QuickSort on Doubly Linked List

03 Jul, 2022
Following is a typical recursive implementation of QuickSort for arrays. The implementation uses last element as pivot. 
C++
Java
Python3
C#
Javascript
/* 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);    }}
/* 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.
"""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 hdef  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 hdef 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.
/* 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
<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. 
 
Implementation:
C++
C
Java
Python3
C#
Javascript
// 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 greaterelements 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 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 liststruct 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 leftof 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 arrvoid 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 Codeint 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;}
// A Java program to sort a linked list using Quicksortclass QuickSort_using_Doubly_LinkedList{    Node head;    /* a node of the doubly linked list */      static class Node{        private int data;        private Node next;        private Node prev;                  Node(int d){            data = d;            next = null;            prev = null;        }    }      // A utility function to find last node of linked list        Node lastNode(Node node){        while(node.next!=null)            node = node.next;        return node;    }        /* Considers last element as pivot, places the pivot element at its   correct position in sorted array, and places all smaller (smaller than   pivot) to left of pivot and all greater elements to right of pivot */    Node partition(Node l,Node h)    {       // set pivot as h element        int x = h.data;                  // similar to i = l-1 for array implementation        Node i = l.prev;                  // Similar to "for (int j = l; j <= h- 1; j++)"        for(Node j=l; j!=h; j=j.next)        {            if(j.data <= x)            {                // Similar to i++ for array                i = (i==null) ? l : i.next;                int temp = i.data;                i.data = j.data;                j.data = temp;            }        }        i = (i==null) ? l : i.next;  // Similar to i++        int temp = i.data;        i.data = h.data;        h.data = temp;        return i;    }          /* A recursive implementation of quicksort for linked list */    void _quickSort(Node l,Node h)    {        if(h!=null && l!=h && l!=h.next){            Node temp = partition(l,h);            _quickSort(l,temp.prev);            _quickSort(temp.next,h);        }    }          // The main function to sort a linked list. It mainly calls _quickSort()    public void quickSort(Node node)    {        // Find last node        Node head = lastNode(node);                  // Call the recursive QuickSort        _quickSort(node,head);    }           // A utility function to print contents of arr     public void printList(Node head)     {        while(head!=null){            System.out.print(head.data+" ");            head = head.next;        }    }          /* Function to insert a node at the beginning of the Doubly Linked List */    void push(int new_Data)    {        Node new_Node = new Node(new_Data);     /* allocate node */                  // if head is null, head = new_Node        if(head==null){            head = new_Node;            return;        }                  /* link the old list 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
# A Python program to sort a linked list using Quicksorthead = None  # a node of the doubly linked listclass Node:    def __init__(self, d):        self.data = d        self.next = None        self.prev = None  # A utility function to find last node of linked listdef 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 arrdef 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
// 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);        }    }
<script>// A Javascript program to sort a linked list using Quicksortlet  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 arrfunction 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>
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.
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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Merge Sort
Bubble Sort Algorithm
QuickSort
Insertion Sort
Selection Sort Algorithm