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<!DOCTYPE html>
<html lang="en">
<head>
<title>Binary Search</title>
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<h1>Binary Search</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn how Binary Search sort works. Also, you will find working examples of Binary Search in C, C++, Java and Python.</p>
<div id="node-1584" class="node node-algorithm clearfix" about="/dsa/binary-search" typeof="sioc:Item foaf:Document">
<span property="dc:title" content="Binary Search" class="rdf-meta element-hidden"></span>
<div class="content">
<p id="definition">Binary Search is a searching algorithm for finding an element's position in a sorted array.</p>
<p>In this approach, the element is always searched in the middle of a portion of an array.</p>
<p class="note-tip">Binary search can be implemented only on a sorted list of items. If the elements are not sorted already, we need to sort them first.</p>
<hr><h2 id="working">Binary Search Working</h2>
<p>Binary Search Algorithm can be implemented in two ways which are discussed below.</p>
<ol><li>Iterative Method</li>
<li>Recursive Method</li>
</ol><p>The recursive method follows <a href="/dsa/divide-and-conquer.html">the divide and conquer</a> approach.</p>
<p>The general steps for both methods are discussed below.</p>
<ol><li>The array in which searching is to be performed is:
<figure><img alt="initial array Binary Search" src="//cdn.programiz.com/sites/tutorial2program/files/binary-search-initial-array.png" title="initial array " width="400" height="107"><figcaption>Initial array</figcaption></figure><br>
Let <code>x = 4</code> be the element to be searched.</li>
<li>Set two pointers low and high at the lowest and the highest positions respectively.
<figure><img alt="setting pointers Binary Search" src="//cdn.programiz.com/sites/tutorial2program/files/binary-search-set-pointers.png" title="setting pointers " width="400" height="166"><figcaption>Setting pointers</figcaption></figure></li>
<li>Find the middle element <var>mid</var> of the array ie. <code>arr[(low + high)/2] = 6</code>.
<figure><img alt="mid element Binary Search" src="//cdn.programiz.com/sites/tutorial2program/files/binary-search-mid.png" title="mid element" width="400" height="166"><figcaption>Mid element</figcaption></figure></li>
<li>If x == mid, then return mid.Else, compare the element to be searched with m.</li>
<li>If <code>x > mid</code>, compare <var>x</var> with the middle element of the elements on the right side of <var>mid</var>. This is done by setting <var>low</var> to <code>low = mid + 1</code>.</li>
<li>Else, compare <var>x</var> with the middle element of the elements on the left side of <var>mid</var>. This is done by setting <var>high</var> to <code>high = mid - 1</code>.
<figure><img alt="finding mid element Binary Search" src="//cdn.programiz.com/sites/tutorial2program/files/binary-search-find-mid.png" title="finding mid element" width="400" height="166"><figcaption>Finding mid element</figcaption></figure></li>
<li>Repeat steps 3 to 6 until low meets high.
<figure><img alt="mid element Binary Search" src="//cdn.programiz.com/sites/tutorial2program/files/binary-search-mid-again.png" title="mid element" width="200" height="162"><figcaption>Mid element</figcaption></figure></li>
<li><code>x = 4</code> is found.
<figure><img alt="found Binary Search" src="//cdn.programiz.com/sites/tutorial2program/files/binary-search-found.png" title="found" width="200" height="162"><figcaption>Found</figcaption></figure></li>
</ol><hr><h2 id="algorithm">Binary Search Algorithm</h2>
<h3>Iteration Method</h3>
<pre>do until the pointers low and high meet each other.
mid = (low + high)/2
if (x == arr[mid])
return mid
else if (x > arr[mid]) // x is on the right side
low = mid + 1
else // x is on the left side
high = mid - 1</pre>
<h3>Recursive Method</h3>
<pre>binarySearch(arr, x, low, high)
if low > high
return False
else
mid = (low + high) / 2
if x == arr[mid]
return mid
else if x > arr[mid] // x is on the right side
return binarySearch(arr, x, mid + 1, high)
else // x is on the right side
return binarySearch(arr, x, low, mid - 1)</pre>
<hr><h2 id="code1">Python, Java, C/C++ Examples (Iterative Method)</h2>
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<div id="py1" onclick="changepy()" class="tabbed-editor__node tabbed-editor__node--active"><a href="#python-code">Python</a></div>
<div id="java1" onclick="changejava()" class="tabbed-editor__node"><a href="#java-code">Java</a></div>
<div id="c1" onclick="changec()" class="tabbed-editor__node"><a href="#c-code">C</a></div>
<div id="cpp1" onclick="changecpp()" class="tabbed-editor__node"><a href="#cpp-code">C++</a></div>
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<div class="code-editor__area code-editor__area--active" id="python-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="python hljs"><span class="hljs-comment"># Binary Search in python</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">binarySearch</span><span class="hljs-params">(array, x, low, high)</span>:</span>
<span class="hljs-comment"># Repeat until the pointers low and high meet each other</span>
<span class="hljs-keyword">while</span> low <= high:
mid = low + (high - low)//<span class="hljs-number">2</span>
<span class="hljs-keyword">if</span> array[mid] == x:
<span class="hljs-keyword">return</span> mid
<span class="hljs-keyword">elif</span> array[mid] < x:
low = mid + <span class="hljs-number">1</span>
<span class="hljs-keyword">else</span>:
high = mid - <span class="hljs-number">1</span>
<span class="hljs-keyword">return</span> <span class="hljs-number">-1</span>
array = [<span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">8</span>, <span class="hljs-number">9</span>]
x = <span class="hljs-number">4</span>
result = binarySearch(array, x, <span class="hljs-number">0</span>, len(array)<span class="hljs-number">-1</span>)
<span class="hljs-keyword">if</span> result != <span class="hljs-number">-1</span>:
<span class="hljs-keyword">print</span>(<span class="hljs-string">"Element is present at index "</span> + str(result))
<span class="hljs-keyword">else</span>:
<span class="hljs-keyword">print</span>(<span class="hljs-string">"Not found"</span>)</code></pre></div>
</div>
<div class="code-editor__area" id="java-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="java hljs"><span class="hljs-comment">// Binary Search in Java</span>
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">BinarySearch</span> </span>{
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">binarySearch</span><span class="hljs-params">(<span class="hljs-keyword">int</span> array[], <span class="hljs-keyword">int</span> x, <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-comment">// Repeat until the pointers low and high meet each other</span>
<span class="hljs-keyword">while</span> (low <= high) {
<span class="hljs-keyword">int</span> mid = low + (high - low) / <span class="hljs-number">2</span>;
<span class="hljs-keyword">if</span> (array[mid] == x)
<span class="hljs-keyword">return</span> mid;
<span class="hljs-keyword">if</span> (array[mid] < x)
low = mid + <span class="hljs-number">1</span>;
<span class="hljs-keyword">else</span>
high = mid - <span class="hljs-number">1</span>;
}
<span class="hljs-keyword">return</span> -<span class="hljs-number">1</span>;
}
<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title">main</span><span class="hljs-params">(String args[])</span> </span>{
BinarySearch ob = <span class="hljs-keyword">new</span> BinarySearch();
<span class="hljs-keyword">int</span> array[] = { <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">8</span>, <span class="hljs-number">9</span> };
<span class="hljs-keyword">int</span> n = array.length;
<span class="hljs-keyword">int</span> x = <span class="hljs-number">4</span>;
<span class="hljs-keyword">int</span> result = ob.binarySearch(array, x, <span class="hljs-number">0</span>, n - <span class="hljs-number">1</span>);
<span class="hljs-keyword">if</span> (result == -<span class="hljs-number">1</span>)
System.out.println(<span class="hljs-string">"Not found"</span>);
<span class="hljs-keyword">else</span>
System.out.println(<span class="hljs-string">"Element found at index "</span> + result);
}
}</code></pre></div>
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<div class="code-editor__area" id="c-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="c hljs cpp"><span class="hljs-comment">// Binary Search in C</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdio.h></span></span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">binarySearch</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> x, <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-comment">// Repeat until the pointers low and high meet each other</span>
<span class="hljs-keyword">while</span> (low <= high) {
<span class="hljs-keyword">int</span> mid = low + (high - low) / <span class="hljs-number">2</span>;
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[mid] == x)
<span class="hljs-keyword">return</span> mid;
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[mid] < x)
low = mid + <span class="hljs-number">1</span>;
<span class="hljs-keyword">else</span>
high = mid - <span class="hljs-number">1</span>;
}
<span class="hljs-keyword">return</span> <span class="hljs-number">-1</span>;
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">(<span class="hljs-keyword">void</span>)</span> </span>{
<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[] = {<span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">8</span>, <span class="hljs-number">9</span>};
<span class="hljs-keyword">int</span> n = <span class="hljs-keyword">sizeof</span>(<span class="hljs-built_in">array</span>) / <span class="hljs-keyword">sizeof</span>(<span class="hljs-built_in">array</span>[<span class="hljs-number">0</span>]);
<span class="hljs-keyword">int</span> x = <span class="hljs-number">4</span>;
<span class="hljs-keyword">int</span> result = binarySearch(<span class="hljs-built_in">array</span>, x, <span class="hljs-number">0</span>, n - <span class="hljs-number">1</span>);
<span class="hljs-keyword">if</span> (result == <span class="hljs-number">-1</span>)
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Not found"</span>);
<span class="hljs-keyword">else</span>
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Element is found at index %d"</span>, result);
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}</code></pre></div>
</div>
<div class="code-editor__area" id="cpp-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="cpp hljs"><span class="hljs-comment">// Binary Search in C++</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><iostream></span></span>
<span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>;
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">binarySearch</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> x, <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-comment">// Repeat until the pointers low and high meet each other</span>
<span class="hljs-keyword">while</span> (low <= high) {
<span class="hljs-keyword">int</span> mid = low + (high - low) / <span class="hljs-number">2</span>;
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[mid] == x)
<span class="hljs-keyword">return</span> mid;
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[mid] < x)
low = mid + <span class="hljs-number">1</span>;
<span class="hljs-keyword">else</span>
high = mid - <span class="hljs-number">1</span>;
}
<span class="hljs-keyword">return</span> <span class="hljs-number">-1</span>;
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">(<span class="hljs-keyword">void</span>)</span> </span>{
<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[] = {<span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">8</span>, <span class="hljs-number">9</span>};
<span class="hljs-keyword">int</span> x = <span class="hljs-number">4</span>;
<span class="hljs-keyword">int</span> n = <span class="hljs-keyword">sizeof</span>(<span class="hljs-built_in">array</span>) / <span class="hljs-keyword">sizeof</span>(<span class="hljs-built_in">array</span>[<span class="hljs-number">0</span>]);
<span class="hljs-keyword">int</span> result = binarySearch(<span class="hljs-built_in">array</span>, x, <span class="hljs-number">0</span>, n - <span class="hljs-number">1</span>);
<span class="hljs-keyword">if</span> (result == <span class="hljs-number">-1</span>)
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Not found"</span>);
<span class="hljs-keyword">else</span>
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Element is found at index %d"</span>, result);
}</code></pre></div>
</div>
</div>
<hr><h2 id="code2">Python, Java, C/C++ Examples (Recursive Method)</h2>
<div class="tabbed-editor">
<div class="tabbed-editor__node tabbed-editor__node--active"><a href="#python-code">Python</a></div>
<div class="tabbed-editor__node"><a href="#java-code">Java</a></div>
<div class="tabbed-editor__node"><a href="#c-code">C</a></div>
<div class="tabbed-editor__node"><a href="#cpp-code">C++</a></div>
</div>
<div class="code-editor code-editor--tabbed">
<div class="code-editor__area code-editor__area--active" id="python-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="python hljs"><span class="hljs-comment"># Binary Search in python</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">binarySearch</span><span class="hljs-params">(array, x, low, high)</span>:</span>
<span class="hljs-keyword">if</span> high >= low:
mid = low + (high - low)//<span class="hljs-number">2</span>
<span class="hljs-comment"># If found at mid, then return it</span>
<span class="hljs-keyword">if</span> array[mid] == x:
<span class="hljs-keyword">return</span> mid
<span class="hljs-comment"># Search the left half</span>
<span class="hljs-keyword">elif</span> array[mid] > x:
<span class="hljs-keyword">return</span> binarySearch(array, x, low, mid<span class="hljs-number">-1</span>)
<span class="hljs-comment"># Search the right half</span>
<span class="hljs-keyword">else</span>:
<span class="hljs-keyword">return</span> binarySearch(array, x, mid + <span class="hljs-number">1</span>, high)
<span class="hljs-keyword">else</span>:
<span class="hljs-keyword">return</span> <span class="hljs-number">-1</span>
array = [<span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">8</span>, <span class="hljs-number">9</span>]
x = <span class="hljs-number">4</span>
result = binarySearch(array, x, <span class="hljs-number">0</span>, len(array)<span class="hljs-number">-1</span>)
<span class="hljs-keyword">if</span> result != <span class="hljs-number">-1</span>:
<span class="hljs-keyword">print</span>(<span class="hljs-string">"Element is present at index "</span> + str(result))
<span class="hljs-keyword">else</span>:
<span class="hljs-keyword">print</span>(<span class="hljs-string">"Not found"</span>)</code></pre></div>
</div>
<div class="code-editor__area" id="java-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="java hljs"><span class="hljs-comment">// Binary Search in Java</span>
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">BinarySearch</span> </span>{
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">binarySearch</span><span class="hljs-params">(<span class="hljs-keyword">int</span> array[], <span class="hljs-keyword">int</span> x, <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-keyword">if</span> (high >= low) {
<span class="hljs-keyword">int</span> mid = low + (high - low) / <span class="hljs-number">2</span>;
<span class="hljs-comment">// If found at mid, then return it</span>
<span class="hljs-keyword">if</span> (array[mid] == x)
<span class="hljs-keyword">return</span> mid;
<span class="hljs-comment">// Search the left half</span>
<span class="hljs-keyword">if</span> (array[mid] > x)
<span class="hljs-keyword">return</span> binarySearch(array, x, low, mid - <span class="hljs-number">1</span>);
<span class="hljs-comment">// Search the right half</span>
<span class="hljs-keyword">return</span> binarySearch(array, x, mid + <span class="hljs-number">1</span>, high);
}
<span class="hljs-keyword">return</span> -<span class="hljs-number">1</span>;
}
<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title">main</span><span class="hljs-params">(String args[])</span> </span>{
BinarySearch ob = <span class="hljs-keyword">new</span> BinarySearch();
<span class="hljs-keyword">int</span> array[] = { <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">8</span>, <span class="hljs-number">9</span> };
<span class="hljs-keyword">int</span> n = array.length;
<span class="hljs-keyword">int</span> x = <span class="hljs-number">4</span>;
<span class="hljs-keyword">int</span> result = ob.binarySearch(array, x, <span class="hljs-number">0</span>, n - <span class="hljs-number">1</span>);
<span class="hljs-keyword">if</span> (result == -<span class="hljs-number">1</span>)
System.out.println(<span class="hljs-string">"Not found"</span>);
<span class="hljs-keyword">else</span>
System.out.println(<span class="hljs-string">"Element found at index "</span> + result);
}
}</code></pre></div>
</div>
<div class="code-editor__area" id="c-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="c hljs cpp"><span class="hljs-comment">// Binary Search in C</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdio.h></span></span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">binarySearch</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> x, <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-keyword">if</span> (high >= low) {
<span class="hljs-keyword">int</span> mid = low + (high - low) / <span class="hljs-number">2</span>;
<span class="hljs-comment">// If found at mid, then return it</span>
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[mid] == x)
<span class="hljs-keyword">return</span> mid;
<span class="hljs-comment">// Search the left half</span>
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[mid] > x)
<span class="hljs-keyword">return</span> binarySearch(<span class="hljs-built_in">array</span>, x, low, mid - <span class="hljs-number">1</span>);
<span class="hljs-comment">// Search the right half</span>
<span class="hljs-keyword">return</span> binarySearch(<span class="hljs-built_in">array</span>, x, mid + <span class="hljs-number">1</span>, high);
}
<span class="hljs-keyword">return</span> <span class="hljs-number">-1</span>;
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">(<span class="hljs-keyword">void</span>)</span> </span>{
<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[] = {<span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">8</span>, <span class="hljs-number">9</span>};
<span class="hljs-keyword">int</span> n = <span class="hljs-keyword">sizeof</span>(<span class="hljs-built_in">array</span>) / <span class="hljs-keyword">sizeof</span>(<span class="hljs-built_in">array</span>[<span class="hljs-number">0</span>]);
<span class="hljs-keyword">int</span> x = <span class="hljs-number">4</span>;
<span class="hljs-keyword">int</span> result = binarySearch(<span class="hljs-built_in">array</span>, x, <span class="hljs-number">0</span>, n - <span class="hljs-number">1</span>);
<span class="hljs-keyword">if</span> (result == <span class="hljs-number">-1</span>)
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Not found"</span>);
<span class="hljs-keyword">else</span>
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Element is found at index %d"</span>, result);
}</code></pre></div>
</div>
<div class="code-editor__area" id="cpp-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="cpp hljs"><span class="hljs-comment">// Binary Search in C++</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><iostream></span></span>
<span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>;
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">binarySearch</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> x, <span class="hljs-keyword">int</span> low, <span class="hljs-keyword">int</span> high)</span> </span>{
<span class="hljs-keyword">if</span> (high >= low) {
<span class="hljs-keyword">int</span> mid = low + (high - low) / <span class="hljs-number">2</span>;
<span class="hljs-comment">// If found at mid, then return it</span>
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[mid] == x)
<span class="hljs-keyword">return</span> mid;
<span class="hljs-comment">// Search the left half</span>
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[mid] > x)
<span class="hljs-keyword">return</span> binarySearch(<span class="hljs-built_in">array</span>, x, low, mid - <span class="hljs-number">1</span>);
<span class="hljs-comment">// Search the right half</span>
<span class="hljs-keyword">return</span> binarySearch(<span class="hljs-built_in">array</span>, x, mid + <span class="hljs-number">1</span>, high);
}
<span class="hljs-keyword">return</span> <span class="hljs-number">-1</span>;
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">(<span class="hljs-keyword">void</span>)</span> </span>{
<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[] = {<span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>, <span class="hljs-number">7</span>, <span class="hljs-number">8</span>, <span class="hljs-number">9</span>};
<span class="hljs-keyword">int</span> x = <span class="hljs-number">4</span>;
<span class="hljs-keyword">int</span> n = <span class="hljs-keyword">sizeof</span>(<span class="hljs-built_in">array</span>) / <span class="hljs-keyword">sizeof</span>(<span class="hljs-built_in">array</span>[<span class="hljs-number">0</span>]);
<span class="hljs-keyword">int</span> result = binarySearch(<span class="hljs-built_in">array</span>, x, <span class="hljs-number">0</span>, n - <span class="hljs-number">1</span>);
<span class="hljs-keyword">if</span> (result == <span class="hljs-number">-1</span>)
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Not found"</span>);
<span class="hljs-keyword">else</span>
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Element is found at index %d"</span>, result);
}</code></pre></div>
</div>
</div>
<hr><h2 id="complexity">Binary Search Complexity</h2>
<p></p><div class="clearfix"></div><p><strong>Time Complexities</strong></p>
<ul><li><strong>Best case complexity</strong>: <code>O(1)</code></li>
<li><strong>Average case complexity</strong>: <code>O(log n)</code></li>
<li><strong>Worst case complexity</strong>: <code>O(log n)</code></li>
</ul><p><strong>Space Complexity</strong></p>
<p>The space complexity of the binary search is <code>O(1)</code>.</p>
<hr><h2 id="application">Binary Search Applications</h2>
<ul><li>In libraries of Java, .Net, C++ STL</li>
<li>While debugging, the binary search is used to pinpoint the place where the error happens.</li>
</ul></div>
</div>
<div class="tutorial-toc"><div class="tutorial-toc__inner"><h3 class="tutorial-toc__title">Table of Contents
<button class="btn btn--clear align-items-center">
<svg class="programiz-icon"><use xlink:href="/sites/all/themes/programiz/assets/feather-sprite.svg#x"></use></svg></button></h3><div class="tutorial-toc__links"><ul><li><a href="#definition">Definition</a></li>
<li><a href="#working">Binary Search Working</a></li>
<li><a href="#algorithm">Binary Search Algorithm</a></li>
<li><a href="#code1">Python, Java, C/C++ Examples (Iterative Method)</a></li>
<li><a href="#code2">Python, Java, C/C++ Examples (Recursive Method)</a></li>
<li><a href="#complexity">Binary Search Complexity</a></li>
<li><a href="#application">Binary Search Applications</a></li>
</ul></div></div></div> </div>
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