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<div class="headertitle"><div class="title">longest_palindromic_subsequence.cpp</div></div>
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<div class="contents">
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<a href="../../d0/d77/longest__palindromic__subsequence_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <cassert></span> </div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <string></span> </div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <vector></span> </div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a> {</div>
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<div class="foldopen" id="foldopen00031" data-start="{" data-end="}">
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"><a class="line" href="../../dd/d24/namespacedynamic__programming.html#afe9f45b6e30ee187509da2d1d0093412"> 31</a></span>std::string <a class="code hl_function" href="../../dd/d24/namespacedynamic__programming.html#afe9f45b6e30ee187509da2d1d0093412">lps</a>(<span class="keyword">const</span> std::string& a) {</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">const</span> <span class="keyword">auto</span> b = std::string(a.rbegin(), a.rend());</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keyword">const</span> <span class="keyword">auto</span> m = a.length();</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keyword">using </span>ind_type = std::string::size_type;</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> std::vector<std::vector<ind_type> > res(m + 1,</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> std::vector<ind_type>(m + 1));</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// Finding the length of the longest</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// palindromic subsequence and storing</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// in a 2D array in bottoms-up manner</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordflow">for</span> (ind_type i = 0; i <= m; i++) {</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">for</span> (ind_type j = 0; j <= m; j++) {</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">if</span> (i == 0 || j == 0) {</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> res[i][j] = 0;</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (a[i - 1] == b[j - 1]) {</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> res[i][j] = res[i - 1][j - 1] + 1;</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> res[i][j] = std::max(res[i - 1][j], res[i][j - 1]);</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> }</div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// Length of longest palindromic subsequence</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">auto</span> idx = res[m][m];</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// Creating string of index+1 length</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> std::string ans(idx, <span class="charliteral">'\0'</span>);</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> ind_type i = m, j = m;</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// starting from right-most bottom-most corner</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// and storing them one by one in ans</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">while</span> (i > 0 && j > 0) {</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// if current characters in a and b are same</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// then it is a part of the ans</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">if</span> (a[i - 1] == b[j - 1]) {</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> ans[idx - 1] = a[i - 1];</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> i--;</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> j--;</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> idx--;</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> }</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// If they are not same, find the larger of the</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// two and move in that direction</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (res[i - 1][j] > res[i][j - 1]) {</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> i--;</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> j--;</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> }</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> }</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">return</span> ans;</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span>}</div>
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</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span>} <span class="comment">// namespace dynamic_programming</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span></div>
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<div class="foldopen" id="foldopen00086" data-start="{" data-end="}">
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"><a class="line" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 86</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
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<div class="line"><a id="l00087" name="l00087"></a><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">"radar"</span>) == <span class="stringliteral">"radar"</span>);</div>
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<div class="line"><a id="l00088" name="l00088"></a><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">"abbcbaa"</span>) == <span class="stringliteral">"abcba"</span>);</div>
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<div class="line"><a id="l00089" name="l00089"></a><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">"bbbab"</span>) == <span class="stringliteral">"bbbb"</span>);</div>
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<div class="line"><a id="l00090" name="l00090"></a><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">""</span>) == <span class="stringliteral">""</span>);</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span>}</div>
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</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span></div>
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<div class="foldopen" id="foldopen00097" data-start="{" data-end="}">
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"><a class="line" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 97</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<div class="line"><a id="l00098" name="l00098"></a><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>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span>}</div>
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</div>
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<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> <a href="#l00086">longest_palindromic_subsequence.cpp:86</a></div></div>
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<div class="ttc" id="alongest__palindromic__subsequence_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d0/d77/longest__palindromic__subsequence_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main Function.</div><div class="ttdef"><b>Definition</b> <a href="#l00097">longest_palindromic_subsequence.cpp:97</a></div></div>
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<div class="ttc" id="anamespacedynamic__programming_html"><div class="ttname"><a href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a></div><div class="ttdoc">Dynamic Programming algorithms.</div></div>
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<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 &a)</div><div class="ttdoc">Function that returns the longest palindromic subsequence of a string.</div><div class="ttdef"><b>Definition</b> <a href="#l00031">longest_palindromic_subsequence.cpp:31</a></div></div>
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