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<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 />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for n_bonacci.cpp:</div>
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<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a> <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:de/d36/namespacen__bonacci"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d36/namespacen__bonacci.html">n_bonacci</a></td></tr>
<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:a6849b68f760be628d5975ab3eddec63d"><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#a6849b68f760be628d5975ab3eddec63d">math::n_bonacci::N_bonacci</a> (const uint64_t &amp;n, const uint64_t &amp;m)</td></tr>
<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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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d27/n__bonacci_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../db/d27/n__bonacci_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 >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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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</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"><span class="lineno"> 120</span> {</div>
<div class="line"><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"><span class="lineno"> 122</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 123</span>}</div>
<div class="ttc" id="an__bonacci_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> n_bonacci.cpp:63</div></div>
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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>(</td>
<td class="paramtype">const uint64_t &amp;&#160;</td>
<td class="paramname"><em>n</em>, </td>
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<td class="paramtype">const uint64_t &amp;&#160;</td>
<td class="paramname"><em>m</em>&#160;</td>
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<p>Finds the N-Bonacci series for the <code>n</code> parameter value and <code>m</code> parameter terms. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>is in the N-Bonacci series </td></tr>
<tr><td class="paramname">m</td><td>is the number of terms in the N-Bonacci sequence </td></tr>
</table>
</dd>
</dl>
<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"><span class="lineno"> 41</span> {</div>
<div class="line"><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"><span class="lineno"> 43</span> </div>
<div class="line"><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"><span class="lineno"> 45</span><span class="comment"> /// preceding N zeros</span></div>
<div class="line"><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"><span class="lineno"> 47</span><span class="comment"> /// also 1</span></div>
<div class="line"><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"><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"><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"><span class="lineno"> 51</span> <span class="comment">// term can be computed using the given formula</span></div>
<div class="line"><span class="lineno"> 52</span> a[i] = 2 * a[i - 1] - a[i - 1 - n];</div>
<div class="line"><span class="lineno"> 53</span> }</div>
<div class="line"><span class="lineno"> 54</span> <span class="keywordflow">return</span> a;</div>
<div class="line"><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&lt; uint64_t &gt;</a></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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<td class="memname">static void test </td>
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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"><span class="lineno"> 63</span> {</div>
<div class="line"><span class="lineno"> 64</span> <span class="comment">// n = 1 m = 1 return [1, 1]</span></div>
<div class="line"><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"><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"><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"><span class="lineno"> 68</span> <span class="comment">// N-bonacci func</span></div>
<div class="line"><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"><span class="lineno"> 70</span> 1, 1}; <span class="comment">// It is the expected output series of length m</span></div>
<div class="line"><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"><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"><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"><span class="lineno"> 74</span> </div>
<div class="line"><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"><span class="lineno"> 76</span> <span class="comment">// 464]</span></div>
<div class="line"><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"><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"><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"><span class="lineno"> 80</span> <span class="comment">// N-bonacci func</span></div>
<div class="line"><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"><span class="lineno"> 82</span> 0, 0, 0, 0, 1, 1, 2, 4,</div>
<div class="line"><span class="lineno"> 83</span> 8, 16, 31, 61, 120, 236, 464}; <span class="comment">// It is the expected output series of</span></div>
<div class="line"><span class="lineno"> 84</span> <span class="comment">// length m</span></div>
<div class="line"><span class="lineno"> 85</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>(arr2), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2),</div>
<div class="line"><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"><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"><span class="lineno"> 88</span> </div>
<div class="line"><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"><span class="lineno"> 90</span> <span class="comment">// 492, 976]</span></div>
<div class="line"><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"><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"><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"><span class="lineno"> 94</span> <span class="comment">// N-bonacci func</span></div>
<div class="line"><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"><span class="lineno"> 96</span> 0, 0, 0, 0, 0, 1, 1, 2, 4,</div>
<div class="line"><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"><span class="lineno"> 98</span> <span class="comment">// of length m</span></div>
<div class="line"><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"><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"><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"><span class="lineno"> 102</span> </div>
<div class="line"><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"><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"><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"><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"><span class="lineno"> 107</span> <span class="comment">// for N-bonacci func</span></div>
<div class="line"><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"><span class="lineno"> 109</span> 0, 0, 0, 0, 0, 0, 0, 0,</div>
<div class="line"><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"><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"><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"><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>
<div class="line"><span class="lineno"> 114</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="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
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<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="aequal_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/equal.html">std::equal</a></div><div class="ttdeci">T equal(T... args)</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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