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<div class="headertitle"><div class="title">catalan_numbers.cpp</div></div>
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<div class="contents">
<a href="../../de/dd9/catalan__numbers_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>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include &lt;cstdint&gt;</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &lt;cstdlib&gt;</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include &lt;functional&gt;</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;numeric&gt;</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span></div>
<div class="foldopen" id="foldopen00022" data-start="{" data-end="};">
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"><a class="line" href="../../dc/d1f/classcatalan__numbers.html"> 22</a></span><span class="keyword">class </span><a class="code hl_class" href="../../dc/d1f/classcatalan__numbers.html">catalan_numbers</a> {</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keyword">using </span>value_type = std::uint64_t;</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> std::vector&lt;value_type&gt; known{1, 1};</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> value_type compute_next() {</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="keywordflow">return</span> std::transform_reduce(known.begin(), known.end(), known.rbegin(),</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">static_cast&lt;</span>value_type<span class="keyword">&gt;</span>(0), std::plus&lt;&gt;(),</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> std::multiplies&lt;&gt;());</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> }</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keywordtype">void</span> add() { known.push_back(this-&gt;compute_next()); }</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keyword">public</span>:</div>
<div class="foldopen" id="foldopen00039" data-start="{" data-end="}">
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"><a class="line" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8"> 39</a></span> value_type <a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(std::size_t n) {</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">while</span> (known.size() &lt;= n) {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> this-&gt;add();</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> }</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">return</span> known[n];</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> }</div>
</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span>};</div>
</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="keywordtype">void</span> test_catalan_numbers_up_to_20() {</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// data verified with https://oeis.org/A000108/</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <a class="code hl_class" href="../../dc/d1f/classcatalan__numbers.html">catalan_numbers</a> cn;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(0) == 1ULL);</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(1) == 1ULL);</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(2) == 2ULL);</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(3) == 5ULL);</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(4) == 14ULL);</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(5) == 42ULL);</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(6) == 132ULL);</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(7) == 429ULL);</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(8) == 1430ULL);</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(9) == 4862ULL);</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(10) == 16796ULL);</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(11) == 58786ULL);</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(12) == 208012ULL);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(13) == 742900ULL);</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(14) == 2674440ULL);</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(15) == 9694845ULL);</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(16) == 35357670ULL);</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(17) == 129644790ULL);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(18) == 477638700ULL);</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(19) == 1767263190ULL);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(20) == 6564120420ULL);</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span>}</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="keywordtype">void</span> test_catalan_numbers_25() {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// data verified with https://oeis.org/A000108/</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <a class="code hl_class" href="../../dc/d1f/classcatalan__numbers.html">catalan_numbers</a> cn;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> assert(cn.<a class="code hl_function" href="../../dc/d1f/classcatalan__numbers.html#a54655c66cf89186d3d1fa90829b28ab8">get</a>(25) == 4861946401452ULL);</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span>}</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> test_catalan_numbers_up_to_20();</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> test_catalan_numbers_25();</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span>}</div>
<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="#l00022">catalan_numbers.cpp:22</a></div></div>
<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="#l00039">catalan_numbers.cpp:39</a></div></div>
<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
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