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QuickSort on Doubly Linked List

  • Difficulty Level : Medium
  • Last Updated : 21 Sep, 2021

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

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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




<script>
/* 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 */
 
function partition (arr,l,h)
{
    let x = arr[h];
    let i = (l - 1);
      
    for(let j = l; j <= h - 1; j++)
    {
        if (arr[j] <= x)
        {
            i++;
            let tmp = arr[i];
            arr[i] = arr[j];
            arr[j] = tmp;
        }
    }  
    let 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 */
function quickSort(A,l,h)
{
    if (l < h)
    {
        
        // Partitioning index
        let p = partition(A, l, h);
        quickSort(A, l, p - 1);
        quickSort(A, p + 1, h);
    }
}
 
 
// This code is contributed by unknown2108
</script>

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 <bits/stdc++.h>
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 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 <stdio.h>
#include <stdlib.h>
 
/* 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

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 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 = 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 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);
        }
    }

Javascript




<script>
// A Javascript program to sort a linked list using Quicksort
let  head;
 
/* a node of the doubly linked list */
class Node
{
    constructor(d)
    {
        this.data = d;
        this.next = null;
        this.prev = null;
    }
}
 
// A utility function to find last node of linked list  
function lastNode(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 */
function partition(l, h)
{
 
    // set pivot as h element
        let x = h.data;
          
        // similar to i = l-1 for array implementation
        let i = l.prev;
          
        // Similar to "for (int j = l; j <= h- 1; j++)"
        for(let j=l; j!=h; j=j.next)
        {
            if(j.data <= x)
            {
                // Similar to i++ for array
                i = (i == null) ? l : i.next;
                let temp = i.data;
                i.data = j.data;
                j.data = temp;
            }
        }
        i = (i == null) ? l : i.next;  // Similar to i++
        let temp = i.data;
        i.data = h.data;
        h.data = temp;
        return i;
}
 
/* A recursive implementation of quicksort for linked list */
function _quickSort(l,h)
{
    if(h != null && l!=h && l != h.next){
            let temp = partition(l, h);
            _quickSort(l,temp.prev);
            _quickSort(temp.next,h);
        }
}
 
// The main function to sort a linked list. It mainly calls _quickSort()
function quickSort(node)
{
    // Find last node
        let head = lastNode(node);
          
        // Call the recursive QuickSort
        _quickSort(node,head);
}
 
// A utility function to print contents of arr
function printList(head)
{
    while(head!=null){
            document.write(head.data+" ");
            head = head.next;
        }
}
 
/* Function to insert a node at the beginning of the Doubly Linked List */
function push(new_Data)
{
    let 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 */
push(5);
push(20);
push(4);
push(3);
push(30);
 
 
document.write("Linked List before sorting <br>");
printList(head);
document.write("<br>Linked List after sorting<br>");
quickSort(head);
printList(head);
 
// This code is contributed by patel2127
</script>

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.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
 




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