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<p><a href="https://en.wikipedia.org/wiki/Exponential_search">Exponential search algorithm</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;cstring&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for exponential_search.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:a0f697e2a3b5193324ab84bd4045088f7"><td class="memTemplParams" colspan="2">template&lt;class Type &gt; </td></tr>
<tr class="memitem:a0f697e2a3b5193324ab84bd4045088f7"><td class="memTemplItemLeft" align="right" valign="top">Type *&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d8/d8a/exponential__search_8cpp.html#a0f697e2a3b5193324ab84bd4045088f7">binary_s</a> (Type *array, size_t size, Type key)</td></tr>
<tr class="separator:a0f697e2a3b5193324ab84bd4045088f7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a67e9c84b4e2eb30e3c5170eabfbb363d"><td class="memTemplParams" colspan="2">template&lt;class Type &gt; </td></tr>
<tr class="memitem:a67e9c84b4e2eb30e3c5170eabfbb363d"><td class="memTemplItemLeft" align="right" valign="top">Type *&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d8/d8a/exponential__search_8cpp.html#a67e9c84b4e2eb30e3c5170eabfbb363d">struzik_search</a> (Type *array, size_t size, Type key)</td></tr>
<tr class="separator:a67e9c84b4e2eb30e3c5170eabfbb363d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d8a/exponential__search_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><a href="https://en.wikipedia.org/wiki/Exponential_search">Exponential search algorithm</a> </p>
<dl class="section copyright"><dt>Copyright</dt><dd>2020 Divide-et-impera-11</dd></dl>
<p>The algorithm try to search the range where the key should be. If it has been found we do a binary search there. The range of the search grows by exponential every time. If the key is larger than the last element of array, the start of block(block_front) will be equal to the end of block(block_size) and the algorithm return null ponter, every other cases the algoritm return fom the loop. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a0f697e2a3b5193324ab84bd4045088f7"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0f697e2a3b5193324ab84bd4045088f7">&#9670;&nbsp;</a></span>binary_s()</h2>
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<div class="memtemplate">
template&lt;class Type &gt; </div>
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<tr>
<td class="mlabels-left">
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<td class="memname">Type* binary_s </td>
<td>(</td>
<td class="paramtype">Type *&#160;</td>
<td class="paramname"><em>array</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">size_t&#160;</td>
<td class="paramname"><em>size</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Type&#160;</td>
<td class="paramname"><em>key</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span></span> </td>
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<p>Binary Search Algorithm (used by <a class="el" href="../../d8/d8a/exponential__search_8cpp.html#a67e9c84b4e2eb30e3c5170eabfbb363d">struzik_search</a>)<br />
</p><ul>
<li>Time Complexity O(log n) where 'n' is the number of elements</li>
<li>Worst Time Complexity O(log n)</li>
<li>Best Time Complexity Ω(1)</li>
<li>Space Complexity O(1)</li>
<li>Auxiliary Space Complexity O(1) <dl class="section return"><dt>Returns</dt><dd>pointer to value in the array </dd>
<dd>
<code>nullptr</code> if value not found </dd></dl>
</li>
</ul>
<div class="fragment"><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; {</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; int32_t lower_index(0), upper_index(size - 1), middle_index;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordflow">while</span> (lower_index &lt;= upper_index) {</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; middle_index = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/floor.html">std::floor</a>((lower_index + upper_index) / 2);</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; </div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">if</span> (*(array + middle_index) &lt; key)</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; lower_index = (middle_index + 1);</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordflow">else</span> <span class="keywordflow">if</span> (*(array + middle_index) &gt; key)</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; upper_index = (middle_index - 1);</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordflow">else</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">return</span> (array + middle_index);</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; }</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; </div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
<div class="memitem">
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<td>(</td>
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<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; {</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="comment">// TEST CASES</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="keywordtype">int</span>* sorted_array = <span class="keyword">new</span> <span class="keywordtype">int</span>[7]{7, 10, 15, 23, 70, 105, 203};</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; assert(struzik_search&lt;int&gt;(sorted_array, 7, 0) == <span class="keyword">nullptr</span>);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; assert(struzik_search&lt;int&gt;(sorted_array, 7, 1000) == <span class="keyword">nullptr</span>);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; assert(struzik_search&lt;int&gt;(sorted_array, 7, 50) == <span class="keyword">nullptr</span>);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; assert(struzik_search&lt;int&gt;(sorted_array, 7, 7) == sorted_array);</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <span class="comment">// TEST CASES</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keyword">delete</span>[] sorted_array;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;}</div>
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<a id="a67e9c84b4e2eb30e3c5170eabfbb363d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a67e9c84b4e2eb30e3c5170eabfbb363d">&#9670;&nbsp;</a></span>struzik_search()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class Type &gt; </div>
<table class="memname">
<tr>
<td class="memname">Type* struzik_search </td>
<td>(</td>
<td class="paramtype">Type *&#160;</td>
<td class="paramname"><em>array</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">size_t&#160;</td>
<td class="paramname"><em>size</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Type&#160;</td>
<td class="paramname"><em>key</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Struzik Search Algorithm(Exponential)</p><ul>
<li>Time Complexity O(log i) where i is the position of search key in the list</li>
<li>Worst Time Complexity O(log i)</li>
<li>Best Time Complexity Ω(1)</li>
<li>Space Complexity O(1)</li>
<li>Auxiliary Space Complexity O(1) </li>
</ul>
<div class="fragment"><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; {</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; uint32_t block_front(0), block_size = size == 0 ? 0 : 1;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">while</span> (block_front != block_size) {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="keywordflow">if</span> (*(array + block_size - 1) &lt; key) {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; block_front = block_size;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; (block_size * 2 - 1 &lt; size) ? (block_size *= 2) : block_size = size;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; }</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordflow">return</span> binary_s&lt;Type&gt;(array + block_front, (block_size - block_front),</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; key);</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; <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160;}</div>
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