Python Program for Find a triplet from three linked lists with sum equal to a given number

Given three linked lists, say a, b and c, find one node from each list such that the sum of the values of the nodes is equal to a given number. 
For example, if the three linked lists are 12->6->29, 23->5->8, and 90->20->59, and the given number is 101, the output should be triple “6 5 90”.
In the following solutions, size of all three linked lists is assumed same for simplicity of analysis. The following solutions work for linked lists of different sizes also.

A simple method to solve this problem is to run three nested loops. The outermost loop picks an element from list a, the middle loop picks an element from b and the innermost loop picks from c. The innermost loop also checks whether the sum of values of current nodes of a, b and c is equal to given number. The time complexity of this method will be O(n^3).
Sorting can be used to reduce the time complexity to O(n*n). Following are the detailed steps. 
1) Sort list b in ascending order, and list c in descending order. 
2) After the b and c are sorted, one by one pick an element from list a and find the pair by traversing both b and c. See isSumSorted() in the following code. The idea is similar to Quadratic algorithm of 3 sum problem.

Following code implements step 2 only. The solution can be easily modified for unsorted lists by adding the merge sort code discussed here. 

Python

# Python program to find a triplet
# from three linked lists with
# sum equal to a given number

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

# A utility function to insert
# a node at the beginning of a
# linked list
def push ( head_ref, new_data) :

    # allocate node
    new_node = Node(0)

    # put in the data
    new_node.data = new_data

    # link the old list of the new node
    new_node.next = (head_ref)

    # move the head to point to the new node
    (head_ref) = new_node

    return head_ref;

# A function to check if there are three elements in a, b
# and c whose sum is equal to givenNumber. The function
# assumes that the list b is sorted in ascending order
# and c is sorted in descending order.
def isSumSorted(headA, headB,headC, givenNumber) :

    a = headA

    # Traverse through all nodes of a
    while (a != None) :

        b = headB
        c = headC

        # For every node of list a, prick two nodes
        # from lists b abd c
        while (b != None and c != None) :

            # If this a triplet with given sum, print
            # it and return true
            sum = a.data + b.data + c.data
            if (sum == givenNumber) :

                print "Triplet Found: " , a.data , " " , b.data , " " , c.data,
                return True

            # If sum of this triplet is smaller, look for
            # greater values in b
            elif (sum < givenNumber):
                b = b.next
            else :# If sum is greater, look for smaller values in c
                c = c.next

        a = a.next # Move ahead in list a

    print("No such triplet")
    return False

# Driver code

# Start with the empty list
headA = None
headB = None
headC = None

# create a linked list 'a' 10.15.5.20
headA = push (headA, 20)
headA = push (headA, 4)
headA = push (headA, 15)
headA = push (headA, 10)

# create a sorted linked list 'b' 2.4.9.10
headB = push (headB, 10)
headB = push (headB, 9)
headB = push (headB, 4)
headB = push (headB, 2)

# create another sorted
# linked list 'c' 8.4.2.1
headC = push (headC, 1)
headC = push (headC, 2)
headC = push (headC, 4)
headC = push (headC, 8)

givenNumber = 25

isSumSorted (headA, headB, headC, givenNumber)

# This code is contributed by Arnab Kundu

Output: 

Triplet Found: 15 2 8

Time complexity: The linked lists b and c can be sorted in O(nLogn) time using Merge Sort (See this). The step 2 takes O(n*n) time. So the overall time complexity is O(nlogn) + O(nlogn) + O(n*n) = O(n*n). 
In this approach, the linked lists b and c are sorted first, so their original order will be lost. If we want to retain the original order of b and c, we can create copy of b and c. 

Please refer complete article on Find a triplet from three linked lists with sum equal to a given number for more details!