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<div class="headertitle"><div class="title">median_search.cpp</div></div>
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<div class="contents">
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<a href="../../d9/d69/median__search_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="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="preprocessor">#include <iostream></span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="preprocessor">#include <cassert></span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d9/dca/namespacesearch.html">search</a> {</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../da/dd4/namespacemedian__search.html">median_search</a> { </div>
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<div class="foldopen" id="foldopen00062" data-start="{" data-end="}">
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"><a class="line" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae"> 62</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">median_of_medians</a>(<span class="keyword">const</span> std::vector<int>& A, <span class="keyword">const</span> <span class="keywordtype">int</span>& idx) {</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordtype">int</span> pivot = 0; <span class="comment">// initialized with zero</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> std::vector<int> a(A.begin(), A.end());</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> std::vector<int> m;</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordtype">int</span> r = a.size();</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i < r; i += 5){</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> std::sort(a.begin() + i, a.begin() + std::min(r, i + 5));</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordtype">int</span> mid = (i + std::min(r, i + 5)) / 2;</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> m.push_back(a[mid]);</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordtype">int</span> sz = int(m.size());</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">if</span>(sz <= 5){</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> std::sort(m.begin(), m.end());</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> pivot = m[(sz- 1) / 2];</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> <span class="keywordflow">else</span>{</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> pivot = <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">median_of_medians</a>(m, idx);</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 class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> std::vector<int> low;</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> std::vector<int> high;</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i < r; i++){</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">if</span>(a[i] < pivot){</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> low.push_back(a[i]);</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> }</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span>(a[i] > pivot){</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> high.push_back(a[i]);</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> }</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordtype">int</span> k = int(low.size());</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">if</span>(idx < k){</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">median_of_medians</a>(low, idx);</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> }</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span>(idx > k){</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">median_of_medians</a>(high, idx-k-1);</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> }</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">else</span>{</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">return</span> pivot;</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</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="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span>} <span class="comment">// namespace median_search</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span>} <span class="comment">// namespace search</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span></div>
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<div class="foldopen" id="foldopen00107" data-start="{" data-end="}">
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"><a class="line" href="../../d9/d69/median__search_8cpp.html#ae1a3968e7947464bee7714f6d43b7002"> 107</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>(){</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> std::vector<int> A{25,21,98,100,76,22,43,60,89,87};</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordtype">int</span> i = 3;</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> assert(A[6] == <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(A, i)); <span class="comment">// A[6] = 43, is the fourth smallest element.</span></div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> std::cout << <span class="stringliteral">"test case:1 passed\n"</span>;</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> </div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> std::vector<int> B{1,2,3,4,5,6};</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordtype">int</span> j = 4;</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> assert(B[4] == <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(B, j)); <span class="comment">// B[4] = 5, is the fifth smallest element.</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> std::cout << <span class="stringliteral">"test case:2 passed\n"</span>;</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> </div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> std::vector<int> C{1,2,3,4,5,1000,8,9,99};</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordtype">int</span> k = 3;</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> assert(C[3] == <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(C, k)); <span class="comment">// C[3] = 4, is the fourth smallest element.</span></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> std::cout << <span class="stringliteral">"test case:3 passed\n"</span>;</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> std::cout << <span class="stringliteral">"--All tests passed--\n"</span>;</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span>}</div>
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</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span></div>
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<div class="foldopen" id="foldopen00128" data-start="{" data-end="}">
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"><a class="line" href="../../d9/d69/median__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 128</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>()</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span>{</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keywordtype">int</span> n = 0;</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> std::cout << <span class="stringliteral">"Enter Size of Array: "</span>;</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> std::cin >> n;</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> std::vector<int> a(n);</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> std::cout << <span class="stringliteral">"Enter Array: "</span>;</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i < n; i++){</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> std::cin >> a[i];</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> }</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> std::cout << <span class="stringliteral">"Median: "</span>; <span class="comment">// Median defination: https://en.wikipedia.org/wiki/Median</span></div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordtype">int</span> x = <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(a, (n - 1) / 2);</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordflow">if</span>(n % 2 == 0){</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keywordtype">int</span> y = <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(a, n / 2);</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> std::cout << (float(x) + float(y))/2.0;</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> }</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keywordflow">else</span>{</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> std::cout << x;</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> }</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> std::cout << <span class="stringliteral">"\nTo find i-th smallest element "</span>;</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> std::cout << <span class="stringliteral">"\nEnter i: "</span>;</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordtype">int</span> idx = 0;</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> std::cin >> idx;</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> idx--;</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> std::cout << idx + 1<< <span class="stringliteral">"-th smallest element: "</span> << <a class="code hl_function" href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a>(a, idx) << <span class="charliteral">'\n'</span>;</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span>}</div>
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</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> </div>
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<div class="ttc" id="amedian__search_8cpp_html_a868847218f694e78bf433a0ff7648bae"><div class="ttname"><a href="../../d9/d69/median__search_8cpp.html#a868847218f694e78bf433a0ff7648bae">search::median_search::median_of_medians</a></div><div class="ttdeci">int median_of_medians(const std::vector< int > &A, const int &idx)</div><div class="ttdef"><b>Definition</b> <a href="#l00062">median_search.cpp:62</a></div></div>
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<div class="ttc" id="amedian__search_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d9/d69/median__search_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition</b> <a href="#l00107">median_search.cpp:107</a></div></div>
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<div class="ttc" id="amedian__search_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d9/d69/median__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition</b> <a href="#l00128">median_search.cpp:128</a></div></div>
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<div class="ttc" id="anamespacemedian__search_html"><div class="ttname"><a href="../../da/dd4/namespacemedian__search.html">median_search</a></div><div class="ttdoc">Functions for Median search algorithm.</div></div>
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<div class="ttc" id="anamespacesearch_html"><div class="ttname"><a href="../../d9/dca/namespacesearch.html">search</a></div><div class="ttdoc">for std::assert</div><div class="ttdef"><b>Definition</b> <a href="../../df/dd5/binary__search_8cpp_source.html#l00047">binary_search.cpp:47</a></div></div>
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