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<p>Implements [Sub-set sum problem] (<a href="https://en.wikipedia.org/wiki/Subset_sum_problem">https://en.wikipedia.org/wiki/Subset_sum_problem</a>) algorithm, which tells whether a subset with target sum exists or not.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;unordered_map&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for subset_sum.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:dd/d24/namespacedynamic__programming" id="r_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>
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<tr class="memitem:dc/d3a/namespacesubset__sum" id="r_dc/d3a/namespacesubset__sum"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d3a/namespacesubset__sum.html">subset_sum</a></td></tr>
<tr class="memdesc:dc/d3a/namespacesubset__sum"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for [Sub-set sum problem] (<a href="https://en.wikipedia.org/wiki/Subset_sum_problem">https://en.wikipedia.org/wiki/Subset_sum_problem</a>) algorithm. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a280fcfb2f6fe49a31c4da572e7032607" id="r_a280fcfb2f6fe49a31c4da572e7032607"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d80/dynamic__programming_2subset__sum_8cpp.html#a280fcfb2f6fe49a31c4da572e7032607">dynamic_programming::subset_sum::subset_sum_recursion</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;arr, int targetSum, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">std::unordered_map</a>&lt; int, bool &gt; &gt; *dp, int index=0)</td></tr>
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<tr class="memitem:ac94e6c0dee11278ac0a5491f1b9a4a50" id="r_ac94e6c0dee11278ac0a5491f1b9a4a50"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d80/dynamic__programming_2subset__sum_8cpp.html#ac94e6c0dee11278ac0a5491f1b9a4a50">dynamic_programming::subset_sum::subset_sum_problem</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;arr, const int targetSum)</td></tr>
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test Function. <br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d80/dynamic__programming_2subset__sum_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implements [Sub-set sum problem] (<a href="https://en.wikipedia.org/wiki/Subset_sum_problem">https://en.wikipedia.org/wiki/Subset_sum_problem</a>) algorithm, which tells whether a subset with target sum exists or not. </p>
<p>In this problem, we use dynamic programming to find if we can pull out a subset from an array whose sum is equal to a given target sum. The overall time complexity of the problem is O(n * targetSum) where n is the size of the array. For example, array = [1, -10, 2, 31, -6], targetSum = -14. Output: true =&gt; We can pick subset [-10, 2, -6] with sum as (-10) + 2 + (-6) = -14. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/KillerAV" target="_blank">KillerAV</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<td class="paramtype">void&#160;</td>
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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"><span class="lineno"> 120</span> {</div>
<div class="line"><span class="lineno"> 121</span> <a class="code hl_function" href="../../d0/dfe/backtracking_2subset__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the test</span></div>
<div class="line"><span class="lineno"> 122</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 123</span>}</div>
<div class="ttc" id="abacktracking_2subset__sum_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d0/dfe/backtracking_2subset__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Test implementations.</div><div class="ttdef"><b>Definition</b> subset_sum.cpp:57</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac94e6c0dee11278ac0a5491f1b9a4a50">&#9670;&#160;</a></span>subset_sum_problem()</h2>
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<td class="memname">bool dynamic_programming::subset_sum::subset_sum_problem </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;&#160;</td>
<td class="paramname"><em>arr</em>, </td>
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<td class="paramtype">const int&#160;</td>
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<p>Function implementing subset sum algorithm using top-down approach </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr</td><td>input array </td></tr>
<tr><td class="paramname">targetSum</td><td>the target sum of the subset </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>true/false based on if the target sum subset exists or not. </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 70</span> {</div>
<div class="line"><span class="lineno"> 71</span> <span class="keywordtype">size_t</span> n = arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 72</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::unordered_map&lt;int, bool&gt;</a>&gt; <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>(n);</div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d6/d80/dynamic__programming_2subset__sum_8cpp.html#a280fcfb2f6fe49a31c4da572e7032607">subset_sum_recursion</a>(arr, targetSum, &amp;<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>);</div>
<div class="line"><span class="lineno"> 74</span>}</div>
<div class="ttc" id="adynamic__programming_2subset__sum_8cpp_html_a280fcfb2f6fe49a31c4da572e7032607"><div class="ttname"><a href="../../d6/d80/dynamic__programming_2subset__sum_8cpp.html#a280fcfb2f6fe49a31c4da572e7032607">dynamic_programming::subset_sum::subset_sum_recursion</a></div><div class="ttdeci">bool subset_sum_recursion(const std::vector&lt; int &gt; &amp;arr, int targetSum, std::vector&lt; std::unordered_map&lt; int, bool &gt; &gt; *dp, int index=0)</div><div class="ttdef"><b>Definition</b> subset_sum.cpp:43</div></div>
<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> partition_problem.cpp:39</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a280fcfb2f6fe49a31c4da572e7032607">&#9670;&#160;</a></span>subset_sum_recursion()</h2>
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<td class="memname">bool dynamic_programming::subset_sum::subset_sum_recursion </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;&#160;</td>
<td class="paramname"><em>arr</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>targetSum</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/unordered_map.html">std::unordered_map</a>&lt; int, bool &gt; &gt; *&#160;</td>
<td class="paramname"><em>dp</em>, </td>
</tr>
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<td class="paramkey"></td>
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<td class="paramtype">int&#160;</td>
<td class="paramname"><em>index</em> = <code>0</code>&#160;</td>
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<p>Recursive function using dynamic programming to find if the required sum subset exists or not. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr</td><td>input array </td></tr>
<tr><td class="paramname">targetSum</td><td>the target sum of the subset </td></tr>
<tr><td class="paramname">dp</td><td>the map storing the results </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>true/false based on if the target sum subset exists or not. </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 45</span> {</div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">if</span> (targetSum == 0) { <span class="comment">// Found a valid subset with required sum.</span></div>
<div class="line"><span class="lineno"> 47</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 48</span> }</div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">if</span> (index == arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()) { <span class="comment">// End of array</span></div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 51</span> }</div>
<div class="line"><span class="lineno"> 52</span> </div>
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">if</span> ((*<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>)[index].count(targetSum)) { <span class="comment">// Answer already present in map</span></div>
<div class="line"><span class="lineno"> 54</span> <span class="keywordflow">return</span> (*<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>)[index][targetSum];</div>
<div class="line"><span class="lineno"> 55</span> }</div>
<div class="line"><span class="lineno"> 56</span> </div>
<div class="line"><span class="lineno"> 57</span> <span class="keywordtype">bool</span> ans =</div>
<div class="line"><span class="lineno"> 58</span> <a class="code hl_function" href="../../d6/d80/dynamic__programming_2subset__sum_8cpp.html#a280fcfb2f6fe49a31c4da572e7032607">subset_sum_recursion</a>(arr, targetSum - arr[index], <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>, index + 1) ||</div>
<div class="line"><span class="lineno"> 59</span> <a class="code hl_function" href="../../d6/d80/dynamic__programming_2subset__sum_8cpp.html#a280fcfb2f6fe49a31c4da572e7032607">subset_sum_recursion</a>(arr, targetSum, <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>, index + 1);</div>
<div class="line"><span class="lineno"> 60</span> (*dp)[index][targetSum] = ans; <span class="comment">// Save ans in dp map.</span></div>
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">return</span> ans;</div>
<div class="line"><span class="lineno"> 62</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<p>Test Function. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 82</span> {</div>
<div class="line"><span class="lineno"> 83</span> <span class="comment">// custom input vector</span></div>
<div class="line"><span class="lineno"> 84</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; custom_input_arr(3);</div>
<div class="line"><span class="lineno"> 85</span> custom_input_arr[0] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>{1, -10, 2, 31, -6};</div>
<div class="line"><span class="lineno"> 86</span> custom_input_arr[1] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>{2, 3, 4};</div>
<div class="line"><span class="lineno"> 87</span> custom_input_arr[2] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a>{0, 1, 0, 1, 0};</div>
<div class="line"><span class="lineno"> 88</span> </div>
<div class="line"><span class="lineno"> 89</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> custom_input_target_sum(3);</div>
<div class="line"><span class="lineno"> 90</span> custom_input_target_sum[0] = -14;</div>
<div class="line"><span class="lineno"> 91</span> custom_input_target_sum[1] = 10;</div>
<div class="line"><span class="lineno"> 92</span> custom_input_target_sum[2] = 2;</div>
<div class="line"><span class="lineno"> 93</span> </div>
<div class="line"><span class="lineno"> 94</span> <span class="comment">// calculated output vector by pal_part Function</span></div>
<div class="line"><span class="lineno"> 95</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> calculated_output(3);</div>
<div class="line"><span class="lineno"> 96</span> </div>
<div class="line"><span class="lineno"> 97</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 3; i++) {</div>
<div class="line"><span class="lineno"> 98</span> calculated_output[i] =</div>
<div class="line"><span class="lineno"> 99</span> <a class="code hl_function" href="../../d6/d80/dynamic__programming_2subset__sum_8cpp.html#ac94e6c0dee11278ac0a5491f1b9a4a50">dynamic_programming::subset_sum::subset_sum_problem</a>(</div>
<div class="line"><span class="lineno"> 100</span> custom_input_arr[i], custom_input_target_sum[i]);</div>
<div class="line"><span class="lineno"> 101</span> }</div>
<div class="line"><span class="lineno"> 102</span> </div>
<div class="line"><span class="lineno"> 103</span> <span class="comment">// expected output vector</span></div>
<div class="line"><span class="lineno"> 104</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> expected_output{<span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>};</div>
<div class="line"><span class="lineno"> 105</span> </div>
<div class="line"><span class="lineno"> 106</span> <span class="comment">// Testing implementation via assert function</span></div>
<div class="line"><span class="lineno"> 107</span> <span class="comment">// It will throw error if any of the expected test fails</span></div>
<div class="line"><span class="lineno"> 108</span> <span class="comment">// Else it will give nothing</span></div>
<div class="line"><span class="lineno"> 109</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 3; i++) {</div>
<div class="line"><span class="lineno"> 110</span> assert(expected_output[i] == calculated_output[i]);</div>
<div class="line"><span class="lineno"> 111</span> }</div>
<div class="line"><span class="lineno"> 112</span> </div>
<div class="line"><span class="lineno"> 113</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;All tests passed successfully!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 114</span>}</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="adynamic__programming_2subset__sum_8cpp_html_ac94e6c0dee11278ac0a5491f1b9a4a50"><div class="ttname"><a href="../../d6/d80/dynamic__programming_2subset__sum_8cpp.html#ac94e6c0dee11278ac0a5491f1b9a4a50">dynamic_programming::subset_sum::subset_sum_problem</a></div><div class="ttdeci">bool subset_sum_problem(const std::vector&lt; int &gt; &amp;arr, const int targetSum)</div><div class="ttdef"><b>Definition</b> subset_sum.cpp:70</div></div>
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