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<div class="headertitle"><div class="title">cut_rod.cpp</div></div>
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<div class="contents">
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<a href="../../d6/d10/cut__rod_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="l00020" name="l00020"></a><span class="lineno"> 20</span> </div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include <array></span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include <cassert></span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include <climits></span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include <iostream></span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a> {</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d8/d36/namespacecut__rod.html">cut_rod</a> {</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="keyword">template</span> <<span class="keywordtype">size_t</span> T></div>
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<div class="foldopen" id="foldopen00045" data-start="{" data-end="}">
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"><a class="line" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa"> 45</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">maxProfitByCuttingRod</a>(<span class="keyword">const</span> std::array<int, T> &price, <span class="keyword">const</span> uint64_t &n) {</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordtype">int</span> *profit =</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">new</span> <span class="keywordtype">int</span>[n + 1]; <span class="comment">// profit[i] will hold maximum profit for i inch rod</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> profit[0] = 0; <span class="comment">// if length of rod is zero, then no profit</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// outer loop will select size of rod, starting from 1 inch to n inch rod.</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// inner loop will evaluate the maximum profit we can get for i inch rod by</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// making every possible cut on it and will store it in profit[i].</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i <= n; i++) {</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">int</span> q = INT_MIN;</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 1; j <= i; j++) {</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> q = std::max(q, price[j - 1] + profit[i - j]);</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> }</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> profit[i] = q;</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> }</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keyword">const</span> int16_t ans = profit[n];</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">delete</span>[] profit;</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">return</span> ans; <span class="comment">// returning maximum profit</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>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span>} <span class="comment">// namespace cut_rod</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span>} <span class="comment">// namespace dynamic_programming</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span></div>
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<div class="foldopen" id="foldopen00072" data-start="{" data-end="}">
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"><a class="line" href="../../d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 72</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// Test 1</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">const</span> int16_t n1 = 8; <span class="comment">// size of rod</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> std::array<int32_t, n1> price1 = {1, 2, 4, 6, 8, 45, 21, 9}; <span class="comment">// price array</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keyword">const</span> int64_t max_profit1 =</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price1, n1);</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keyword">const</span> int64_t expected_max_profit1 = 47;</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> assert(max_profit1 == expected_max_profit1);</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> std::cout << <span class="stringliteral">"Maximum profit with "</span> << n1 << <span class="stringliteral">" inch road is "</span> << max_profit1</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> << std::endl;</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// Test 2</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keyword">const</span> int16_t n2 = 30; <span class="comment">// size of rod</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> std::array<int32_t, n2> price2 = {</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> 1, 5, 8, 9, 10, 17, 17, 20, 24, 30, <span class="comment">// price array</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> 41, 42, 43, 44, 45, 46, 47, 48, 49, 50};</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keyword">const</span> int64_t max_profit2 =</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price2, n2);</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keyword">const</span> int32_t expected_max_profit2 = 90;</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> assert(max_profit2 == expected_max_profit2);</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> std::cout << <span class="stringliteral">"Maximum profit with "</span> << n2 << <span class="stringliteral">" inch road is "</span> << max_profit2</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> << std::endl;</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// Test 3</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keyword">const</span> int16_t n3 = 5; <span class="comment">// size of rod</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> std::array<int32_t, n3> price3 = {2, 9, 17, 23, 45}; <span class="comment">// price array</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">const</span> int64_t max_profit3 =</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price3, n3);</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keyword">const</span> int64_t expected_max_profit3 = 45;</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> assert(max_profit3 == expected_max_profit3);</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> std::cout << <span class="stringliteral">"Maximum profit with "</span> << n3 << <span class="stringliteral">" inch road is "</span> << max_profit3</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> << std::endl;</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span>}</div>
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</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span></div>
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<div class="foldopen" id="foldopen00111" data-start="{" data-end="}">
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"><a class="line" href="../../d6/d10/cut__rod_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 111</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="comment">// Testing</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <a class="code hl_function" href="../../d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span>}</div>
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</div>
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<div class="ttc" id="acut__rod_8cpp_html_a1cc523a30c18c63eac58220c3c494cfa"><div class="ttname"><a href="../../d6/d10/cut__rod_8cpp.html#a1cc523a30c18c63eac58220c3c494cfa">dynamic_programming::cut_rod::maxProfitByCuttingRod</a></div><div class="ttdeci">int maxProfitByCuttingRod(const std::array< int, T > &price, const uint64_t &n)</div><div class="ttdoc">Cuts the rod in different pieces and stores the maximum profit for each piece of the rod.</div><div class="ttdef"><b>Definition</b> <a href="#l00045">cut_rod.cpp:45</a></div></div>
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<div class="ttc" id="acut__rod_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function to test above algorithm.</div><div class="ttdef"><b>Definition</b> <a href="#l00072">cut_rod.cpp:72</a></div></div>
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<div class="ttc" id="acut__rod_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d6/d10/cut__rod_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="#l00111">cut_rod.cpp:111</a></div></div>
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<div class="ttc" id="anamespacecut__rod_html"><div class="ttname"><a href="../../d8/d36/namespacecut__rod.html">cut_rod</a></div><div class="ttdoc">Implementation of cutting a rod problem.</div></div>
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<div class="ttc" id="anamespacedynamic__programming_html"><div class="ttname"><a href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a></div><div class="ttdoc">Dynamic Programming algorithms.</div></div>
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