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<p>Algorithm of <a href="https://en.wikipedia.org/wiki/Radix_sort">Radix sort</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
<code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for radix_sort2.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:d5/d91/namespacesorting"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html">sorting</a></td></tr>
<tr class="memdesc:d5/d91/namespacesorting"><td class="mdescLeft">&#160;</td><td class="mdescRight">Sorting algorithms. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:da/dda/namespaceradix__sort"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dda/namespaceradix__sort.html">radix_sort</a></td></tr>
<tr class="memdesc:da/dda/namespaceradix__sort"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Radix_sort">Radix sort</a> algorithm. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a302672a25ef4561eb41b4f9ef8e518b2"><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="../../d8/d61/radix__sort2_8cpp.html#a302672a25ef4561eb41b4f9ef8e518b2">sorting::radix_sort::step_ith</a> (uint16_t cur_digit, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt; &amp;ar)</td></tr>
<tr class="memdesc:a302672a25ef4561eb41b4f9ef8e518b2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to sort vector according to current digit using stable sorting. <a href="../../d8/d61/radix__sort2_8cpp.html#a302672a25ef4561eb41b4f9ef8e518b2">More...</a><br /></td></tr>
<tr class="separator:a302672a25ef4561eb41b4f9ef8e518b2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8df9406972cda58c209b30ebae295daa"><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="../../d8/d61/radix__sort2_8cpp.html#a8df9406972cda58c209b30ebae295daa">sorting::radix_sort::radix</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt; &amp;ar)</td></tr>
<tr class="memdesc:a8df9406972cda58c209b30ebae295daa"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to sort vector digit by digit. <a href="../../d8/d61/radix__sort2_8cpp.html#a8df9406972cda58c209b30ebae295daa">More...</a><br /></td></tr>
<tr class="separator:a8df9406972cda58c209b30ebae295daa"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to test the above algorithm. <a href="../../d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">More...</a><br /></td></tr>
<tr class="separator:a483bb8ccf42aaf7375a83e91490eda1e"><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="../../d8/d61/radix__sort2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d8/d61/radix__sort2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">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>Algorithm of <a href="https://en.wikipedia.org/wiki/Radix_sort">Radix sort</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Suyashjaiswal">Suyash Jaiswal</a> Sort the vector of unsigned integers using radix sort i.e. sorting digit by digit using <a href="https://en.wikipedia.org/wiki/Counting_sort">Counting Sort</a> as subroutine. Running time of radix sort is O(d*(n+b)) where b is the base for representing numbers and d in the max digits in input integers and n is number of unsigned integers. consider example for n = 5, aray elements = 432,234,143,332,123 sorting digit by digit sorting according to 1) 1st digit place =&gt; 432, 332, 143, 123, 234</dd></dl>
<p>2) 2nd digit place =&gt; 123, 432, 332, 234, 143</p>
<p>3) 3rd digit place =&gt; 123, 143, 234, 332, 432</p>
<p>using count sort at each step, which is stable. stable =&gt; already sorted according to previous digits. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
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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="l00115"></a><span class="lineno"> 115</span>&#160; {</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <a class="code" href="../../d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8df9406972cda58c209b30ebae295daa">&#9670;&nbsp;</a></span>radix()</h2>
<div class="memitem">
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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; sorting::radix_sort::radix </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; uint64_t &gt; &amp;&#160;</td>
<td class="paramname"><em>ar</em></td><td>)</td>
<td></td>
</tr>
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</div><div class="memdoc">
<p>Function to sort vector digit by digit. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">ar</td><td>- vector to be sorted </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>sorted vector </dd></dl>
<div class="fragment"><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; {</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; uint64_t max_ele = *<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max_element.html">max_element</a>(ar.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), ar.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()); <span class="comment">// returns the max element.</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> temp = ar;</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; max_ele / i &gt; 0;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; i *= 10) { <span class="comment">// loop breaks when i &gt; max_ele because no further digits</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="comment">// left to makes changes in aray.</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; temp = <a class="code" href="../../d8/d61/radix__sort2_8cpp.html#a302672a25ef4561eb41b4f9ef8e518b2">step_ith</a>(i,temp);</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; }</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <span class="keywordflow">for</span> (uint64_t i : temp) {</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</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; <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&quot;</span>;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <span class="keywordflow">return</span> temp;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a302672a25ef4561eb41b4f9ef8e518b2">&#9670;&nbsp;</a></span>step_ith()</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; sorting::radix_sort::step_ith </td>
<td>(</td>
<td class="paramtype">uint16_t&#160;</td>
<td class="paramname"><em>cur_digit</em>, </td>
</tr>
<tr>
<td class="paramkey"></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; uint64_t &gt; &amp;&#160;</td>
<td class="paramname"><em>ar</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>Function to sort vector according to current digit using stable sorting. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">cur_digit</td><td>- sort according to the cur_digit </td></tr>
<tr><td class="paramname">ar</td><td>- vector to be sorted </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html" title="STL class.">std::vector</a> sorted till ith digit </dd></dl>
<div class="fragment"><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; { <span class="comment">// sorting according to current digit.</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordtype">int</span> n = ar.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> position(10, 0);</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; position[(ar[i] / cur_digit) %</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; 10]++; <span class="comment">// counting frequency of 0-9 at cur_digit.</span></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">int</span> cur = 0;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 10; ++i) {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordtype">int</span> a = position[i];</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; position[i] = cur; <span class="comment">// assingning starting position of 0-9.</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; cur += a;</div>
<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; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> temp(n);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; temp[position[(ar[i] / cur_digit) % 10]] =</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; ar[i]; <span class="comment">// storing ar[i] in ar[i]&#39;s cur_digit expected position of</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="comment">// this step.</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; position[(ar[i] / cur_digit) %</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; 10]++; <span class="comment">// incrementing ar[i]&#39;s cur_digit position by 1, as</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <span class="comment">// current place used by ar[i].</span></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="keywordflow">return</span> temp;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">&#9670;&nbsp;</a></span>tests()</h2>
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<td class="memname">static void tests </td>
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<p>Function to test the above algorithm. </p>
<dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
<p>Test 1</p>
<p>Test 2</p>
<div class="fragment"><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; {<span class="comment"></span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160;<span class="comment"> /// Test 1</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;<span class="comment"></span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> ar1 = {432, 234, 143, 332, 123};</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; ar1 = <a class="code" href="../../d8/d61/radix__sort2_8cpp.html#a8df9406972cda58c209b30ebae295daa">sorting::radix_sort::radix</a>(ar1);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(ar1.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), ar1.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()));<span class="comment"></span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160;<span class="comment"> /// Test 2</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160;<span class="comment"></span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> ar2 = {213, 3214, 123, 111, 112, 142,</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; 133, 132, 32, 12, 113};</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; ar2 = <a class="code" href="../../d8/d61/radix__sort2_8cpp.html#a8df9406972cda58c209b30ebae295daa">sorting::radix_sort::radix</a>(ar2);</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(ar2.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), ar2.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()));</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160;}</div>
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<div class="ttc" id="aradix__sort2_8cpp_html_a302672a25ef4561eb41b4f9ef8e518b2"><div class="ttname"><a href="../../d8/d61/radix__sort2_8cpp.html#a302672a25ef4561eb41b4f9ef8e518b2">sorting::radix_sort::step_ith</a></div><div class="ttdeci">std::vector&lt; uint64_t &gt; step_ith(uint16_t cur_digit, const std::vector&lt; uint64_t &gt; &amp;ar)</div><div class="ttdoc">Function to sort vector according to current digit using stable sorting.</div><div class="ttdef"><b>Definition:</b> radix_sort2.cpp:50</div></div>
<div class="ttc" id="amax_element_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max_element.html">std::max_element</a></div><div class="ttdeci">T max_element(T... args)</div></div>
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<div class="ttc" id="aradix__sort2_8cpp_html_a8df9406972cda58c209b30ebae295daa"><div class="ttname"><a href="../../d8/d61/radix__sort2_8cpp.html#a8df9406972cda58c209b30ebae295daa">sorting::radix_sort::radix</a></div><div class="ttdeci">std::vector&lt; uint64_t &gt; radix(const std::vector&lt; uint64_t &gt; &amp;ar)</div><div class="ttdoc">Function to sort vector digit by digit.</div><div class="ttdef"><b>Definition:</b> radix_sort2.cpp:79</div></div>
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