Quicksort is a Divide and Conquer Algorithm that is used for sorting the elements. In this algorithm, we choose a pivot and partitions the given array according to the pivot. Quicksort algorithm is a mostly used algorithm because this algorithm is cache-friendly and performs in-place sorting of the elements means no extra space requires for sorting the elements.
Note:
Quicksort algorithm is generally unstable algorithm because quick sort cannot be able to maintain the relative
order of the elements.
Three partitions are possible for the Quicksort algorithm:
- Naive partition: In this partition helps to maintain the relative order of the elements but this partition takes O(n) extra space.
- Lomuto partition: In this partition, The last element chooses as a pivot in this partition. The pivot acquires its required position after partition but more comparison takes place in this partition.
- Hoare’s partition: In this partition, The first element chooses as a pivot in this partition. The pivot displaces its required position after partition but less comparison takes place as compared to the Lomuto partition.
1. Naive partition
Algorithm:
Naivepartition(arr[],l,r)
1. Make a Temporary array temp[r-l+1] length
2. Choose last element as a pivot element
3. Run two loops:
-> Store all the elements in the temp array that are less than pivot element
-> Store the pivot element
-> Store all the elements in the temp array that are greater than pivot element.
4.Update all the elements of arr[] with the temp[] array
QuickSort(arr[], l, r)
If r > l
1. Find the partition point of the array
m = Naivepartition(a,l,r)
2. Call Quicksort for less than partition point
Call Quicksort(arr, l, m-1)
3. Call Quicksort for greater than the partition point
Call Quicksort(arr, m+1, r)
Java
// Java program to demonstrate the naive partition// in quick sortimport java.io.*;import java.util.*;public class GFG { static int partition(int a[], int start, int high) { // Creating temporary int temp[] = new int[(high - start) + 1]; // Choosing a pivot int pivot = a[high]; int index = 0; // smaller number for (int i = start; i <= high; ++i) { if (a[i] < pivot) { temp[index++] = a[i]; } } // pivot position int position = index; // Placing the pivot to its original position temp[index++] = pivot; for (int i = start; i <= high; ++i) { if (a[i] > pivot) { temp[index++] = a[i]; } } // Change the original array for (int i = start; i <= high; ++i) { a[i] = temp[i - start]; } // return the position of the pivot return position; } static void quicksort(int numbers[], int start, int end) { if (start < end) { int point = partition(numbers, start, end); quicksort(numbers, start, point - 1); quicksort(numbers, point + 1, end); } } // Function to print the array static void print(int numbers[]) { for (int a : numbers) { System.out.print(a + " "); } } public static void main(String[] args) { int numbers[] = { 3, 2, 1, 78, 9798, 97 }; // rearrange using naive partition quicksort(numbers, 0, numbers.length - 1); print(numbers); }} |
Output
1 2 3 78 97 9798
2. Lomuto partition
- Lomuto’s Partition Algorithm (unstable algorithm)
Lomutopartition(arr[], lo, hi)
pivot = arr[hi]
i = lo // place for swapping
for j := lo to hi – 1 do
if arr[j] <= pivot then
swap arr[i] with arr[j]
i = i + 1
swap arr[i] with arr[hi]
return i
QuickSort(arr[], l, r)
If r > l
1. Find the partition point of the array
m =Lomutopartition(a,l,r)
2. Call Quicksort for less than partition point
Call Quicksort(arr, l, m-1)
3. Call Quicksort for greater than the partition point
Call Quicksort(arr, m+1, r)
Java
// Java program to demonstrate the Lomuto partition// in quick sortimport java.util.*;public class GFG { static int sort(int numbers[], int start, int last) { int pivot = numbers[last]; int index = start - 1; int temp = 0; for (int i = start; i < last; ++i) { if (numbers[i] < pivot) { ++index; // swap the position temp = numbers[index]; numbers[index] = numbers[i]; numbers[i] = temp; } } int pivotposition = ++index; temp = numbers[index]; numbers[index] = pivot; numbers[last] = temp; return pivotposition; } static void quicksort(int numbers[], int start, int end) { if (start < end) { int pivot_position = sort(numbers, start, end); quicksort(numbers, start, pivot_position - 1); quicksort(numbers, pivot_position + 1, end); } } static void print(int numbers[]) { for (int a : numbers) { System.out.print(a + " "); } } public static void main(String[] args) { int numbers[] = { 4, 5, 1, 2, 4, 5, 6 }; quicksort(numbers, 0, numbers.length - 1); print(numbers); }} |
Output
1 2 4 4 5 5 6
3. Hoare’s Partition
Hoare’s Partition Scheme works by initializing two indexes that start at two ends, the two indexes move toward each other until an inversion is (A smaller value on the left side and a greater value on the right side) found. When an inversion is found, two values are swapped and the process is repeated.
Algorithm:
Hoarepartition(arr[], lo, hi)
pivot = arr[lo]
i = lo - 1 // Initialize left index
j = hi + 1 // Initialize right index
// Find a value in left side greater
// than pivot
do
i = i + 1
while arr[i] < pivot
// Find a value in right side smaller
// than pivot
do
j--;
while (arr[j] > pivot);
if i >= j then
return j
swap arr[i] with arr[j]
QuickSort(arr[], l, r)
If r > l
1. Find the partition point of the array
m =Hoarepartition(a,l,r)
2. Call Quicksort for less than partition point
Call Quicksort(arr, l, m)
3. Call Quicksort for greater than the partition point
Call Quicksort(arr, m+1, r)
Java
// Java implementation of QuickSort// using Hoare's partition schemeimport java.io.*;class GFG { // This function takes first element as pivot, and // places all the elements smaller than the pivot on the // left side and all the elements greater than the pivot // on the right side. It returns the index of the last // element on the smaller side static int partition(int[] arr, int low, int high) { int pivot = arr[low]; int i = low - 1, j = high + 1; while (true) { // Find leftmost element greater // than or equal to pivot do { i++; } while (arr[i] < pivot); // Find rightmost element smaller // than or equal to pivot do { j--; } while (arr[j] > pivot); // If two pointers met. if (i >= j) return j; // swap(arr[i], arr[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 static 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); quickSort(arr, pi + 1, high); } } // Function to print an array static void printArray(int[] arr, int n) { for (int i = 0; i < n; ++i) System.out.print(" " + arr[i]); System.out.println(); } // Driver Code static public void main(String[] args) { int[] arr = { 10, 17, 18, 9, 11, 15 }; int n = arr.length; quickSort(arr, 0, n - 1); printArray(arr, n); }} |
Output
9 10 11 15 17 18
