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<h1>Radix Sort Algorithm</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn about the radix sort algorithm and its implementation in Python, Java, C, and C++.</p>
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<span property="dc:title" content="Radix Sort Algorithm" class="rdf-meta element-hidden"></span>
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<p id="definition">Radix sort is <a href="/dsa.html">a sorting algorithm</a> that sorts the elements by first grouping the individual digits of the same <strong>place value</strong>. Then, sort the elements according to their increasing/decreasing order.</p>
<p>Suppose, we have an array of 8 elements. First, we will sort elements based on the value of the unit place. Then, we will sort elements based on the value of the tenth place. This process goes on until the last significant place.</p>
<p>Let the initial array be <code>[121, 432, 564, 23, 1, 45, 788]</code>. It is sorted according to radix sort as shown in the figure below.</p>
<figure><img alt="Radix Sort Working" src="https://www.programiz.com/sites/tutorial2program/files/Radix-sort-0_0.png" title="Working of Radix Sort" width="500" height="474"><figcaption>Working of Radix Sort</figcaption></figure><p>Please go through <a href="/dsa/counting-sort.html">the counting sort</a> before reading this article because counting sort is used as an intermediate sort in radix sort.</p>
<hr><h2 id="working">Working of Radix Sort</h2>
<ol><li>Find the largest element in the array, i.e. <var>max</var>. Let <code>X</code> be the number of digits in <code>max</code>. <code>X</code> is calculated because we have to go through all the significant places of all elements.<br><br>
In this array <code>[121, 432, 564, 23, 1, 45, 788]</code>, we have the largest number 788. It has 3 digits. Therefore, the loop should go up to hundreds place (3 times).</li>
<li>Now, go through each significant place one by one.<br><br>
Use any stable sorting technique to sort the digits at each significant place. We have used counting sort for this.<br><br>
Sort the elements based on the unit place digits (<code>X=0</code>).
<figure><img alt="Radix Sort working with Counting Sort as intermediate step" src="https://www.programiz.com/sites/tutorial2program/files/Radix-sort-one.png" title="Radix Sort Steps" width="650" height="395"><figcaption>Using counting sort to sort elements based on unit place</figcaption></figure></li>
<li>Now, sort the elements based on digits at tens place.
<figure><img alt="Radix Sort Step" src="https://www.programiz.com/sites/tutorial2program/files/Radix-sort-ten.png" title="Radix Sort Step" width="500" height="96"><figcaption>Sort elements based on tens place</figcaption></figure></li>
<li>Finally, sort the elements based on the digits at hundreds place.
<figure><img alt="Selection Sort Step" src="https://www.programiz.com/sites/tutorial2program/files/Radix-sort-hundred.png" title="Selection Sort Step" width="500" height="96"><figcaption>Sort elements based on hundreds place</figcaption></figure></li>
</ol><hr><h2 id="algorithm">Radix Sort Algorithm</h2>
<pre style="max-height: 600px;"><code class="dsa hljs properties"><span class="hljs-attr">radixSort(array)</span>
<span class="hljs-attr">d</span> <span class="hljs-string"><- maximum number of digits in the largest element</span>
<span class="hljs-attr">create</span> <span class="hljs-string">d buckets of size 0-9</span>
<span class="hljs-attr">for</span> <span class="hljs-string">i <- 0 to d</span>
<span class="hljs-attr">sort</span> <span class="hljs-string">the elements according to ith place digits using countingSort</span>
<span class="hljs-meta">countingSort(array,</span> <span class="hljs-string">d)</span>
<span class="hljs-attr">max</span> <span class="hljs-string"><- find largest element among dth place elements</span>
<span class="hljs-attr">initialize</span> <span class="hljs-string">count array with all zeros</span>
<span class="hljs-attr">for</span> <span class="hljs-string">j <- 0 to size</span>
<span class="hljs-attr">find</span> <span class="hljs-string">the total count of each unique digit in dth place of elements and</span>
<span class="hljs-attr">store</span> <span class="hljs-string">the count at jth index in count array</span>
<span class="hljs-attr">for</span> <span class="hljs-string">i <- 1 to max</span>
<span class="hljs-attr">find</span> <span class="hljs-string">the cumulative sum and store it in count array itself</span>
<span class="hljs-attr">for</span> <span class="hljs-string">j <- size down to 1</span>
<span class="hljs-attr">restore</span> <span class="hljs-string">the elements to array</span>
<span class="hljs-attr">decrease</span> <span class="hljs-string">count of each element restored by 1</span></code></pre>
<hr><h2 id="code">Radix Sort Code in Python, Java, and C/C++</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>
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<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"># Radix sort in Python</span>
<span class="hljs-comment"># Using counting sort to sort the elements in the basis of significant places</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">countingSort</span><span class="hljs-params">(array, place)</span>:</span>
size = len(array)
output = [<span class="hljs-number">0</span>] * size
count = [<span class="hljs-number">0</span>] * <span class="hljs-number">10</span>
<span class="hljs-comment"># Calculate count of elements</span>
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(<span class="hljs-number">0</span>, size):
index = array[i] // place
count[index % <span class="hljs-number">10</span>] += <span class="hljs-number">1</span>
<span class="hljs-comment"># Calculate cumulative count</span>
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(<span class="hljs-number">1</span>, <span class="hljs-number">10</span>):
count[i] += count[i - <span class="hljs-number">1</span>]
<span class="hljs-comment"># Place the elements in sorted order</span>
i = size - <span class="hljs-number">1</span>
<span class="hljs-keyword">while</span> i >= <span class="hljs-number">0</span>:
index = array[i] // place
output[count[index % <span class="hljs-number">10</span>] - <span class="hljs-number">1</span>] = array[i]
count[index % <span class="hljs-number">10</span>] -= <span class="hljs-number">1</span>
i -= <span class="hljs-number">1</span>
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(<span class="hljs-number">0</span>, size):
array[i] = output[i]
<span class="hljs-comment"># Main function to implement radix sort</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">radixSort</span><span class="hljs-params">(array)</span>:</span>
<span class="hljs-comment"># Get maximum element</span>
max_element = max(array)
<span class="hljs-comment"># Apply counting sort to sort elements based on place value.</span>
place = <span class="hljs-number">1</span>
<span class="hljs-keyword">while</span> max_element // place > <span class="hljs-number">0</span>:
countingSort(array, place)
place *= <span class="hljs-number">10</span>
data = [<span class="hljs-number">121</span>, <span class="hljs-number">432</span>, <span class="hljs-number">564</span>, <span class="hljs-number">23</span>, <span class="hljs-number">1</span>, <span class="hljs-number">45</span>, <span class="hljs-number">788</span>]
radixSort(data)
<span class="hljs-keyword">print</span>(data)</code></pre></div>
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<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">// Radix Sort in Java Programming</span>
<span class="hljs-keyword">import</span> java.util.Arrays;
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">RadixSort</span> </span>{
<span class="hljs-comment">// Using counting sort to sort the elements in the basis of significant places</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">countingSort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> array[], <span class="hljs-keyword">int</span> size, <span class="hljs-keyword">int</span> place)</span> </span>{
<span class="hljs-keyword">int</span>[] output = <span class="hljs-keyword">new</span> <span class="hljs-keyword">int</span>[size + <span class="hljs-number">1</span>];
<span class="hljs-keyword">int</span> max = array[<span class="hljs-number">0</span>];
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">1</span>; i < size; i++) {
<span class="hljs-keyword">if</span> (array[i] > max)
max = array[i];
}
<span class="hljs-keyword">int</span>[] count = <span class="hljs-keyword">new</span> <span class="hljs-keyword">int</span>[max + <span class="hljs-number">1</span>];
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < max; ++i)
count[i] = <span class="hljs-number">0</span>;
<span class="hljs-comment">// Calculate count of elements</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; i++)
count[(array[i] / place) % <span class="hljs-number">10</span>]++;
<span class="hljs-comment">// Calculate cumulative count</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">1</span>; i < <span class="hljs-number">10</span>; i++)
count[i] += count[i - <span class="hljs-number">1</span>];
<span class="hljs-comment">// Place the elements in sorted order</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = size - <span class="hljs-number">1</span>; i >= <span class="hljs-number">0</span>; i--) {
output[count[(array[i] / place) % <span class="hljs-number">10</span>] - <span class="hljs-number">1</span>] = array[i];
count[(array[i] / place) % <span class="hljs-number">10</span>]--;
}
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; i++)
array[i] = output[i];
}
<span class="hljs-comment">// Function to get the largest element from an array</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">getMax</span><span class="hljs-params">(<span class="hljs-keyword">int</span> array[], <span class="hljs-keyword">int</span> n)</span> </span>{
<span class="hljs-keyword">int</span> max = array[<span class="hljs-number">0</span>];
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">1</span>; i < n; i++)
<span class="hljs-keyword">if</span> (array[i] > max)
max = array[i];
<span class="hljs-keyword">return</span> max;
}
<span class="hljs-comment">// Main function to implement radix sort</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">radixSort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> array[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-comment">// Get maximum element</span>
<span class="hljs-keyword">int</span> max = getMax(array, size);
<span class="hljs-comment">// Apply counting sort to sort elements based on place value.</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> place = <span class="hljs-number">1</span>; max / place > <span class="hljs-number">0</span>; place *= <span class="hljs-number">10</span>)
countingSort(array, size, place);
}
<span class="hljs-comment">// Driver code</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>{
<span class="hljs-keyword">int</span>[] data = { <span class="hljs-number">121</span>, <span class="hljs-number">432</span>, <span class="hljs-number">564</span>, <span class="hljs-number">23</span>, <span class="hljs-number">1</span>, <span class="hljs-number">45</span>, <span class="hljs-number">788</span> };
<span class="hljs-keyword">int</span> size = data.length;
RadixSort rs = <span class="hljs-keyword">new</span> RadixSort();
rs.radixSort(data, size);
System.out.println(<span class="hljs-string">"Sorted Array in Ascending Order: "</span>);
System.out.println(Arrays.toString(data));
}
}</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">// Radix Sort in C Programming</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdio.h></span></span>
<span class="hljs-comment">// Function to get the largest element from an array</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">getMax</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> n)</span> </span>{
<span class="hljs-keyword">int</span> max = <span class="hljs-built_in">array</span>[<span class="hljs-number">0</span>];
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">1</span>; i < n; i++)
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[i] > max)
max = <span class="hljs-built_in">array</span>[i];
<span class="hljs-keyword">return</span> max;
}
<span class="hljs-comment">// Using counting sort to sort the elements in the basis of significant places</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">countingSort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size, <span class="hljs-keyword">int</span> place)</span> </span>{
<span class="hljs-keyword">int</span> output[size + <span class="hljs-number">1</span>];
<span class="hljs-keyword">int</span> max = (<span class="hljs-built_in">array</span>[<span class="hljs-number">0</span>] / place) % <span class="hljs-number">10</span>;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">1</span>; i < size; i++) {
<span class="hljs-keyword">if</span> (((<span class="hljs-built_in">array</span>[i] / place) % <span class="hljs-number">10</span>) > max)
max = <span class="hljs-built_in">array</span>[i];
}
<span class="hljs-keyword">int</span> count[max + <span class="hljs-number">1</span>];
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < max; ++i)
count[i] = <span class="hljs-number">0</span>;
<span class="hljs-comment">// Calculate count of elements</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; i++)
count[(<span class="hljs-built_in">array</span>[i] / place) % <span class="hljs-number">10</span>]++;
<span class="hljs-comment">// Calculate cumulative count</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">1</span>; i < <span class="hljs-number">10</span>; i++)
count[i] += count[i - <span class="hljs-number">1</span>];
<span class="hljs-comment">// Place the elements in sorted order</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = size - <span class="hljs-number">1</span>; i >= <span class="hljs-number">0</span>; i--) {
output[count[(<span class="hljs-built_in">array</span>[i] / place) % <span class="hljs-number">10</span>] - <span class="hljs-number">1</span>] = <span class="hljs-built_in">array</span>[i];
count[(<span class="hljs-built_in">array</span>[i] / place) % <span class="hljs-number">10</span>]--;
}
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; i++)
<span class="hljs-built_in">array</span>[i] = output[i];
}
<span class="hljs-comment">// Main function to implement radix sort</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">radixsort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-comment">// Get maximum element</span>
<span class="hljs-keyword">int</span> max = getMax(<span class="hljs-built_in">array</span>, size);
<span class="hljs-comment">// Apply counting sort to sort elements based on place value.</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> place = <span class="hljs-number">1</span>; max / place > <span class="hljs-number">0</span>; place *= <span class="hljs-number">10</span>)
countingSort(<span class="hljs-built_in">array</span>, size, place);
}
<span class="hljs-comment">// Print an array</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printArray</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; ++i) {
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"%d "</span>, <span class="hljs-built_in">array</span>[i]);
}
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n"</span>);
}
<span class="hljs-comment">// Driver code</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[] = {<span class="hljs-number">121</span>, <span class="hljs-number">432</span>, <span class="hljs-number">564</span>, <span class="hljs-number">23</span>, <span class="hljs-number">1</span>, <span class="hljs-number">45</span>, <span class="hljs-number">788</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>]);
radixsort(<span class="hljs-built_in">array</span>, n);
printArray(<span class="hljs-built_in">array</span>, n);
}</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">// Radix Sort in C++ Programming</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-comment">// Function to get the largest element from an array</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">getMax</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> n)</span> </span>{
<span class="hljs-keyword">int</span> max = <span class="hljs-built_in">array</span>[<span class="hljs-number">0</span>];
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">1</span>; i < n; i++)
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[i] > max)
max = <span class="hljs-built_in">array</span>[i];
<span class="hljs-keyword">return</span> max;
}
<span class="hljs-comment">// Using counting sort to sort the elements in the basis of significant places</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">countingSort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size, <span class="hljs-keyword">int</span> place)</span> </span>{
<span class="hljs-keyword">const</span> <span class="hljs-keyword">int</span> max = <span class="hljs-number">10</span>;
<span class="hljs-keyword">int</span> output[size];
<span class="hljs-keyword">int</span> count[max];
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < max; ++i)
count[i] = <span class="hljs-number">0</span>;
<span class="hljs-comment">// Calculate count of elements</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; i++)
count[(<span class="hljs-built_in">array</span>[i] / place) % <span class="hljs-number">10</span>]++;
<span class="hljs-comment">// Calculate cumulative count</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">1</span>; i < max; i++)
count[i] += count[i - <span class="hljs-number">1</span>];
<span class="hljs-comment">// Place the elements in sorted order</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = size - <span class="hljs-number">1</span>; i >= <span class="hljs-number">0</span>; i--) {
output[count[(<span class="hljs-built_in">array</span>[i] / place) % <span class="hljs-number">10</span>] - <span class="hljs-number">1</span>] = <span class="hljs-built_in">array</span>[i];
count[(<span class="hljs-built_in">array</span>[i] / place) % <span class="hljs-number">10</span>]--;
}
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; i++)
<span class="hljs-built_in">array</span>[i] = output[i];
}
<span class="hljs-comment">// Main function to implement radix sort</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">radixsort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-comment">// Get maximum element</span>
<span class="hljs-keyword">int</span> max = getMax(<span class="hljs-built_in">array</span>, size);
<span class="hljs-comment">// Apply counting sort to sort elements based on place value.</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> place = <span class="hljs-number">1</span>; max / place > <span class="hljs-number">0</span>; place *= <span class="hljs-number">10</span>)
countingSort(<span class="hljs-built_in">array</span>, size, place);
}
<span class="hljs-comment">// Print an array</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printArray</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-keyword">int</span> i;
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">0</span>; i < size; i++)
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">array</span>[i] << <span class="hljs-string">" "</span>;
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>;
}
<span class="hljs-comment">// Driver code</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[] = {<span class="hljs-number">121</span>, <span class="hljs-number">432</span>, <span class="hljs-number">564</span>, <span class="hljs-number">23</span>, <span class="hljs-number">1</span>, <span class="hljs-number">45</span>, <span class="hljs-number">788</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>]);
radixsort(<span class="hljs-built_in">array</span>, n);
printArray(<span class="hljs-built_in">array</span>, n);
}</code></pre></div>
</div>
</div>
<hr><h2 id="complexity">Radix Sort Complexity</h2>
<div class="table-responsive">
<table border="0"><tbody><tr><th><strong>Time Complexity</strong></th>
<td> </td>
</tr><tr><td>Best</td>
<td>O(n+k)</td>
</tr><tr><td>Worst</td>
<td>O(n+k)</td>
</tr><tr><td>Average</td>
<td>O(n+k)</td>
</tr><tr><th><strong>Space Complexity</strong></th>
<td>O(max)</td>
</tr><tr><th><strong>Stability</strong></th>
<td>Yes</td>
</tr></tbody></table></div>
<hr><p>Since radix sort is a non-comparative algorithm, it has advantages over comparative sorting algorithms.</p>
<p>For the radix sort that uses counting sort as an intermediate stable sort, the time complexity is <code>O(d(n+k))</code>.</p>
<p></p><div class="clearfix"></div><p>Here, <code>d</code> is the number cycle and <code>O(n+k)</code> is the time complexity of counting sort.</p>
<p>Thus, radix sort has linear time complexity which is better than <code>O(nlog n)</code> of comparative sorting algorithms.</p>
<p>If we take very large digit numbers or the number of other bases like 32-bit and 64-bit numbers then it can perform in linear time however the intermediate sort takes large space.</p>
<p>This makes radix sort space inefficient. This is the reason why this sort is not used in software libraries.</p>
<hr><h2 id="application">Radix Sort Applications</h2>
<p>Radix sort is implemented in</p>
<ul><li>DC3 algorithm (Kärkkäinen-Sanders-Burkhardt) while making a suffix array.</li>
<li>places where there are numbers in large ranges.</li>
</ul><hr><h2>Similar Sorting Algorithms</h2>
<ol><li><a href="/dsa/quick-sort.html">Quicksort</a></li>
<li><a href="/dsa/merge-sort.html">Merge Sort</a></li>
<li><a href="/dsa/bucket-sort.html">Bucket Sort</a></li>
<li><a href="/dsa/counting-sort.html">Counting Sort</a></li>
</ol></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">Working of Radix Sort</a></li>
<li><a href="#algorithm">Radix Sort Algorithm</a></li>
<li><a href="#code">Radix Sort Code in Python, Java, and C/C++</a></li>
<li><a href="#complexity">Complexity</a></li>
<li><a href="#application">Applications</a></li>
</ul></div></div></div> </div>
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