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<div class="summary">
<a href="#define-members">Macros</a> &#124;
<a href="#func-members">Functions</a> </div>
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<div class="title">brent_method_extrema.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">brent_method_extrema.cpp File Reference</div></div>
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<p>Find real extrema of a univariate real function in a given interval using <a href="https://en.wikipedia.org/wiki/Brent%27s_method">Brent's method</a>.
<p>Find real extrema of a univariate real function in a given interval using <a href="https://en.wikipedia.org/wiki/Brent%27s_method" target="_blank">Brent's method</a>.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
@@ -112,48 +111,45 @@ Include dependency graph for brent_method_extrema.cpp:</div>
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#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html#a525335710b53cb064ca56b936120431e">_USE_MATH_DEFINES</a></td></tr>
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<tr class="memdesc:a525335710b53cb064ca56b936120431e"><td class="mdescLeft">&#160;</td><td class="mdescRight">required for MS Visual C++ <br /></td></tr>
<tr class="separator:a525335710b53cb064ca56b936120431e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a002b2f4894492820fe708b1b7e7c5e70"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></td></tr>
<tr class="memdesc:a002b2f4894492820fe708b1b7e7c5e70"><td class="mdescLeft">&#160;</td><td class="mdescRight">system accuracy limit <a href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">More...</a><br /></td></tr>
<tr class="separator:a002b2f4894492820fe708b1b7e7c5e70"><td class="memSeparator" colspan="2">&#160;</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a1aa76a6d5fd4d333f9072beff1dc486b"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt; double(double)&gt; &amp;f, double lim_a, double lim_b)</td></tr>
<tr class="memdesc:a1aa76a6d5fd4d333f9072beff1dc486b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the real root of a function in the given interval. <a href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">More...</a><br /></td></tr>
<tr class="separator:a1aa76a6d5fd4d333f9072beff1dc486b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top"><a id="a1440a7779ac56f47a3f355ce4a8c7da0"></a>
void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
<tr class="memdesc:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to find root for the function \(f(x)= (x-2)^2\) in the interval \([1,5]\) <br />
Expected result = 2. <br /></td></tr>
Expected result = 2. <a href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">More...</a><br /></td></tr>
<tr class="separator:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0283886819c7c140a023582b7269e2d0"><td class="memItemLeft" align="right" valign="top"><a id="a0283886819c7c140a023582b7269e2d0"></a>
void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a> ()</td></tr>
<tr class="memitem:a0283886819c7c140a023582b7269e2d0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a> ()</td></tr>
<tr class="memdesc:a0283886819c7c140a023582b7269e2d0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to find root for the function \(f(x)= x^{\frac{1}{x}}\) in the interval \([-2,10]\) <br />
Expected result: \(e\approx 2.71828182845904509\). <br /></td></tr>
Expected result: \(e\approx 2.71828182845904509\). <a href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">More...</a><br /></td></tr>
<tr class="separator:a0283886819c7c140a023582b7269e2d0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6d0455dd5c30adda100e95f0423c786e"><td class="memItemLeft" align="right" valign="top"><a id="a6d0455dd5c30adda100e95f0423c786e"></a>
void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a> ()</td></tr>
<tr class="memitem:a6d0455dd5c30adda100e95f0423c786e"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a> ()</td></tr>
<tr class="memdesc:a6d0455dd5c30adda100e95f0423c786e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to find <em>maxima</em> for the function \(f(x)= \cos x\) in the interval \([0,12]\) <br />
Expected result: \(\pi\approx 3.14159265358979312\). <br /></td></tr>
Expected result: \(\pi\approx 3.14159265358979312\). <a href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">More...</a><br /></td></tr>
<tr class="separator:a6d0455dd5c30adda100e95f0423c786e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d01/brent__method__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Find real extrema of a univariate real function in a given interval using <a href="https://en.wikipedia.org/wiki/Brent%27s_method">Brent's method</a>. </p>
<p>Refer the algorithm discoverer's publication <a href="https://maths-people.anu.edu.au/~brent/pd/rpb011i.pdf">online</a> and also associated book: </p><blockquote class="doxtable">
<p>R. P. Brent, Algorithms for Minimization without Derivatives, Prentice-Hall, Englewood Cliffs, New Jersey, 1973 </p>
<div class="textblock"><p >Find real extrema of a univariate real function in a given interval using <a href="https://en.wikipedia.org/wiki/Brent%27s_method" target="_blank">Brent's method</a>. </p>
<p >Refer the algorithm discoverer's publication <a href="https://maths-people.anu.edu.au/~brent/pd/rpb011i.pdf" target="_blank">online</a> and also associated book: </p><blockquote class="doxtable">
<p >R. P. Brent, Algorithms for Minimization without Derivatives, Prentice-Hall, Englewood Cliffs, New Jersey, 1973 </p>
</blockquote>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d6/d7a/golden__search__extrema_8cpp.html" title="Find extrema of a univariate real function in a given interval using golden section search algorithm.">golden_search_extrema.cpp</a></dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Macro Definition Documentation</h2>
<a id="a002b2f4894492820fe708b1b7e7c5e70"></a>
<a id="a002b2f4894492820fe708b1b7e7c5e70" name="a002b2f4894492820fe708b1b7e7c5e70"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a002b2f4894492820fe708b1b7e7c5e70">&#9670;&nbsp;</a></span>EPSILON</h2>
<div class="memitem">
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</tr>
</table>
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<b>Value:</b><div class="fragment"><div class="line"> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>( \</div>
<div class="line"> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits&lt;double&gt;::epsilon</a>())</div>
<b>Value:</b><div class="fragment"><div class="line"> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>( \</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits&lt;double&gt;::epsilon</a>())</div>
<div class="ttc" id="anumeric_limits_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits</a></div></div>
<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
</div><!-- fragment -->
@@ -174,7 +170,7 @@ void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../.
</div>
</div>
<h2 class="groupheader">Function Documentation</h2>
<a id="a1aa76a6d5fd4d333f9072beff1dc486b"></a>
<a id="a1aa76a6d5fd4d333f9072beff1dc486b" name="a1aa76a6d5fd4d333f9072beff1dc486b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a1aa76a6d5fd4d333f9072beff1dc486b">&#9670;&nbsp;</a></span>get_minima()</h2>
<div class="memitem">
@@ -216,106 +212,106 @@ void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../.
</dd>
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<dl class="section return"><dt>Returns</dt><dd>root found in the interval </dd></dl>
<div class="fragment"><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; uint32_t iters = 0;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; </div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">if</span> (lim_a &gt; lim_b) {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(lim_a, lim_b);</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::abs(lim_a - lim_b) &lt;= <a class="code" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>) {</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Search range must be greater than &quot;</span> &lt;&lt; <a class="code" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordflow">return</span> lim_a;</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; }</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="comment">// golden ratio value</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> M_GOLDEN_RATIO = (3.f - <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(5.f)) / 2.f;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordtype">double</span> v = lim_a + M_GOLDEN_RATIO * (lim_b - lim_a);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordtype">double</span> u, w = v, x = v;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordtype">double</span> fu, fv = f(v);</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="keywordtype">double</span> fw = fv, fx = fv;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <span class="keywordtype">double</span> mid_point = (lim_a + lim_b) / 2.f;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="keywordtype">double</span> p = 0, q = 0, r = 0;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordtype">double</span> d, e = 0;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordtype">double</span> tolerance, tolerance2;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; mid_point = (lim_a + lim_b) / 2.f;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; tolerance = <a class="code" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> * std::abs(x);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; tolerance2 = 2 * tolerance;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; </div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="keywordflow">if</span> (std::abs(e) &gt; tolerance2) {</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// fit parabola</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; r = (x - w) * (fx - fv);</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; q = (x - v) * (fx - fw);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; p = (x - v) * q - (x - w) * r;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; q = 2.f * (q - r);</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="keywordflow">if</span> (q &gt; 0)</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; p = -p;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordflow">else</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; q = -q;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; r = e;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; e = d;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; }</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="keywordflow">if</span> (std::abs(p) &lt; std::abs(0.5 * q * r) &amp;&amp; p &lt; q * (lim_b - x)) {</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="comment">// parabolic interpolation step</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; d = p / q;</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; u = x + d;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="keywordflow">if</span> (u - lim_a &lt; tolerance2 || lim_b - u &lt; tolerance2)</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; d = x &lt; mid_point ? tolerance : -tolerance;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="comment">// golden section interpolation step</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; e = (x &lt; mid_point ? lim_b : lim_a) - x;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; d = M_GOLDEN_RATIO * e;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; }</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <span class="comment">// evaluate not too close to x</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="keywordflow">if</span> (std::abs(d) &gt;= tolerance)</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; u = d;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keywordflow">else</span> <span class="keywordflow">if</span> (d &gt; 0)</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; u = tolerance;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <span class="keywordflow">else</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; u = -tolerance;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; u += x;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; fu = f(u);</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="comment">// update variables</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <span class="keywordflow">if</span> (fu &lt;= fx) {</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <span class="keywordflow">if</span> (u &lt; x)</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; lim_b = x;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="keywordflow">else</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; lim_a = x;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; v = w;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; fv = fw;</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; w = x;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; fw = fx;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; x = u;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; fx = fu;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; <span class="keywordflow">if</span> (u &lt; x)</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; lim_a = u;</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <span class="keywordflow">else</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; lim_b = u;</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <span class="keywordflow">if</span> (fu &lt;= fw || x == w) {</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; v = w;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; fv = fw;</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; w = u;</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; fw = fu;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (fu &lt;= fv || v == x || v == w) {</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; v = u;</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; fv = fu;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; }</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; }</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; iters++;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; } <span class="keywordflow">while</span> (std::abs(x - mid_point) &gt; (tolerance - (lim_b - lim_a) / 2.f));</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; (iters: &quot;</span> &lt;&lt; iters &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; </div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> {</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> uint32_t iters = 0;</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">if</span> (lim_a &gt; lim_b) {</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(lim_a, lim_b);</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (std::abs(lim_a - lim_b) &lt;= <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>) {</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Search range must be greater than &quot;</span> &lt;&lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">return</span> lim_a;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> }</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// golden ratio value</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">const</span> <span class="keywordtype">double</span> M_GOLDEN_RATIO = (3.f - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(5.f)) / 2.f;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordtype">double</span> v = lim_a + M_GOLDEN_RATIO * (lim_b - lim_a);</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordtype">double</span> u, w = v, x = v;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordtype">double</span> fu, fv = f(v);</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordtype">double</span> fw = fv, fx = fv;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordtype">double</span> mid_point = (lim_a + lim_b) / 2.f;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">double</span> p = 0, q = 0, r = 0;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordtype">double</span> d, e = 0;</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordtype">double</span> tolerance, tolerance2;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">do</span> {</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> mid_point = (lim_a + lim_b) / 2.f;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> tolerance = <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a> * std::abs(x);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> tolerance2 = 2 * tolerance;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">if</span> (std::abs(e) &gt; tolerance2) {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// fit parabola</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> r = (x - w) * (fx - fv);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> q = (x - v) * (fx - fw);</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> p = (x - v) * q - (x - w) * r;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> q = 2.f * (q - r);</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">if</span> (q &gt; 0)</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> p = -p;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> q = -q;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> r = e;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> e = d;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> }</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">if</span> (std::abs(p) &lt; std::abs(0.5 * q * r) &amp;&amp; p &lt; q * (lim_b - x)) {</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// parabolic interpolation step</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> d = p / q;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> u = x + d;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">if</span> (u - lim_a &lt; tolerance2 || lim_b - u &lt; tolerance2)</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> d = x &lt; mid_point ? tolerance : -tolerance;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// golden section interpolation step</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> e = (x &lt; mid_point ? lim_b : lim_a) - x;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> d = M_GOLDEN_RATIO * e;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// evaluate not too close to x</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">if</span> (std::abs(d) &gt;= tolerance)</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> u = d;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (d &gt; 0)</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> u = tolerance;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> u = -tolerance;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> u += x;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> fu = f(u);</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// update variables</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordflow">if</span> (fu &lt;= fx) {</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">if</span> (u &lt; x)</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> lim_b = x;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> lim_a = x;</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> v = w;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> fv = fw;</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> w = x;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> fw = fx;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> x = u;</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> fx = fu;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordflow">if</span> (u &lt; x)</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> lim_a = u;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> lim_b = u;</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordflow">if</span> (fu &lt;= fw || x == w) {</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> v = w;</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> fv = fw;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> w = u;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> fw = fu;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (fu &lt;= fv || v == x || v == w) {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> v = u;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> fv = fu;</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> }</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> }</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> iters++;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> } <span class="keywordflow">while</span> (std::abs(x - mid_point) &gt; (tolerance - (lim_b - lim_a) / 2.f));</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot; (iters: &quot;</span> &lt;&lt; iters &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:23</div></div>
<div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160; {</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(18);</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160; </div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Computations performed with machine epsilon: &quot;</span> &lt;&lt; <a class="code" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160; &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160; </div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160; <a class="code" href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160; <a class="code" href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160; <a class="code" href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160; </div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160;}</div>
<p >Main function </p>
<div class="fragment"><div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> {</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(18);</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> </div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Computations performed with machine epsilon: &quot;</span> &lt;&lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> </div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a>();</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> </div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span>}</div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdoc">Test function to find root for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:165</div></div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdoc">Test function to find root for the function in the interval Expected result = 2.</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:143</div></div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdoc">Test function to find maxima for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:188</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">&#9670;&nbsp;</a></span>test1()</h2>
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<td class="memname">void test1 </td>
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<p>Test function to find root for the function \(f(x)= (x-2)^2\) in the interval \([1,5]\) <br />
Expected result = 2. </p>
<div class="fragment"><div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> {</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="comment">// define the function to minimize as a lambda function</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; f1 = [](<span class="keywordtype">double</span> x) {</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordflow">return</span> (x - 2) * (x - 2);</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> };</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> </div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1.... &quot;</span>;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> </div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(f1, -1, 5);</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot;...&quot;</span>;</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> </div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> assert(std::abs(minima - 2) &lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span>}</div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a1aa76a6d5fd4d333f9072beff1dc486b"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a></div><div class="ttdeci">double get_minima(const std::function&lt; double(double)&gt; &amp;f, double lim_a, double lim_b)</div><div class="ttdoc">Get the real root of a function in the given interval.</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:35</div></div>
<div class="ttc" id="afunction_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">&#9670;&nbsp;</a></span>test2()</h2>
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<td class="memname">void test2 </td>
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<p>Test function to find root for the function \(f(x)= x^{\frac{1}{x}}\) in the interval \([-2,10]\) <br />
Expected result: \(e\approx 2.71828182845904509\). </p>
<div class="fragment"><div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> {</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// define the function to maximize as a lambda function</span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="comment">// since we are maximixing, we negated the function return value</span></div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) {</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keywordflow">return</span> -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, 1.f / x);</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> };</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> </div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2.... &quot;</span>;</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> </div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -2, 5);</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> </div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_E &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> </div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> assert(std::abs(minima - M_E) &lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span>}</div>
<div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6d0455dd5c30adda100e95f0423c786e">&#9670;&nbsp;</a></span>test3()</h2>
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<td class="memname">void test3 </td>
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<p>Test function to find <em>maxima</em> for the function \(f(x)= \cos x\) in the interval \([0,12]\) <br />
Expected result: \(\pi\approx 3.14159265358979312\). </p>
<div class="fragment"><div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> {</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="comment">// define the function to maximize as a lambda function</span></div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="comment">// since we are maximixing, we negated the function return value</span></div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(<span class="keywordtype">double</span>)&gt; func = [](<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(x); };</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> </div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3.... &quot;</span>;</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> </div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="keywordtype">double</span> minima = <a class="code hl_function" href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a>(func, -4, 12);</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> </div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; minima &lt;&lt; <span class="stringliteral">&quot; (&quot;</span> &lt;&lt; M_PI &lt;&lt; <span class="stringliteral">&quot;)...&quot;</span>;</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> </div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> assert(std::abs(minima - M_PI) &lt; <a class="code hl_define" href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a>);</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span>}</div>
<div class="ttc" id="acos_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a></div><div class="ttdeci">T cos(T... args)</div></div>
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<div class="title">ST</div> </div>
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<p>Builds the sparse table for computing min/max/gcd/lcm/...etc for any contiguous sub-segment of the array.This is an example of computing the index of the minimum value. </p><dl class="section return"><dt>Returns</dt><dd>void @complexity: O(n.log(n))&lt; precomputing <code>log2(i+1)</code></dd></dl>
<p >Builds the sparse table for computing min/max/gcd/lcm/...etc for any contiguous sub-segment of the array.This is an example of computing the index of the minimum value. </p><dl class="section return"><dt>Returns</dt><dd>void @complexity: O(n.log(n))&lt; precomputing <code>log2(i+1)</code></dd></dl>
<dl class="section note"><dt>Note</dt><dd>notice how we deal with the range of length <code>pow(2,i)</code>, and we can reuse the computation that we did for the range of length <code>pow(2,i-1)</code>.</dd></dl>
<p>So, ST[j][i] = min( ST[j-1][i], ST[j-1][i + pow(2,j-1)]). [2][3] = min(ST[1][3], ST[1][5])</p>
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<p>Functions for the <a href="https://www.geeksforgeeks.org/wildcard-pattern-matching/">Wildcard Matching</a> problem.
<p>Functions for the <a href="https://www.geeksforgeeks.org/wildcard-pattern-matching/" target="_blank">Wildcard Matching</a> problem.
<a href="../../db/d03/namespacewildcard__matching.html#details">More...</a></p>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Functions for the <a href="https://www.geeksforgeeks.org/wildcard-pattern-matching/">Wildcard Matching</a> problem. </p>
<div class="textblock"><p >Functions for the <a href="https://www.geeksforgeeks.org/wildcard-pattern-matching/" target="_blank">Wildcard Matching</a> problem. </p>
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Functions</h2></td></tr>
<tr class="memitem:acfff36db81326fb990a643ab198ee8a5"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d07/spiral__print_8cpp.html#acfff36db81326fb990a643ab198ee8a5">genArray</a> (int **a, int r, int c)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Print the elements of a matrix traversing it spirally. </p>
<div class="textblock"><p >Print the elements of a matrix traversing it spirally. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="acfff36db81326fb990a643ab198ee8a5"></a>
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<p>Arrange sequence of numbers from '1' in a matrix form </p><dl class="params"><dt>Parameters</dt><dd>
<p >Arrange sequence of numbers from '1' in a matrix form </p><dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramdir">[out]</td><td class="paramname">a</td><td>matrix to fill </td></tr>
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<div class="fragment"><div class="line"><a name="l00012"></a><span class="lineno"> 12</span>&#160; {</div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; c; j++) {</div>
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<p>main function </p>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="keywordtype">int</span> **a = <span class="keyword">new</span> <span class="keywordtype">int</span> *[r];</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; </div>
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<p >main function </p>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <a class="code hl_function" href="../../db/d07/spiral__print_8cpp.html#a850d3f55e1a8d227176cdcc67352c197">spiralPrint</a>(a, r, c);</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; r; i++) <span class="keyword">delete</span>[] a[i];</div>
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<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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<div class="ttc" id="aspiral__print_8cpp_html_acfff36db81326fb990a643ab198ee8a5"><div class="ttname"><a href="../../db/d07/spiral__print_8cpp.html#acfff36db81326fb990a643ab198ee8a5">genArray</a></div><div class="ttdeci">void genArray(int **a, int r, int c)</div><div class="ttdef"><b>Definition:</b> spiral_print.cpp:12</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a850d3f55e1a8d227176cdcc67352c197">&#9670;&nbsp;</a></span>spiralPrint()</h2>
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<p>Traverse the matrix spirally and print the sequence of elements </p><dl class="params"><dt>Parameters</dt><dd>
<p >Traverse the matrix spirally and print the sequence of elements </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">a</td><td>matrix to read from </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">r</td><td>number of rows </td></tr>
@@ -260,48 +259,48 @@ Here is the call graph for this function:</div>
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<p>Print start row</p>
<p>Print the end col</p>
<p>Print the end row</p>
<p>Print the start Col</p>
<div class="fragment"><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; {</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordtype">int</span> startRow = 0, endRow = r - 1;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordtype">int</span> startCol = 0, endCol = c - 1;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="keywordtype">int</span> cnt = 0;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordflow">while</span> (startRow &lt;= endRow &amp;&amp; startCol &lt;= endCol) {<span class="comment"></span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160;<span class="comment"> /// Print start row</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160;<span class="comment"></span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = startCol; i &lt;= endCol; i++, cnt++) {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; a[startRow][i] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; }</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; startRow++;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160;<span class="comment"> /// Print the end col</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;<span class="comment"></span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = startRow; i &lt;= endRow; i++, cnt++) {</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; a[i][endCol] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; }</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; endCol--;</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160;<span class="comment"> /// Print the end row</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160;<span class="comment"></span> <span class="keywordflow">if</span> (cnt == r * c) {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordflow">break</span>;</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = endCol; i &gt;= startCol; i--, cnt++) {</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; a[endRow][i] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; endRow--;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;<span class="comment"> /// Print the start Col</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;<span class="comment"></span> <span class="keywordflow">if</span> (cnt == r * c) {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; }</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = endRow; i &gt;= startRow; i--, cnt++) {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; a[i][startCol] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; }</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; startCol++;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; }</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160;}</div>
<p >Print start row</p>
<p >Print the end col</p>
<p >Print the end row</p>
<p >Print the start Col</p>
<div class="fragment"><div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> {</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordtype">int</span> startCol = 0, endCol = c - 1;</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment"> /// Print start row</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; a[startRow][i] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> startRow++;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment"></span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment"> /// Print the end col</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment"></span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = startRow; i &lt;= endRow; i++, cnt++) {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; a[i][endCol] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> }</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment"> /// Print the end row</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment"></span> <span class="keywordflow">if</span> (cnt == r * c) {</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = endCol; i &gt;= startCol; i--, cnt++) {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; a[endRow][i] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> endRow--;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment"></span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment"> /// Print the start Col</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment"></span> <span class="keywordflow">if</span> (cnt == r * c) {</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = endRow; i &gt;= startRow; i--, cnt++) {</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; a[i][startCol] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> }</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> startCol++;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> }</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span>}</div>
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<div class="title">prime_factorization.cpp File Reference</div> </div>
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Functions</h2></td></tr>
<tr class="memitem:affe577b9bce8f604f5e2f861c63c7099"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">SieveOfEratosthenes</a> (int N)</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d0d/prime__factorization_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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Variables</h2></td></tr>
<tr class="memitem:a7fe38b570a51e448430d6a0f072c2f23"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a> [1000006]</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Prime factorization of positive integers. </p>
<div class="textblock"><p >Prime factorization of positive integers. </p>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main program </p>
<div class="fragment"><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordtype">int</span> num;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t\tComputes the prime factorization\n\n&quot;</span>;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Type in a number: &quot;</span>;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; num;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">SieveOfEratosthenes</a>(num);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization</a>(num);</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="comment">// Prime factors with their powers in the given number in new line</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">auto</span> it : <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a>) {</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; it.first &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; it.second &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; }</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;}</div>
<p >Main program </p>
<div class="fragment"><div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> {</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordtype">int</span> num;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t\tComputes the prime factorization\n\n&quot;</span>;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Type in a number: &quot;</span>;</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; num;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <a class="code hl_function" href="../../db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">SieveOfEratosthenes</a>(num);</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <a class="code hl_function" href="../../db/d0d/prime__factorization_8cpp.html#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization</a>(num);</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// Prime factors with their powers in the given number in new line</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> it : <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a>) {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; it.first &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; it.second &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> }</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span>}</div>
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0ece0145fb29a5cf48378c23dde2da46">&#9670;&nbsp;</a></span>prime_factorization()</h2>
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<p>Prime factorization of a number </p>
<div class="fragment"><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordtype">int</span> number = num;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; </div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i] &lt;= num; i++) {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordtype">int</span> count = 0;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="comment">// termination condition</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keywordflow">if</span> (number == 1) {</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; }</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordflow">while</span> (number % <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i] == 0) {</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; count++;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; number = number / <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i];</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordflow">if</span> (count)</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a>.push_back(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(<a class="code" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i], count));</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; }</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;}</div>
<p >Prime factorization of a number </p>
<div class="fragment"><div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordtype">int</span> number = num;</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i] &lt;= num; i++) {</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordtype">int</span> count = 0;</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// termination condition</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordflow">if</span> (number == 1) {</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">while</span> (number % <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i] == 0) {</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> count++;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> number = number / <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i];</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> </div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">if</span> (count)</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a>.push_back(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(<a class="code hl_variable" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i], count));</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> }</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span>}</div>
<div class="ttc" id="amake_pair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a></div><div class="ttdeci">T make_pair(T... args)</div></div>
<div class="ttc" id="aprime__factorization_8cpp_html_af097796783684712b8326e5b82bfd4fe"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a></div><div class="ttdeci">std::vector&lt; int &gt; prime_numbers</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:16</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#affe577b9bce8f604f5e2f861c63c7099">&#9670;&nbsp;</a></span>SieveOfEratosthenes()</h2>
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<p>Calculating prime number upto a given range </p>
<div class="fragment"><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; {</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; <span class="comment">// initializes the array isprime</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/memset.html">memset</a>(<a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>, <span class="keyword">true</span>, <span class="keyword">sizeof</span> <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>);</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; </div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i &lt;= <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[i]) {</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 2 * i; j &lt;= <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j += i) <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[j] = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; }</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; }</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i &lt;= <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[i])</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(i);</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; }</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160;}</div>
<p >Calculating prime number upto a given range </p>
<div class="fragment"><div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> {</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// initializes the array isprime</span></div>
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<div class="ttc" id="amemset_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/memset.html">std::memset</a></div><div class="ttdeci">T memset(T... args)</div></div>
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<h2 class="groupheader">Variable Documentation</h2>
<a id="acfb0df439a4beae5a34ef131ce737c1b"></a>
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<p>list of prime factor-pairs </p>
<p >list of prime factor-pairs </p>
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<p>Declaring variables for maintaing prime numbers and to check whether a number is prime or not </p>
<p >Declaring variables for maintaing prime numbers and to check whether a number is prime or not </p>
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<p>list of prime numbers </p>
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<div class="title">0_1_knapsack.cpp File Reference</div> </div>
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<p>Implementation of <a href="https://en.wikipedia.org/wiki/Knapsack_problem">0-1 Knapsack Problem</a>
<p>Implementation of <a href="https://en.wikipedia.org/wiki/Knapsack_problem" target="_blank">0-1 Knapsack Problem</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
@@ -111,16 +110,16 @@ Include dependency graph for 0_1_knapsack.cpp:</div>
</div>
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</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="namespaces"></a>
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Namespaces</h2></td></tr>
<tr class="memitem:dd/d24/namespacedynamic__programming"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a></td></tr>
<tr class="memitem:dd/d24/namespacedynamic__programming"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a></td></tr>
<tr class="memdesc:dd/d24/namespacedynamic__programming"><td class="mdescLeft">&#160;</td><td class="mdescRight">Dynamic Programming algorithms. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:d7/daf/namespace_knapsack"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/daf/namespace_knapsack.html">Knapsack</a></td></tr>
<tr class="memitem:d7/daf/namespace_knapsack"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/daf/namespace_knapsack.html">Knapsack</a></td></tr>
<tr class="memdesc:d7/daf/namespace_knapsack"><td class="mdescLeft">&#160;</td><td class="mdescRight">Implementation of 0-1 <a class="el" href="../../d7/daf/namespace_knapsack.html" title="Implementation of 0-1 Knapsack problem.">Knapsack</a> problem. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a15edf30f336885e5b851f6b7199c6cd1"><td class="memTemplParams" colspan="2">template&lt;size_t n&gt; </td></tr>
<tr class="memitem:a15edf30f336885e5b851f6b7199c6cd1"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">dynamic_programming::knapsack::maxKnapsackValue</a> (const int capacity, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt; &amp;weight, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt; &amp;value)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Knapsack_problem">0-1 Knapsack Problem</a> </p>
<p>Given weights and values of n items, put these items in a knapsack of capacity <code>W</code> to get the maximum total value in the knapsack. In other words, given two integer arrays <code>val[0..n-1]</code> and <code>wt[0..n-1]</code> which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of <code>val[]</code> such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property)</p>
<div class="textblock"><p >Implementation of <a href="https://en.wikipedia.org/wiki/Knapsack_problem" target="_blank">0-1 Knapsack Problem</a> </p>
<p >Given weights and values of n items, put these items in a knapsack of capacity <code>W</code> to get the maximum total value in the knapsack. In other words, given two integer arrays <code>val[0..n-1]</code> and <code>wt[0..n-1]</code> which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of <code>val[]</code> such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property)</p>
<h3><a class="anchor" id="autotoc_md58"></a>
Algorithm</h3>
<p>The idea is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than <code>W</code>. From all such subsets, pick the maximum value subset.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Anmol3299">Anmol</a> </dd>
<p >The idea is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than <code>W</code>. From all such subsets, pick the maximum value subset.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Anmol3299" target="_blank">Anmol</a> </dd>
<dd>
<a href="https://github.com/Pardeep009">Pardeep</a> </dd></dl>
<a href="https://github.com/Pardeep009" target="_blank">Pardeep</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
<div class="memitem">
@@ -161,11 +160,11 @@ Algorithm</h3>
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; {</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; <span class="comment">// Testing</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <a class="code" href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> {</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// Testing</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span>}</div>
<div class="ttc" id="a0__1__knapsack_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function to test above algorithm.</div><div class="ttdef"><b>Definition:</b> 0_1_knapsack.cpp:96</div></div>
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Here is the call graph for this function:</div>
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</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a15edf30f336885e5b851f6b7199c6cd1">&#9670;&nbsp;</a></span>maxKnapsackValue()</h2>
<div class="memitem">
@@ -226,43 +225,43 @@ template&lt;size_t n&gt; </div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>maximum value obtainable with given capacity. </dd></dl>
<div class="fragment"><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; {</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a> &gt; maxValue(n + 1,</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(capacity + 1, 0));</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="comment">// outer loop will select no of items allowed</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="comment">// inner loop will select capcity of knapsack bag</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordtype">int</span> items = <span class="keyword">sizeof</span>(weight) / <span class="keyword">sizeof</span>(weight[0]);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; items + 1; ++i) {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; capacity + 1; ++j) {</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="comment">// if no of items is zero or capacity is zero, then maxValue</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="comment">// will be zero</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; maxValue[i][j] = 0;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (weight[i - 1] &lt;= j) {</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="comment">// if the ith item&#39;s weight(in actual array it will be at i-1)</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// is less than or equal to the allowed weight i.e. j then we</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="comment">// can pick that item for our knapsack. maxValue will be the</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="comment">// obtained either by picking the current item or by not picking</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="comment">// current item</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="comment">// picking current item</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="keywordtype">int</span> profit1 = value[i - 1] + maxValue[i - 1][j - weight[i - 1]];</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; </div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="comment">// not picking current item</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordtype">int</span> profit2 = maxValue[i - 1][j];</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; maxValue[i][j] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(profit1, profit2);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="comment">// as weight of current item is greater than allowed weight, so</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="comment">// maxProfit will be profit obtained by excluding current item.</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; maxValue[i][j] = maxValue[i - 1][j];</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; }</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; }</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; }</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; </div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="comment">// returning maximum value</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <span class="keywordflow">return</span> maxValue[items][capacity];</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a> &gt; maxValue(n + 1,</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(capacity + 1, 0));</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// outer loop will select no of items allowed</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// inner loop will select capcity of knapsack bag</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordtype">int</span> items = <span class="keyword">sizeof</span>(weight) / <span class="keyword">sizeof</span>(weight[0]);</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; items + 1; ++i) {</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j &lt; capacity + 1; ++j) {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// if no of items is zero or capacity is zero, then maxValue</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// will be zero</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (weight[i - 1] &lt;= j) {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// if the ith item&#39;s weight(in actual array it will be at i-1)</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// is less than or equal to the allowed weight i.e. j then we</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// can pick that item for our knapsack. maxValue will be the</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// obtained either by picking the current item or by not picking</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// current item</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// picking current item</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordtype">int</span> profit1 = value[i - 1] + maxValue[i - 1][j - weight[i - 1]];</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// not picking current item</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordtype">int</span> profit2 = maxValue[i - 1][j];</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> maxValue[i][j] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(profit1, profit2);</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// as weight of current item is greater than allowed weight, so</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// maxProfit will be profit obtained by excluding current item.</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> maxValue[i][j] = maxValue[i - 1][j];</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> }</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> }</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// returning maximum value</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">return</span> maxValue[items][capacity];</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span>}</div>
<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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<p>Function to test above algorithm. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; {</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="comment">// Test 1</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> n1 = 3; <span class="comment">// number of items</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n1&gt;</a> weight1 = {10, 20, 30}; <span class="comment">// weight of each item</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n1&gt;</a> value1 = {60, 100, 120}; <span class="comment">// value of each item</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> capacity1 = 50; <span class="comment">// capacity of carrying bag</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> max_value1 = <a class="code" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">dynamic_programming::knapsack::maxKnapsackValue</a>(</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; capacity1, weight1, value1);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> expected_max_value1 = 220;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; assert(max_value1 == expected_max_value1);</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum Knapsack value with &quot;</span> &lt;&lt; n1 &lt;&lt; <span class="stringliteral">&quot; items is &quot;</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; &lt;&lt; max_value1 &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <span class="comment">// Test 2</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> n2 = 4; <span class="comment">// number of items</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n2&gt;</a> weight2 = {24, 10, 10, 7}; <span class="comment">// weight of each item</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n2&gt;</a> value2 = {24, 18, 18, 10}; <span class="comment">// value of each item</span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> capacity2 = 25; <span class="comment">// capacity of carrying bag</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> max_value2 = <a class="code" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">dynamic_programming::knapsack::maxKnapsackValue</a>(</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; capacity2, weight2, value2);</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> expected_max_value2 = 36;</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; assert(max_value2 == expected_max_value2);</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; &lt;&lt; max_value2 &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> {</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// Test 1</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n1 = 3; <span class="comment">// number of items</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n1&gt;</a> weight1 = {10, 20, 30}; <span class="comment">// weight of each item</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n1&gt;</a> value1 = {60, 100, 120}; <span class="comment">// value of each item</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keyword">const</span> <span class="keywordtype">int</span> capacity1 = 50; <span class="comment">// capacity of carrying bag</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keyword">const</span> <span class="keywordtype">int</span> max_value1 = <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">dynamic_programming::knapsack::maxKnapsackValue</a>(</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> capacity1, weight1, value1);</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keyword">const</span> <span class="keywordtype">int</span> expected_max_value1 = 220;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> assert(max_value1 == expected_max_value1);</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum Knapsack value with &quot;</span> &lt;&lt; n1 &lt;&lt; <span class="stringliteral">&quot; items is &quot;</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> &lt;&lt; max_value1 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// Test 2</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n2 = 4; <span class="comment">// number of items</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n2&gt;</a> weight2 = {24, 10, 10, 7}; <span class="comment">// weight of each item</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n2&gt;</a> value2 = {24, 18, 18, 10}; <span class="comment">// value of each item</span></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keyword">const</span> <span class="keywordtype">int</span> capacity2 = 25; <span class="comment">// capacity of carrying bag</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keyword">const</span> <span class="keywordtype">int</span> max_value2 = <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">dynamic_programming::knapsack::maxKnapsackValue</a>(</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> capacity2, weight2, value2);</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keyword">const</span> <span class="keywordtype">int</span> expected_max_value2 = 36;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> assert(max_value2 == expected_max_value2);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Maximum Knapsack value with &quot;</span> &lt;&lt; n2 &lt;&lt; <span class="stringliteral">&quot; items is &quot;</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> &lt;&lt; max_value2 &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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Public Attributes</h2></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a class="el" href="../../db/d8b/struct_node.html">Node</a> object that holds key </p>
<div class="textblock"><p ><a class="el" href="../../db/d8b/struct_node.html">Node</a> object that holds key </p>
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<p>Implementation of the <a href="http://oeis.org/wiki/N-bonacci_numbers">N-bonacci</a> series.
<p>Implementation of the <a href="http://oeis.org/wiki/N-bonacci_numbers" target="_blank">N-bonacci</a> series.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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<tr class="memdesc:de/d36/namespacen__bonacci"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="http://oeis.org/wiki/N-bonacci_numbers" target="_blank">N-bonacci</a> implementation. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a767bc5427e0ebaf88ab5a7572a7d852e"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d27/n__bonacci_8cpp.html#a767bc5427e0ebaf88ab5a7572a7d852e">math::n_bonacci::N_bonacci</a> (const uint64_t &amp;n, const uint64_t &amp;m)</td></tr>
<tr class="memdesc:a767bc5427e0ebaf88ab5a7572a7d852e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Finds the N-Bonacci series for the <code>n</code> parameter value and <code>m</code> parameter terms. <a href="../../db/d27/n__bonacci_8cpp.html#a767bc5427e0ebaf88ab5a7572a7d852e">More...</a><br /></td></tr>
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<tr class="memdesc:a6849b68f760be628d5975ab3eddec63d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Finds the N-Bonacci series for the <code>n</code> parameter value and <code>m</code> parameter terms. <a href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">More...</a><br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of the <a href="http://oeis.org/wiki/N-bonacci_numbers">N-bonacci</a> series. </p>
<p>In general, in N-bonacci sequence, we generate sum of preceding N numbers from the next term.</p>
<p>For example, a 3-bonacci sequence is the following: 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81 In this code we take N and M as input where M is the number of terms to be printed of the N-bonacci series</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy">Swastika Gupta</a> </dd></dl>
<div class="textblock"><p >Implementation of the <a href="http://oeis.org/wiki/N-bonacci_numbers" target="_blank">N-bonacci</a> series. </p>
<p >In general, in N-bonacci sequence, we generate sum of preceding N numbers from the next term.</p>
<p >For example, a 3-bonacci sequence is the following: 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81 In this code we take N and M as input where M is the number of terms to be printed of the N-bonacci series</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy" target="_blank">Swastika Gupta</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; {</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <a class="code" href="../../db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> {</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a767bc5427e0ebaf88ab5a7572a7d852e">&#9670;&nbsp;</a></span>N_bonacci()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a6849b68f760be628d5975ab3eddec63d">&#9670;&nbsp;</a></span>N_bonacci()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;uint64_t&gt; math::n_bonacci::N_bonacci </td>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt; math::n_bonacci::N_bonacci </td>
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<td class="paramtype">const uint64_t &amp;&#160;</td>
<td class="paramname"><em>n</em>, </td>
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<dl class="section return"><dt>Returns</dt><dd>the n-bonacci sequence as vector array </dd></dl>
<p>we initialise the (n-1)th term as 1 which is the sum of preceding N zeros</p>
<p>similarily the sum of preceding N zeros and the (N+1)th 1 is also 1</p>
<div class="fragment"><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; {</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> a(m, 0); <span class="comment">// we create an empty array of size m</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; </div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; a[n - 1] = 1; <span class="comment">/// we initialise the (n-1)th term as 1 which is the sum of</span><span class="comment"></span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160;<span class="comment"> /// preceding N zeros</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160;<span class="comment"></span> a[n] = 1; <span class="comment">/// similarily the sum of preceding N zeros and the (N+1)th 1 is</span><span class="comment"></span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160;<span class="comment"> /// also 1</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160;<span class="comment"></span> <span class="keywordflow">for</span> (uint64_t i = n + 1; i &lt; m; i++) {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="comment">// this is an optimized solution that works in O(M) time and takes O(M)</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="comment">// extra space here we use the concept of the sliding window the current</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="comment">// term can be computed using the given formula</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; a[i] = 2 * a[i - 1] - a[i - 1 - n];</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; }</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160;}</div>
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<p >we initialise the (n-1)th term as 1 which is the sum of preceding N zeros</p>
<p >similarily the sum of preceding N zeros and the (N+1)th 1 is also 1</p>
<div class="fragment"><div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> {</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> a(m, 0); <span class="comment">// we create an empty array of size m</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> a[n - 1] = 1; <span class="comment">/// we initialise the (n-1)th term as 1 which is the sum of</span><span class="comment"></span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment"> /// preceding N zeros</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment"></span> a[n] = 1; <span class="comment">/// similarily the sum of preceding N zeros and the (N+1)th 1 is</span><span class="comment"></span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment"> /// also 1</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment"></span> <span class="keywordflow">for</span> (uint64_t i = n + 1; i &lt; m; i++) {</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// this is an optimized solution that works in O(M) time and takes O(M)</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// extra space here we use the concept of the sliding window the current</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// term can be computed using the given formula</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> a[i] = 2 * a[i - 1] - a[i - 1 - n];</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> }</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">return</span> a;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span>}</div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; {</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="comment">// n = 1 m = 1 return [1, 1]</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test&quot;</span>;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr1 = <a class="code" href="../../db/d27/n__bonacci_8cpp.html#a767bc5427e0ebaf88ab5a7572a7d852e">math::n_bonacci::N_bonacci</a>(</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; 1, 1); <span class="comment">// first input is the param n and second one is the param m for</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="comment">// N-bonacci func</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array1 = {</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; 1, 1}; <span class="comment">// It is the expected output series of length m</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr1), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr1),</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array1)));</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; </div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="comment">// n = 5 m = 15 return [0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236,</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="comment">// 464]</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test&quot;</span>;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr2 = <a class="code" href="../../db/d27/n__bonacci_8cpp.html#a767bc5427e0ebaf88ab5a7572a7d852e">math::n_bonacci::N_bonacci</a>(</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; 5, 15); <span class="comment">// first input is the param n and second one is the param m for</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="comment">// N-bonacci func</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array2 = {</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; 0, 0, 0, 0, 1, 1, 2, 4,</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; 8, 16, 31, 61, 120, 236, 464}; <span class="comment">// It is the expected output series of</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="comment">// length m</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2),</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array2)));</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; </div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="comment">// n = 6 m = 17 return [0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 63, 125, 248,</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; <span class="comment">// 492, 976]</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test&quot;</span>;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr3 = <a class="code" href="../../db/d27/n__bonacci_8cpp.html#a767bc5427e0ebaf88ab5a7572a7d852e">math::n_bonacci::N_bonacci</a>(</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; 6, 17); <span class="comment">// first input is the param n and second one is the param m for</span></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="comment">// N-bonacci func</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array3 = {</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; 0, 0, 0, 0, 0, 1, 1, 2, 4,</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; 8, 16, 32, 63, 125, 248, 492, 976}; <span class="comment">// It is the expected output series</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="comment">// of length m</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3),</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array3)));</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; </div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <span class="comment">// n = 56 m = 15 return [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test&quot;</span>;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr4 = <a class="code" href="../../db/d27/n__bonacci_8cpp.html#a767bc5427e0ebaf88ab5a7572a7d852e">math::n_bonacci::N_bonacci</a>(</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; 56, 15); <span class="comment">// first input is the param n and second one is the param m</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <span class="comment">// for N-bonacci func</span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array4 = {</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; 0, 0, 0, 0, 0, 0, 0, 0,</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; 0, 0, 0, 0, 0, 0, 0}; <span class="comment">// It is the expected output series of length m</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4),</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array4)));</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> {</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// n = 1 m = 1 return [1, 1]</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test&quot;</span>;</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr1 = <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">math::n_bonacci::N_bonacci</a>(</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> 1, 1); <span class="comment">// first input is the param n and second one is the param m for</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// N-bonacci func</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array1 = {</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> 1, 1}; <span class="comment">// It is the expected output series of length m</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr1), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr1),</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array1)));</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// n = 5 m = 15 return [0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236,</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// 464]</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test&quot;</span>;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr2 = <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">math::n_bonacci::N_bonacci</a>(</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> 5, 15); <span class="comment">// first input is the param n and second one is the param m for</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// N-bonacci func</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array2 = {</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> 0, 0, 0, 0, 1, 1, 2, 4,</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// length m</span></div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array2)));</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// n = 6 m = 17 return [0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 63, 125, 248,</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// 492, 976]</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test&quot;</span>;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr3 = <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">math::n_bonacci::N_bonacci</a>(</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> 6, 17); <span class="comment">// first input is the param n and second one is the param m for</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// N-bonacci func</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array3 = {</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> 0, 0, 0, 0, 0, 1, 1, 2, 4,</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> 8, 16, 32, 63, 125, 248, 492, 976}; <span class="comment">// It is the expected output series</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// of length m</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3),</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array3)));</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// n = 56 m = 15 return [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test&quot;</span>;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr4 = <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">math::n_bonacci::N_bonacci</a>(</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> 56, 15); <span class="comment">// first input is the param n and second one is the param m</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="comment">// for N-bonacci func</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> output_array4 = {</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> 0, 0, 0, 0, 0, 0, 0, 0,</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> 0, 0, 0, 0, 0, 0, 0}; <span class="comment">// It is the expected output series of length m</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4),</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(output_array4)));</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="ttc" id="an__bonacci_8cpp_html_a767bc5427e0ebaf88ab5a7572a7d852e"><div class="ttname"><a href="../../db/d27/n__bonacci_8cpp.html#a767bc5427e0ebaf88ab5a7572a7d852e">math::n_bonacci::N_bonacci</a></div><div class="ttdeci">std::vector&lt; uint64_t &gt; N_bonacci(const uint64_t &amp;n, const uint64_t &amp;m)</div><div class="ttdoc">Finds the N-Bonacci series for the n parameter value and m parameter terms.</div><div class="ttdef"><b>Definition:</b> n_bonacci.cpp:41</div></div>
<div class="ttc" id="an__bonacci_8cpp_html_a6849b68f760be628d5975ab3eddec63d"><div class="ttname"><a href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">math::n_bonacci::N_bonacci</a></div><div class="ttdeci">std::vector&lt; uint64_t &gt; N_bonacci(const uint64_t &amp;n, const uint64_t &amp;m)</div><div class="ttdoc">Finds the N-Bonacci series for the n parameter value and m parameter terms.</div><div class="ttdef"><b>Definition:</b> n_bonacci.cpp:41</div></div>
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<p>Solve the <a href="https://en.wikipedia.org/wiki/Tower_of_Hanoi">Tower of Hanoi</a> problem.
<p>Solve the <a href="https://en.wikipedia.org/wiki/Tower_of_Hanoi" target="_blank">Tower of Hanoi</a> problem.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
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<tr class="memitem:a746d9a3984bba88fd6dd91978f6931ed"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a> (const struct <a class="el" href="../../d2/d2c/structtower.html">tower</a> *const F, const struct <a class="el" href="../../d2/d2c/structtower.html">tower</a> *const T, const struct <a class="el" href="../../d2/d2c/structtower.html">tower</a> *const U)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Solve the <a href="https://en.wikipedia.org/wiki/Tower_of_Hanoi">Tower of Hanoi</a> problem. </p>
<div class="textblock"><p >Solve the <a href="https://en.wikipedia.org/wiki/Tower_of_Hanoi" target="_blank">Tower of Hanoi</a> problem. </p>
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<p>Main function </p>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; </div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; </div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(no, &amp;F, &amp;U, &amp;T);</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="keywordflow">return</span> 0;</div>
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<p >Main function </p>
<div class="fragment"><div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> {</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nEnter number of discs : &quot;</span>;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; no;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = no; i &gt; 0; i--) {</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> F.values[F.top++] = i;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> }</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a>(&amp;F, &amp;T, &amp;U);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(no, &amp;F, &amp;U, &amp;T);</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span>}</div>
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="astructtower_html"><div class="ttname"><a href="../../d2/d2c/structtower.html">tower</a></div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:11</div></div>
@@ -173,13 +172,13 @@ Functions</h2></td></tr>
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<h2 class="memtitle"><span class="permalink"><a href="#af4cfc41e546f1f8d25f01e0804e8b61d">&#9670;&nbsp;</a></span>mov()</h2>
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<p>Move one disc from one tower to another </p><dl class="params"><dt>Parameters</dt><dd>
<p >Move one disc from one tower to another </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">From</td><td>tower to move disk <em>from</em> </td></tr>
<tr><td class="paramdir">[in,out]</td><td class="paramname">To</td><td>tower to move disk <em>to</em> </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; --From-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; To-&gt;<a class="code" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[To-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>] = From-&gt;<a class="code" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[From-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>];</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; ++To-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> {</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> --From-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>;</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> To-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[To-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>] = From-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[From-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>];</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> ++To-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span>}</div>
<div class="ttc" id="astructtower_html_a3ebb75c13c57d51a8a1ba1ea54a515e9"><div class="ttname"><a href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">tower::values</a></div><div class="ttdeci">int values[10]</div><div class="ttdoc">Values in the tower.</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:13</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a746d9a3984bba88fd6dd91978f6931ed">&#9670;&nbsp;</a></span>show()</h2>
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<p>Display the towers </p>
<div class="fragment"><div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160; {</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\n\tF : &quot;</span>;</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; F-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; F-&gt;<a class="code" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; }</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\tU : &quot;</span>;</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; U-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; U-&gt;<a class="code" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; }</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\tT : &quot;</span>;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; T-&gt;<a class="code" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; T-&gt;<a class="code" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; }</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160;}</div>
<p >Display the towers </p>
<div class="fragment"><div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> {</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\n\tF : &quot;</span>;</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; F-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; F-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> }</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\tU : &quot;</span>;</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; U-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; U-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> }</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\tT : &quot;</span>;</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; T-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#acb535964abd34c47678a4ade0628223d">top</a>; i++) {</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; T-&gt;<a class="code hl_variable" href="../../d2/d2c/structtower.html#a3ebb75c13c57d51a8a1ba1ea54a515e9">values</a>[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> }</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ab037f72a5eac476535a6cfbbcb965417">&#9670;&nbsp;</a></span>TH()</h2>
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<p>Recursive algorithm to solve the puzzle </p><dl class="params"><dt>Parameters</dt><dd>
<p >Recursive algorithm to solve the puzzle </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>starting number of disks </td></tr>
<tr><td class="paramdir">[in,out]</td><td class="paramname">From</td><td>tower to move disks from </td></tr>
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<div class="fragment"><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; {</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>(From, To);</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a>(From, To, Using);</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(n - 1, From, To, Using);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>(From, To);</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a>(From, To, Using);</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(n - 1, Using, From, To);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; }</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>(From, To);</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a>(From, To, Using);</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(n - 1, From, To, Using);</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>(From, To);</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#a746d9a3984bba88fd6dd91978f6931ed">show</a>(From, To, Using);</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <a class="code hl_function" href="../../db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">TH</a>(n - 1, Using, From, To);</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span>}</div>
<div class="ttc" id="atower__of__hanoi_8cpp_html_af4cfc41e546f1f8d25f01e0804e8b61d"><div class="ttname"><a href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a></div><div class="ttdeci">void mov(tower *From, tower *To)</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:39</div></div>
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<p>Implementation of the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/">Wave sort</a> algorithm.
<p>Implementation of the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/" target="_blank">Wave sort</a> algorithm.
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<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
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Functions</h2></td></tr>
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<tr class="memdesc:aa3e61ec7fbcf7f9b52de306e6dd6a41c"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main function implements that implements the Wave Sort algorithm. <a href="../../db/d3f/wave__sort_8cpp.html#aa3e61ec7fbcf7f9b52de306e6dd6a41c">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/">Wave sort</a> algorithm. </p>
<p>Wave Sort is a sorting algorithm that works in \(O(nlogn)\) time assuming the sort function used works in \(O(nlogn)\) time. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy">Swastika Gupta</a> </dd></dl>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; {</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <span class="comment">// [10, 90, 49, 2, 1, 5, 23] return [2, 1, 10, 5, 49, 23, 90]</span></div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array1 = {10, 90, 49, 2, 1, 5, 23};</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr1 = <a class="code" href="../../db/d3f/wave__sort_8cpp.html#aa3e61ec7fbcf7f9b52de306e6dd6a41c">sorting::wave_sort::waveSort</a>(array1, 7);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o1 = {2, 1, 10, 5, 49, 23, 90};</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; assert(arr1 == o1);</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="comment">// [1, 3, 4, 2, 7, 8] return [2, 1, 4, 3, 8, 7]</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array2 = {1, 3, 4, 2, 7, 8};</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2... &quot;</span>;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr2 = <a class="code" href="../../db/d3f/wave__sort_8cpp.html#aa3e61ec7fbcf7f9b52de306e6dd6a41c">sorting::wave_sort::waveSort</a>(array2, 6);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o2 = {2, 1, 4, 3, 8, 7};</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; assert(arr2 == o2);</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <span class="comment">// [3, 3, 3, 3] return [3, 3, 3, 3]</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array3 = {3, 3, 3, 3};</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr3 = <a class="code" href="../../db/d3f/wave__sort_8cpp.html#aa3e61ec7fbcf7f9b52de306e6dd6a41c">sorting::wave_sort::waveSort</a>(array3, 4);</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o3 = {3, 3, 3, 3};</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; assert(arr3 == o3);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="comment">// [9, 4, 6, 8, 14, 3] return [4, 3, 8, 6, 14, 9]</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array4 = {9, 4, 6, 8, 14, 3};</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 4... &quot;</span>;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr4 = <a class="code" href="../../db/d3f/wave__sort_8cpp.html#aa3e61ec7fbcf7f9b52de306e6dd6a41c">sorting::wave_sort::waveSort</a>(array4, 6);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o4 = {4, 3, 8, 6, 14, 9};</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; assert(arr4 == o4);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> {</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// [10, 90, 49, 2, 1, 5, 23] return [2, 1, 10, 5, 49, 23, 90]</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array1 = {10, 90, 49, 2, 1, 5, 23};</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1... &quot;</span>;</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr1 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array1, 7);</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o1 = {2, 1, 10, 5, 49, 23, 90};</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> assert(arr1 == o1);</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// [1, 3, 4, 2, 7, 8] return [2, 1, 4, 3, 8, 7]</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array2 = {1, 3, 4, 2, 7, 8};</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2... &quot;</span>;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr2 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array2, 6);</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o2 = {2, 1, 4, 3, 8, 7};</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> assert(arr2 == o2);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// [3, 3, 3, 3] return [3, 3, 3, 3]</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array3 = {3, 3, 3, 3};</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 3... &quot;</span>;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr3 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array3, 4);</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o3 = {3, 3, 3, 3};</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> assert(arr3 == o3);</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// [9, 4, 6, 8, 14, 3] return [4, 3, 8, 6, 14, 9]</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> array4 = {9, 4, 6, 8, 14, 3};</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 4... &quot;</span>;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr4 = <a class="code hl_function" href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a>(array4, 6);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> o4 = {4, 3, 8, 6, 14, 9};</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> assert(arr4 == o4);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int64_t &gt;</a></div></div>
<div class="ttc" id="awave__sort_8cpp_html_aa3e61ec7fbcf7f9b52de306e6dd6a41c"><div class="ttname"><a href="../../db/d3f/wave__sort_8cpp.html#aa3e61ec7fbcf7f9b52de306e6dd6a41c">sorting::wave_sort::waveSort</a></div><div class="ttdeci">std::vector&lt; T &gt; waveSort(const std::vector&lt; T &gt; &amp;in_arr, int64_t n)</div><div class="ttdoc">The main function implements that implements the Wave Sort algorithm.</div><div class="ttdef"><b>Definition:</b> wave_sort.cpp:34</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
<div class="ttc" id="awave__sort_8cpp_html_a7d4f243b9dc13ace4ef77e30dbc56f12"><div class="ttname"><a href="../../db/d3f/wave__sort_8cpp.html#a7d4f243b9dc13ace4ef77e30dbc56f12">sorting::wave_sort::waveSort</a></div><div class="ttdeci">std::vector&lt; T &gt; waveSort(const std::vector&lt; T &gt; &amp;in_arr, int64_t n)</div><div class="ttdoc">The main function implements that implements the Wave Sort algorithm.</div><div class="ttdef"><b>Definition:</b> wave_sort.cpp:34</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa3e61ec7fbcf7f9b52de306e6dd6a41c">&#9670;&nbsp;</a></span>waveSort()</h2>
<a id="a7d4f243b9dc13ace4ef77e30dbc56f12" name="a7d4f243b9dc13ace4ef77e30dbc56f12"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7d4f243b9dc13ace4ef77e30dbc56f12">&#9670;&nbsp;</a></span>waveSort()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;T&gt; sorting::wave_sort::waveSort </td>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; sorting::wave_sort::waveSort </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>in_arr</em>, </td>
@@ -282,24 +281,24 @@ template&lt;typename T &gt; </div>
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<dl class="section return"><dt>Returns</dt><dd>arr the wave sorted array </dd></dl>
<div class="fragment"><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; {</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> arr(in_arr);</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordflow">for</span> (int64_t i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; arr[i] = in_arr[i];</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; }</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a>(arr.begin(), arr.end());</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordflow">for</span> (int64_t i = 0; i &lt; n - 1; i += 2) { <span class="comment">// swap all the adjacent elements</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(arr[i], arr[i + 1]);</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; }</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordflow">return</span> arr;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> {</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> arr(in_arr);</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
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<p>Heavy light decomposition algorithm.
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<p>Storage mechanism using <a href="https://en.wikipedia.org/wiki/Quadratic_probing">quadratic probing hash</a> keys.
<p>Storage mechanism using <a href="https://en.wikipedia.org/wiki/Quadratic_probing" target="_blank">quadratic probing hash</a> keys.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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bool&#160;</td><td class="memItemRight" valign="bottom"><b>quadratic_probing::rehashing</b></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Storage mechanism using <a href="https://en.wikipedia.org/wiki/Quadratic_probing">quadratic probing hash</a> keys. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/achance6">achance6</a> </dd>
<div class="textblock"><p >Storage mechanism using <a href="https://en.wikipedia.org/wiki/Quadratic_probing" target="_blank">quadratic probing hash</a> keys. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/achance6" target="_blank">achance6</a> </dd>
<dd>
<a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
<a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
<dl class="section note"><dt>Note</dt><dd>The implementation can be optimized by using OOP style. </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<p>Main function </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
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<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2. Remove key.&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3. Find key.&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4. Generate Hash. (Numeric only)&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5. Display Hash table.&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;6. Exit.&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; cmd;</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160; <span class="keywordflow">switch</span> (cmd) {</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160; <span class="keywordflow">case</span> 1:</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to add = &quot;</span>;</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160; <a class="code" href="../../d4/dd2/namespacequadratic__probing.html#a312143ed316d48978084c025ff8d9768">quadratic_probing::addInfo</a>(key);</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160; <span class="keywordflow">case</span> 2:</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to remove = &quot;</span>;</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160; <a class="code" href="../../d4/dd2/namespacequadratic__probing.html#a69fe1f7c36fe004ba83eef2ca82e7e30">quadratic_probing::removalInfo</a>(key);</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160; <span class="keywordflow">case</span> 3: {</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to search = &quot;</span>;</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160; <a class="code" href="../../da/dd1/structquadratic__probing_1_1_entry.html">quadratic_probing::Entry</a> entry =</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160; quadratic_probing::table[<a class="code" href="../../d4/dd2/namespacequadratic__probing.html#ab431981b54c0bae1b2956f716aee1dcf">quadratic_probing::quadraticProbe</a>(</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160; key, <span class="keyword">true</span>)];</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>&#160; <span class="keywordflow">if</span> (entry.<a class="code" href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">key</a> == quadratic_probing::notPresent) {</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key not present&quot;</span>;</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160; }</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>&#160; }</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160; <span class="keywordflow">case</span> 4:</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter element to generate hash = &quot;</span>;</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash of &quot;</span> &lt;&lt; key</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>&#160; &lt;&lt; <span class="stringliteral">&quot; is = &quot;</span> &lt;&lt; <a class="code" href="../../d4/dd2/namespacequadratic__probing.html#a2093d91dd3d377cf0a5c939e45dcefc7">quadratic_probing::hashFxn</a>(key);</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>&#160; <span class="keywordflow">case</span> 5:</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>&#160; <a class="code" href="../../d4/dd2/namespacequadratic__probing.html#a40d617ebf4d6ba21bcda8d8d1faa2357">quadratic_probing::display</a>();</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>&#160; <span class="keywordflow">default</span>:</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>&#160; loop = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>&#160; <span class="comment">// delete[] table;</span></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>&#160; }</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>&#160; }</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>&#160;}</div>
<p >Main function </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<div class="fragment"><div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> {</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keywordtype">int</span> cmd = 0, hash = 0, key = 0;</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the initial size of Hash Table. = &quot;</span>;</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; totalSize;</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> table = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Entry&gt;</a>(totalSize);</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="keywordtype">bool</span> loop = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="keywordflow">while</span> (loop) {</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;PLEASE CHOOSE -&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1. Add key. (Numeric only)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2. Remove key.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3. Find key.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4. Generate Hash. (Numeric only)&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;5. Display Hash table.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;6. Exit.&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; cmd;</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="keywordflow">switch</span> (cmd) {</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <span class="keywordflow">case</span> 1:</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to add = &quot;</span>;</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a312143ed316d48978084c025ff8d9768">quadratic_probing::addInfo</a>(key);</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="keywordflow">case</span> 2:</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to remove = &quot;</span>;</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a69fe1f7c36fe004ba83eef2ca82e7e30">quadratic_probing::removalInfo</a>(key);</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="keywordflow">case</span> 3: {</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter key to search = &quot;</span>;</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <a class="code hl_struct" href="../../da/dd1/structquadratic__probing_1_1_entry.html">quadratic_probing::Entry</a> entry =</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> quadratic_probing::table[<a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#ab431981b54c0bae1b2956f716aee1dcf">quadratic_probing::quadraticProbe</a>(</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> key, <span class="keyword">true</span>)];</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="keywordflow">if</span> (entry.<a class="code hl_variable" href="../../da/dd1/structquadratic__probing_1_1_entry.html#a75f72858f08a2fc8b94402de98db12d8">key</a> == quadratic_probing::notPresent) {</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Key not present&quot;</span>;</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> }</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> }</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="keywordflow">case</span> 4:</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter element to generate hash = &quot;</span>;</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; key;</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Hash of &quot;</span> &lt;&lt; key</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> &lt;&lt; <span class="stringliteral">&quot; is = &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a2093d91dd3d377cf0a5c939e45dcefc7">quadratic_probing::hashFxn</a>(key);</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <span class="keywordflow">case</span> 5:</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <a class="code hl_function" href="../../d4/dd2/namespacequadratic__probing.html#a40d617ebf4d6ba21bcda8d8d1faa2357">quadratic_probing::display</a>();</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> <span class="keywordflow">default</span>:</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> loop = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="comment">// delete[] table;</span></div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> }</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> }</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span>}</div>
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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