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<p>Implementation of <a href="https://en.wikipedia.org/wiki/Knapsack_problem" target="_blank">0-1 Knapsack Problem</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for 0_1_knapsack.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:dd/d24/namespacedynamic__programming"><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>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:d7/daf/namespace_knapsack"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/daf/namespace_knapsack.html">Knapsack</a></td></tr>
<tr class="memdesc:d7/daf/namespace_knapsack"><td class="mdescLeft">&#160;</td><td class="mdescRight">Implementation of 0-1 <a class="el" href="../../d7/daf/namespace_knapsack.html" title="Implementation of 0-1 Knapsack problem.">Knapsack</a> problem. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a15edf30f336885e5b851f6b7199c6cd1"><td class="memTemplParams" colspan="2">template&lt;size_t n&gt; </td></tr>
<tr class="memitem:a15edf30f336885e5b851f6b7199c6cd1"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">dynamic_programming::knapsack::maxKnapsackValue</a> (const int capacity, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt; &amp;weight, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt; &amp;value)</td></tr>
<tr class="memdesc:a15edf30f336885e5b851f6b7199c6cd1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Picking up all those items whose combined weight is below given capacity and calculating value of those picked items.Trying all possible combinations will yield the maximum knapsack value. <a href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">More...</a><br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to test above algorithm. <a href="../../db/d16/0__1__knapsack_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/d16/0__1__knapsack_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../db/d16/0__1__knapsack_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation of <a href="https://en.wikipedia.org/wiki/Knapsack_problem" target="_blank">0-1 Knapsack Problem</a> </p>
<p >Given weights and values of n items, put these items in a knapsack of capacity <code>W</code> to get the maximum total value in the knapsack. In other words, given two integer arrays <code>val[0..n-1]</code> and <code>wt[0..n-1]</code> which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of <code>val[]</code> such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property)</p>
<h3><a class="anchor" id="autotoc_md59"></a>
Algorithm</h3>
<p >The idea is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than <code>W</code>. From all such subsets, pick the maximum value subset.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Anmol3299" target="_blank">Anmol</a> </dd>
<dd>
<a href="https://github.com/Pardeep009" target="_blank">Pardeep</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> {</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// Testing</span></div>
<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>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span>}</div>
<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 above algorithm.</div><div class="ttdef"><b>Definition:</b> 0_1_knapsack.cpp:96</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a15edf30f336885e5b851f6b7199c6cd1">&#9670;&nbsp;</a></span>maxKnapsackValue()</h2>
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template&lt;size_t n&gt; </div>
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<td class="memname">int dynamic_programming::knapsack::maxKnapsackValue </td>
<td>(</td>
<td class="paramtype">const int&#160;</td>
<td class="paramname"><em>capacity</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt; &amp;&#160;</td>
<td class="paramname"><em>weight</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt; &amp;&#160;</td>
<td class="paramname"><em>value</em>&#160;</td>
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<p>Picking up all those items whose combined weight is below given capacity and calculating value of those picked items.Trying all possible combinations will yield the maximum knapsack value. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">n</td><td>size of the weight and value array </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">capacity</td><td>capacity of the carrying bag </td></tr>
<tr><td class="paramname">weight</td><td>array representing weight of items </td></tr>
<tr><td class="paramname">value</td><td>array representing value of items </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>maximum value obtainable with given capacity. </dd></dl>
<div class="fragment"><div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a> &gt; maxValue(n + 1,</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>(capacity + 1, 0));</div>
<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>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// inner loop will select capcity of knapsack bag</span></div>
<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>
<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 &lt; items + 1; ++i) {</div>
<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 &lt; capacity + 1; ++j) {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
<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>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// will be zero</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> maxValue[i][j] = 0;</div>
<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] &lt;= j) {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// if the ith item&#39;s weight(in actual array it will be at i-1)</span></div>
<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>
<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>
<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>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// current item</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// picking current item</span></div>
<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>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// not picking current item</span></div>
<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>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> maxValue[i][j] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(profit1, profit2);</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// as weight of current item is greater than allowed weight, so</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// maxProfit will be profit obtained by excluding current item.</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> maxValue[i][j] = maxValue[i - 1][j];</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> }</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> }</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// returning maximum value</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">return</span> maxValue[items][capacity];</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span>}</div>
<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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<p>Function to test above algorithm. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> {</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// Test 1</span></div>
<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>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n1&gt;</a> weight1 = {10, 20, 30}; <span class="comment">// weight of each item</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n1&gt;</a> value1 = {60, 100, 120}; <span class="comment">// value of each item</span></div>
<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>
<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 = <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">dynamic_programming::knapsack::maxKnapsackValue</a>(</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> capacity1, weight1, value1);</div>
<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>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> assert(max_value1 == expected_max_value1);</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</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;Maximum Knapsack value with &quot;</span> &lt;&lt; n1 &lt;&lt; <span class="stringliteral">&quot; items is &quot;</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> &lt;&lt; max_value1 &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"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// Test 2</span></div>
<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>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n2&gt;</a> weight2 = {24, 10, 10, 7}; <span class="comment">// weight of each item</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n2&gt;</a> value2 = {24, 18, 18, 10}; <span class="comment">// value of each item</span></div>
<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>
<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 = <a class="code hl_function" href="../../db/d16/0__1__knapsack_8cpp.html#a15edf30f336885e5b851f6b7199c6cd1">dynamic_programming::knapsack::maxKnapsackValue</a>(</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> capacity2, weight2, value2);</div>
<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>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> assert(max_value2 == expected_max_value2);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</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;Maximum Knapsack value with &quot;</span> &lt;&lt; n2 &lt;&lt; <span class="stringliteral">&quot; items is &quot;</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> &lt;&lt; max_value2 &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"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span>}</div>
<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&lt; int, n &gt; &amp;weight, const std::array&lt; int, n &gt; &amp;value)</div><div class="ttdoc">Picking up all those items whose combined weight is below given capacity and calculating value of tho...</div><div class="ttdef"><b>Definition:</b> 0_1_knapsack.cpp:51</div></div>
<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</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>
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