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Advanced Quick Sort (Hybrid Algorithm)

  • Difficulty Level : Hard
  • Last Updated : 04 Aug, 2021

Prerequisites: Insertion Sort, Quick Sort, Selection Sort
In this article, a Hybrid algorithm with the combination of quick sort and insertion sort is implemented. As the name suggests, the Hybrid algorithm combines more than one algorithm. 
Why Hybrid algorithm: 
Quicksort algorithm is efficient if the size of the input is very large. But, insertion sort is more efficient than quick sort in case of small arrays as the number of comparisons and swaps are less compared to quicksort. So we combine the two algorithms to sort efficiently using both approaches.
Note: Selectionsort algorithm can also be used to combine with quicksort. Though the time complexity is of O(N2), these algorithms prove to be efficient in this case because these are used only when the size of the array is less than a threshold value(10 in this article). 
 

Dry run of the algorithm: 
 

Let arr[] = {24, 97, 40, 67, 88, 85, 15, 66, 53, 44, 26, 48, 16, 52, 45, 23, 90, 18, 49, 80}
 

Example pictorial explanation

Example explanation

 

Approach: The idea is to use recursion and continuously find the size of the array. If the size is greater than the threshold value(10), then the quicksort function is called for that portion of the array. Else, insertion sort is called. 
Below is the implementation of the Hybrid algorithm: 
 



C++




// C++ implementation of the above approach
 
#include<bits/stdc++.h>
using namespace std;
 
// Function to perform the insertion sort
 
void insertion_sort(int arr[], int low, int n)
  {
 
    for(int i=low+1;i<n+1;i++)
    {
      int val = arr[i] ;
      int j = i ;
    while (j>low && arr[j-1]>val)
      {
        arr[j]= arr[j-1] ;
      j-= 1;
    }
    arr[j]= val ;
    }
 
  }
 
//The following two functions are used
// to perform quicksort on the array.
 
 
// Partition function for quicksort
 
int partition(int arr[], int low, int high)
{
  int pivot = arr[high] ;
  int i ,j;
  i = low;
  j = low;
 
  for (int i = low; i < high; i++)
     {
      if(arr[i]<pivot)
      {
        int temp = arr[i];
      arr[i] = arr[j];
      arr[j] = temp;
      j += 1;
      }
    }
   
    int temp = arr[j];
    arr[j] = arr[high];
    arr[high] = temp;
 
  return j;
  }
 
 
// Function to call the partition function
// and perform quick sort on the array
 
 
void quick_sort(int arr[], int low,int high)
{
  if (low < high)
  {
    int pivot = partition(arr, low, high);
    quick_sort(arr, low, pivot-1) ;
    quick_sort(arr, pivot + 1, high) ;
   
   
  }
}
 
// Hybrid function -> Quick + Insertion sort
 
void hybrid_quick_sort(int arr[], int low, int high)
{
  while (low < high)
    {
 
    // If the size of the array is less
    // than threshold apply insertion sort
    // and stop recursion
 
    if (high-low + 1 < 10)
      {
        insertion_sort(arr, low, high);
      break;
    }
 
    else
       
        {
          int pivot = partition(arr, low, high) ;
 
      // Optimised quicksort which works on
      // the smaller arrays first
 
      // If the left side of the pivot
      // is less than right, sort left part
      // and move to the right part of the array
 
      if (pivot-low<high-pivot)
        {
          hybrid_quick_sort(arr, low, pivot - 1);
        low = pivot + 1;
      }
      else
        {
 
        // If the right side of pivot is less
        // than left, sort right side and
        // move to the left side
           
        hybrid_quick_sort(arr, pivot + 1, high);
        high = pivot-1;
        }
 
     }
 
   }
}
// Driver Code
int main()
{
 int  arr[21] = { 24, 97, 40, 67, 88, 85, 15,
  66, 53, 44, 26, 48, 16, 52,
  45, 23, 90, 18, 49, 80, 23 };
 
hybrid_quick_sort(arr, 0, 20);
   
  for(int i = 0; i < 21; i++)
    cout << arr[i] << ", ";
}
 
// This code is contributed by ishayadav2918


Java




/*package whatever //do not write package name here */
import java.io.*;
class GFG {
 
    private static void insertionSort(int a[], int low,
                                     int high)
    {
        for (int i = low + 1; i <= high; i++) {
            for (int j = i - 1; j >= low; j--) {
                if (a[j] > a[j + 1]) {
                    // Swap
                    int temp = a[j];
                    a[j] = a[j + 1];
                    a[j + 1] = temp;
                }
                else
                    break;
            }
        }
    }
 
    private static int partition(int arr[], int low,
                                int high)
    {
        int pivot = arr[high];
        int i = low;
        int j = low;
 
        while (i <= high) {
            if (arr[i] > pivot)
                i++;
            else {
                int temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;
                i++;
                j++;
            }
        }
        return j - 1;
    }
 
    public static void hybridQuickSort(int arr[], int low,
                                       int high)
    {
        while (low < high) {
            // Check if array size on which we will be working is less than 10
            if (high - low < 10) {
                insertionSort(arr, low, high);
                break;
            }
            else {
                int pivot = partition(arr, low, high);
 
                // We will do recursion on small size
                // subarray So we can check pivot - low  and
                // pivot - high
 
                if (pivot - low < pivot - high) {
                    hybridQuickSort(arr, low, pivot - 1);
                    low = pivot + 1;
                }
                else {
                    hybridQuickSort(arr, pivot + 1, high);
                    high = pivot - 1;
                }
            }
        }
    }
   
  // Driver code
    public static void main(String[] args)
    {
 
        int arr[]
            = { 24, 97, 40, 67, 88, 85, 15, 66, 53, 44, 26,
                48, 16, 52, 45, 23, 90, 18, 49, 80, 23 };
 
        hybridQuickSort(arr, 0, arr.length - 1);
        for (int i : arr)
            System.out.print(i + "  ");
    }
}
 
// This code is contribute  by @mahi_07


Python3




# Python implementation of the above approach
 
# Function to perform the insertion sort
def insertion_sort(arr, low, n):
    for i in range(low + 1, n + 1):
        val = arr[i]
        j = i
        while j>low and arr[j-1]>val:
            arr[j]= arr[j-1]
            j-= 1
        arr[j]= val
 
# The following two functions are used
# to perform quicksort on the array.
 
# Partition function for quicksort
def partition(arr, low, high):
    pivot = arr[high]
    i = j = low
    for i in range(low, high):
        if arr[i]<pivot:
            a[i], a[j]= a[j], a[i]
            j+= 1
    a[j], a[high]= a[high], a[j]
    return j
 
# Function to call the partition function
# and perform quick sort on the array
def quick_sort(arr, low, high):
    if low<high:
        pivot = partition(arr, low, high)
        quick_sort(arr, low, pivot-1)
        quick_sort(arr, pivot + 1, high)
        return arr
 
# Hybrid function -> Quick + Insertion sort
def hybrid_quick_sort(arr, low, high):
    while low<high:
 
        # If the size of the array is less
        # than threshold apply insertion sort
        # and stop recursion
        if high-low + 1<10:
            insertion_sort(arr, low, high)
            break
 
        else:
            pivot = partition(arr, low, high)
 
            # Optimised quicksort which works on
            # the smaller arrays first
 
            # If the left side of the pivot
            # is less than right, sort left part
            # and move to the right part of the array
            if pivot-low<high-pivot:
                hybrid_quick_sort(arr, low, pivot-1)
                low = pivot + 1
            else:
                # If the right side of pivot is less
                # than left, sort right side and
                # move to the left side
                hybrid_quick_sort(arr, pivot + 1, high)
                high = pivot-1
 
# Driver code
 
a = [ 24, 97, 40, 67, 88, 85, 15,
      66, 53, 44, 26, 48, 16, 52,
      45, 23, 90, 18, 49, 80, 23 ]
hybrid_quick_sort(a, 0, 20)
print(a)


Output

15, 16, 18, 23, 23, 24, 26, 40, 44, 45, 48, 49, 52, 53, 66, 67, 80, 85, 88, 90, 97, 

Time Complexity: O(N^2)
Auxiliary Space: O(N)

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