As we know, the single pivot quick sort takes a pivot from one of the ends of the array and partitioning the array, so that all elements are left to the pivot are less than or equal to the pivot, and all elements that are right to the pivot are greater than the pivot.
The idea of dual pivot quick sort is to take two pivots, one in the left end of the array and the second, in the right end of the array. The left pivot must be less than or equal to the right pivot, so we swap them if necessary.
Then, we begin partitioning the array into three parts: in the first part, all elements will be less than the left pivot, in the second part all elements will be greater or equal to the left pivot and also will be less than or equal to the right pivot, and in the third part all elements will be greater than the right pivot. Then, we shift the two pivots to their appropriate positions as we see in the below bar, and after that we begin quicksorting these three parts recursively, using this method.
Dual pivot quick sort is a little bit faster than the original single pivot quicksort. But still, the worst case will remain O(n^2) when the array is already sorted in an increasing or decreasing order.
An example:
C++
// C++ program to implement dual pivot QuickSort#include <iostream>using namespace std; int partition(int* arr, int low, int high, int* lp); void swap(int* a, int* b){ int temp = *a; *a = *b; *b = temp;} void DualPivotQuickSort(int* arr, int low, int high){ if (low < high) { // lp means left pivot, and rp means right pivot. int lp, rp; rp = partition(arr, low, high, &lp); DualPivotQuickSort(arr, low, lp - 1); DualPivotQuickSort(arr, lp + 1, rp - 1); DualPivotQuickSort(arr, rp + 1, high); }} int partition(int* arr, int low, int high, int* lp){ if (arr[low] > arr[high]) swap(&arr[low], &arr[high]); // p is the left pivot, and q is the right pivot. int j = low + 1; int g = high - 1, k = low + 1, p = arr[low], q = arr[high]; while (k <= g) { // if elements are less than the left pivot if (arr[k] < p) { swap(&arr[k], &arr[j]); j++; } // if elements are greater than or equal // to the right pivot else if (arr[k] >= q) { while (arr[g] > q && k < g) g--; swap(&arr[k], &arr[g]); g--; if (arr[k] < p) { swap(&arr[k], &arr[j]); j++; } } k++; } j--; g++; // bring pivots to their appropriate positions. swap(&arr[low], &arr[j]); swap(&arr[high], &arr[g]); // returning the indices of the pivots. *lp = j; // because we cannot return two elements // from a function. return g;} // Driver codeint main(){ int arr[] = { 24, 8, 42, 75, 29, 77, 38, 57 }; DualPivotQuickSort(arr, 0, 7); cout << "Sorted array: "; for (int i = 0; i < 8; i++) cout << arr[i] << " "; cout << endl;} // This code is contributed by SHUBHAMSINGH10 |
C
// C program to implement dual pivot QuickSort#include <stdio.h> int partition(int* arr, int low, int high, int* lp); void swap(int* a, int* b){ int temp = *a; *a = *b; *b = temp;} void DualPivotQuickSort(int* arr, int low, int high){ if (low < high) { // lp means left pivot, and rp means right pivot. int lp, rp; rp = partition(arr, low, high, &lp); DualPivotQuickSort(arr, low, lp - 1); DualPivotQuickSort(arr, lp + 1, rp - 1); DualPivotQuickSort(arr, rp + 1, high); }} int partition(int* arr, int low, int high, int* lp){ if (arr[low] > arr[high]) swap(&arr[low], &arr[high]); // p is the left pivot, and q is the right pivot. int j = low + 1; int g = high - 1, k = low + 1, p = arr[low], q = arr[high]; while (k <= g) { // if elements are less than the left pivot if (arr[k] < p) { swap(&arr[k], &arr[j]); j++; } // if elements are greater than or equal // to the right pivot else if (arr[k] >= q) { while (arr[g] > q && k < g) g--; swap(&arr[k], &arr[g]); g--; if (arr[k] < p) { swap(&arr[k], &arr[j]); j++; } } k++; } j--; g++; // bring pivots to their appropriate positions. swap(&arr[low], &arr[j]); swap(&arr[high], &arr[g]); // returning the indices of the pivots. *lp = j; // because we cannot return two elements // from a function. return g;} // Driver codeint main(){ int arr[] = { 24, 8, 42, 75, 29, 77, 38, 57 }; DualPivotQuickSort(arr, 0, 7); printf("Sorted array: "); for (int i = 0; i < 8; i++) printf("%d ", arr[i]); printf("\n"); return 0;} |
Java
// Java program to implement// dual pivot QuickSortclass GFG{ static void swap(int[] arr, int i, int j){ int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp;} static void dualPivotQuickSort(int[] arr, int low, int high){ if (low < high) { // piv[] stores left pivot and right pivot. // piv[0] means left pivot and // piv[1] means right pivot int[] piv; piv = partition(arr, low, high); dualPivotQuickSort(arr, low, piv[0] - 1); dualPivotQuickSort(arr, piv[0] + 1, piv[1] - 1); dualPivotQuickSort(arr, piv[1] + 1, high); }} static int[] partition(int[] arr, int low, int high){ if (arr[low] > arr[high]) swap(arr, low, high); // p is the left pivot, and q // is the right pivot. int j = low + 1; int g = high - 1, k = low + 1, p = arr[low], q = arr[high]; while (k <= g) { // If elements are less than the left pivot if (arr[k] < p) { swap(arr, k, j); j++; } // If elements are greater than or equal // to the right pivot else if (arr[k] >= q) { while (arr[g] > q && k < g) g--; swap(arr, k, g); g--; if (arr[k] < p) { swap(arr, k, j); j++; } } k++; } j--; g++; // Bring pivots to their appropriate positions. swap(arr, low, j); swap(arr, high, g); // Returning the indices of the pivots // because we cannot return two elements // from a function, we do that using an array. return new int[] { j, g };} // Driver codepublic static void main(String[] args){ int[] arr = { 24, 8, 42, 75, 29, 77, 38, 57 }; dualPivotQuickSort(arr, 0, 7); System.out.print("Sorted array: "); for (int i = 0; i < 8; i++) System.out.print(arr[i] + " "); System.out.println();}} // This code is contributed by Gourish Sadhu |
Python3
# Python3 program to implement # dual pivot QuickSortdef dualPivotQuickSort(arr, low, high): if low < high: # lp means left pivot and rp # means right pivot lp, rp = partition(arr, low, high) dualPivotQuickSort(arr, low, lp - 1) dualPivotQuickSort(arr, lp + 1, rp - 1) dualPivotQuickSort(arr, rp + 1, high) def partition(arr, low, high): if arr[low] > arr[high]: arr[low], arr[high] = arr[high], arr[low] # p is the left pivot, and q is the right pivot. j = k = low + 1 g, p, q = high - 1, arr[low], arr[high] while k <= g: # If elements are less than the left pivot if arr[k] < p: arr[k], arr[j] = arr[j], arr[k] j += 1 # If elements are greater than or equal # to the right pivot elif arr[k] >= q: while arr[g] > q and k < g: g -= 1 arr[k], arr[g] = arr[g], arr[k] g -= 1 if arr[k] < p: arr[k], arr[j] = arr[j], arr[k] j += 1 k += 1 j -= 1 g += 1 # Bring pivots to their appropriate positions. arr[low], arr[j] = arr[j], arr[low] arr[high], arr[g] = arr[g], arr[high] # Returning the indices of the pivots return j, g # Driver codearr = [ 24, 8, 42, 75, 29, 77, 38, 57 ]dualPivotQuickSort(arr, 0, 7) print('Sorted array: ', end = '')for i in arr: print(i, end = ' ') print() # This code is contributed by Gourish Sadhu |
Output:
Sorted array: 8 24 29 38 42 57 75 77
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