Following is a typical recursive implementation of QuickSort for arrays. The implementation uses last element as pivot.
Java
/* A typical recursive implementation of Quicksort for array*/ /* 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 */static int partition (int []arr, int l, int h){ int x = arr[h]; int i = (l - 1); for(int j = l; j <= h - 1; j++) { if (arr[j] <= x) { i++; int tmp = arr[i]; arr[i] = arr[j]; arr[j] = tmp; } } int tmp = arr[i + 1]; arr[i + 1] = arr[h]; arr[h] = tmp; return(i + 1);} /* A[] --> Array to be sorted, l --> Starting index, h --> Ending index */static void quickSort(int []A, int l, int h){ if (l < h) { // Partitioning index int p = partition(A, l, h); quickSort(A, l, p - 1); quickSort(A, p + 1, h); }}// This code is contributed by pratham76. |
Can we use the same algorithm for Linked List?
Following is C++ implementation for the doubly linked list. The idea is simple, we first find out pointer to the last node. Once we have a pointer to the last node, we can recursively sort the linked list using pointers to first and last nodes of a linked list, similar to the above recursive function where we pass indexes of first and last array elements. The partition function for a linked list is also similar to partition for arrays. Instead of returning index of the pivot element, it returns a pointer to the pivot element. In the following implementation, quickSort() is just a wrapper function, the main recursive function is _quickSort() which is similar to quickSort() for array implementation.
Java
// A Java program to sort a linked list using Quicksortclass QuickSort_using_Doubly_LinkedList{ Node head; /* a node of the doubly linked list */ static class Node{ private int data; private Node next; private Node prev; Node(int d){ data = d; next = null; prev = null; } } // A utility function to find last node of linked list Node lastNode(Node node){ while(node.next!=null) node = node.next; return node; } /* Considers 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 */ Node partition(Node l,Node h) { // set pivot as h element int x = h.data; // similar to i = l-1 for array implementation Node i = l.prev; // Similar to "for (int j = l; j <= h- 1; j++)" for(Node j=l; j!=h; j=j.next) { if(j.data <= x) { // Similar to i++ for array i = (i==null) ? l : i.next; int temp = i.data; i.data = j.data; j.data = temp; } } i = (i==null) ? l : i.next; // Similar to i++ int temp = i.data; i.data = h.data; h.data = temp; return i; } /* A recursive implementation of quicksort for linked list */ void _quickSort(Node l,Node h) { if(h!=null && l!=h && l!=h.next){ Node temp = partition(l,h); _quickSort(l,temp.prev); _quickSort(temp.next,h); } } // The main function to sort a linked list. It mainly calls _quickSort() public void quickSort(Node node) { // Find last node Node head = lastNode(node); // Call the recursive QuickSort _quickSort(node,head); } // A utility function to print contents of arr public void printList(Node head) { while(head!=null){ System.out.print(head.data+" "); head = head.next; } } /* Function to insert a node at the beginning of the Doubly Linked List */ void push(int new_Data) { Node new_Node = new Node(new_Data); /* allocate node */ // if head is null, head = new_Node if(head==null){ head = new_Node; return; } /* link the old list of the new node */ new_Node.next = head; /* change prev of head node to new node */ head.prev = new_Node; /* since we are adding at the beginning, prev is always NULL */ new_Node.prev = null; /* move the head to point to the new node */ head = new_Node; } /* Driver program to test above function */ public static void main(String[] args){ QuickSort_using_Doubly_LinkedList list = new QuickSort_using_Doubly_LinkedList(); list.push(5); list.push(20); list.push(4); list.push(3); list.push(30); System.out.println("Linked List before sorting "); list.printList(list.head); System.out.println("Linked List after sorting"); list.quickSort(list.head); list.printList(list.head); }}// This code has been contributed by Amit Khandelwal |
Output :
Linked List before sorting 30 3 4 20 5 Linked List after sorting 3 4 5 20 30
Time Complexity: Time complexity of the above implementation is same as time complexity of QuickSort() for arrays. It takes O(n^2) time in the worst case and O(nLogn) in average and best cases. The worst case occurs when the linked list is already sorted.
Space Complexity: O(n). The extra space is due to the function call stack.
Can we implement random quicksort for a linked list?
Quicksort can be implemented for Linked List only when we can pick a fixed point as the pivot (like the last element in the above implementation). Random QuickSort cannot be efficiently implemented for Linked Lists by picking random pivot.
Please refer complete article on QuickSort on Doubly Linked List for more details!
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