Python Program For QuickSort On Doubly Linked List
Last Updated :
03 May, 2023
Following is a typical recursive implementation of QuickSort for arrays. The implementation uses last element as pivot.
Python3
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 )
def quickSort(A, l, h):
if (l < h):
p = partition(A, l, h)
quickSort(A, l, p - 1 )
quickSort(A, p + 1 , h)
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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
head = None
class Node:
def __init__( self , d):
self .data = d
self . next = None
self .prev = None
def lastNode(node):
while (node. next ! = None ):
node = node. next ;
return node;
def partition(l, h):
x = h.data;
i = l.prev;
j = l
while (j ! = h):
if (j.data < = x):
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 ;
temp = i.data;
i.data = h.data;
h.data = temp;
return i;
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);
def quickSort(node):
head = lastNode(node);
_quickSort(node,head);
def printList(head):
while (head ! = None ):
print (head.data, end = " " );
head = head. next ;
def push(new_Data):
global head;
new_Node = Node(new_Data);
if (head = = None ):
head = new_Node;
return ;
new_Node. next = head;
head.prev = new_Node;
new_Node.prev = None ;
head = new_Node;
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);
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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!
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