Dados dos números representados por listas enlazadas, escribe una función que devuelva el encabezado de la nueva lista enlazada que representa el número que es el producto de esos números.
Ejemplos:
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
Ya hemos discutido una solución en la publicación a continuación.
Multiplica dos números representados por listas enlazadas
La solución discutida anteriormente almacena el resultado en un número entero. Aquí almacenamos el resultado en una tercera lista para que se puedan manejar números grandes.
¿Recuerdas la multiplicación de la vieja escuela? imitamos ese proceso. En papel, tomamos el último dígito de un número y lo multiplicamos por el segundo número y escribimos el producto. Ahora deje la última columna y de la misma manera cada dígito de un número se multiplica con cada dígito de otro número y cada vez que el resultado se escribe dejando una última columna. luego agregue estas columnas que forman el número. Ahora asuma estas columnas como Nodes de la lista enlazada resultante. Hacemos la lista enlazada resultante de forma inversa.
Algoritmo:
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
Implementación:
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 multiply 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;
// Assign 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 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 multiply 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;
// Assign 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) {
printf("%d", Node->data);
if (Node->next)
printf("->");
Node = Node->next;
}
printf("\n");
}
// 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);
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 Class
class 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 length
def 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 length 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 than 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 code
if __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
Producción:
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
Nota: podemos ocuparnos del Node resultante que puede tener más de 1 dígito fuera del ciclo, simplemente recorra la lista de resultados y agregue el acarreo al siguiente dígito antes de invertir.
Publicación traducida automáticamente
Artículo escrito por Shubham_Raghuwanshi y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA