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<div class="headertitle"><div class="title">n_bonacci.cpp</div></div>
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<div class="contents">
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<a href="../../db/d27/n__bonacci_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <cassert></span> </div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <iostream></span> </div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include <vector></span> </div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d47/namespacemath.html">math</a> {</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../de/d36/namespacen__bonacci.html">n_bonacci</a> {</div>
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<div class="foldopen" id="foldopen00040" data-start="{" data-end="}">
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"><a class="line" href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d"> 40</a></span>std::vector<uint64_t> <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#a6849b68f760be628d5975ab3eddec63d">N_bonacci</a>(<span class="keyword">const</span> uint64_t &n, <span class="keyword">const</span> uint64_t &m) {</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> std::vector<uint64_t> a(</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> m, 0); <span class="comment">// we create an array of size m filled with zeros</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">if</span> (m < n || n == 0) {</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">return</span> a;</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> }</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> a[n - 1] = 1; </div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">if</span> (n == m) {</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordflow">return</span> a;</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> }</div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> a[n] = 1; </div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">for</span> (uint64_t i = n + 1; i < m; i++) {</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// this is an optimized solution that works in O(M) time and takes O(M)</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// extra space here we use the concept of the sliding window the current</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// term can be computed using the given formula</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> a[i] = 2 * a[i - 1] - a[i - 1 - n];</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> }</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">return</span> a;</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span>}</div>
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</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span>} <span class="comment">// namespace n_bonacci</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span>} <span class="comment">// namespace math</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
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<div class="foldopen" id="foldopen00069" data-start="{" data-end="}">
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"><a class="line" href="../../db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 69</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keyword">struct </span><a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a> {</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keyword">const</span> uint64_t n;</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keyword">const</span> uint64_t m;</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keyword">const</span> std::vector<uint64_t> expected;</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(<span class="keyword">const</span> uint64_t in_n, <span class="keyword">const</span> uint64_t in_m,</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> std::initializer_list<uint64_t> <a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>)</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> : n(in_n), m(in_m), expected(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>) {</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> assert(<a class="code hl_variable" href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a>.size() == m);</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> };</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">const</span> std::vector<TestCase> test_cases = {</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(0, 0, {}),</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(0, 1, {0}),</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(0, 2, {0, 0}),</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(1, 0, {}),</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(1, 1, {1}),</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(1, 2, {1, 1}),</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(1, 3, {1, 1, 1}),</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(5, 15, {0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236, 464}),</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> 6, 17,</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> {0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 63, 125, 248, 492, 976}),</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <a class="code hl_struct" href="../../da/d86/struct_test_case.html">TestCase</a>(56, 15, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})};</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> </div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &tc : test_cases) {</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> assert(math::n_bonacci::N_bonacci(tc.n, tc.m) == tc.expected);</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> }</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span>}</div>
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</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> </div>
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<div class="foldopen" id="foldopen00104" data-start="{" data-end="}">
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"><a class="line" href="../../db/d27/n__bonacci_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 104</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../db/d27/n__bonacci_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</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>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span>}</div>
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</div>
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<div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition</b> <a href="../../d1/df3/hash__search_8cpp_source.html#l00024">hash_search.cpp:24</a></div></div>
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<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< uint64_t > N_bonacci(const uint64_t &n, const uint64_t &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> <a href="#l00040">n_bonacci.cpp:40</a></div></div>
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<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> <a href="#l00069">n_bonacci.cpp:69</a></div></div>
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<div class="ttc" id="an__bonacci_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../db/d27/n__bonacci_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00104">n_bonacci.cpp:104</a></div></div>
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<div class="ttc" id="anamespacemath_html"><div class="ttname"><a href="../../dd/d47/namespacemath.html">math</a></div><div class="ttdoc">for assert</div></div>
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<div class="ttc" id="anamespacen__bonacci_html"><div class="ttname"><a href="../../de/d36/namespacen__bonacci.html">n_bonacci</a></div><div class="ttdoc">Functions for the N-bonacci implementation.</div></div>
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<div class="ttc" id="astruct_test_case_html"><div class="ttname"><a href="../../da/d86/struct_test_case.html">TestCase</a></div><div class="ttdoc">represents single example inputs and expected output of the function longest_common_string_length</div><div class="ttdef"><b>Definition</b> <a href="../../da/d0d/longest__common__string_8cpp_source.html#l00054">longest_common_string.cpp:54</a></div></div>
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