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<p>Program to find the Longest Palindormic Subsequence of a string.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for longest_palindromic_subsequence.cpp:</div>
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Functions</h2></td></tr>
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<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>
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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="../../d0/d77/longest__palindromic__subsequence_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<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>
<p><a href="https://en.wikipedia.org/wiki/Palindrome">Palindrome</a> string sequence of characters which reads the same backward as forward <a href="https://en.wikipedia.org/wiki/Subsequence">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">Anjali Jha</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a6f73ddd8cd83d784036f131dfc6540c4">&#9670;&nbsp;</a></span>lps()</h2>
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<p>Function that returns the longest palindromic subsequence of a string </p>
<div class="fragment"><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; {</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> b = a;</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/reverse.html">reverse</a>(b.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), b.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>());</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="keywordtype">int</span> m = a.length();</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a> &gt; res(m + 1);</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="comment">// Finding the length of the longest</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="comment">// palindromic subsequence and storing</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="comment">// in a 2D array in bottoms-up manner</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= m; i++) {</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt;= m; j++) {</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; res[i][j] = 0;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a[i - 1] == b[j - 1]) {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; res[i][j] = res[i - 1][j - 1] + 1;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; res[i][j] = <a class="codeRef" 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"><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; }</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="comment">// Length of longest palindromic subsequence</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordtype">int</span> idx = res[m][m];</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="comment">// Creating string of index+1 length</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(idx + 1, <span class="charliteral">&#39;\0&#39;</span>);</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordtype">int</span> i = m, j = m;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="comment">// starting from right-most bottom-most corner</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="comment">// and storing them one by one in ans</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordflow">while</span> (i &gt; 0 &amp;&amp; j &gt; 0) {</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <span class="comment">// if current characters in a and b are same</span></div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="comment">// then it is a part of the ans</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordflow">if</span> (a[i - 1] == b[j - 1]) {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[idx - 1] = a[i - 1];</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; i--;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; j--;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; idx--;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; }</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="comment">// If they are not same, find the larger of the</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="comment">// two and move in that direction</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordflow">else</span> <span class="keywordflow">if</span> (res[i - 1][j] &gt; res[i][j - 1]) {</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; i--;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; j--;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; }</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; }</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main Function </p>
<div class="fragment"><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; {</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <a class="code" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae1a3968e7947464bee7714f6d43b7002">&#9670;&nbsp;</a></span>test()</h2>
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<p>Test function </p>
<div class="fragment"><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; {</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="comment">// lps(&quot;radar&quot;) return &quot;radar&quot;</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; assert(<a class="code" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a6f73ddd8cd83d784036f131dfc6540c4">lps</a>(<span class="stringliteral">&quot;radar&quot;</span>) == <span class="stringliteral">&quot;radar&quot;</span>);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="comment">// lps(&quot;abbcbaa&quot;) return &quot;abcba&quot;</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; assert(<a class="code" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a6f73ddd8cd83d784036f131dfc6540c4">lps</a>(<span class="stringliteral">&quot;abbcbaa&quot;</span>) == <span class="stringliteral">&quot;abcba&quot;</span>);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="comment">// lps(&quot;bbbab&quot;) return &quot;bbbb&quot;</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; assert(<a class="code" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a6f73ddd8cd83d784036f131dfc6540c4">lps</a>(<span class="stringliteral">&quot;bbbab&quot;</span>) == <span class="stringliteral">&quot;bbbb&quot;</span>);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160;}</div>
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