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<p>Calculate the length of the <a href="https://en.wikipedia.org/wiki/Longest_increasing_subsequence" target="_blank">longest increasing subsequence</a> in an array.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;climits&gt;</code><br />
<code>#include &lt;cstdint&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 longest_increasing_subsequence.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:"><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>
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Functions</h2></td></tr>
<tr class="memitem:a0a2215194e58786c34db1ccaf8031079" id="r_a0a2215194e58786c34db1ccaf8031079"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d24/namespacedynamic__programming.html#a0a2215194e58786c34db1ccaf8031079">dynamic_programming::LIS</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;a, const uint32_t &amp;n)</td></tr>
<tr class="memdesc:a0a2215194e58786c34db1ccaf8031079"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate the longest increasing subsequence for the specified numbers. <br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="memitem:abf9e6b7e6f15df4b525a2e7705ba3089" id="r_abf9e6b7e6f15df4b525a2e7705ba3089"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#abf9e6b7e6f15df4b525a2e7705ba3089">main</a> (int argc, char const *argv[])</td></tr>
<tr class="memdesc:abf9e6b7e6f15df4b525a2e7705ba3089"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Calculate the length of the <a href="https://en.wikipedia.org/wiki/Longest_increasing_subsequence" target="_blank">longest increasing subsequence</a> in an array. </p>
<p>In computer science, the longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence's elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible. This subsequence is not necessarily contiguous, or unique. Longest increasing subsequences are studied in the context of various disciplines related to mathematics, including algorithmics, random matrix theory, representation theory, and physics. The longest increasing subsequence problem is solvable in time O(n log n), where n denotes the length of the input sequence.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd>
<dd>
<a href="https://github.com/Panquesito7" target="_blank">David Leal</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="abf9e6b7e6f15df4b525a2e7705ba3089" name="abf9e6b7e6f15df4b525a2e7705ba3089"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abf9e6b7e6f15df4b525a2e7705ba3089">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>argc</em></span>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
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<p>Main function. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">argc</td><td>commandline argument count (ignored) </td></tr>
<tr><td class="paramname">argv</td><td>commandline array of arguments (ignored) </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 81</span> {</div>
<div class="line"><span class="lineno"> 82</span> uint32_t n = 0;</div>
<div class="line"><span class="lineno"> 83</span> </div>
<div class="line"><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;Enter size of array: &quot;</span>;</div>
<div class="line"><span class="lineno"> 85</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
<div class="line"><span class="lineno"> 86</span> </div>
<div class="line"><span class="lineno"> 87</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(n);</div>
<div class="line"><span class="lineno"> 88</span> </div>
<div class="line"><span class="lineno"> 89</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 array elements: &quot;</span>;</div>
<div class="line"><span class="lineno"> 90</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</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_istream.html">std::cin</a> &gt;&gt; a[i];</div>
<div class="line"><span class="lineno"> 92</span> }</div>
<div class="line"><span class="lineno"> 93</span> </div>
<div class="line"><span class="lineno"> 94</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;\nThe result is: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../dd/d24/namespacedynamic__programming.html#a0a2215194e58786c34db1ccaf8031079">dynamic_programming::LIS</a>(a, n)</div>
<div class="line"><span class="lineno"> 95</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"> 96</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 97</span> </div>
<div class="line"><span class="lineno"> 98</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 99</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>
<div class="ttc" id="alongest__increasing__subsequence_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> longest_increasing_subsequence.cpp:64</div></div>
<div class="ttc" id="anamespacedynamic__programming_html_a0a2215194e58786c34db1ccaf8031079"><div class="ttname"><a href="../../dd/d24/namespacedynamic__programming.html#a0a2215194e58786c34db1ccaf8031079">dynamic_programming::LIS</a></div><div class="ttdeci">uint64_t LIS(const std::vector&lt; uint64_t &gt; &amp;a, const uint32_t &amp;n)</div><div class="ttdoc">Calculate the longest increasing subsequence for the specified numbers.</div><div class="ttdef"><b>Definition</b> longest_increasing_subsequence.cpp:40</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>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</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>
<p>&lt; The longest increasing subsequence is <code>{2,3,4,5,8}</code></p>
<div class="fragment"><div class="line"><span class="lineno"> 64</span> {</div>
<div class="line"><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;uint64_t&gt;</a> a = {15, 21, 2, 3, 4, 5, 8, 4, 1, 1};</div>
<div class="line"><span class="lineno"> 66</span> uint32_t n = a.size();</div>
<div class="line"><span class="lineno"> 67</span> </div>
<div class="line"><span class="lineno"> 68</span> uint32_t <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../dd/d24/namespacedynamic__programming.html#a0a2215194e58786c34db1ccaf8031079">dynamic_programming::LIS</a>(a, n);</div>
<div class="line"><span class="lineno"> 69</span> assert(result ==</div>
<div class="line"><span class="lineno"> 70</span> 5); <span class="comment">///&lt; The longest increasing subsequence is `{2,3,4,5,8}`</span></div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><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;Self-test implementations 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"> 73</span>}</div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition</b> fibonacci_sum.cpp:77</div></div>
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