Python Program For Partitioning A Linked List Around A Given Value And Keeping The Original Order

Last Updated : 22 Jun, 2022

Given a linked list and a value x, partition it such that all nodes less than x come first, then all nodes with a value equal to x, and finally nodes with a value greater than or equal to x. The original relative order of the nodes in each of the three partitions should be preserved. The partition must work in place.
Examples:

Input: 1->4->3->2->5->2->3, 
        x = 3
Output: 1->2->2->3->3->4->5

Input: 1->4->2->10 
        x = 3
Output: 1->2->4->10

Input: 10->4->20->10->3 
        x = 3
Output: 3->10->4->20->10

To solve this problem we can use partition method of Quick Sort but this would not preserve the original relative order of the nodes in each of the two partitions.
Below is the algorithm to solve this problem :

Initialize first and last nodes of below three linked lists as NULL.
- Linked list of values smaller than x.
- Linked list of values equal to x.
- Linked list of values greater than x.
Now iterate through the original linked list. If a node's value is less than x then append it at the end of the smaller list. If the value is equal to x, then at the end of the equal list. And if a value is greater, then at the end of the greater list.
Now concatenate three lists.

Below is the implementation of the above idea.

Python3

# Python3 program to partition a 
# linked list around a given value. 

# Link list Node 
class Node: 
    def __init__(self):
        self.data = 0
        self.next = None

# A utility function to create 
# a new node 
def newNode(data): 
    new_node = Node() 
    new_node.data = data 
    new_node.next = None
    return new_node 

# Function to make two separate lists 
# and return head after concatenating 
def partition( head, x) :

    # Let us initialize first and last 
    # nodes of three linked lists 
    # 1) Linked list of values smaller 
    #    than x. 
    # 2) Linked list of values equal 
    #    to x. 
    # 3) Linked list of values greater 
    #    than x.
    smallerHead = None
    smallerLast = None
    greaterLast = None
    greaterHead = None
    equalHead = None
    equalLast = None

    # Now iterate original list and connect 
    # nodes of appropriate linked lists. 
    while (head != None) :
    
        # If current node is equal to x, 
        # append it to the list of x values 
        if (head.data == x): 
        
            if (equalHead == None): 
                equalHead = equalLast = head 
            else:
            
                equalLast.next = head 
                equalLast = equalLast.next
            
        # If current node is less than X, 
        # append it to the list of smaller 
        # values 
        elif (head.data < x): 
        
            if (smallerHead == None): 
                smallerLast = smallerHead = head 
            else:
            
                smallerLast.next = head 
                smallerLast = head 
        
        else :

        # Append to the list of greater values         
            if (greaterHead == None) :
                greaterLast = greaterHead = head 
            else:
            
                greaterLast.next = head 
                greaterLast = head 
            
        head = head.next
    
    # Fix end of greater linked list to None 
    # if this list has some nodes 
    if (greaterLast != None) :
        greaterLast.next = None

    # Connect three lists 

    # If smaller list is empty 
    if (smallerHead == None) :
    
        if (equalHead == None) :
            return greaterHead 
        equalLast.next = greaterHead 
        return equalHead 
    
    # If smaller list is not empty 
    # and equal list is empty 
    if (equalHead == None) :
    
        smallerLast.next = greaterHead 
        return smallerHead 
    
    # If both smaller and equal list 
    # are non-empty 
    smallerLast.next = equalHead 
    equalLast.next = greaterHead 
    return smallerHead 

# Function to print linked list 
def printList(head) :

    temp = head 
    while (temp != None): 
    
        print(temp.data ,end= " ") 
        temp = temp.next
    
# Driver code 
# Start with the empty list 
head = newNode(10) 
head.next = newNode(4) 
head.next.next = newNode(5) 
head.next.next.next = newNode(30) 
head.next.next.next.next = newNode(2) 
head.next.next.next.next.next = newNode(50) 

x = 3
head = partition(head, x) 
printList(head) 
# This code is contributed by Arnab Kundu.