C++ Program To Multiply Two Numbers Represented By Linked Lists

Given two numbers represented by linked lists, write a function that returns the multiplication of these two linked lists.

Examples:

Input: 9->4->6
        8->4
Output: 79464

Input: 3->2->1
        1->2
Output: 3852

Solution: 
Traverse both lists and generate the required numbers to be multiplied and then return the multiplied values of the two numbers. 
Algorithm to generate the number from linked list representation: 

1) Initialize a variable to zero
2) Start traversing the linked list
3) Add the value of the first node to this variable
4) From the second node, multiply the variable by 10
   and also take the modulus of this value by 10^9+7
   and then add the value of the node to this 
   variable.
5) Repeat step 4 until we reach the last node of the list. 

Use the above algorithm with both linked lists to generate the numbers. 

Below is the program for multiplying two numbers represented as linked lists:  

C++

// C++ program to Multiply two numbers
// represented as linked lists
#include<bits/stdc++.h>
#include<stdio.h>
using namespace std;

// Linked list node
struct Node
{
    int data;
    struct Node* next;
};

// Function to create a new node
// with given data
struct Node *newNode(int data)
{
    struct Node *new_node =
           (struct Node *) malloc(sizeof(struct Node));
    new_node->data = data;
    new_node->next = NULL;
    return new_node;
}

// Function to insert a node at the
// beginning of the Linked List
void push(struct Node** head_ref,
          int new_data)
{
    // Allocate node
    struct Node* new_node =
           newNode(new_data);

    // Link the old list off the
    // new node
    new_node->next = (*head_ref);

    // Move the head to point to the
    // new node
    (*head_ref) = new_node;
}

// Multiply contents of two linked lists
long long multiplyTwoLists (Node* first,
                            Node* second)
{
    long long N= 1000000007;
    long long num1 = 0, num2 = 0;
    while (first || second)
    {
        if(first)
        {
            num1 = (((num1) * 10) % N +
                      first -> data);
            first = first -> next;
        }

        if(second)
        {
            num2 = (((num2) * 10) % N +
                      second -> data);
            second = second->next;
        }

    }
    return (((num1 % N) *
             (num2 % N)) % N);
}

// A utility function to print a
// linked list
void printList(struct Node *node)
{
    while(node != NULL)
    {
        cout << node -> data;
        if(node -> next)
            cout << "->";
        node = node -> next;
    }
    cout << "";
}

// Driver code
int main()
{
    struct Node* first = NULL;
    struct Node* second = NULL;

    // Create first list 9->4->6
    push(&first, 6);
    push(&first, 4);
    push(&first, 9);
    printf("First List is: ");
    printList(first);

    // Create second list 8->4
    push(&second, 4);
    push(&second, 8);
    printf("Second List is: ");
    printList(second);

    // Multiply the two lists and see result
    cout << "Result is: ";
    cout << multiplyTwoLists(first,
                             second);
    return 0;
}

Output:

First List is: 9->4->6
Second List is: 8->4
Result is: 79464

Time Complexity: O(max(n1, n2)), where n1 and n2 represents the number of nodes present in the first and second linked list respectively.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

Please refer complete article on Multiply two numbers represented by Linked Lists for more details!