Explain Quick Sort in detail?

Software Development
#1

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

  • Always pick the first element as a pivot.
  • Always pick the last element as a pivot (implemented below)
  • Pick a random element as a pivot.
  • Pick median as the pivot.

The key process in quickSort is a partition(). The target of partitions is, given an array and an element x of an array as the pivot, put x at its correct position in a sorted array and 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.

Following are the implementations of QuickSort:

#include <bits/stdc++.h>
using namespace std; 
  
// A utility function to swap two elements 
void swap(int* a, int* b) 
{ 
    int t = *a; 
    *a = *b; 
    *b = t; 
} 
  
/* This function takes last element as pivot, places 
the pivot element at its correct position in sorted 
array, and places all smaller (smaller than pivot) 
to left of pivot and all greater elements to right 
of pivot */
int partition (int arr[], int low, int high) 
{ 
    int pivot = arr[high]; // pivot 
    int i = (low - 1); // Index of smaller element and indicates the right position of pivot found so far
  
    for (int j = low; j <= high - 1; j++) 
    { 
        // If current element is smaller than the pivot 
        if (arr[j] < pivot) 
        { 
            i++; // increment index of smaller element 
            swap(&arr[i], &arr[j]); 
        } 
    } 
    swap(&arr[i + 1], &arr[high]); 
    return (i + 1); 
} 
  
/* 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 < high) 
    { 
        /* pi is partitioning index, arr[p] is now 
        at right place */
        int pi = partition(arr, low, high); 
  
        // Separately sort elements before 
        // partition and after partition 
        quickSort(arr, low, pi - 1); 
        quickSort(arr, pi + 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[] = {10, 7, 8, 9, 1, 5}; 
    int n = sizeof(arr) / sizeof(arr[0]); 
    quickSort(arr, 0, n - 1); 
    cout << "Sorted array: \n"; 
    printArray(arr, n); 
    return 0; 
}

Output

Sorted array: 
1 5 7 8 9 10 

//Time taken by QuickSort, in general, can be written as follows. 
// T(n) = T(k) + T(n-k-1) + (n)