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<div class="headertitle"><div class="title">0_1_knapsack.cpp</div></div>
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<a href="../../db/d16/0__1__knapsack_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="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include <array></span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include <cassert></span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include <iostream></span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</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="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="keyword">namespace </span>knapsack {</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="keyword">template</span> <<span class="keywordtype">size_t</span> n></div>
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<div class="foldopen" id="foldopen00051" data-start="{" data-end="}">
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"><a class="line" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1"> 51</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">maxKnapsackValue</a>(<span class="keyword">const</span> <span class="keywordtype">int</span> capacity, <span class="keyword">const</span> std::array<int, n> &weight,</div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keyword">const</span> std::array<int, n> &value) {</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> std::vector<std::vector<int> > maxValue(n + 1,</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> std::vector<int>(capacity + 1, 0));</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// outer loop will select no of items allowed</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// inner loop will select the capacity of the knapsack bag</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordtype">int</span> items = <span class="keyword">sizeof</span>(weight) / <span class="keyword">sizeof</span>(weight[0]);</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i < items + 1; ++i) {</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; j < capacity + 1; ++j) {</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// if no of items is zero or capacity is zero, then maxValue</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// will be zero</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> maxValue[i][j] = 0;</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (weight[i - 1] <= j) {</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// if the ith item's weight(in the actual array it will be at i-1)</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// is less than or equal to the allowed weight i.e. j then we</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// can pick that item for our knapsack. maxValue will be the</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// obtained either by picking the current item or by not picking</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// current item</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// picking the current item</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordtype">int</span> profit1 = value[i - 1] + maxValue[i - 1][j - weight[i - 1]];</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// not picking the current item</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordtype">int</span> profit2 = maxValue[i - 1][j];</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> maxValue[i][j] = std::max(profit1, profit2);</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// as the weight of the current item is greater than the allowed weight, so</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// maxProfit will be profit obtained by excluding the current item.</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> maxValue[i][j] = maxValue[i - 1][j];</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> }</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// returning maximum value</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">return</span> maxValue[items][capacity];</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span>}</div>
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</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span>} <span class="comment">// namespace knapsack</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>} <span class="comment">// namespace dynamic_programming</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
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<div class="foldopen" id="foldopen00096" data-start="{" data-end="}">
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"><a class="line" href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 96</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// Test 1</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n1 = 3; <span class="comment">// number of items</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> std::array<int, n1> weight1 = {10, 20, 30}; <span class="comment">// weight of each item</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> std::array<int, n1> value1 = {60, 100, 120}; <span class="comment">// value of each item</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keyword">const</span> <span class="keywordtype">int</span> capacity1 = 50; <span class="comment">// capacity of carrying bag</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keyword">const</span> <span class="keywordtype">int</span> max_value1 = dynamic_programming::knapsack::maxKnapsackValue(</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> capacity1, weight1, value1);</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keyword">const</span> <span class="keywordtype">int</span> expected_max_value1 = 220;</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> assert(max_value1 == expected_max_value1);</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> std::cout << <span class="stringliteral">"Maximum Knapsack value with "</span> << n1 << <span class="stringliteral">" items is "</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> << max_value1 << std::endl;</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// Test 2</span></div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n2 = 4; <span class="comment">// number of items</span></div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> std::array<int, n2> weight2 = {24, 10, 10, 7}; <span class="comment">// weight of each item</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> std::array<int, n2> value2 = {24, 18, 18, 10}; <span class="comment">// value of each item</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keyword">const</span> <span class="keywordtype">int</span> capacity2 = 25; <span class="comment">// capacity of carrying bag</span></div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keyword">const</span> <span class="keywordtype">int</span> max_value2 = dynamic_programming::knapsack::maxKnapsackValue(</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> capacity2, weight2, value2);</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keyword">const</span> <span class="keywordtype">int</span> expected_max_value2 = 36;</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> assert(max_value2 == expected_max_value2);</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> std::cout << <span class="stringliteral">"Maximum Knapsack value with "</span> << n2 << <span class="stringliteral">" items is "</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> << max_value2 << std::endl;</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span>}</div>
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</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> </div>
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<div class="foldopen" id="foldopen00126" data-start="{" data-end="}">
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"><a class="line" href="../../db/d16/0__1__knapsack_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 126</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// Testing</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span>}</div>
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</div>
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<div class="ttc" id="a0__1__knapsack_8cpp_html_a15edf30f336885e5b851f6b7199c6cd1"><div class="ttname"><a href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">dynamic_programming::knapsack::maxKnapsackValue</a></div><div class="ttdeci">int maxKnapsackValue(const int capacity, const std::array< int, n > &weight, const std::array< int, n > &value)</div><div class="ttdoc">Picking up all those items whose combined weight is below the given capacity and calculating the valu...</div><div class="ttdef"><b>Definition</b> <a href="#l00051">0_1_knapsack.cpp:51</a></div></div>
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<div class="ttc" id="a0__1__knapsack_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function to test the above algorithm.</div><div class="ttdef"><b>Definition</b> <a href="#l00096">0_1_knapsack.cpp:96</a></div></div>
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<div class="ttc" id="a0__1__knapsack_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../db/d16/0__1__knapsack_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="#l00126">0_1_knapsack.cpp:126</a></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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