C++ Program For 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);
    }
}

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
";
    printList(a);

    quickSort(a);

    cout << "Linked List after sorting
";
    printList(a);

    return 0;
}

// This code is contributed by rathbhupendra

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.

Space Complexity: O(n). The extra space is due to the function call stack.

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.

Please refer complete article on QuickSort on Doubly Linked List for more details!