C++ Program For Finding 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. 

C++

// C++ program to find a triplet
// from three linked lists with
// sum equal to a given number
#include <bits/stdc++.h>
using namespace std;

/* Link list node */
class Node
{
    public:
    int data;
    Node* next;
};

/* A utility function to insert
a node at the beginning of a
linked list*/
void push (Node** head_ref, int new_data)
{
    /* allocate node */
    Node* new_node = new Node();

    /* 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;
}

/* 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. */
bool isSumSorted(Node *headA, Node *headB,
                Node *headC, int givenNumber)
{
    Node *a = headA;

    // Traverse through all nodes of a
    while (a != NULL)
    {
        Node *b = headB;
        Node *c = headC;

        // For every node of list a, prick two nodes
        // from lists b abd c
        while (b != NULL && c != NULL)
        {
            // If this a triplet with given sum, print
            // it and return true
            int sum = a->data + b->data + c->data;
            if (sum == givenNumber)
            {
            cout << "Triplet Found: " << a->data << " " <<
                                b->data << " " << c->data;
            return true;
            }

            // If sum of this triplet is smaller, look for
            // greater values in b
            else if (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
    }

    cout << "No such triplet";
    return false;
}


/* Driver code*/
int main()
{
    /* Start with the empty list */
    Node* headA = NULL;
    Node* headB = NULL;
    Node* headC = NULL;

    /*create a linked list 'a' 10->15->5->20 */
    push (&headA, 20);
    push (&headA, 4);
    push (&headA, 15);
    push (&headA, 10);

    /*create a sorted linked list 'b' 2->4->9->10 */
    push (&headB, 10);
    push (&headB, 9);
    push (&headB, 4);
    push (&headB, 2);

    /*create another sorted
    linked list 'c' 8->4->2->1 */
    push (&headC, 1);
    push (&headC, 2);
    push (&headC, 4);
    push (&headC, 8);

    int givenNumber = 25;

    isSumSorted (headA, headB, headC, givenNumber);

    return 0;
}

// This code is contributed by rathbhupendra

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!