Merge sort is often preferred for sorting a linked list. The slow random-access performance of a linked list makes some other algorithms (such as quicksort) perform poorly, and others (such as heapsort) completely impossible.
Let the head be the first node of the linked list to be sorted and headRef be the pointer to head. Note that we need a reference to head in MergeSort() as the below implementation changes next links to sort the linked lists (not data at the nodes), so the head node has to be changed if the data at the original head is not the smallest value in the linked list.
MergeSort(headRef) 1) If the head is NULL or there is only one element in the Linked List then return. 2) Else divide the linked list into two halves. FrontBackSplit(head, &a, &b); /* a and b are two halves */ 3) Sort the two halves a and b. MergeSort(a); MergeSort(b); 4) Merge the sorted a and b (using SortedMerge() discussed here) and update the head pointer using headRef. *headRef = SortedMerge(a, b);
# Python3 program to merge sort of linked list # create Node using class Node. class Node:
def __init__( self , data):
self .data = data
self . next = None
class LinkedList:
def __init__( self ):
self .head = None
# push new value to linked list
# using append method
def append( self , new_value):
# Allocate new node
new_node = Node(new_value)
# if head is None, initialize it to new node
if self .head is None :
self .head = new_node
return
curr_node = self .head
while curr_node. next is not None :
curr_node = curr_node. next
# Append the new node at the end
# of the linked list
curr_node. next = new_node
def sortedMerge( self , a, b):
result = None
# Base cases
if a = = None :
return b
if b = = None :
return a
# pick either a or b and recur..
if a.data < = b.data:
result = a
result. next = self .sortedMerge(a. next , b)
else :
result = b
result. next = self .sortedMerge(a, b. next )
return result
def mergeSort( self , h):
# Base case if head is None
if h = = None or h. next = = None :
return h
# get the middle of the list
middle = self .getMiddle(h)
nexttomiddle = middle. next
# set the next of middle node to None
middle. next = None
# Apply mergeSort on left list
left = self .mergeSort(h)
# Apply mergeSort on right list
right = self .mergeSort(nexttomiddle)
# Merge the left and right lists
sortedlist = self .sortedMerge(left, right)
return sortedlist
# Utility function to get the middle
# of the linked list
def getMiddle( self , head):
if (head = = None ):
return head
slow = head
fast = head
while (fast. next ! = None and fast. next . next ! = None ):
slow = slow. next
fast = fast. next . next
return slow
# Utility function to print the linked list def printList(head):
if head is None :
print ( ' ' )
return
curr_node = head
while curr_node:
print (curr_node.data, end = " " )
curr_node = curr_node. next
print ( ' ' )
# Driver Code if __name__ = = '__main__' :
li = LinkedList()
# Let us create a unsorted linked list
# to test the functions created.
# The list shall be a: 2->3->20->5->10->15
li.append( 15 )
li.append( 10 )
li.append( 5 )
li.append( 20 )
li.append( 3 )
li.append( 2 )
# Apply merge Sort
li.head = li.mergeSort(li.head)
print ( "Sorted Linked List is:" )
printList(li.head)
# This code is contributed by Vikas Chitturi |
Sorted Linked List is: 2 3 5 10 15 20
Time Complexity: O(n*log n)
Space Complexity: O(n*log n)
Approach 2: This approach is simpler and uses log n space.
mergeSort():
- If the size of the linked list is 1 then return the head
- Find mid using The Tortoise and The Hare Approach
- Store the next of mid in head2 i.e. the right sub-linked list.
- Now Make the next midpoint null.
- Recursively call mergeSort() on both left and right sub-linked list and store the new head of the left and right linked list.
- Call merge() given the arguments new heads of left and right sub-linked lists and store the final head returned after merging.
- Return the final head of the merged linkedlist.
merge(head1, head2):
- Take a pointer say merged to store the merged list in it and store a dummy node in it.
- Take a pointer temp and assign merge to it.
- If the data of head1 is less than the data of head2, then, store head1 in next of temp & move head1 to the next of head1.
- Else store head2 in next of temp & move head2 to the next of head2.
- Move temp to the next of temp.
- Repeat steps 3, 4 & 5 until head1 is not equal to null and head2 is not equal to null.
- Now add any remaining nodes of the first or the second linked list to the merged linked list.
- Return the next of merged(that will ignore the dummy and return the head of the final merged linked list)
# Python program for the above approach # Node Class class Node:
def __init__( self ,key):
self .data = key
self . next = None
# Function to merge sort def mergeSort(head):
if (head. next = = None ):
return head
mid = findMid(head)
head2 = mid. next
mid. next = None
newHead1 = mergeSort(head)
newHead2 = mergeSort(head2)
finalHead = merge(newHead1, newHead2)
return finalHead
# Function to merge two linked lists def merge(head1,head2):
merged = Node( - 1 )
temp = merged
# While head1 is not null and head2
# is not null
while (head1 ! = None and head2 ! = None ):
if (head1.data < head2.data):
temp. next = head1
head1 = head1. next
else :
temp. next = head2
head2 = head2. next
temp = temp. next
# While head1 is not null
while (head1 ! = None ):
temp. next = head1
head1 = head1. next
temp = temp. next
# While head2 is not null
while (head2 ! = None ):
temp. next = head2
head2 = head2. next
temp = temp. next
return merged. next
# Find mid using The Tortoise and The Hare approach def findMid(head):
slow = head
fast = head. next
while (fast ! = None and fast. next ! = None ):
slow = slow. next
fast = fast. next . next
return slow
# Function to print list def printList(head):
while (head ! = None ):
print (head.data,end = " " )
head = head. next
# Driver Code head = Node( 7 )
temp = head
temp. next = Node( 10 );
temp = temp. next ;
temp. next = Node( 5 );
temp = temp. next ;
temp. next = Node( 20 );
temp = temp. next ;
temp. next = Node( 3 );
temp = temp. next ;
temp. next = Node( 2 );
temp = temp. next ;
# Apply merge Sort head = mergeSort(head);
print ("
Sorted Linked List is :
"); printList(head); # This code is contributed by avanitrachhadiya2155 |
Output:
Sorted Linked List is: 2 3 5 7 10 20
Time Complexity: O(n*log n)
Space Complexity: O(log n)
Please refer complete article on Merge Sort for Linked Lists for more details!