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# QuickSort on Doubly Linked List

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 swapping 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`

## Javascript

 ``

Time Complexity : O(N log N)

Auxiliary Space : O(N)

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.

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 ` `beginning 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 of 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 of 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` `import` `java.io.*;` `public` `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 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(``"\nLinked List after sorting"``);` `            ``list.quickSort(list.head);` `            ``list.printList(list.head);` `        `  `    ``}` `}`   `// This code has been contributed by Amit Khandelwal`

## Python3

 `# A Python program to sort a linked list using Quicksort` `head ``=` `None`   `# a node of the doubly linked list` `class` `Node:` `    ``def` `__init__(``self``, d):` `        ``self``.data ``=` `d` `        ``self``.``next` `=` `None` `        ``self``.prev ``=` `None`   `# A utility function to find last node of linked list` `def` `lastNode(node):` `    ``while``(node.``next` `!``=` `None``):` `            ``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 ` `def` `partition(l, h):`   `    ``# set pivot as h element` `        ``x ``=` `h.data;` `         `  `        ``# similar to i = l-1 for array implementation` `        ``i ``=` `l.prev;` `        `  `        ``j ``=` `l` `        `  `        ``# Similar to "for (int j = l; j <= h- 1; j++)"` `        ``while``(j !``=` `h):` `            ``if``(j.data <``=` `x):` `              `  `                ``# Similar to i++ for array` `                ``i ``=` `l ``if``(i ``=``=` `None``) ``else` `i.``next``;`   `                ``temp ``=` `i.data;` `                ``i.data ``=` `j.data;` `                ``j.data ``=` `temp;` `            ``j ``=` `j.``next` `                        `  `        ``i ``=` `l ``if` `(i ``=``=` `None``) ``else` `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 ` `def` `_quickSort(l,h):` `    ``if``(h !``=` `None` `and` `l !``=` `h ``and` `l !``=` `h.``next``):` `            ``temp ``=` `partition(l, h);` `            ``_quickSort(l,temp.prev);` `            ``_quickSort(temp.``next``, h);` `        `  `# The main function to sort a linked list. It mainly calls _quickSort()` `def` `quickSort(node):` `  `  `    ``# Find last node` `        ``head ``=` `lastNode(node);` `         `  `        ``# Call the recursive QuickSort` `        ``_quickSort(node,head);`   `# A utility function to print contents of arr` `def` `printList(head):` `    ``while``(head !``=` `None``):` `            ``print``(head.data, end``=``" "``);` `            ``head ``=` `head.``next``;` `        `  `# Function to insert a node at the beginning of the Doubly Linked List ` `def` `push(new_Data):` `    ``global` `head;` `    ``new_Node ``=` `Node(new_Data);     ``# allocate node ` `         `  `    ``# if head is null, head = new_Node` `    ``if``(head ``=``=` `None``):` `        ``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 ``=` `None``;` `        `  `    ``# move the head to point to the new node ` `    ``head ``=` `new_Node;`   `# Driver program to test above function ` `push(``5``);` `push(``20``);` `push(``4``);` `push(``3``);` `push(``30``);`     `print``(``"Linked List before sorting "``);` `printList(head);` `print``(``"\nLinked List after sorting"``);` `quickSort(head);` `printList(head);`   `# This code is contributed by _saurabh_jaiswal`

## 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` `        ``beginning 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 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 */`   `            ``/* 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);` `        ``}` `    ``}`

## Javascript

 ``

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 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.

Auxiliary Space: O(n)

The extra space is due to the function call stack.

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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