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<div class="headertitle"><div class="title">interpolation_search.cpp</div></div>
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<div class="contents">
<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">/******************************************************************************</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * @file</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> * @brief [Interpolation search</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> * algorithm](https://en.wikipedia.org/wiki/interpolation_search)</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> *</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> * @details</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment"> * interpolation search resembles the method by which people search a telephone</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment"> * directory for a name (the key value by which the book&#39;s entries are ordered):</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment"> * in each step the algorithm calculates where in the remaining search space</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment"> * the sought item might be, based on the key values at the bounds of the search</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"> * space and the value of the sought key, usually via a linear interpolation.</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment"> * The key value actually found at this estimated position is then compared to</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"> * the key value being sought. If it is not equal, then depending on the</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment"> * comparison, the remaining search space is reduced to the part before or</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"> * after the estimated position. This method will only work if calculations</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment"> * on the size of differences between key values are sensible.</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment"></span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment"> * ### Complexities</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment"> *</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment"> * //n is the number of element in the array.</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment"> *</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment"> * Worst-case time complexity O(n) (when items are distributed</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment"> exponentially)</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment"> * Average time complexity O(log2(log2 n))</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment"> * space complexity 0(1)</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment"> *</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment"> * @author [Lajat Manekar](https://github.com/Lazeeez)</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment"> * @author Unknown author</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment"> *******************************************************************************/</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#include &lt;algorithm&gt;</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">/******************************************************************************</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment"> * @namespace search</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment"> * @brief Searching algorithms</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment"> *******************************************************************************/</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d9/dca/namespacesearch.html">search</a> {</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><span class="comment">/******************************************************************************</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment"> * @namespace interpolation_search</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment"> * @brief Functions for the [Interpolation</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment"> *Search](https://en.wikipedia.org/wiki/interpolation_search) algorithm</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment"> *implementation</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment"> *******************************************************************************/</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="keyword">namespace </span>interpolation_search {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">/******************************************************************************</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment"> * @brief The main function which implements interpolation search</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment"> * @param arr vector to be searched in</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment"> * @param number value to be searched</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment"> * @returns integer index of `number` in vector `arr`</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment"> *******************************************************************************/</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span>uint64_t interpolationSearch(<span class="keyword">const</span> std::vector&lt;uint64_t&gt; &amp;arr,</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> uint64_t number) {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> uint64_t size = arr.size();</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> uint64_t low = 0, high = (size - 1);</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// Since vector is sorted, an element present in array must be in range</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// defined by corner</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">while</span> (low &lt;= high &amp;&amp; number &gt;= arr[low] &amp;&amp; number &lt;= arr[high]) {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">if</span> (low == high) {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">if</span> (arr[low] == number) {</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keywordflow">return</span> low;</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> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// Probing the position with keeping uniform distribution in mind.</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> uint64_t pos =</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> low +</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> ((<span class="keyword">static_cast&lt;</span>uint64_t<span class="keyword">&gt;</span>(high - low) / (arr[high] - arr[low])) *</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> (number - arr[low]));</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">if</span> (arr[pos] == number) {</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">return</span> pos; <span class="comment">// Condition of target found</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> }</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">if</span> (arr[pos] &lt; number) {</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> low = pos + 1; <span class="comment">// If x is larger, x is in upper part</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> high = pos - 1; <span class="comment">// If x is smaller, x is in the lower part</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> }</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span>}</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> </div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span>} <span class="comment">// namespace interpolation_search</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span>} <span class="comment">// namespace search</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">/*******************************************************************************</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment"> * @brief Self-test implementation</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="comment"> * @returns void</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment"> *******************************************************************************/</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_namespace" href="../../d9/df4/namespacetests.html">tests</a>() {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// testcase</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// array = [10, 12, 13, 16, 18, 19, 20, 21, 1, 2, 3, 4, 22, 23, 24, 33, 35,</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// 42, 47] , Value = 33 should return 15</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> std::vector&lt;uint64_t&gt; arr = {{10, 12, 13, 16, 18, 19, 20, 21, 1, 2, 3, 4,</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> 22, 23, 24, 33, 35, 42, 47}};</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> sort(arr.begin(), arr.end());</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> uint64_t number = 33; <span class="comment">// Element to be searched</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> uint64_t expected_answer = 15;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> uint64_t derived_answer =</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> search::interpolation_search::interpolationSearch(arr, number);</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Testcase: &quot;</span>;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> assert(derived_answer == expected_answer);</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed!\n&quot;</span>;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span>}</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span><span class="comment">/*******************************************************************************</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="comment"> * @brief Main function</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment"> * @returns 0 on exit</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="comment"> *******************************************************************************/</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <a class="code hl_namespace" href="../../d9/df4/namespacetests.html">tests</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span>}</div>
<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
<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>
<div class="ttc" id="anamespacetests_html"><div class="ttname"><a href="../../d9/df4/namespacetests.html">tests</a></div><div class="ttdoc">Testcases to check Union of Two Arrays.</div></div>
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