Python Program For QuickSort On Doubly Linked List

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

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.

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.

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("
Linked List after sorting");
quickSort(head);
printList(head);

# This code is contributed by _saurabh_jaiswal

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!