# QuickSort on Doubly Linked List

Following is a typical recursive implementation of QuickSort for arrays. The implementation uses last element as pivot.

 `/* 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 */` `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++; ` `            ``swap (&arr[i], &arr[j]); ` `        ``} ` `    ``} ` `    ``swap (&arr[i + 1], &arr[h]); ` `    ``return` `(i + 1); ` `} ` ` `  `/* A[] --> Array to be sorted, l  --> Starting index, h  --> Ending index */` `void` `quickSort(``int` `A[], ``int` `l, ``int` `h) ` `{ ` `    ``if` `(l < h) ` `    ``{         ` `        ``int` `p = partition(A, l, h); ``/* Partitioning index */` `        ``quickSort(A, l, p - 1);   ` `        ``quickSort(A, p + 1, h); ` `    ``} ` `} `

Can we use same algorithm for Linked List?
Following is C++ implementation for doubly linked list. The idea is simple, we first find out pointer to last node. Once we have pointer to last node, we can recursively sort the linked list using pointers to first and last nodes of linked list, similar to the above recursive function where we pass indexes of first and last array elements. The partition function for linked list is also similar to partition for arrays. Instead of returning index of the pivot element, it returns 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. ## C++

 `// A C++ program to sort a linked list using Quicksort  ` `#include ` `using` `namespace` `std; ` ` `  `/* a node of the doubly linked list */` `class` `Node  ` `{  ` `    ``public``: ` `    ``int` `data;  ` `    ``Node *next;  ` `    ``Node *prev;  ` `};  ` ` `  `/* A utility function to swap two elements */` `void` `swap ( ``int``* a, ``int``* b )  ` `{ ``int` `t = *a; *a = *b; *b = t; }  ` ` `  `// A utility function to find ` `// last node of linked list  ` `Node *lastNode(Node *root)  ` `{  ` `    ``while` `(root && root->next)  ` `        ``root = root->next;  ` `    ``return` `root;  ` `}  ` ` `  `/* 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;  ` ` `  `            ``swap(&(i->data), &(j->data));  ` `        ``}  ` `    ``}  ` `    ``i = (i == NULL)? l : i->next; ``// Similar to i++  ` `    ``swap(&(i->data), &(h->data));  ` `    ``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 *p = partition(l, h);  ` `        ``_quickSort(l, p->prev);  ` `        ``_quickSort(p->next, h);  ` `    ``}  ` `}  ` ` `  `// The main function to sort a linked list. ` `// It mainly calls _quickSort()  ` `void` `quickSort(Node *head)  ` `{  ` `    ``// Find last node  ` `    ``Node *h = lastNode(head);  ` ` `  `    ``// Call the recursive QuickSort  ` `    ``_quickSort(head, h);  ` `}  ` ` `  `// A utility function to print contents of arr  ` `void` `printList(Node *head)  ` `{  ` `    ``while` `(head)  ` `    ``{  ` `        ``cout << head->data << ``" "``;  ` `        ``head = head->next;  ` `    ``}  ` `    ``cout << endl;  ` `}  ` ` `  `/* Function to insert a node at the  ` `beginging of the Doubly Linked List */` `void` `push(Node** head_ref, ``int` `new_data)  ` `{  ` `    ``Node* new_node = ``new` `Node; ``/* allocate node */` `    ``new_node->data = new_data;  ` ` `  `    ``/* since we are adding at the ` `    ``begining, prev is always NULL */` `    ``new_node->prev = NULL;  ` ` `  `    ``/* link the old list off the new node */` `    ``new_node->next = (*head_ref);  ` ` `  `    ``/* change prev of head node to new node */` `    ``if` `((*head_ref) != NULL) (*head_ref)->prev = new_node ;  ` ` `  `    ``/* move the head to point to the new node */` `    ``(*head_ref) = new_node;  ` `}  ` ` `  `/* Driver code */` `int` `main()  ` `{  ` `    ``Node *a = NULL;  ` `    ``push(&a, 5);  ` `    ``push(&a, 20);  ` `    ``push(&a, 4);  ` `    ``push(&a, 3);  ` `    ``push(&a, 30);  ` ` `  `    ``cout << ````"Linked List before sorting "````;  ` `    ``printList(a);  ` ` `  `    ``quickSort(a);  ` ` `  `    ``cout << ````"Linked List after sorting "````;  ` `    ``printList(a);  ` ` `  `    ``return` `0;  ` `}  ` ` `  `// This code is contributed by rathbhupendra `

## C

 `// A C program to sort a linked list using Quicksort ` `#include ` `#include ` `using` `namespace` `std; ` ` `  `/* a node of the doubly linked list */` `struct` `Node ` `{ ` `    ``int` `data; ` `    ``struct` `Node *next; ` `    ``struct` `Node *prev; ` `}; ` ` `  `/* A utility function to swap two elements */` `void` `swap ( ``int``* a, ``int``* b ) ` `{   ``int` `t = *a;      *a = *b;       *b = t;   } ` ` `  `// A utility function to find last node of linked list ` `struct` `Node *lastNode(Node *root) ` `{ ` `    ``while` `(root && root->next) ` `        ``root = root->next; ` `    ``return` `root; ` `} ` ` `  `/* 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; ` ` `  `            ``swap(&(i->data), &(j->data)); ` `        ``} ` `    ``} ` `    ``i = (i == NULL)? l : i->next; ``// Similar to i++ ` `    ``swap(&(i->data), &(h->data)); ` `    ``return` `i; ` `} ` ` `  `/* A recursive implementation of quicksort for linked list */` `void` `_quickSort(``struct` `Node* l, ``struct` `Node *h) ` `{ ` `    ``if` `(h != NULL && l != h && l != h->next) ` `    ``{ ` `        ``struct` `Node *p = partition(l, h); ` `        ``_quickSort(l, p->prev); ` `        ``_quickSort(p->next, h); ` `    ``} ` `} ` ` `  `// The main function to sort a linked list. It mainly calls _quickSort() ` `void` `quickSort(``struct` `Node *head) ` `{ ` `    ``// Find last node ` `    ``struct` `Node *h = lastNode(head); ` ` `  `    ``// Call the recursive QuickSort ` `    ``_quickSort(head, h); ` `} ` ` `  `// A utility function to print contents of arr ` `void` `printList(``struct` `Node *head) ` `{ ` `    ``while` `(head) ` `    ``{ ` `        ``cout << head->data << ``"  "``; ` `        ``head = head->next; ` `    ``} ` `    ``cout << endl; ` `} ` ` `  `/* Function to insert a node at the beginging of the Doubly Linked List */` `void` `push(``struct` `Node** head_ref, ``int` `new_data) ` `{ ` `    ``struct` `Node* new_node = ``new` `Node;     ``/* allocate node */` `    ``new_node->data  = new_data; ` ` `  `    ``/* since we are adding at the begining, prev is always NULL */` `    ``new_node->prev = NULL; ` ` `  `    ``/* link the old list off the new node */` `    ``new_node->next = (*head_ref); ` ` `  `    ``/* change prev of head node to new node */` `    ``if` `((*head_ref) !=  NULL)  (*head_ref)->prev = new_node ; ` ` `  `    ``/* move the head to point to the new node */` `    ``(*head_ref)    = new_node; ` `} ` ` `  `/* Driver program to test above function */` `int` `main() ` `{ ` `    ``struct` `Node *a = NULL; ` `    ``push(&a, 5); ` `    ``push(&a, 20); ` `    ``push(&a, 4); ` `    ``push(&a, 3); ` `    ``push(&a, 30); ` ` `  `    ``cout << ````"Linked List before sorting "````; ` `    ``printList(a); ` ` `  `    ``quickSort(a); ` ` `  `    ``cout << ````"Linked List after sorting "````; ` `    ``printList(a); ` ` `  `    ``return` `0; ` `} `

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## Java

 `// A Java program to sort a linked list using Quicksort ` `class` `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 beginging 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 off 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 begining, 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 `

## C#

 `// A C# program to sort a linked list using Quicksort  ` `using` `System;  ` ` `  `public` `class` `QuickSort_using_Doubly_LinkedList ` `{  ` `    ``Node head;  ` `     `  `/* a node of the doubly linked list */` `    ``public` `class` `Node{  ` `        ``public` `int` `data;  ` `        ``public` `Node next;  ` `        ``public` `Node prev;  ` `         `  `        ``public` `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;  ` `        ``int` `temp; ` `         `  `        ``// 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;  ` `                ``temp = i.data;  ` `                ``i.data = j.data;  ` `                ``j.data = temp;  ` `            ``}  ` `        ``}  ` `        ``i = (i == ``null``) ? l : i.next; ``// Similar to i++  ` `        ``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``){  ` `            ``Console.Write(head.data+``" "``);  ` `            ``head = head.next;  ` `        ``}  ` `    ``}  ` `     `  `    ``/* Function to insert a node at the  ` `    ``beginging 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 off 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 ` `        ``begining, prev is always NULL */` `        ``new_Node.prev = ``null``;  ` `         `  `        ``/* move the head to point to the new node */` `        ``head = new_Node;  ` `    ``}  ` `     `  `    ``/* Driver code */` `    ``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);  ` `             `  `             `  `            ``Console.WriteLine(``"Linked List before sorting "``);  ` `            ``list.printList(list.head);  ` `            ``Console.WriteLine(````" Linked List after sorting"````);  ` `            ``list.quickSort(list.head);  ` `            ``list.printList(list.head);  ` `    ``}  ` `}  ` ` `  `// This code is contributed by 29AjayKumar `

Output :

```Linked List before sorting
30  3  4  20  5
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 worst case and O(nLogn) in average and best cases. The worst case occurs when the linked list is already sorted.

Can we implement random quick sort for linked list?
Quicksort can be implemented for Linked List only when we can pick a fixed point as pivot (like last element in above implementation). Random QuickSort cannot be efficiently implemented for Linked Lists by picking random pivot.

Exercise:
The above implementation is for doubly linked list. Modify it for singly linked list. Note that we don’t have prev pointer in singly linked list.
Refer QuickSort on Singly Linked List for solution.