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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>
<tr class="memitem:a6f73ddd8cd83d784036f131dfc6540c4"><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#a6f73ddd8cd83d784036f131dfc6540c4">lps</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> a)</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" 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>
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<h2 class="memtitle"><span class="permalink"><a href="#a6f73ddd8cd83d784036f131dfc6540c4">&#9670;&nbsp;</a></span>lps()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> lps </td>
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<p >Function that returns the longest palindromic subsequence of a string </p>
<div class="fragment"><div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> {</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> b = a;</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/reverse.html">reverse</a>(b.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>(), b.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>());</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordtype">int</span> m = a.length();</div>
<div class="line"><a id="l00029" name="l00029"></a><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;std::vector&lt;int&gt;</a> &gt; res(m + 1);</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// Finding the length of the longest</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// palindromic subsequence and storing</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// in a 2D array in bottoms-up manner</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= m; i++) {</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt;= m; j++) {</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> res[i][j] = 0;</div>
<div class="line"><a id="l00038" name="l00038"></a><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"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> res[i][j] = res[i - 1][j - 1] + 1;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00041" name="l00041"></a><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"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> }</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> }</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> }</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// Length of longest palindromic subsequence</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordtype">int</span> idx = res[m][m];</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// Creating string of index+1 length</span></div>
<div class="line"><a id="l00048" name="l00048"></a><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> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(idx + 1, <span class="charliteral">&#39;\0&#39;</span>);</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordtype">int</span> i = m, j = m;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// starting from right-most bottom-most corner</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// and storing them one by one in ans</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">while</span> (i &gt; 0 &amp;&amp; j &gt; 0) {</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// if current characters in a and b are same</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// then it is a part of the ans</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">if</span> (a[i - 1] == b[j - 1]) {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>[idx - 1] = a[i - 1];</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> i--;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> j--;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> idx--;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// If they are not same, find the larger of the</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// two and move in that direction</span></div>
<div class="line"><a id="l00064" name="l00064"></a><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"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> i--;</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> j--;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> }</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> }</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span>}</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 id="l00087" name="l00087"></a><span class="lineno"> 87</span> {</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</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"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>}</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 id="l00075" name="l00075"></a><span class="lineno"> 75</span> {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// lps(&quot;radar&quot;) return &quot;radar&quot;</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> assert(<a class="code hl_function" 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 id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// lps(&quot;abbcbaa&quot;) return &quot;abcba&quot;</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> assert(<a class="code hl_function" 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 id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// lps(&quot;bbbab&quot;) return &quot;bbbb&quot;</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> assert(<a class="code hl_function" 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 id="l00082" name="l00082"></a><span class="lineno"> 82</span>}</div>
<div class="ttc" id="alongest__palindromic__subsequence_8cpp_html_a6f73ddd8cd83d784036f131dfc6540c4"><div class="ttname"><a href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#a6f73ddd8cd83d784036f131dfc6540c4">lps</a></div><div class="ttdeci">std::string lps(std::string a)</div><div class="ttdef"><b>Definition:</b> longest_palindromic_subsequence.cpp:25</div></div>
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