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<p>Provides utilities to compute Catalan numbers using dynamic programming. A Catalan numbers satisfy these recurrence relations: C(0) = C(1) = 1; C(n) = sum(C(i).C(n-i-1)), for i = 0 to n-1 Read more about Catalan numbers here: <a href="https://en.wikipedia.org/wiki/Catalan_number">https://en.wikipedia.org/wiki/Catalan_number</a> <a href="https://oeis.org/A000108/">https://oeis.org/A000108/</a>.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cassert></code><br />
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<code>#include <cstdint></code><br />
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<code>#include <cstdlib></code><br />
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<code>#include <functional></code><br />
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<code>#include <numeric></code><br />
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<code>#include <vector></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for catalan_numbers.cpp:</div>
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<p><a href="../../de/dd9/catalan__numbers_8cpp_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-nested-classes" class="groupheader"><a id="nested-classes" name="nested-classes"></a>
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Classes</h2></td></tr>
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<tr class="memitem:catalan_5Fnumbers" id="r_catalan_5Fnumbers"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d1f/classcatalan__numbers.html">catalan_numbers</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">computes and caches Catalan numbers <a href="../../dc/d1f/classcatalan__numbers.html#details">More...</a><br /></td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:af232ca32e11f2fad3fbcd016582736f6" id="r_af232ca32e11f2fad3fbcd016582736f6"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#af232ca32e11f2fad3fbcd016582736f6">test_catalan_numbers_up_to_20</a> ()</td></tr>
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<tr class="memitem:a5aba76282165e591c9872df9fe3ce173" id="r_a5aba76282165e591c9872df9fe3ce173"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a5aba76282165e591c9872df9fe3ce173">test_catalan_numbers_25</a> ()</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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</table>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Provides utilities to compute Catalan numbers using dynamic programming. A Catalan numbers satisfy these recurrence relations: C(0) = C(1) = 1; C(n) = sum(C(i).C(n-i-1)), for i = 0 to n-1 Read more about Catalan numbers here: <a href="https://en.wikipedia.org/wiki/Catalan_number">https://en.wikipedia.org/wiki/Catalan_number</a> <a href="https://oeis.org/A000108/">https://oeis.org/A000108/</a>. </p>
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<p class="definition">Definition in file <a class="el" href="../../de/dd9/catalan__numbers_8cpp_source.html">catalan_numbers.cpp</a>.</p>
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</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p class="definition">Definition at line <a class="el" href="../../de/dd9/catalan__numbers_8cpp_source.html#l00079">79</a> of file <a class="el" href="../../de/dd9/catalan__numbers_8cpp_source.html">catalan_numbers.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 79</span> {</div>
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<div class="line"><span class="lineno"> 80</span> test_catalan_numbers_up_to_20();</div>
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<div class="line"><span class="lineno"> 81</span> test_catalan_numbers_25();</div>
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<div class="line"><span class="lineno"> 82</span>}</div>
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<a id="a5aba76282165e591c9872df9fe3ce173" name="a5aba76282165e591c9872df9fe3ce173"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a5aba76282165e591c9872df9fe3ce173">◆ </a></span>test_catalan_numbers_25()</h2>
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<td class="memname">void test_catalan_numbers_25 </td>
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<td>(</td>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p class="definition">Definition at line <a class="el" href="../../de/dd9/catalan__numbers_8cpp_source.html#l00073">73</a> of file <a class="el" href="../../de/dd9/catalan__numbers_8cpp_source.html">catalan_numbers.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 73</span> {</div>
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<div class="line"><span class="lineno"> 74</span> <span class="comment">// data verified with https://oeis.org/A000108/</span></div>
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<div class="line"><span class="lineno"> 75</span> <a class="code hl_class" href="../../dc/d1f/classcatalan__numbers.html">catalan_numbers</a> cn;</div>
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<div class="line"><span class="lineno"> 76</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(25) == 4861946401452ULL);</div>
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<div class="line"><span class="lineno"> 77</span>}</div>
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<div class="ttc" id="aclasscatalan__numbers_html"><div class="ttname"><a href="../../dc/d1f/classcatalan__numbers.html">catalan_numbers</a></div><div class="ttdoc">computes and caches Catalan numbers</div><div class="ttdef"><b>Definition</b> <a href="../../de/dd9/catalan__numbers_8cpp_source.html#l00022">catalan_numbers.cpp:22</a></div></div>
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<div class="ttc" id="aclasscatalan__numbers_html_a54655c66cf89186d3d1fa90829b28ab8"><div class="ttname"><a href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">catalan_numbers::get</a></div><div class="ttdeci">value_type get(std::size_t n)</div><div class="ttdoc">computes the n-th Catalan number and updates the cache.</div><div class="ttdef"><b>Definition</b> <a href="../../de/dd9/catalan__numbers_8cpp_source.html#l00039">catalan_numbers.cpp:39</a></div></div>
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<a id="af232ca32e11f2fad3fbcd016582736f6" name="af232ca32e11f2fad3fbcd016582736f6"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#af232ca32e11f2fad3fbcd016582736f6">◆ </a></span>test_catalan_numbers_up_to_20()</h2>
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<td class="memname">void test_catalan_numbers_up_to_20 </td>
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<td>(</td>
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<p class="definition">Definition at line <a class="el" href="../../de/dd9/catalan__numbers_8cpp_source.html#l00047">47</a> of file <a class="el" href="../../de/dd9/catalan__numbers_8cpp_source.html">catalan_numbers.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 47</span> {</div>
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<div class="line"><span class="lineno"> 48</span> <span class="comment">// data verified with https://oeis.org/A000108/</span></div>
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<div class="line"><span class="lineno"> 49</span> <a class="code hl_class" href="../../dc/d1f/classcatalan__numbers.html">catalan_numbers</a> cn;</div>
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<div class="line"><span class="lineno"> 50</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(0) == 1ULL);</div>
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<div class="line"><span class="lineno"> 51</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(1) == 1ULL);</div>
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<div class="line"><span class="lineno"> 52</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(2) == 2ULL);</div>
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<div class="line"><span class="lineno"> 53</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(3) == 5ULL);</div>
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<div class="line"><span class="lineno"> 54</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(4) == 14ULL);</div>
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<div class="line"><span class="lineno"> 55</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(5) == 42ULL);</div>
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<div class="line"><span class="lineno"> 56</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(6) == 132ULL);</div>
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<div class="line"><span class="lineno"> 57</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(7) == 429ULL);</div>
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<div class="line"><span class="lineno"> 58</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(8) == 1430ULL);</div>
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<div class="line"><span class="lineno"> 59</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(9) == 4862ULL);</div>
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<div class="line"><span class="lineno"> 60</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(10) == 16796ULL);</div>
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<div class="line"><span class="lineno"> 61</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(11) == 58786ULL);</div>
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<div class="line"><span class="lineno"> 62</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(12) == 208012ULL);</div>
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<div class="line"><span class="lineno"> 63</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(13) == 742900ULL);</div>
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<div class="line"><span class="lineno"> 64</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(14) == 2674440ULL);</div>
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<div class="line"><span class="lineno"> 65</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(15) == 9694845ULL);</div>
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<div class="line"><span class="lineno"> 66</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(16) == 35357670ULL);</div>
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<div class="line"><span class="lineno"> 67</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(17) == 129644790ULL);</div>
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<div class="line"><span class="lineno"> 68</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(18) == 477638700ULL);</div>
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<div class="line"><span class="lineno"> 69</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(19) == 1767263190ULL);</div>
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<div class="line"><span class="lineno"> 70</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(20) == 6564120420ULL);</div>
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<div class="line"><span class="lineno"> 71</span>}</div>
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