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<div class="headertitle"><div class="title">unbounded_0_1_knapsack.cpp</div></div>
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<div class="contents">
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<a href="../../d9/dec/unbounded__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="l00026" name="l00026"></a><span class="lineno"> 26</span> </div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include <cassert></span> <span class="comment">// For using assert function to validate test cases</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#include <cstdint></span> <span class="comment">// For fixed-width integer types like std::uint16_t</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="preprocessor">#include <iostream></span> <span class="comment">// Standard input-output stream</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="preprocessor">#include <vector></span> <span class="comment">// Standard library for using dynamic arrays (vectors)</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</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="l00037" name="l00037"></a><span class="lineno"> 37</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="keyword">namespace </span>unbounded_knapsack {</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span></div>
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<div class="foldopen" id="foldopen00058" data-start="{" data-end="}">
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"><a class="line" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#afe447a5979582174908695952c8a079c"> 58</a></span>std::uint16_t <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#afe447a5979582174908695952c8a079c">KnapSackFilling</a>(std::uint16_t i, std::uint16_t W,</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keyword">const</span> std::vector<std::uint16_t>& val,</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">const</span> std::vector<std::uint16_t>& wt,</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> std::vector<std::vector<int>>& <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>) {</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">if</span> (i == 0) {</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">if</span> (wt[0] <= W) {</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">return</span> (W / wt[0]) *</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> val[0]; <span class="comment">// Take as many of the first item as possible</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">return</span> 0; <span class="comment">// Can't take the first item</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> }</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> }</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">if</span> (<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][W] != -1)</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][W]; <span class="comment">// Return result if available</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordtype">int</span> nottake =</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#afe447a5979582174908695952c8a079c">KnapSackFilling</a>(i - 1, W, val, wt, <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>); <span class="comment">// Value without taking item i</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> take = 0;</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">if</span> (W >= wt[i]) {</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> take = val[i] + <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#afe447a5979582174908695952c8a079c">KnapSackFilling</a>(i, W - wt[i], val, wt,</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>); <span class="comment">// Value taking item i</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> }</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][W] =</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> std::max(take, nottake); <span class="comment">// Store and return the maximum value</span></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>
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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="foldopen" id="foldopen00093" data-start="{" data-end="}">
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"><a class="line" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef"> 93</a></span>std::uint16_t <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef">unboundedKnapsack</a>(std::uint16_t N, std::uint16_t W,</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keyword">const</span> std::vector<std::uint16_t>& val,</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keyword">const</span> std::vector<std::uint16_t>& wt) {</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">if</span> (N == 0)</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">return</span> 0; <span class="comment">// Expect 0 since no items</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> std::vector<std::vector<int>> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>(</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> N, std::vector<int>(W + 1, -1)); <span class="comment">// Initialize memoization table</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#afe447a5979582174908695952c8a079c">KnapSackFilling</a>(N - 1, W, val, wt, <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>); <span class="comment">// Start the calculation</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span>}</div>
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</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> </div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span>} <span class="comment">// namespace unbounded_knapsack</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span>} <span class="comment">// namespace dynamic_programming</span></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="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e"> 111</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>() {</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="comment">// Test Case 1</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> std::uint16_t N1 = 4; <span class="comment">// Number of items</span></div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> std::vector<std::uint16_t> wt1 = {1, 3, 4, 5}; <span class="comment">// Weights of the items</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> std::vector<std::uint16_t> val1 = {6, 1, 7, 7}; <span class="comment">// Values of the items</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> std::uint16_t W1 = 8; <span class="comment">// Maximum capacity of the knapsack</span></div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// Test the function and assert the expected output</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> assert(<a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef">dynamic_programming::unbounded_knapsack::unboundedKnapsack</a>(</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> N1, W1, val1, wt1) == 48);</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> std::cout << <span class="stringliteral">"Maximum Knapsack value "</span></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> << <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef">dynamic_programming::unbounded_knapsack::unboundedKnapsack</a>(</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> N1, W1, val1, wt1)</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> << std::endl;</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> </div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// Test Case 2</span></div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> std::uint16_t N2 = 3; <span class="comment">// Number of items</span></div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> std::vector<std::uint16_t> wt2 = {10, 20, 30}; <span class="comment">// Weights of the items</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> std::vector<std::uint16_t> val2 = {60, 100, 120}; <span class="comment">// Values of the items</span></div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> std::uint16_t W2 = 5; <span class="comment">// Maximum capacity of the knapsack</span></div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// Test the function and assert the expected output</span></div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> assert(<a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef">dynamic_programming::unbounded_knapsack::unboundedKnapsack</a>(</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> N2, W2, val2, wt2) == 0);</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> std::cout << <span class="stringliteral">"Maximum Knapsack value "</span></div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> << <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef">dynamic_programming::unbounded_knapsack::unboundedKnapsack</a>(</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> N2, W2, val2, wt2)</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> << std::endl;</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> </div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// Test Case 3</span></div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> std::uint16_t N3 = 3; <span class="comment">// Number of items</span></div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> std::vector<std::uint16_t> wt3 = {2, 4, 6}; <span class="comment">// Weights of the items</span></div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> std::vector<std::uint16_t> val3 = {5, 11, 13}; <span class="comment">// Values of the items</span></div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> std::uint16_t W3 = 27; <span class="comment">// Maximum capacity of the knapsack</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="comment">// Test the function and assert the expected output</span></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> assert(<a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef">dynamic_programming::unbounded_knapsack::unboundedKnapsack</a>(</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> N3, W3, val3, wt3) == 27);</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> std::cout << <span class="stringliteral">"Maximum Knapsack value "</span></div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> << <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef">dynamic_programming::unbounded_knapsack::unboundedKnapsack</a>(</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> N3, W3, val3, wt3)</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> << std::endl;</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> </div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="comment">// Test Case 4</span></div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> std::uint16_t N4 = 0; <span class="comment">// Number of items</span></div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> std::vector<std::uint16_t> wt4 = {}; <span class="comment">// Weights of the items</span></div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> std::vector<std::uint16_t> val4 = {}; <span class="comment">// Values of the items</span></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> std::uint16_t W4 = 10; <span class="comment">// Maximum capacity of the knapsack</span></div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> assert(<a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef">dynamic_programming::unbounded_knapsack::unboundedKnapsack</a>(</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> N4, W4, val4, wt4) == 0);</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> std::cout << <span class="stringliteral">"Maximum Knapsack value for empty arrays: "</span></div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> << <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef">dynamic_programming::unbounded_knapsack::unboundedKnapsack</a>(</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> N4, W4, val4, wt4)</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> << std::endl;</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> </div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> std::cout << <span class="stringliteral">"All test cases passed!"</span> << std::endl;</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span>}</div>
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</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span></div>
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<div class="foldopen" id="foldopen00170" data-start="{" data-end="}">
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"><a class="line" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 170</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <a class="code hl_function" href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// Run self test implementation</span></div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span>}</div>
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</div>
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<div class="ttc" id="anamespacedp_html"><div class="ttname"><a href="../../df/d88/namespacedp.html">dp</a></div><div class="ttdoc">for std::vector</div><div class="ttdef"><b>Definition</b> <a href="../../de/d8c/partition__problem_8cpp_source.html#l00039">partition_problem.cpp:39</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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<div class="ttc" id="aunbounded__0__1__knapsack_8cpp_html_a1bcff7f76de48fa7f629480f8f18b5ef"><div class="ttname"><a href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a1bcff7f76de48fa7f629480f8f18b5ef">dynamic_programming::unbounded_knapsack::unboundedKnapsack</a></div><div class="ttdeci">std::uint16_t unboundedKnapsack(std::uint16_t N, std::uint16_t W, const std::vector< std::uint16_t > &val, const std::vector< std::uint16_t > &wt)</div><div class="ttdoc">Wrapper function to initiate the unbounded knapsack calculation.</div><div class="ttdef"><b>Definition</b> <a href="#l00093">unbounded_0_1_knapsack.cpp:93</a></div></div>
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<div class="ttc" id="aunbounded__0__1__knapsack_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">self test implementation</div><div class="ttdef"><b>Definition</b> <a href="#l00111">unbounded_0_1_knapsack.cpp:111</a></div></div>
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<div class="ttc" id="aunbounded__0__1__knapsack_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d9/dec/unbounded__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="#l00170">unbounded_0_1_knapsack.cpp:170</a></div></div>
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<div class="ttc" id="aunbounded__0__1__knapsack_8cpp_html_afe447a5979582174908695952c8a079c"><div class="ttname"><a href="../../d9/dec/unbounded__0__1__knapsack_8cpp.html#afe447a5979582174908695952c8a079c">dynamic_programming::unbounded_knapsack::KnapSackFilling</a></div><div class="ttdeci">std::uint16_t KnapSackFilling(std::uint16_t i, std::uint16_t W, const std::vector< std::uint16_t > &val, const std::vector< std::uint16_t > &wt, std::vector< std::vector< int > > &dp)</div><div class="ttdoc">Recursive function to calculate the maximum value obtainable using an unbounded knapsack approach.</div><div class="ttdef"><b>Definition</b> <a href="#l00058">unbounded_0_1_knapsack.cpp:58</a></div></div>
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