Documentation for 4f4585d4c1

2026-03-21 04:18:34 +08:00 · 2023-05-20 01:28:48 +00:00
parent 1aa699dc74
commit 84985ecf11
45 changed files with 346 additions and 313 deletions
--- a/d0/d77/longestpalindromicsubsequence_8cpp.html
+++ b/d0/d77/longestpalindromicsubsequence_8cpp.html
@@ -98,12 +98,13 @@ $(document).ready(function(){initNavTree('d0/d77/longest__palindromic__subsequen

 <div class="header">
  <div class="summary">
+<a href="#namespaces">Namespaces</a> &#124;
 <a href="#func-members">Functions</a>  </div>
  <div class="headertitle"><div class="title">longest_palindromic_subsequence.cpp File Reference</div></div>
 </div><!--header-->
 <div class="contents">

-<p>Program to find the Longest Palindormic Subsequence of a string.  
+<p>Program to find the <a href="https://www.geeksforgeeks.org/longest-palindromic-subsequence-dp-12/" target="_blank">Longest Palindormic Subsequence</a> of a string.  
 <a href="#details">More...</a></p>
 <div class="textblock"><code>#include &lt;cassert&gt;</code><br />
 <code>#include &lt;string&gt;</code><br />
@@ -115,97 +116,29 @@ Include dependency graph for longest_palindromic_subsequence.cpp:</div>
 </div>
 </div>
 </div><table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
+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>
+</table><table class="memberdecls">
 <tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
 Functions</h2></td></tr>
-<tr class="memitem:a4f863610aebbc218f90a7adfde240cb4"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a4f863610aebbc218f90a7adfde240cb4">lps</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;a)</td></tr>
-<tr class="separator:a4f863610aebbc218f90a7adfde240cb4"><td class="memSeparator" colspan="2">&#160;</td></tr>
-<tr class="memitem:ae1a3968e7947464bee7714f6d43b7002"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a> ()</td></tr>
-<tr class="separator:ae1a3968e7947464bee7714f6d43b7002"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:afe9f45b6e30ee187509da2d1d0093412"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d24/namespacedynamic__programming.html#afe9f45b6e30ee187509da2d1d0093412">dynamic_programming::lps</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;a)</td></tr>
+<tr class="memdesc:afe9f45b6e30ee187509da2d1d0093412"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function that returns the longest palindromic subsequence of a string.  <br /></td></tr>
+<tr class="separator:afe9f45b6e30ee187509da2d1d0093412"><td class="memSeparator" colspan="2">&#160;</td></tr>
+<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
+<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations.  <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="../../d0/d77/longest__palindromic__subsequence_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
+<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main Function.  <br /></td></tr>
 <tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
-<div class="textblock"><p>Program to find the Longest Palindormic Subsequence of a string. </p>
+<div class="textblock"><p>Program to find the <a href="https://www.geeksforgeeks.org/longest-palindromic-subsequence-dp-12/" target="_blank">Longest Palindormic Subsequence</a> of a string. </p>
 <p><a href="https://en.wikipedia.org/wiki/Palindrome" target="_blank">Palindrome</a> string sequence of characters which reads the same backward as forward <a href="https://en.wikipedia.org/wiki/Subsequence" target="_blank">Subsequence</a> is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.</p>
 <dl class="section author"><dt>Author</dt><dd><a href="https://github.com/anjali1903" target="_blank">Anjali Jha</a> </dd></dl>
 </div><h2 class="groupheader">Function Documentation</h2>
-<a id="a4f863610aebbc218f90a7adfde240cb4" name="a4f863610aebbc218f90a7adfde240cb4"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#a4f863610aebbc218f90a7adfde240cb4">&#9670;&#160;</a></span>lps()</h2>
-
-<div class="memitem">
-<div class="memproto">
-      <table class="memname">
-        <tr>
-          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> lps </td>
-          <td>(</td>
-          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
-          <td class="paramname"><em>a</em></td><td>)</td>
-          <td></td>
-        </tr>
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-</div><div class="memdoc">
-<p>for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> Function that returns the longest palindromic subsequence of a string </p>
-<div class="fragment"><div class="line"><span class="lineno">   24</span>                                  {</div>
-<div class="line"><span class="lineno">   25</span>    <span class="keyword">const</span> <span class="keyword">auto</span> b = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(a.rbegin(), a.rend());</div>
-<div class="line"><span class="lineno">   26</span>    <span class="keyword">const</span> <span class="keyword">auto</span> m = a.length();</div>
-<div class="line"><span class="lineno">   27</span>    <span class="keyword">using </span>ind_type = std::string::size_type;</div>
-<div class="line"><span class="lineno">   28</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;ind_type&gt;</a> &gt; res(m + 1,</div>
-<div class="line"><span class="lineno">   29</span>                                            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;ind_type&gt;</a>(m + 1));</div>
-<div class="line"><span class="lineno">   30</span> </div>
-<div class="line"><span class="lineno">   31</span>    <span class="comment">// Finding the length of the longest</span></div>
-<div class="line"><span class="lineno">   32</span>    <span class="comment">// palindromic subsequence and storing</span></div>
-<div class="line"><span class="lineno">   33</span>    <span class="comment">// in a 2D array in bottoms-up manner</span></div>
-<div class="line"><span class="lineno">   34</span>    <span class="keywordflow">for</span> (ind_type i = 0; i &lt;= m; i++) {</div>
-<div class="line"><span class="lineno">   35</span>        <span class="keywordflow">for</span> (ind_type j = 0; j &lt;= m; j++) {</div>
-<div class="line"><span class="lineno">   36</span>            <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
-<div class="line"><span class="lineno">   37</span>                res[i][j] = 0;</div>
-<div class="line"><span class="lineno">   38</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a[i - 1] == b[j - 1]) {</div>
-<div class="line"><span class="lineno">   39</span>                res[i][j] = res[i - 1][j - 1] + 1;</div>
-<div class="line"><span class="lineno">   40</span>            } <span class="keywordflow">else</span> {</div>
-<div class="line"><span class="lineno">   41</span>                res[i][j] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(res[i - 1][j], res[i][j - 1]);</div>
-<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>    }</div>
-<div class="line"><span class="lineno">   45</span>    <span class="comment">// Length of longest palindromic subsequence</span></div>
-<div class="line"><span class="lineno">   46</span>    <span class="keyword">auto</span> idx = res[m][m];</div>
-<div class="line"><span class="lineno">   47</span>    <span class="comment">// Creating string of index+1 length</span></div>
-<div class="line"><span class="lineno">   48</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> ans(idx, <span class="charliteral">&#39;\0&#39;</span>);</div>
-<div class="line"><span class="lineno">   49</span>    ind_type i = m, j = m;</div>
-<div class="line"><span class="lineno">   50</span> </div>
-<div class="line"><span class="lineno">   51</span>    <span class="comment">// starting from right-most bottom-most corner</span></div>
-<div class="line"><span class="lineno">   52</span>    <span class="comment">// and storing them one by one in ans</span></div>
-<div class="line"><span class="lineno">   53</span>    <span class="keywordflow">while</span> (i &gt; 0 &amp;&amp; j &gt; 0) {</div>
-<div class="line"><span class="lineno">   54</span>        <span class="comment">// if current characters in a and b are same</span></div>
-<div class="line"><span class="lineno">   55</span>        <span class="comment">// then it is a part of the ans</span></div>
-<div class="line"><span class="lineno">   56</span>        <span class="keywordflow">if</span> (a[i - 1] == b[j - 1]) {</div>
-<div class="line"><span class="lineno">   57</span>            ans[idx - 1] = a[i - 1];</div>
-<div class="line"><span class="lineno">   58</span>            i--;</div>
-<div class="line"><span class="lineno">   59</span>            j--;</div>
-<div class="line"><span class="lineno">   60</span>            idx--;</div>
-<div class="line"><span class="lineno">   61</span>        }</div>
-<div class="line"><span class="lineno">   62</span>        <span class="comment">// If they are not same, find the larger of the</span></div>
-<div class="line"><span class="lineno">   63</span>        <span class="comment">// two and move in that direction</span></div>
-<div class="line"><span class="lineno">   64</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (res[i - 1][j] &gt; res[i][j - 1]) {</div>
-<div class="line"><span class="lineno">   65</span>            i--;</div>
-<div class="line"><span class="lineno">   66</span>        } <span class="keywordflow">else</span> {</div>
-<div class="line"><span class="lineno">   67</span>            j--;</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> </div>
-<div class="line"><span class="lineno">   71</span>    <span class="keywordflow">return</span> ans;</div>
-<div class="line"><span class="lineno">   72</span>}</div>
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-Here is the call graph for this function:</div>
-<div class="dyncontent">
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 <h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>

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        </tr>
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 </div><div class="memdoc">
-<p>Main Function </p>
-<div class="fragment"><div class="line"><span class="lineno">   85</span>           {</div>
-<div class="line"><span class="lineno">   86</span>    <a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();  <span class="comment">// execute the tests</span></div>
-<div class="line"><span class="lineno">   87</span>    <span class="keywordflow">return</span> 0;</div>
-<div class="line"><span class="lineno">   88</span>}</div>
-<div class="ttc" id="alongest__palindromic__subsequence_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> longest_palindromic_subsequence.cpp:75</div></div>
+
+<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">   97</span>           {</div>
+<div class="line"><span class="lineno">   98</span>    <a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();  <span class="comment">// execute the tests</span></div>
+<div class="line"><span class="lineno">   99</span>    <span class="keywordflow">return</span> 0;</div>
+<div class="line"><span class="lineno">  100</span>}</div>
+<div class="ttc" id="alongest__palindromic__subsequence_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> longest_palindromic_subsequence.cpp:86</div></div>
 </div><!-- fragment --><div class="dynheader">
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-<a id="ae1a3968e7947464bee7714f6d43b7002" name="ae1a3968e7947464bee7714f6d43b7002"></a>
-<h2 class="memtitle"><span class="permalink"><a href="#ae1a3968e7947464bee7714f6d43b7002">&#9670;&#160;</a></span>test()</h2>
+<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
+<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>

 <div class="memitem">
 <div class="memproto">
+<table class="mlabels">
+  <tr>
+  <td class="mlabels-left">
      <table class="memname">
        <tr>
-          <td class="memname">void test </td>
+          <td class="memname">static void test </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td></td>
        </tr>
      </table>
+  </td>
+  <td class="mlabels-right">
+<span class="mlabels"><span class="mlabel">static</span></span>  </td>
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 </div><div class="memdoc">
-<p>Test function </p>
-<div class="fragment"><div class="line"><span class="lineno">   75</span>            {</div>
-<div class="line"><span class="lineno">   76</span>    assert(<a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a4f863610aebbc218f90a7adfde240cb4">lps</a>(<span class="stringliteral">&quot;radar&quot;</span>) == <span class="stringliteral">&quot;radar&quot;</span>);</div>
-<div class="line"><span class="lineno">   77</span>    assert(<a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a4f863610aebbc218f90a7adfde240cb4">lps</a>(<span class="stringliteral">&quot;abbcbaa&quot;</span>) == <span class="stringliteral">&quot;abcba&quot;</span>);</div>
-<div class="line"><span class="lineno">   78</span>    assert(<a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a4f863610aebbc218f90a7adfde240cb4">lps</a>(<span class="stringliteral">&quot;bbbab&quot;</span>) == <span class="stringliteral">&quot;bbbb&quot;</span>);</div>
-<div class="line"><span class="lineno">   79</span>    assert(<a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a4f863610aebbc218f90a7adfde240cb4">lps</a>(<span class="stringliteral">&quot;&quot;</span>) == <span class="stringliteral">&quot;&quot;</span>);</div>
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+
+<p>Self-test implementations. </p>
+<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
+<div class="fragment"><div class="line"><span class="lineno">   86</span>                   {</div>
+<div class="line"><span class="lineno">   87</span>    assert(<a class="code hl_function" href="../../dd/d24/namespacedynamic__programming.html#afe9f45b6e30ee187509da2d1d0093412">dynamic_programming::lps</a>(<span class="stringliteral">&quot;radar&quot;</span>) == <span class="stringliteral">&quot;radar&quot;</span>);</div>
+<div class="line"><span class="lineno">   88</span>    assert(<a class="code hl_function" href="../../dd/d24/namespacedynamic__programming.html#afe9f45b6e30ee187509da2d1d0093412">dynamic_programming::lps</a>(<span class="stringliteral">&quot;abbcbaa&quot;</span>) == <span class="stringliteral">&quot;abcba&quot;</span>);</div>
+<div class="line"><span class="lineno">   89</span>    assert(<a class="code hl_function" href="../../dd/d24/namespacedynamic__programming.html#afe9f45b6e30ee187509da2d1d0093412">dynamic_programming::lps</a>(<span class="stringliteral">&quot;bbbab&quot;</span>) == <span class="stringliteral">&quot;bbbb&quot;</span>);</div>
+<div class="line"><span class="lineno">   90</span>    assert(<a class="code hl_function" href="../../dd/d24/namespacedynamic__programming.html#afe9f45b6e30ee187509da2d1d0093412">dynamic_programming::lps</a>(<span class="stringliteral">&quot;&quot;</span>) == <span class="stringliteral">&quot;&quot;</span>);</div>
+<div class="line"><span class="lineno">   91</span>}</div>
+<div class="ttc" id="anamespacedynamic__programming_html_afe9f45b6e30ee187509da2d1d0093412"><div class="ttname"><a href="../../dd/d24/namespacedynamic__programming.html#afe9f45b6e30ee187509da2d1d0093412">dynamic_programming::lps</a></div><div class="ttdeci">std::string lps(const std::string &amp;a)</div><div class="ttdoc">Function that returns the longest palindromic subsequence of a string.</div><div class="ttdef"><b>Definition:</b> longest_palindromic_subsequence.cpp:31</div></div>
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+<h2 class="memtitle"><span class="permalink"><a href="#afe9f45b6e30ee187509da2d1d0093412">&#9670;&#160;</a></span>lps()</h2>
+
+<div class="memitem">
+<div class="memproto">
+      <table class="memname">
+        <tr>
+          <td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> dynamic_programming::lps </td>
+          <td>(</td>
+          <td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
+          <td class="paramname"><em>a</em></td><td>)</td>
+          <td></td>
+        </tr>
+      </table>
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+
+<p>Function that returns the longest palindromic subsequence of a string. </p>
+<dl class="params"><dt>Parameters</dt><dd>
+  <table class="params">
+    <tr><td class="paramname">a</td><td>string whose longest palindromic subsequence is to be found </td></tr>
+  </table>
+  </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>longest palindromic subsequence of the string </dd></dl>
+<div class="fragment"><div class="line"><span class="lineno">   31</span>                                  {</div>
+<div class="line"><span class="lineno">   32</span>    <span class="keyword">const</span> <span class="keyword">auto</span> b = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(a.rbegin(), a.rend());</div>
+<div class="line"><span class="lineno">   33</span>    <span class="keyword">const</span> <span class="keyword">auto</span> m = a.length();</div>
+<div class="line"><span class="lineno">   34</span>    <span class="keyword">using </span>ind_type = std::string::size_type;</div>
+<div class="line"><span class="lineno">   35</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;ind_type&gt;</a> &gt; res(m + 1,</div>
+<div class="line"><span class="lineno">   36</span>                                            <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;ind_type&gt;</a>(m + 1));</div>
+<div class="line"><span class="lineno">   37</span> </div>
+<div class="line"><span class="lineno">   38</span>    <span class="comment">// Finding the length of the longest</span></div>
+<div class="line"><span class="lineno">   39</span>    <span class="comment">// palindromic subsequence and storing</span></div>
+<div class="line"><span class="lineno">   40</span>    <span class="comment">// in a 2D array in bottoms-up manner</span></div>
+<div class="line"><span class="lineno">   41</span>    <span class="keywordflow">for</span> (ind_type i = 0; i &lt;= m; i++) {</div>
+<div class="line"><span class="lineno">   42</span>        <span class="keywordflow">for</span> (ind_type j = 0; j &lt;= m; j++) {</div>
+<div class="line"><span class="lineno">   43</span>            <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
+<div class="line"><span class="lineno">   44</span>                res[i][j] = 0;</div>
+<div class="line"><span class="lineno">   45</span>            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a[i - 1] == b[j - 1]) {</div>
+<div class="line"><span class="lineno">   46</span>                res[i][j] = res[i - 1][j - 1] + 1;</div>
+<div class="line"><span class="lineno">   47</span>            } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   48</span>                res[i][j] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(res[i - 1][j], res[i][j - 1]);</div>
+<div class="line"><span class="lineno">   49</span>            }</div>
+<div class="line"><span class="lineno">   50</span>        }</div>
+<div class="line"><span class="lineno">   51</span>    }</div>
+<div class="line"><span class="lineno">   52</span>    <span class="comment">// Length of longest palindromic subsequence</span></div>
+<div class="line"><span class="lineno">   53</span>    <span class="keyword">auto</span> idx = res[m][m];</div>
+<div class="line"><span class="lineno">   54</span>    <span class="comment">// Creating string of index+1 length</span></div>
+<div class="line"><span class="lineno">   55</span>    <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> ans(idx, <span class="charliteral">&#39;\0&#39;</span>);</div>
+<div class="line"><span class="lineno">   56</span>    ind_type i = m, j = m;</div>
+<div class="line"><span class="lineno">   57</span> </div>
+<div class="line"><span class="lineno">   58</span>    <span class="comment">// starting from right-most bottom-most corner</span></div>
+<div class="line"><span class="lineno">   59</span>    <span class="comment">// and storing them one by one in ans</span></div>
+<div class="line"><span class="lineno">   60</span>    <span class="keywordflow">while</span> (i &gt; 0 &amp;&amp; j &gt; 0) {</div>
+<div class="line"><span class="lineno">   61</span>        <span class="comment">// if current characters in a and b are same</span></div>
+<div class="line"><span class="lineno">   62</span>        <span class="comment">// then it is a part of the ans</span></div>
+<div class="line"><span class="lineno">   63</span>        <span class="keywordflow">if</span> (a[i - 1] == b[j - 1]) {</div>
+<div class="line"><span class="lineno">   64</span>            ans[idx - 1] = a[i - 1];</div>
+<div class="line"><span class="lineno">   65</span>            i--;</div>
+<div class="line"><span class="lineno">   66</span>            j--;</div>
+<div class="line"><span class="lineno">   67</span>            idx--;</div>
+<div class="line"><span class="lineno">   68</span>        }</div>
+<div class="line"><span class="lineno">   69</span>        <span class="comment">// If they are not same, find the larger of the</span></div>
+<div class="line"><span class="lineno">   70</span>        <span class="comment">// two and move in that direction</span></div>
+<div class="line"><span class="lineno">   71</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (res[i - 1][j] &gt; res[i][j - 1]) {</div>
+<div class="line"><span class="lineno">   72</span>            i--;</div>
+<div class="line"><span class="lineno">   73</span>        } <span class="keywordflow">else</span> {</div>
+<div class="line"><span class="lineno">   74</span>            j--;</div>
+<div class="line"><span class="lineno">   75</span>        }</div>
+<div class="line"><span class="lineno">   76</span>    }</div>
+<div class="line"><span class="lineno">   77</span> </div>
+<div class="line"><span class="lineno">   78</span>    <span class="keywordflow">return</span> ans;</div>
+<div class="line"><span class="lineno">   79</span>}</div>
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