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# C++ Program for QuickSort

• Difficulty Level : Easy
• Last Updated : 21 Dec, 2022

Similar to the Merge Sort algorithm, the Quick Sort algorithm is a Divide and Conquer algorithm. It initially selects an element as a pivot element and partitions the given array around the picked pivot. There are many different versions of quickSort that pick pivot in different ways.

1. Always pick the first element as a pivot (implemented below).
2. Always pick the last element as the pivot.
3. Pick a random element as a pivot.
4. Pick median as a pivot.

The key process in quickSort is the partition() process. The aim of the partition() function is to receive an array and an element x of the array as a pivot, put x at its correct position in a sorted array and then put all smaller elements (smaller than x) before x, and put all greater elements (greater than x) after x. All this should be done in linear time i.e.  Big O(n) .
Pseudo Code for recursive QuickSort function :

```/* low  --> Starting index,  high  --> Ending index */
quickSort(arr[], low, high)
{
if (low < high)
{
/* pi is partitioning index, arr[p] is now
at right place */
pi = partition(arr, low, high);

quickSort(arr, low, pi - 1);  // Before pi
quickSort(arr, pi + 1, high); // After pi
}
}```

## CPP

 `// C++ Implementation of the Quick Sort Algorithm.` `#include ` `using` `namespace` `std;`   `int` `partition(``int` `arr[], ``int` `start, ``int` `end)` `{`   `    ``int` `pivot = arr[start];`   `    ``int` `count = 0;` `    ``for` `(``int` `i = start + 1; i <= end; i++) {` `        ``if` `(arr[i] <= pivot)` `            ``count++;` `    ``}`   `    ``// Giving pivot element its correct position` `    ``int` `pivotIndex = start + count;` `    ``swap(arr[pivotIndex], arr[start]);`   `    ``// Sorting left and right parts of the pivot element` `    ``int` `i = start, j = end;`   `    ``while` `(i < pivotIndex && j > pivotIndex) {`   `        ``while` `(arr[i] <= pivot) {` `            ``i++;` `        ``}`   `        ``while` `(arr[j] > pivot) {` `            ``j--;` `        ``}`   `        ``if` `(i < pivotIndex && j > pivotIndex) {` `            ``swap(arr[i++], arr[j--]);` `        ``}` `    ``}`   `    ``return` `pivotIndex;` `}`   `void` `quickSort(``int` `arr[], ``int` `start, ``int` `end)` `{`   `    ``// base case` `    ``if` `(start >= end)` `        ``return``;`   `    ``// partitioning the array` `    ``int` `p = partition(arr, start, end);`   `    ``// Sorting the left part` `    ``quickSort(arr, start, p - 1);`   `    ``// Sorting the right part` `    ``quickSort(arr, p + 1, end);` `}`   `int` `main()` `{`   `    ``int` `arr[] = { 9, 3, 4, 2, 1, 8 };` `    ``int` `n = 6;`   `    ``quickSort(arr, 0, n - 1);`   `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``cout << arr[i] << ``" "``;` `    ``}`   `    ``return` `0;` `}`

Output

`1 2 3 4 8 9 `

### Method-2 :

This method’s space complexity is O(n). As we will take an extra array in partition function like in merge function of merge sort

#### Algorithm explanation and steps of partition function:

• Make a new array of size equal to given array.
• push all the smaller elements than pivotElement to the new array.
• Push pivotElement to new array now.
• finally, push all the greater elements than pivotElement to the new array.
• Now, copy the new array to the original array.
• Store the index of the pivotElement from the original array. Return this index.

After this, all the elements in the original array are in the order : smaller than pivotElement -> pivotElement -> greater than pivotElement.

Time Complexity : θ(nlogn).

Space Complexity : O(n).

## C++

 `// added by Manish Sharma`   `#include ` `using` `namespace` `std;`   `int` `partition(``int``* arr, ``int` `start, ``int` `end)` `{   ` `      ``// assuming last element as pivotElement` `    ``int` `index = 0, pivotElement = arr[end], pivotIndex;` `    ``int``* temp = ``new` `int``[end - start + 1]; ``// making an array whose size is equal to current partition range...` `    ``for` `(``int` `i = start; i <= end; i++) ``// pushing all the elements in temp which are smaller than pivotElement` `    ``{` `        ``if``(arr[i] < pivotElement)` `        ``{` `            ``temp[index] = arr[i];` `            ``index++;` `        ``}` `    ``}`   `    ``temp[index] = pivotElement; ``// pushing pivotElement in temp` `    ``index++;`   `    ``for` `(``int` `i = start; i < end; i++) ``// pushing all the elements in temp which are greater than pivotElement` `    ``{` `        ``if``(arr[i] > pivotElement)` `        ``{` `            ``temp[index] = arr[i];` `            ``index++;` `        ``}` `    ``}` `  ``// all the elements now in temp array are order : ` `  ``// leftmost elements are lesser than pivotElement and rightmost elements are greater than pivotElement` `              `  `    `  `    `  `    ``index = 0;` `    ``for` `(``int` `i = start; i <= end; i++) ``// copying all the elements to original array i.e arr` `    ``{   ` `        ``if``(arr[i] == pivotElement)` `        ``{` `              ``// for getting pivot index in the original array.` `              ``// we need the pivotIndex value in the original and not in the temp array` `            ``pivotIndex = i;` `        ``}` `        ``arr[i] = temp[index];` `        ``index++;` `    ``}` `    ``return` `pivotIndex; ``// returning pivotIndex` `}`   `void` `quickSort(``int``* arr, ``int` `start, ``int` `end)` `{  ` `    ``if``(start < end)` `    ``{   ` `        ``int` `partitionIndex = partition(arr, start, end); ``// for getting partition` `        ``quickSort(arr, start, partitionIndex - 1); ``// sorting left side array` `        ``quickSort(arr, partitionIndex + 1, end); ``// sorting right side array` `    ``}` `    ``return``;` `}`   `int` `main() ` `{    ` `    ``int` `size = 9;` `    ``int` `arr[size] = {5, 12, 7, 1, 13, 2 ,23, 11, 18};` `      `  `      ``cout << ``"Unsorted array : "``;` `    ``for` `(``int` `i = 0; i < size; i++)` `    ``{` `        ``cout << arr[i] << ``" "``;` `    ``}` `    ``printf``(``"\n"``);`   `    ``quickSort(arr, 0, size - 1);` `    `  `      ``cout << ``"Sorted array : "``;` `    ``for` `(``int` `i = 0; i < size; i++)` `    ``{` `       ``cout << arr[i] << ``" "``;` `    ``}` `  `  `      ``return` `0;` `}`

Output

```Unsorted array : 5 12 7 1 13 2 23 11 18
Sorted array : 1 2 5 7 11 12 13 18 23 ```

Please refer complete article on QuickSort for more details!

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