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<p>Implementation of the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem">Subset Sum</a> problem.
<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;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:db/dc0/namespacebacktracking"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html">backtracking</a></td></tr>
<tr class="memdesc:db/dc0/namespacebacktracking"><td class="mdescLeft">&#160;</td><td class="mdescRight">Backtracking algorithms. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:de/d95/namespace_subsets"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d95/namespace_subsets.html">Subsets</a></td></tr>
<tr class="memdesc:de/d95/namespace_subsets"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem">Subset Sum</a> problem. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a7cb50d36a59427a33f64a266dac83d99"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d5a/subset__sum_8cpp.html#a7cb50d36a59427a33f64a266dac83d99">backtracking::subset_sum::number_of_subsets</a> (int32_t sum, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int32_t &gt; &amp;in_arr)</td></tr>
<tr class="memdesc:a7cb50d36a59427a33f64a266dac83d99"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main function implements count of subsets. <a href="../../d2/d5a/subset__sum_8cpp.html#a7cb50d36a59427a33f64a266dac83d99">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="../../d2/d5a/subset__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test implementations. <a href="../../d2/d5a/subset__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d5a/subset__sum_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d2/d5a/subset__sum_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem">Subset Sum</a> problem. </p>
<p>We are given an array and a sum value. The algorithm finds all the subsets of that array with sum equal to the given sum and return such subsets count. This approach will have exponential time complexity. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy">Swastika Gupta</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<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 name="l00103"></a><span class="lineno"> 103</span>&#160; {</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <a class="code" href="../../d2/d5a/subset__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160;}</div>
<div class="ttc" id="asubset__sum_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d2/d5a/subset__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="#a7cb50d36a59427a33f64a266dac83d99">&#9670;&nbsp;</a></span>number_of_subsets()</h2>
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<td class="memname">uint64_t backtracking::subset_sum::number_of_subsets </td>
<td>(</td>
<td class="paramtype">int32_t&#160;</td>
<td class="paramname"><em>sum</em>, </td>
</tr>
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<td class="paramkey"></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; int32_t &gt; &amp;&#160;</td>
<td class="paramname"><em>in_arr</em>&#160;</td>
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<p>The main function implements count of subsets. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">sum</td><td>is the required sum of any subset </td></tr>
<tr><td class="paramname">in_arr</td><td>is the input array </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>count of the number of subsets with required sum </dd></dl>
<div class="fragment"><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; int32_t nelement = in_arr.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; uint64_t count_of_subset = 0;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordflow">for</span> (int32_t i = 0; i &lt; (1 &lt;&lt; (nelement)); i++) {</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; int32_t <a class="code" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a> = 0;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">for</span> (int32_t j = 0; j &lt; nelement; j++) {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">if</span> (i &amp; (1 &lt;&lt; j)) {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <a class="code" href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">check</a> += (in_arr[j]);</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; }</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; }</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordflow">if</span> (check == <a class="code" href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">sum</a>) {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; count_of_subset++;</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; }</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; }</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">return</span> count_of_subset;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160;}</div>
<div class="ttc" id="anamespacemachine__learning_html_a5305cc18d11943d3dc0d66e70d7e9c44"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector&lt; std::valarray&lt; T &gt;&gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:232</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>
<div class="ttc" id="aword__break_8cpp_html_a272b0f5cdb4e41fd6dee4538b808c06a"><div class="ttname"><a href="../../d3/d84/word__break_8cpp.html#a272b0f5cdb4e41fd6dee4538b808c06a">dynamic_programming::word_break::check</a></div><div class="ttdeci">bool check(const std::string &amp;s, const std::unordered_set&lt; std::string &gt; &amp;strSet, int pos, std::vector&lt; int &gt; *dp)</div><div class="ttdoc">Function that checks if the string passed in param can be segmented from position 'pos',...</div><div class="ttdef"><b>Definition:</b> word_break.cpp:80</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>Test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; {</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="comment">// 1st test</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test &quot;</span>;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array1 = {-7, -3, -2, 5, 8}; <span class="comment">// input array</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; assert(backtracking::subset_sum::number_of_subsets(0, array1) ==</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; 2); <span class="comment">// first argument in subset_sum function is the required sum and</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="comment">// second is the input array</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// 2nd test</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test &quot;</span>;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array2 = {1, 2, 3, 3};</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; assert(backtracking::subset_sum::number_of_subsets(6, array2) ==</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; 3); <span class="comment">// here we are expecting 3 subsets which sum up to 6 i.e.</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="comment">// {(1,2,3),(1,2,3),(3,3)}</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; </div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="comment">// 3rd test</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test &quot;</span>;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> array3 = {1, 1, 1, 1};</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; assert(backtracking::subset_sum::number_of_subsets(1, array3) ==</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; 4); <span class="comment">// here we are expecting 4 subsets which sum up to 1 i.e.</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="comment">// {(1),(1),(1),(1)}</span></div>
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];

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