Multiply two numbers represented as linked lists into a third list
Given two numbers represented by linked lists, write a function that returns the head of the new linked list that represents the number that is the product of those numbers.
Examples:
Input : 9->4->6
8->4
Output : 7->9->4->6->4
Input : 9->9->9->4->6->9
9->9->8->4->9
Output : 9->9->7->9->5->9->8->0->1->8->1
We have already discussed a solution in below post.
Multiply two numbers represented by Linked Lists
The solution discussed above store result in an integer. Her we store result in a third list so that large numbers can be handled.
Remember old school multiplication? we imitate that process. On paper, we take the last digit of a number and multiply with the second number and write the product. Now leave the last column and same way each digit of one number is multiplied with every digit of other number and every time result is written by leaving one last column. then add these columns that forms the number. Now assume these columns as nodes of the resultant linked list. We make resultant linked list in reversed fashion.
Algorithm
Reverse both linked lists
Make a linked list of maximum result size (m + n + 1)
For each node of one list
For each node of second list
a) Multiply nodes
b) Add digit in result LL at corresponding
position
c) Now resultant node itself can be higher
than one digit
d) Make carry for next node
Leave one last column means next time start
From next node in result list
Reverse the resulted linked list
C++
// C++ program to Multiply two numbers // represented as linked lists #include <bits/stdc++.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; } // Function to reverse the linked list and return // its length int reverse(struct Node** head_ref) { struct Node* prev = NULL; struct Node* current = *head_ref; struct Node* next; int len = 0; while (current != NULL) { len++; next = current->next; current->next = prev; prev = current; current = next; } *head_ref = prev; return len; } // Function to make an empty linked list of // given size struct Node* make_empty_list(int size) { struct Node* head = NULL; while (size--) push(&head, 0); return head; } // Multiply contents of two linked lists => store // in another list and return its head struct Node* multiplyTwoLists(struct Node* first, struct Node* second) { // reverse the lists to muliply from end // m and n lengths of linked lists to make // and empty list int m = reverse(&first), n = reverse(&second); // make a list that will contain the result // of multiplication. // m+n+1 can be max size of the list struct Node* result = make_empty_list(m + n + 1); // pointers for traverse linked lists and also // to reverse them after struct Node *second_ptr = second, *result_ptr1 = result, *result_ptr2, *first_ptr; // multiply each Node of second list with first while (second_ptr) { int carry = 0; // each time we start from the next of Node // from which we started last time result_ptr2 = result_ptr1; first_ptr = first; while (first_ptr) { // multiply a first list's digit with a // current second list's digit int mul = first_ptr->data * second_ptr->data + carry; // Assigne the product to corresponding Node // of result result_ptr2->data += mul % 10; // now resultant Node itself can have more // than 1 digit carry = mul / 10 + result_ptr2->data / 10; result_ptr2->data = result_ptr2->data % 10; first_ptr = first_ptr->next; result_ptr2 = result_ptr2->next; } // if carry is remaining from last multiplication if (carry > 0) { result_ptr2->data += carry; } result_ptr1 = result_ptr1->next; second_ptr = second_ptr->next; } // reverse the result_list as it was populated // from last Node reverse(&result); reverse(&first); reverse(&second); // remove if there are zeros at starting while (result->data == 0) { struct Node* temp = result; result = result->next; free(temp); } // Return head of multiplication list return result; } // 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 << endl; } // Driver program to test above function int main(void) { struct Node* first = NULL; struct Node* second = NULL; // create first list 9->9->9->4->6->9 push(&first, 9); push(&first, 6); push(&first, 4); push(&first, 9); push(&first, 9); push(&first, 9); cout<<"First List is: "; printList(first); // create second list 9->9->8->4->9 push(&second, 9); push(&second, 4); push(&second, 8); push(&second, 9); push(&second, 9); cout<<"Second List is: "; printList(second); // Multiply the two lists and see result struct Node* result = multiplyTwoLists(first, second); cout << "Resultant list is: "; printList(result); return 0; } // This code is contributed by SHUBHAMSINGH10 |
C
// C program to Multiply two numbers// represented as linked lists#include <stdio.h>#include <stdlib.h> // Linked list Nodestruct Node { int data; struct Node* next;}; // Function to create a new Node// with given datastruct 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 Listvoid 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;} // Function to reverse the linked list and return// its lengthint reverse(struct Node** head_ref){ struct Node* prev = NULL; struct Node* current = *head_ref; struct Node* next; int len = 0; while (current != NULL) { len++; next = current->next; current->next = prev; prev = current; current = next; } *head_ref = prev; return len;} // Function to make an empty linked list of// given sizestruct Node* make_empty_list(int size){ struct Node* head = NULL; while (size--) push(&head, 0); return head;} // Multiply contents of two linked lists => store// in another list and return its headstruct Node* multiplyTwoLists(struct Node* first, struct Node* second){ // reverse the lists to muliply from end // m and n lengths of linked lists to make // and empty list int m = reverse(&first), n = reverse(&second); // make a list that will contain the result // of multiplication. // m+n+1 can be max size of the list struct Node* result = make_empty_list(m + n + 1); // pointers for traverse linked lists and also // to reverse them after struct Node *second_ptr = second, *result_ptr1 = result, *result_ptr2, *first_ptr; // multiply each Node of second list with first while (second_ptr) { int carry = 0; // each time we start from the next of Node // from which we started last time result_ptr2 = result_ptr1; first_ptr = first; while (first_ptr) { // multiply a first list's digit with a // current second list's digit int mul = first_ptr->data * second_ptr->data + carry; // Assigne the product to corresponding Node // of result result_ptr2->data += mul % 10; // now resultant Node itself can have more // than 1 digit carry = mul / 10 + result_ptr2->data / 10; result_ptr2->data = result_ptr2->data % 10; first_ptr = first_ptr->next; result_ptr2 = result_ptr2->next; } // if carry is remaining from last multiplication if (carry > 0) { result_ptr2->data += carry; } result_ptr1 = result_ptr1->next; second_ptr = second_ptr->next; } // reverse the result_list as it was populated // from last Node reverse(&result); reverse(&first); reverse(&second); // remove if there are zeros at starting while (result->data == 0) { struct Node* temp = result; result = result->next; free(temp); } // Return head of multiplication list return result;} // A utility function to print a linked listvoid printList(struct Node* Node){ while (Node != NULL) { printf("%d", Node->data); if (Node->next) printf("->"); Node = Node->next; } printf("\n");} // Driver program to test above functionint main(void){ struct Node* first = NULL; struct Node* second = NULL; // create first list 9->9->9->4->6->9 push(&first, 9); push(&first, 6); push(&first, 4); push(&first, 9); push(&first, 9); push(&first, 9); printf("First List is: "); printList(first); // create second list 9->9->8->4->9 push(&second, 9); push(&second, 4); push(&second, 8); push(&second, 9); push(&second, 9); printf("Second List is: "); printList(second); // Multiply the two lists and see result struct Node* result = multiplyTwoLists(first, second); printf("Resultant list is: "); printList(result); return 0;} |
Python3
# Python3 program to multiply two numbers # represented as linked lists # Node class class Node: # Function to initialize the node object def __init__(self, data): self.data = data self.next = None # Linked List Classclass LinkedList: # Function to initialize the # LinkedList class. def __init__(self): # Initialize head as None self.head = None # This function insert a new node at the # beginning of the linked list def push(self, new_data): # Create a new Node new_node = Node(new_data) # Make next of new Node as head new_node.next = self.head # Move the head to point to new Node self.head = new_node # Method to print the linked list def printList(self): # Object to iterate # the list ptr = self.head # Loop to iterate list while(ptr != None): print(ptr.data, '->', end = '') # Moving the iterating object # to next node ptr = ptr.next print() # Function to reverse the linked# list and return its lengthdef reverse(head_ref): # Initialising prev and current # at None and starting node # respectively. prev = None current = head_ref.head Len = 0 # Loop to reverse the link # of each node in the list while(current != None): Len += 1 Next = current.next current.next = prev prev = current current = Next # Assigning new starting object # to main head object. head_ref.head = prev # Returning the lemgth of # linked list. return Len # Function to define an empty# linked list of given size and# each element as zero.def make_empty_list(size): head = LinkedList() while(size): head.push(0) size -= 1 # Returns the head object. return head # Multiply contents of two linked# list store it in other list and# return its head.def multiplyTwoLists(first, second): # Reverse the list to multiply from # end m and n lengths of linked list # to make and empty list m = reverse(first) n = reverse(second) # Make a list that will contain the # result of multiplication. # m+n+1 can be max size of the list. result = make_empty_list(m + n + 1) # Objects for traverse linked list # and also to reverse them after. second_ptr = second.head result_ptr1 = result.head # Multiply each node of second # list with first. while(second_ptr != None): carry = 0 # Each time we start from next # node from which we started last # time. result_ptr2 = result_ptr1 first_ptr = first.head while(first_ptr != None): # Multiply a first list's digit # with a current second list's digit. mul = ((first_ptr.data) * (second_ptr.data) + carry) # Assign the product to corresponding # node of result. result_ptr2.data += mul % 10 # Now resultant node itself can have # more then one digit. carry = ((mul // 10) + (result_ptr2.data // 10)) result_ptr2.data = result_ptr2.data % 10 first_ptr = first_ptr.next result_ptr2 = result_ptr2.next # If carry is remaining from # last multiplication if(carry > 0): result_ptr2.data += carry result_ptr1 = result_ptr1.next second_ptr = second_ptr.next # Reverse the result_list as it # was populated from last node reverse(result) reverse(first) reverse(second) # Remove starting nodes # containing zeroes. start = result.head while(start.data == 0): result.head = start.next start = start.next # Return the resultant multiplicated # linked list. return result # Driver codeif __name__=='__main__': first = LinkedList() second = LinkedList() # Pushing elements at start of # first linked list. first.push(9) first.push(6) first.push(4) first.push(9) first.push(9) first.push(9) # Printing first linked list print("First list is: ", end = '') first.printList() # Pushing elements at start of # second linked list. second.push(9) second.push(4) second.push(8) second.push(9) second.push(9) # Printing second linked list. print("Second List is: ", end = '') second.printList() # Multiply two linked list and # print the result. result = multiplyTwoLists(first, second) print("Resultant list is: ", end = '') result.printList() # This code is contributed by Amit Mangal |
Output:
First List is: 9->9->9->4->6->9 Second List is: 9->9->8->4->9 Resultant list is: 9->9->7->9->5->9->8->0->1->8->1
Note: we can take care of resultant node that can have more than 1 digit outside the loop just traverse the result list and add carry to next digit before reversing.
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