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QuickSort on Doubly Linked List
• Difficulty Level : Medium
• Last Updated : 13 Apr, 2021

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

## C++

 `/* 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);``    ``}``}`

## 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.`

## Python3

 `"""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``"""` `"""`` ``i --> is the first index in the array`` ``x --> is the last index in the array`` ``tmp --> is a temporary variable for swaping values (integer)``"""``# array arr, integer l, integer h``def`  `partition (arr, l, h):``    ``x ``=` `arr[h]``    ``i ``=` `(l ``-` `1``)``    ``for` `j ``in` `range``(l, h):``        ``if` `(arr[j] <``=` `x):``            ``i ``+``=``1``            ``tmp ``=` `arr[i]``            ``arr[i] ``=` `arr[j]``            ``arr[j] ``=` `tmp` `    ``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``"""` `# array A, integer l, integer h``def` `quickSort(A, l, h):``    ``if` `(l < h):``        ``p ``=` `partition(A, l, h) ``# pivot index``        ``quickSort(A, l, p ``-` `1``) ``# left``        ``quickSort(A, p ``+` `1``, h) ``# right` `# This code is contributed by humphreykibet.`

## C#

 `/* 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 rutvik_56`

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. ## 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``    ``beginning, 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 \n"``;``    ``printList(a);` `    ``quickSort(a);` `    ``cout << ``"Linked List after sorting \n"``;``    ``printList(a);` `    ``return` `0;``}` `// This code is contributed by rathbhupendra`

## C

 `// C program to sort a linked list using Quicksort``#include ``#include ` `/* 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(``struct` `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 */``struct` `Node* partition(``struct` `Node *l, ``struct` `Node *h)``{``    ``// set pivot as h element``    ``int` `x = h->data;` `    ``// similar to i = l-1 for array implementation``    ``struct` `Node *i = l->prev;` `    ``// Similar to "for (int j = l; j <= h- 1; j++)"``    ``for` `(``struct` `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)``    ``{``        ``printf``(``"%d "``, head->data);``        ``head = head->next;``    ``}``    ``printf``(``"\n"``);``}` `/* Function to insert a node at the``beginning of the Doubly Linked List */``void` `push(``struct` `Node** head_ref, ``int` `new_data)``{``    ``struct` `Node* new_node = (``struct` `Node*)``               ``malloc``(``sizeof``(``struct` `Node)); ``/* allocate node */``    ``new_node->data = new_data;` `    ``/* since we are adding at the beginning,``    ``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(``int` `argc, ``char` `**argv)``{``    ``struct` `Node *a = NULL;``    ``push(&a, 5);``    ``push(&a, 20);``    ``push(&a, 4);``    ``push(&a, 3);``    ``push(&a, 30);` `    ``printf``(``"Linked List before sorting \n"``);``    ``printList(a);` `    ``quickSort(a);` `    ``printf``(``"Linked List after sorting \n"``);``    ``printList(a);` `    ``return` `0;``}`

## 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 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 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 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(``"\nLinked 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;``    ``/* 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;``              ``/* Prev and Next are left Null */``        ``}``    ``}` `    ``public` `class` `DoublyLinkedList``    ``{``        ``private` `Node _head;``        ``public` `Node Head``        ``{``            ``get` `=> _head;``            ``set` `=> _head = value;``        ``}` `        ``// A utility function to find the last node of linked list``        ``private` `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 a sorted array,``        ``and places all smaller (smaller than``        ``pivot) to left of pivot and all``        ``greater elements to right of pivot */``        ``private` `Node Partition(Node last, Node head)``        ``{``            ``// set pivot as h element``            ``int` `pivot = head.Data;` `            ``// similar to i = l-1 for array implementation``            ``Node i = last.Prev;``            ``int` `temp;` `            ``// Similar to "for (int j = l; j <= h- 1; j++)"``            ``for` `(Node j = last; j != head; j = j.Next)``            ``{``                ``if` `(j.Data <= pivot)``                ``{``                    ``// Similar to i++ for array``                    ``i = (i == ``null``) ? last : i.Next;``                    ``temp = i.Data;``                    ``i.Data = j.Data;``                    ``j.Data = temp;``                ``}``            ``}``            ``i = (i == ``null``) ? last : i.Next; ``// Similar to i++``            ``temp = i.Data;``            ``i.Data = head.Data;``            ``head.Data = temp;``            ``return` `i;``        ``}` `        ``/* A recursive implementation of``        ``quicksort for linked list */``        ``private` `void` `RecursiveQuickSort(Node last, Node head)``        ``{``            ``if` `(head != ``null` `&& last != head && last != head.Next)``            ``{``                ``Node temp = Partition(last, head);``                ``RecursiveQuickSort(last, temp.Prev);``                ``RecursiveQuickSort(temp.Next, head);``            ``}``        ``}` `        ``// 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``            ``RecursiveQuickSort(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 */``        ``public` `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``            ``beginning, prev is always NULL */` `            ``/* move the head to point to the new node */``            ``_head = new_Node;``        ``}` `        ``/* Driver code */``    ``}``    ``public` `class` `QuickSort_using_Doubly_LinkedList``    ``{``        ``public` `static` `void` `Main(String[] args)``        ``{``            ``var` `list = ``new` `DoublyLinkedList();` `            ``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(``"\nLinked List after sorting"``);``            ``list.QuickSort(list.Head);``            ``list.PrintList(list.Head);``        ``}``    ``}`

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.
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.

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

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