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<p>SCS is a string Z which is the shortest supersequence of strings X and Y (may not be continuous in Z, but order is maintained).
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;string&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
<code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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Include dependency graph for shortest_common_supersequence.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:dynamic_5Fprogramming" id="r_dynamic_5Fprogramming"><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="memitem:shortest_5Fcommon_5Fsupersequence" id="r_shortest_5Fcommon_5Fsupersequence"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/deb/namespaceshortest__common__supersequence.html">shortest_common_supersequence</a></td></tr>
<tr class="memdesc:d3/deb/namespaceshortest__common__supersequence"><td class="mdescLeft">&#160;</td><td class="mdescRight">Shortest Common Super Sequence algorithm. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:ad2ee8d7e67da9f6eb85146b08dad95e6" id="r_ad2ee8d7e67da9f6eb85146b08dad95e6"><td class="memItemLeft" align="right" valign="top">std::string&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ad2ee8d7e67da9f6eb85146b08dad95e6">dynamic_programming::shortest_common_supersequence::scs</a> (const std::string &amp;str1, const std::string &amp;str2)</td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<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="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>SCS is a string Z which is the shortest supersequence of strings X and Y (may not be continuous in Z, but order is maintained). </p>
<p>The idea is to use lookup table method as used in LCS. For example: example 1:- X: 'ABCXYZ', Y: 'ABZ' then Z will be 'ABCXYZ' (y is not continuous but in order)</p>
<p>For example: example 2:- X: 'AGGTAB', Y: 'GXTXAYB' then Z will be 'AGGXTXAYB' </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/ridhishjain" target="_blank">Ridhish Jain</a> </dd></dl>
<dl class="section see"><dt>See also</dt><dd>more on <a href="https://en.wikipedia.org/wiki/Shortest_common_supersequence_problem" target="_blank">SCS</a> </dd>
<dd>
related <a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe" title="Problem statement for a system with first-order differential equations. Updates the system differenti...">problem</a> <a href="https://leetcode.com/problems/shortest-common-supersequence/" target="_blank">Leetcode</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../d7/d65/shortest__common__supersequence_8cpp_source.html">shortest_common_supersequence.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" 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</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>Main function (driver code) </p>
<p class="definition">Definition at line <a class="el" href="../../d7/d65/shortest__common__supersequence_8cpp_source.html#l00164">164</a> of file <a class="el" href="../../d7/d65/shortest__common__supersequence_8cpp_source.html">shortest_common_supersequence.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 164</span> {</div>
<div class="line"><span class="lineno"> 165</span> <span class="comment">// test for implementation</span></div>
<div class="line"><span class="lineno"> 166</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
<div class="line"><span class="lineno"> 167</span> </div>
<div class="line"><span class="lineno"> 168</span> <span class="comment">// user input</span></div>
<div class="line"><span class="lineno"> 169</span> std::string s1, s2;</div>
<div class="line"><span class="lineno"> 170</span> std::cin &gt;&gt; s1;</div>
<div class="line"><span class="lineno"> 171</span> std::cin &gt;&gt; s2;</div>
<div class="line"><span class="lineno"> 172</span> </div>
<div class="line"><span class="lineno"> 173</span> std::string ans;</div>
<div class="line"><span class="lineno"> 174</span> </div>
<div class="line"><span class="lineno"> 175</span> <span class="comment">// user output</span></div>
<div class="line"><span class="lineno"> 176</span> ans = <a class="code hl_function" href="#ad2ee8d7e67da9f6eb85146b08dad95e6">dynamic_programming::shortest_common_supersequence::scs</a>(s1, s2);</div>
<div class="line"><span class="lineno"> 177</span> std::cout &lt;&lt; ans;</div>
<div class="line"><span class="lineno"> 178</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 179</span>}</div>
<div class="ttc" id="ashortest__common__supersequence_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d65/shortest__common__supersequence_8cpp_source.html#l00124">shortest_common_supersequence.cpp:124</a></div></div>
<div class="ttc" id="ashortest__common__supersequence_8cpp_html_ad2ee8d7e67da9f6eb85146b08dad95e6"><div class="ttname"><a href="#ad2ee8d7e67da9f6eb85146b08dad95e6">dynamic_programming::shortest_common_supersequence::scs</a></div><div class="ttdeci">std::string scs(const std::string &amp;str1, const std::string &amp;str2)</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d65/shortest__common__supersequence_8cpp_source.html#l00042">shortest_common_supersequence.cpp:42</a></div></div>
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<a id="ad2ee8d7e67da9f6eb85146b08dad95e6" name="ad2ee8d7e67da9f6eb85146b08dad95e6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad2ee8d7e67da9f6eb85146b08dad95e6">&#9670;&#160;</a></span>scs()</h2>
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<td class="memname">std::string dynamic_programming::shortest_common_supersequence::scs </td>
<td>(</td>
<td class="paramtype">const std::string &amp;</td> <td class="paramname"><span class="paramname"><em>str1</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const std::string &amp;</td> <td class="paramname"><span class="paramname"><em>str2</em></span>&#160;)</td>
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<p>Function implementing Shortest Common Super-Sequence algorithm using look-up table method. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">str1</td><td>first string 'X' </td></tr>
<tr><td class="paramname">str2</td><td>second string 'Y' </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>string 'Z', superSequence of X and Y </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d7/d65/shortest__common__supersequence_8cpp_source.html#l00042">42</a> of file <a class="el" href="../../d7/d65/shortest__common__supersequence_8cpp_source.html">shortest_common_supersequence.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 42</span> {</div>
<div class="line"><span class="lineno"> 43</span> </div>
<div class="line"><span class="lineno"> 44</span> <span class="comment">// Edge cases</span></div>
<div class="line"><span class="lineno"> 45</span> <span class="comment">// If either str1 or str2 or both are empty</span></div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">if</span>(str1.empty() &amp;&amp; str2.empty()) {</div>
<div class="line"><span class="lineno"> 47</span> <span class="keywordflow">return</span> <span class="stringliteral">&quot;&quot;</span>;</div>
<div class="line"><span class="lineno"> 48</span> }</div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span>(str1.empty()) {</div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">return</span> str2;</div>
<div class="line"><span class="lineno"> 51</span> }</div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span>(str2.empty()) {</div>
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">return</span> str1;</div>
<div class="line"><span class="lineno"> 54</span> }</div>
<div class="line"><span class="lineno"> 55</span> </div>
<div class="line"><span class="lineno"> 56</span> <span class="comment">// creating lookup table</span></div>
<div class="line"><span class="lineno"> 57</span> std::vector &lt;std::vector &lt;int&gt;&gt; lookup(str1.length() + 1, std::vector &lt;int&gt; (str2.length() + 1, 0));</div>
<div class="line"><span class="lineno"> 58</span> </div>
<div class="line"><span class="lineno"> 59</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=1; i &lt;= str1.length(); i++) {</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=1; j &lt;= str2.length(); j++) {</div>
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">if</span>(str1[i-1] == str2[j-1]) {</div>
<div class="line"><span class="lineno"> 62</span> lookup[i][j] = lookup[i-1][j-1] + 1;</div>
<div class="line"><span class="lineno"> 63</span> }</div>
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 65</span> lookup[i][j] = std::max(lookup[i-1][j], lookup[i][j-1]);</div>
<div class="line"><span class="lineno"> 66</span> }</div>
<div class="line"><span class="lineno"> 67</span> }</div>
<div class="line"><span class="lineno"> 68</span> }</div>
<div class="line"><span class="lineno"> 69</span> </div>
<div class="line"><span class="lineno"> 70</span> <span class="comment">// making supersequence</span></div>
<div class="line"><span class="lineno"> 71</span> <span class="comment">// i and j are initially pointed towards end of strings</span></div>
<div class="line"><span class="lineno"> 72</span> <span class="comment">// Super-sequence will be constructed backwards</span></div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordtype">int</span> i=str1.length();</div>
<div class="line"><span class="lineno"> 74</span> <span class="keywordtype">int</span> j=str2.length();</div>
<div class="line"><span class="lineno"> 75</span> std::string s;</div>
<div class="line"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">while</span>(i&gt;0 &amp;&amp; j&gt;0) {</div>
<div class="line"><span class="lineno"> 78</span> </div>
<div class="line"><span class="lineno"> 79</span> <span class="comment">// If the characters at i and j of both strings are same</span></div>
<div class="line"><span class="lineno"> 80</span> <span class="comment">// We only need to add them once in s</span></div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">if</span>(str1[i-1] == str2[j-1]) {</div>
<div class="line"><span class="lineno"> 82</span> s.push_back(str1[i-1]);</div>
<div class="line"><span class="lineno"> 83</span> i--;</div>
<div class="line"><span class="lineno"> 84</span> j--;</div>
<div class="line"><span class="lineno"> 85</span> }</div>
<div class="line"><span class="lineno"> 86</span> <span class="comment">// otherwise we check lookup table for recurrences of characters</span></div>
<div class="line"><span class="lineno"> 87</span> <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordflow">if</span>(lookup[i-1][j] &gt; lookup[i][j-1]) {</div>
<div class="line"><span class="lineno"> 89</span> s.push_back(str1[i-1]);</div>
<div class="line"><span class="lineno"> 90</span> i--;</div>
<div class="line"><span class="lineno"> 91</span> }</div>
<div class="line"><span class="lineno"> 92</span> <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 93</span> s.push_back(str2[j-1]);</div>
<div class="line"><span class="lineno"> 94</span> j--;</div>
<div class="line"><span class="lineno"> 95</span> }</div>
<div class="line"><span class="lineno"> 96</span> }</div>
<div class="line"><span class="lineno"> 97</span> }</div>
<div class="line"><span class="lineno"> 98</span> </div>
<div class="line"><span class="lineno"> 99</span> <span class="comment">// copying remaining elements</span></div>
<div class="line"><span class="lineno"> 100</span> <span class="comment">// if j becomes 0 before i</span></div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordflow">while</span>(i &gt; 0) {</div>
<div class="line"><span class="lineno"> 102</span> s.push_back(str1[i-1]);</div>
<div class="line"><span class="lineno"> 103</span> i--;</div>
<div class="line"><span class="lineno"> 104</span> }</div>
<div class="line"><span class="lineno"> 105</span> </div>
<div class="line"><span class="lineno"> 106</span> <span class="comment">// if i becomes 0 before j</span></div>
<div class="line"><span class="lineno"> 107</span> <span class="keywordflow">while</span>(j &gt; 0) {</div>
<div class="line"><span class="lineno"> 108</span> s.push_back(str2[j-1]);</div>
<div class="line"><span class="lineno"> 109</span> j--;</div>
<div class="line"><span class="lineno"> 110</span> }</div>
<div class="line"><span class="lineno"> 111</span> </div>
<div class="line"><span class="lineno"> 112</span> <span class="comment">// As the super sequence is constructd backwards</span></div>
<div class="line"><span class="lineno"> 113</span> <span class="comment">// reversing the string before returning gives us the correct output </span></div>
<div class="line"><span class="lineno"> 114</span> reverse(s.begin(), s.end());</div>
<div class="line"><span class="lineno"> 115</span> <span class="keywordflow">return</span> s;</div>
<div class="line"><span class="lineno"> 116</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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<td class="memname">void test </td>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
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<p>Test Function </p><dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d7/d65/shortest__common__supersequence_8cpp_source.html#l00124">124</a> of file <a class="el" href="../../d7/d65/shortest__common__supersequence_8cpp_source.html">shortest_common_supersequence.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 124</span> {</div>
<div class="line"><span class="lineno"> 125</span> <span class="comment">// custom input vector</span></div>
<div class="line"><span class="lineno"> 126</span> std::vector &lt;std::vector &lt;std::string&gt;&gt; scsStrings {</div>
<div class="line"><span class="lineno"> 127</span> {<span class="stringliteral">&quot;ABCXYZ&quot;</span>, <span class="stringliteral">&quot;ABZ&quot;</span>},</div>
<div class="line"><span class="lineno"> 128</span> {<span class="stringliteral">&quot;ABZ&quot;</span>, <span class="stringliteral">&quot;ABCXYZ&quot;</span>},</div>
<div class="line"><span class="lineno"> 129</span> {<span class="stringliteral">&quot;AGGTAB&quot;</span>, <span class="stringliteral">&quot;GXTXAYB&quot;</span>},</div>
<div class="line"><span class="lineno"> 130</span> {<span class="stringliteral">&quot;X&quot;</span>, <span class="stringliteral">&quot;Y&quot;</span>},</div>
<div class="line"><span class="lineno"> 131</span> };</div>
<div class="line"><span class="lineno"> 132</span> </div>
<div class="line"><span class="lineno"> 133</span> <span class="comment">// calculated output vector by scs function</span></div>
<div class="line"><span class="lineno"> 134</span> std::vector &lt;std::string&gt; calculatedOutput(4, <span class="stringliteral">&quot;&quot;</span>);</div>
<div class="line"><span class="lineno"> 135</span> <span class="keywordtype">int</span> i=0;</div>
<div class="line"><span class="lineno"> 136</span> <span class="keywordflow">for</span>(<span class="keyword">auto</span> &amp; scsString : scsStrings) {</div>
<div class="line"><span class="lineno"> 137</span> </div>
<div class="line"><span class="lineno"> 138</span> calculatedOutput[i] = <a class="code hl_function" href="#ad2ee8d7e67da9f6eb85146b08dad95e6">dynamic_programming::shortest_common_supersequence::scs</a>(</div>
<div class="line"><span class="lineno"> 139</span> scsString[0], scsString[1]</div>
<div class="line"><span class="lineno"> 140</span> );</div>
<div class="line"><span class="lineno"> 141</span> i++;</div>
<div class="line"><span class="lineno"> 142</span> }</div>
<div class="line"><span class="lineno"> 143</span> </div>
<div class="line"><span class="lineno"> 144</span> <span class="comment">// expected output vector acc to problem statement</span></div>
<div class="line"><span class="lineno"> 145</span> std::vector &lt;std::string&gt; expectedOutput {</div>
<div class="line"><span class="lineno"> 146</span> <span class="stringliteral">&quot;ABCXYZ&quot;</span>,</div>
<div class="line"><span class="lineno"> 147</span> <span class="stringliteral">&quot;ABCXYZ&quot;</span>,</div>
<div class="line"><span class="lineno"> 148</span> <span class="stringliteral">&quot;AGGXTXAYB&quot;</span>,</div>
<div class="line"><span class="lineno"> 149</span> <span class="stringliteral">&quot;XY&quot;</span></div>
<div class="line"><span class="lineno"> 150</span> };</div>
<div class="line"><span class="lineno"> 151</span> </div>
<div class="line"><span class="lineno"> 152</span> <span class="comment">// Testing implementation via assert function</span></div>
<div class="line"><span class="lineno"> 153</span> <span class="comment">// It will throw error if any of the expected test fails</span></div>
<div class="line"><span class="lineno"> 154</span> <span class="comment">// Else it will give nothing</span></div>
<div class="line"><span class="lineno"> 155</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0; i &lt; scsStrings.size(); i++) {</div>
<div class="line"><span class="lineno"> 156</span> assert(expectedOutput[i] == calculatedOutput[i]);</div>
<div class="line"><span class="lineno"> 157</span> }</div>
<div class="line"><span class="lineno"> 158</span> </div>
<div class="line"><span class="lineno"> 159</span> std::cout &lt;&lt; <span class="stringliteral">&quot;All tests passed successfully!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 160</span> <span class="keywordflow">return</span>;</div>
<div class="line"><span class="lineno"> 161</span>}</div>
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