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<!DOCTYPE html>
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<title>Quick Sort Visualizer - Step-by-Step Animation, Code & Complexity | EasySorting</title>
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content="Visualize Quick Sort's pivot-based partitioning step by step. Understand average O(n log n) performance, randomized quick sort, with code in C, C++, Java, Python, and JavaScript." />
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<h1>Quick Sort</h1>
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<span class="info" id="pivot"></span>
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<span class="info" id="pi"></span>
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<h3>How to use ?</h3>
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<div class="ans">
<p>
Enter an array separated by commas as : 16,15,15,10,1 or just press the hand icon to generate a
random array then press enter or Sort button. Sorting
will
start
and
you can watch each pass as it gets sorted.
When it shows green it means the two of them are
being
compared
when red shows, it means the left number is greater than right number so it needs swapping
The blue color means the number is
at its
correct position and thus sorted
it will continue to check other numbers until it reaches end.
</p>
</div>
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<div class="sorting-algorithm-container">
<h1 class="algorithm-title scroll-animate">Quick Sort Overview</h1>
<section class="history scroll-animate">
<h2 class="section-title">History</h2>
<p>Quick sort was developed by Tony Hoare in 1960. It is a divide-and-conquer algorithm that is
efficient for large datasets. Quick sort has become one of the most widely used sorting algorithms
due to its performance in practice and its ability to sort in place.</p>
</section>
<section class="current-uses scroll-animate">
<h2 class="section-title">Current Uses</h2>
<ul>
<li><strong>General Purpose:</strong> Used in a variety of applications, including databases and
memory sorting.</li>
<li><strong>Libraries:</strong> Often implemented in standard libraries for programming languages
due to its efficiency.</li>
<li><strong>Embedded Systems:</strong> Commonly used in systems with limited resources for efficient
sorting.</li>
</ul>
</section>
<section class="complexity scroll-animate">
<h2 class="section-title">Time and Space Complexity</h2>
<h3>Time Complexity</h3>
<ul>
<li><strong>Best Case:</strong> <code>O(n log n)</code> - When the pivot divides the array into
nearly equal halves.</li>
<li><strong>Average Case:</strong> <code>O(n log n)</code> - The average case performance is
efficient.</li>
<li><strong>Worst Case:</strong> <code>O(n<sup>2</sup>)</code> - Occurs when the smallest or largest
element
is always chosen as the pivot.</li>
</ul>
<h3>Space Complexity</h3>
<p><strong>Space Complexity:</strong> <code>O(log n)</code> - Due to the recursive stack space used
during the algorithm's execution.</p>
</section>
<section class="pseudo-code scroll-animate">
<h2 class="section-title">Pseudo Code</h2>
<div class="code-container">
<button class="copy-btn" onclick="copyToClipboard(this)">Copy</button>
<pre class="pseudo-code-code"><code><!-- This is the pseudo code for Quick Sort -->function quickSort(arr, low, high):
if low < high:
pi = partition(arr, low, high)
quickSort(arr, low, pi - 1)
quickSort(arr, pi + 1, high)
function partition(arr, low, high):
pivot = arr[high]
i = low - 1
for j from low to high - 1:
if arr[j] <= pivot:
i = i + 1
swap arr[i] and arr[j]
swap arr[i + 1] and arr[high]
return i + 1</code></pre>
</div>
</section>
<section class="characteristics scroll-animate">
<h2 class="section-title">Key Characteristics</h2>
<ul>
<li><strong>In-Place:</strong> Quick sort requires minimal additional storage space.</li>
<li><strong>Not Stable:</strong> The algorithm is not stable due to the way it swaps elements.</li>
</ul>
</section>
<section class="summary scroll-animate">
<h2 class="section-title">Summary</h2>
<p>Quick sort is a highly efficient sorting algorithm that utilizes the divide-and-conquer strategy.
Despite its worst-case time complexity of <code>O(n<sup>2</sup>)</code>, it is widely used due to
its
average-case efficiency and practical performance.</p>
</section>
<section class="how-it-works scroll-animate">
<h2 class="section-title">How Quick Sort Works</h2>
<p>Quick sort is a divide-and-conquer algorithm built around the idea of a <strong>pivot</strong>. Its
efficiency comes from partitioning the array in place:</p>
<ol class="algorithm-steps">
<li><strong>Choose a pivot</strong> element (any element - often the last, first, or a random
one).</li>
<li><strong>Partition</strong> the array so that every element smaller than the pivot comes before
it, and every element larger comes after it. The pivot is now in its final sorted position.</li>
<li><strong>Recursively</strong> quick sort the sub-array to the left of the pivot and the
sub-array to the right.</li>
<li><strong>Terminate</strong> when a sub-array has zero or one element - the whole array is then
sorted.</li>
</ol>
<p>On average quick sort makes <code>O(n log n)</code> comparisons and is famously cache-friendly,
which is why it is so fast in practice - but its worst case is <code>O(n²)</code> when the pivot is
consistently the smallest or largest element (randomizing the pivot avoids this).</p>
</section>
<section class="application-code scroll-animate">
<h2 class="section-title">When To Use Quick Sort</h2>
<ul class="algorithm-list-inline">
<li><strong>Random or shuffled data:</strong> excellent expected performance with low overhead.</li>
<li><strong>Average-case sensitive workloads:</strong> cache-friendly partitioning beats merge sort
in most comparisons.</li>
<li><strong>In-place sorting:</strong> uses only O(log n) stack space.</li>
<li><strong>Base of Introsort:</strong> combined with heap and insertion sort for production C++
std::sort.</li>
</ul>
</section>
<section class="related-visualizations scroll-animate">
<h2 class="section-title">Related Sorting Visualizers</h2>
<p>Quick sort is an in-place but unstable comparison sort. Compare it with related algorithms:</p>
<div class="related-links">
<a href="./mergeSort.html">Merge Sort Visualizer</a> -
<a href="./heapSort.html">Heap Sort Visualizer</a> -
<a href="./insertionSort.html">Insertion Sort Visualizer</a> -
<a href="./shellSort.html">Shell Sort Visualizer</a> -
<a href="./bubbleSort.html">Bubble Sort Visualizer</a>
</div>
<p>Compare all algorithms side by side in the <a href="./summary.html">Sorting Algorithm Complexity
Summary</a>.</p>
<p>Prefer a plain-English answer? See <a href="./sortingAlgorithms.html">Which sorting algorithm
should I use?</a>, benchmark every algorithm live in the <a href="./sortingAlgorithmRace.html">Sorting
Algorithm Race</a>, or learn <a href="./bigONotation.html">Big O notation</a> with charts.</p>
</section>
<section class="language-code-container">
<h1 class="scroll-animate">Quick Sort Code Implementation</h1>
<div class="language-selector scroll-animate">
<button data-language="c">C</button>
<button data-language="cpp">C++</button>
<button data-language="javascript">JavaScript</button>
<button data-language="python">Python</button>
<button data-language="java">Java</button>
</div>
<pre class="inside-code-container">
<code id="code-display"></code>
</pre>
<button class="language-copy-button scroll-animate">Copy</button>
</section>
</div>
</div>
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<script src="./app.js"></script>
<script>
const yearEl = document.getElementById('year');
if (yearEl) yearEl.textContent = new Date().getFullYear();
const codeSnippets = {
javascript: `// JavaScript code for Quick Sort
function quickSort(arr) {
if (arr.length <= 1) {
return arr;
}
const pivot = arr[arr.length - 1];
const left = [];
const right = [];
for (let i = 0; i < arr.length - 1; i++) {
if (arr[i] < pivot) {
left.push(arr[i]);
} else {
right.push(arr[i]);
}
}
return [...quickSort(left), pivot, ...quickSort(right)];
}
let arr = [16, 15, 15, 10, 1];
console.log('Before sorting:', arr);
arr = quickSort(arr);
console.log('After sorting:', arr);`,
c: `// C code for Quick Sort
#include <stdio.h>
void quickSort(int arr[], int low, int high) {
if (low < high) {
int pivot = arr[high];
int i = low - 1;
for (int j = low; j < high; j++) {
if (arr[j] < pivot) {
i++;
int temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
}
}
int temp = arr[i + 1];
arr[i + 1] = arr[high];
arr[high] = temp;
quickSort(arr, low, i);
quickSort(arr, i + 2, high);
}
}
int main() {
int arr[] = {16, 15, 15, 10, 1};
int n = sizeof(arr) / sizeof(arr[0]);
printf("Before sorting: ");
for (int i = 0; i < n; i++) {
printf("%d ", arr[i]);
}
quickSort(arr, 0, n - 1);
printf("\\nAfter sorting: ");
for (int i = 0; i < n; i++) {
printf("%d ", arr[i]);
}
return 0;
}`,
cpp: `// C++ code for Quick Sort
#include <iostream>
#include <vector>
using namespace std;
void quickSort(vector<int>& arr, int low, int high) {
if (low < high) {
int pivot = arr[high];
int i = low - 1;
for (int j = low; j < high; j++) {
if (arr[j] < pivot) {
i++;
swap(arr[i], arr[j]);
}
}
swap(arr[i + 1], arr[high]);
quickSort(arr, low, i);
quickSort(arr, i + 2, high);
}
}
int main() {
vector<int> arr = {16, 15, 15, 10, 1};
cout << "Before sorting: ";
for (int num : arr) {
cout << num << " ";
}
quickSort(arr, 0, arr.size() - 1);
cout << "\\nAfter sorting: ";
for (int num : arr) {
cout << num << " ";
}
return 0;
}`,
java: `// Java code for Quick Sort
public class SortingAlgorithm {
public static void quickSort(int[] arr, int low, int high) {
if (low < high) {
int pivot = arr[high];
int i = low - 1;
for (int j = low; j < high; j++) {
if (arr[j] < pivot) {
i++;
int temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
}
}
int temp = arr[i + 1];
arr[i + 1] = arr[high];
arr[high] = temp;
quickSort(arr, low, i);
quickSort(arr, i + 2, high);
}
}
public static void main(String[] args) {
int[] arr = {16, 15, 15, 10, 1};
System.out.print("Before sorting: ");
for (int num : arr) {
System.out.print(num + " ");
}
quickSort(arr, 0, arr.length - 1);
System.out.print("\\nAfter sorting: ");
for (int num : arr) {
System.out.print(num + " ");
}
}
}`,
python: `# Python code for Quick Sort
def quickSort(arr, low, high):
if low < high:
pivot = arr[high]
i = low - 1
for j in range(low, high):
if arr[j] < pivot:
i += 1
arr[i], arr[j] = arr[j], arr[i]
arr[i + 1], arr[high] = arr[high], arr[i + 1]
quickSort(arr, low, i)
quickSort(arr, i + 2, high)
arr = [16, 15, 15, 10, 1]
print('Before sorting:', arr)
quickSort(arr, 0, len(arr) - 1)
print('After sorting:', arr)
`
};
const sortBtn = document.getElementById("sort-btn");
const inputBox = document.getElementById("input-num");
const passesDiv = document.getElementById("passes");
const howto = document.getElementById("howto");
const skipBtn = document.getElementById("skip");
const fastBtn = document.getElementById("fast-btn");
let ms = 1000, randomizer = false;
const toggleCheckbox = document.getElementById("toggle-randomized");
const toggleLabel = document.getElementById("toggle-label");
// Event listener to update label based on toggle state
toggleCheckbox.addEventListener("change", () => {
toggleLabel.textContent = toggleCheckbox.checked ? "Randomized" : "Normal";
randomizer = toggleCheckbox.checked ? true : false;
});
sortBtn.addEventListener("click", () => {
if (sortBtn.textContent == "Sorting...") return;
let input = inputBox.value.trim();
if (input == "") {
alert("Please enter some values ! ");
return;
}
ms = 1000;
displayBtn("inline");
sortBtn.textContent = "Sorting...";
const values = input.split(',');
const numDiv = document.getElementById("num-div");
numDiv.innerHTML = `<span class="pointer" id="left-pointer">L</span>
<span class="pointer" id="right-pointer">R</span>`;
document.querySelectorAll(".pointer").forEach(pointer => pointer.style.opacity = "1");
passesDiv.innerHTML = "";
howto.innerHTML = "";
howto.style.visibility = "hidden";
let sorted = [];
changeText("");
let randomized = randomizer;
document.getElementById("passInfo").style.display = "flex";
for (let i = 0; i < values.length; i++) {
let el = document.createElement("div");
el.className = "num-wrapper";
let li = document.createElement("div");
li.className = "num";
li.textContent = values[i];
values[i] = parseFloat(values[i]);
let li1 = document.createElement("p");
li1.classList = "ij";
li1.textContent = i;
el.appendChild(li1);
el.appendChild(li);
numDiv.appendChild(el);
}
const divs = document.querySelectorAll(".num");
quickSort1();
async function quickSort1() {
document.getElementById("pi").style.display = "none";
await sleep(ms);
let i, j, pivot, count = 0;
async function partition(values, low, high) {
toggleBorder(divs, low, high);
if (randomized) {
let randomPivotIndex = low + Math.floor(Math.random() * (high - low + 1));
document.getElementById("pivot").textContent = "Index " + randomPivotIndex + " is selected as the random pivot.";
await sleep(ms);
divs[randomPivotIndex].classList.add("swapping");
divs[high].classList.add("swapping");
await sleep(ms);
document.getElementById("pivot").textContent = "Swapping " + randomPivotIndex + "index and " + high + " index.";
await sleep(ms);
[values[randomPivotIndex], values[high]] = [values[high], values[randomPivotIndex]];
divs[randomPivotIndex].textContent = values[randomPivotIndex];
divs[high].textContent = values[high];
divs[randomPivotIndex].classList.remove("swapping");
divs[high].classList.remove("swapping");
document.getElementById("pivot").textContent = "Pivot is now " + values[high];
await sleep(ms);
await sleep(ms);
}
pivot = values[high];
divs[high].classList.add("pivot");
document.getElementById("pivot").textContent = "Pivot = " + pivot;
document.getElementById("low").textContent = "Low = " + low;
document.getElementById("high").textContent = "High = " + high;
await sleep(ms);
i = low - 1;
updateLeftPointer(numDiv, divs, i);
for (j = low; j <= high - 1; j++) {
updateRightPointer(numDiv, divs, j);
divs[j].classList.add("comparing");
if (values[j] < pivot) {
i++;
updateLeftPointer(numDiv, divs, i);
[values[i], values[j]] = [values[j], values[i]];
divs[j].classList.remove("comparing");
divs[i].classList.add("swapping");
divs[j].classList.add("swapping");
await sleep(ms);
divs[i].textContent = values[i];
divs[j].textContent = values[j];
await sleep(ms);
divs[i].classList.remove("swapping");
divs[j].classList.remove("swapping");
await sleep(ms);
continue;
}
await sleep(ms);
divs[j].classList.remove("comparing");
await sleep(ms);
}
[values[i + 1], values[high]] = [values[high], values[i + 1]];
await sleep(ms);
divs[high].classList.remove("pivot");
divs[i + 1].classList.add("swapping");
divs[high].classList.add("swapping");
await sleep(ms);
divs[i + 1].textContent = values[i + 1];
divs[high].textContent = values[high];
divs[i + 1].classList.remove("swapping");
divs[high].classList.remove("swapping");
divs[i + 1].classList.add("sorted");
sorted.push(i + 1);
await sleep(ms);
if (low == high - 1 || low == high) {
divs[low].classList.add("sorted");
sorted.push(low);
}
count++;
let passes = createDiv("numbers", "num", values, sorted, count, i + 1);
passesDiv.appendChild(passes);
toggleBorder(divs, low, high);
return i + 1;
}
async function quickSort(values, low, high) {
if (low < high) {
let pi = await partition(values, low, high);
document.getElementById("pi").style.display = "block";
document.getElementById("pi").textContent = "Partition index = " + pi;
await quickSort(values, low, pi - 1);
await quickSort(values, pi + 1, high);
}
}
await quickSort(values, 0, values.length - 1);
sortedArray = values.join(", ");
changeText("Array is Sorted");
howto.style.visibility = "visible";
document.querySelector("#left-pointer").style.left = "-35px";
document.querySelector("#right-pointer").style.left = "-25px";
howto.innerHTML = "The array is successfully sorted.There were " + values.length + " numbers.The sorted array is : <br>" + sortedArray;
const btn = document.createElement("button");
btn.textContent = "Copy";
btn.className = "copy-btn";
btn.id = "ans-copy-btn";
btn.addEventListener("click", () => {
navigator.clipboard.writeText(sortedArray);
btn.textContent = "Copied!";
setTimeout(() => {
btn.textContent = "Copy";
}, 2000);
});
howto.appendChild(btn);
displayBtn("none");
sortBtn.textContent = "Sort";
}
});
function toggleBorder(divs, low, high) {
if (low >= 0)
divs[low].classList.toggle("border-left");
if (high < divs.length)
divs[high].classList.toggle("border-right");
}
function updateLeftPointer(numDiv, divs, low) {
let numbersRect = numDiv.getBoundingClientRect();
let leftPointer = document.querySelector("#left-pointer");
if (low < 0) {
leftPointer.style.left = "-30px";
}
else if (low >= divs.length) {
leftPointer.style.right = "-15px";
}
else {
let divsRect = divs[low].getBoundingClientRect();
divsRect = parseInt(divsRect.left - numbersRect.left);
leftPointer.style.left = divsRect + 15 + "px";
let bottom = divs[low].getBoundingClientRect();
bottom = bottom.bottom;
bottom = bottom - numbersRect.top;
leftPointer.style.top = bottom + 3 + "px";
}
}
function updateRightPointer(numDiv, divs, high) {
let rightPointer = document.querySelector("#right-pointer");
let numbersRect = numDiv.getBoundingClientRect();
if (high < 0) {
rightPointer.style.left = "-20px";
}
else if (high >= divs.length) {
rightPointer.style.right = leftPos + "-35px";
}
else {
let divsRect = divs[high].getBoundingClientRect();
divsRect = parseInt(divsRect.left) - parseInt(numbersRect.left);
rightPointer.style.left = divsRect + 25 + "px";
let bottom = divs[high].getBoundingClientRect();
bottom = bottom.bottom;
bottom = bottom - numbersRect.top;
rightPointer.style.top = bottom + 3 + "px";
}
}
function changeText(content) {
document.querySelector("#pivot").textContent = content;
document.querySelector("#low").textContent = "";
document.querySelector("#high").textContent = "";
document.querySelector("#pi").textContent = "";
}
function createDiv(cn1, cn2, content, sorted, passCount, pivot) {
const outerDiv = document.createElement("div");
outerDiv.className = cn1;
const li = document.createElement("div");
li.className = cn2;