Implement Quicksort with first element as pivot

Last Updated : 27 May, 2024

QuickSort is a Divide and Conquer algorithm. It picks an element as a pivot and partitions the given array around the pivot. There are many different versions of quickSort that pick the pivot in different ways.

Always pick the first element as a pivot.
Always pick the last element as a pivot.
Pick a random element as a pivot.
Pick the median as the pivot.

Note: Here we will be implementing quick sort by picking the first element as the pivot.

Quick Sort by picking the first element as the Pivot:

The key function in quick sort is a partition. The target of partitions is to put the pivot in its correct position if the array is sorted and the smaller (or equal) to its left and higher elements to its right and do all this in linear time.

Partition Algorithm:

There can be many ways to do partition, the following pseudo-code adopts the method given in the CLRS book.

We start from the leftmost element and keep track of the index of smaller (or equal) elements as i.
While traversing, if we find a smaller (or equal) element, we swap the current element with arr[i].
Otherwise, we ignore the current element.

Pseudo Code for recursive QuickSort function:

// low –> Starting index, high –> Ending index

quickSort(arr[], low, high) {
if (low < high) {

// pi is partitioning index, arr[pi] is now at right place
pi = partition(arr, low, high);
quickSort(arr, low, pi – 1); // Before pi
quickSort(arr, pi + 1, high); // After pi
}
}

Pseudo code for partition() function

/* This function takes first element as pivot, places the pivot element at its correct position in sorted array, and places all smaller (smaller than or equal to pivot) to left of pivot and all greater elements to right of pivot */

partition (arr[], low, high) {
// first element as pivot
pivot = arr[low]
k = high
for (i = high; i > low; i--) {
if (arr[i] > pivot){
swap arr[i] and arr[k];
k--;
}
}
swap arr[k] and arr[low]
return k;
}

Illustration of partition() :

Consider: arr[] = { 7, 6, 10, 5, 9, 2, 1, 15, 7 }

First Partition: low = 0, high = 8, pivot = arr[low] = 7
Initialize index of right most element k = high = 8.

Traverse from i = high to low:
if arr[i] is greater than pivot:
Swap arr[i] and arr[k].
Decrement k;
At the end swap arr[low] and arr[k].
Now the correct position of pivot is index 5

First partition
Second Partition: low = 0, high = 4, pivot = arr[low] = 2
Similarly initialize k = high = 4;

The correct position of 2 becomes index 1. And the left part is only one element and the right part has {6, 5, 7}.

Partition of the left half
On the other hand partition happens on the segment [6, 8] i.e., the array {10, 9, 15}.
Here low = 6, high = 8, pivot = 10 and k = 8.

The correct position of 10 becomes index 7 and the right and left part both has only one element.

Partition of the right half
Third partition: Here partition the segment {6, 5, 7}. The low = 2, high = 4, pivot = 6 and k = 4.
If the same process is applied, we get correct position of 6 as index 3 and the left and the right part is having only one element.

Third partition
The total array becomes sorted in this way. Check the below image for the recursion tree

Recursion tree for partitions

Follow the below steps to implement the approach.

Use a recursive function (say quickSort) to initialize the function.
Call the partition function to partition the array and inside the partition function do the following
- Take the first element as pivot and initialize and iterator k = high.
- Iterate in a for loop from i = high to low+1:
  - If arr[i] is greater than pivot then swap arr[i] and arr[k] and decrement k.
- After the iteration is swap the pivot with arr[k].
- Return k-1 as the point of partition.
Now recursively call quickSort for the left half and right half of the partition index.

Implementation of the above approach.

C++

#include <bits/stdc++.h> using namespace std;  /*This function takes first element as pivot, the function places the pivot element(first element) on its sorted position and all the element lesser than pivot will placed left to it, and all the element greater than pivot placed right to it.*/  int partition(int arr[], int low, int high) {      // First element as pivot     int pivot = arr[low];       int k = high;     for (int i = high; i > low; i--) {         if (arr[i] > pivot)             swap(arr[i], arr[k--]);     }     swap(arr[low], arr[k]);     // As we got pivot element index is end     // now pivot element is at its sorted position     // return pivot element index (end)     return k; }  /* The main function that implements QuickSort arr[] --> Array to be sorted, low --> Starting index, high --> Ending index */ void quickSort(int arr[], int low, int high) {     // If low is lesser than high     if (low < high) {         // idx is index of pivot element which is at its         // sorted position         int idx = partition(arr, low, high);          // Separately sort elements before         // partition and after partition         quickSort(arr, low, idx - 1);         quickSort(arr, idx + 1, high);     } }  /* Function to print an array */ void printArray(int arr[], int size) {     int i;     for (i = 0; i < size; i++)         cout << arr[i] << " ";     cout << endl; }  // Driver Code int main() {     int arr[] = { 7, 6, 10, 5, 9, 2, 1, 15, 7 };     int n = sizeof(arr) / sizeof(arr[0]);     quickSort(arr, 0, n - 1);     cout << "Sorted array: \n";     printArray(arr, n);     return 0; }  // This Code is contributed by Harsh Raghav

#include <stdio.h>  void swap(int *a, int *b) {     int temp = *a;     *a = *b;     *b = temp; }  int partition(int arr[], int low, int high) {     int pivot = arr[low]; // Choosing the pivot element     int start = low;     int end = high;     int k = high;      // Iterate from the end of the array to the start     for (int i = high; i > low; i--) {         // If the current element is greater than the pivot,         // swap it with the element at index k and decrement k         if (arr[i] > pivot)             swap(&arr[i], &arr[k--]);     }      // Swap the pivot element with the element at index k     swap(&arr[low], &arr[k]);      return k; // Return the index of the pivot element after partitioning }  void quickSort(int arr[], int low, int high) {     if (low < high) {         // Partition the array and get the index of the pivot element         int idx = partition(arr, low, high);          // Recursively sort the subarrays before and after the pivot element         quickSort(arr, low, idx - 1);         quickSort(arr, idx + 1, high);     } }  void printArray(int arr[], int size) {     for (int i = 0; i < size; i++)         printf("%d ", arr[i]);     printf("\n"); }  int main() {     int arr[] = {7, 6, 10, 5, 9, 2, 1, 15, 7};     int n = sizeof(arr) / sizeof(arr[0]);      // Call quickSort to sort the array     quickSort(arr, 0, n - 1);      printf("Sorted array: \n");     printArray(arr, n);      return 0; }

Java

import java.util.Arrays;  class QuickSort {     /* This function takes first element as pivot, the     function places the pivot element(first element) on its     sorted position and all the element lesser than pivot     will placed left to it, and all the element greater than     pivot placed right to it.*/     int partition(int arr[], int low, int high)     {         // First element as pivot         int pivot = arr[low];         int st = low; // st points to the starting of array         int end             = high; // end points to the ending of the array         int k = high;         for (int i = high; i > low; i--) {             if (arr[i] > pivot)                 swap(arr, i, k--);         }         swap(arr, low, k);         // As we got pivot element index is end         // now pivot element is at its sorted position         // return pivot element index (end)         return k;     }      // Function to swap two elements     public static void swap(int[] arr, int i, int j)     {         int temp = arr[i];         arr[i] = arr[j];         arr[j] = temp;     }      /* The main function that implements QuickSort     arr[] --> Array to be sorted,     low --> Starting index,     high --> Ending index */     void quickSort(int arr[], int low, int high)     {         // If low is lesser than high         if (low < high) {             // idx is index of pivot element which is at its             // sorted position             int idx = partition(arr, low, high);              // Separately sort elements before             // partition and after partition             quickSort(arr, low, idx - 1);             quickSort(arr, idx + 1, high);         }     }      /* Function to print an array */     void printArray(int arr[], int size)     {         int i;         for (i = 0; i < size; i++)             System.out.print(arr[i] + " ");         System.out.println();     }      // Driver Code     public static void main(String args[])     {         int arr[] = { 7, 6, 10, 5, 9, 2, 1, 15, 7 };         int n = arr.length;          QuickSort ob = new QuickSort();         ob.quickSort(arr, 0, n - 1);          System.out.println("Sorted array");         ob.printArray(arr, n);     } }

Python

# This function takes first element as pivot, the function # places the pivot element(first element) on its sorted # position and all the element lesser than pivot will placed # left to it, and all the element greater than pivot placed # right to it. def partition(array, low, high):        # First Element as pivot     pivot = array[low]          # st points to the starting of array     start = low + 1          # end points to the ending of the array     end = high      while True:         # It indicates we have already moved all the elements to their correct side of the pivot         while start <= end and array[end] >= pivot:             end = end - 1          # Opposite process         while start <= end and array[start] <= pivot:             start = start + 1          # Case in which we will exit the loop         if start <= end:             array[start], array[end] = array[end], array[start]             # The loop continues         else:             # We exit out of the loop             break      array[low], array[end] = array[end], array[low]     # As we got pivot element index is end     # now pivot element is at its sorted position     # return pivot element index (end)     return end  # The main function that implements QuickSort # arr[] --> Array to be sorted, # low --> Starting index, # high --> Ending index def quick_sort(array, start, end):      # If low is lesser than high     if start < end:                # idx is index of pivot element which is at its         # sorted position         idx = partition(array, start, end)                  # Separately sort elements before         # partition and after partition         quick_sort(array, start, idx-1)         quick_sort(array, idx+1, end)  # Function to print an array def print_arr(arr, n):     for i in range(n):         print(arr[i], end=" ")     print()  # Driver Code arr1 = [7, 6, 10, 5, 9, 2, 1, 15, 7] quick_sort(arr1, 0, len(arr1)-1) print_arr(arr1, len(arr1))  # This code is contributed by Aditya Sharma

using System;  class QuickSort {     /* This function takes first element as pivot, the     function places the pivot element(first element) on its     sorted position and all the element lesser than pivot     will placed left to it, and all the element greater than     pivot placed right to it.*/     int partition(int[] arr, int low, int high)     {         // First element as pivot         int pivot = arr[low];         int st = low; // st points to the starting of array         int end = high; // end points to the ending of the array         int k = high;         for (int i = high; i > low; i--)         {             if (arr[i] > pivot)             {                 swap(arr, i, k--);             }         }         swap(arr, low, k);         // As we got pivot element index is end         // now pivot element is at its sorted position         // return pivot element index (end)         return k;     }      // Function to swap two elements     public static void swap(int[] arr, int i, int j)     {         int temp = arr[i];         arr[i] = arr[j];         arr[j] = temp;     }      /* The main function that implements QuickSort     arr[] --> Array to be sorted,     low --> Starting index,     high --> Ending index */     void quickSort(int[] arr, int low, int high)     {         // If low is lesser than high         if (low < high)         {             // idx is index of pivot element which is at its             // sorted position             int idx = partition(arr, low, high);              // Separately sort elements before             // partition and after partition             quickSort(arr, low, idx - 1);             quickSort(arr, idx + 1, high);         }     }      /* Function to print an array */     void printArray(int[] arr, int size)     {         int i;         for (i = 0; i < size; i++)             Console.Write(arr[i] + " ");         Console.WriteLine();     }      // Driver Code     public static void Main()     {         int[] arr = { 7, 6, 10, 5, 9, 2, 1, 15, 7 };         int n = arr.Length;          QuickSort ob = new QuickSort();         ob.quickSort(arr, 0, n - 1);          Console.WriteLine("Sorted array");         ob.printArray(arr, n);     } }

JavaScript

function partition(function partition(array, low, high) {   // First Element as pivot   let pivot = array[low];    // st points to the starting of array   let start = low + 1;    // end points to the ending of the array   let end = high;    while (true) {     // It indicates we have already moved all the elements to their correct side of the pivot     while (start <= end && array[end] >= pivot) {       end--;     }      // Opposite process     while (start <= end && array[start] <= pivot) {       start++;     }      // Case in which we will exit the loop     if (start <= end) {       [array[start], array[end]] = [array[end], array[start]];       // The loop continues     } else {       // We exit out of the loop       break;     }   }    [array[low], array[end]] = [array[end], array[low]];   // As we got pivot element index is end   // now pivot element is at its sorted position   // return pivot element index (end)   return end; }  function quick_sort(array, start, end) {   // If low is lesser than high   if (start < end) {     // idx is index of pivot element which is at its     // sorted position     let idx = partition(array, start, end);      // Separately sort elements before     // partition and after partition     quick_sort(array, start, idx - 1);     quick_sort(array, idx + 1, end);   } }  function print_arr(arr) {   console.log(arr.join(" ")); }  // Driver Code let arr1 = [7, 6, 10, 5, 9, 2, 1, 15, 7]; quick_sort(arr1, 0, arr1.length - 1); console.log("Sorted array: "); print_arr(arr1);   //contributed by Aditya Sharma

Output

Sorted array:  1 2 5 6 7 7 9 10 15

Complexity Analysis:

Time Complexity:
- Average Case: O(N * logN), where N is the length of the array.
- Best Case: O(N * logN)
- Worst Case: O(N²)
Auxiliary Space: O(1)

Advanced Quick Sort (Hybrid Algorithm)

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Article Tags :

Practice Tags :

Sorting

Implement Quicksort with first element as pivot

Quick Sort by picking the first element as the Pivot:

Partition Algorithm:

Pseudo Code for recursive QuickSort function:

Pseudo code for partition() function

Illustration of partition() :

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