Dados dos polinomios representados por dos arrays, escribe una función que suma dos polinomios dados.
Ejemplo:
Input: A[] = {5, 0, 10, 6}
B[] = {1, 2, 4}
Output: sum[] = {6, 2, 14, 6}
The first input array represents "5 + 0x^1 + 10x^2 + 6x^3"
The second array represents "1 + 2x^1 + 4x^2"
And Output is "6 + 2x^1 + 14x^2 + 6x^3"
Recomendamos encarecidamente minimizar su navegador y probarlo usted mismo primero.
La suma es más sencilla que la multiplicación de polinomios . Inicializamos el resultado como uno de los dos polinomios, luego recorremos el otro polinomio y sumamos todos los términos al resultado.
add(A[0..m-1], B[0..n01])
1) Create a sum array sum[] of size equal to maximum of 'm' and 'n'
2) Copy A[] to sum[].
3) Traverse array B[] and do following for every element B[i]
sum[i] = sum[i] + B[i]
4) Return sum[].
La siguiente es la implementación del algoritmo anterior.
C++
// Simple C++ program to add two polynomials
#include <iostream>
using namespace std;
// A utility function to return maximum of two integers
int max(int m, int n) { return (m > n)? m: n; }
// A[] represents coefficients of first polynomial
// B[] represents coefficients of second polynomial
// m and n are sizes of A[] and B[] respectively
int *add(int A[], int B[], int m, int n)
{
int size = max(m, n);
int *sum = new int[size];
// Initialize the product polynomial
for (int i = 0; i<m; i++)
sum[i] = A[i];
// Take ever term of first polynomial
for (int i=0; i<n; i++)
sum[i] += B[i];
return sum;
}
// A utility function to print a polynomial
void printPoly(int poly[], int n)
{
for (int i=0; i<n; i++)
{
cout << poly[i];
if (i != 0)
cout << "x^" << i ;
if (i != n-1)
cout << " + ";
}
}
// Driver program to test above functions
int main()
{
// The following array represents polynomial 5 + 10x^2 + 6x^3
int A[] = {5, 0, 10, 6};
// The following array represents polynomial 1 + 2x + 4x^2
int B[] = {1, 2, 4};
int m = sizeof(A)/sizeof(A[0]);
int n = sizeof(B)/sizeof(B[0]);
cout << "First polynomial is \n";
printPoly(A, m);
cout << "\nSecond polynomial is \n";
printPoly(B, n);
int *sum = add(A, B, m, n);
int size = max(m, n);
cout << "\nsum polynomial is \n";
printPoly(sum, size);
return 0;
}
Java
// Java program to add two polynomials
class GFG {
// A utility function to return maximum of two integers
static int max(int m, int n) {
return (m > n) ? m : n;
}
// A[] represents coefficients of first polynomial
// B[] represents coefficients of second polynomial
// m and n are sizes of A[] and B[] respectively
static int[] add(int A[], int B[], int m, int n) {
int size = max(m, n);
int sum[] = new int[size];
// Initialize the product polynomial
for (int i = 0; i < m; i++) {
sum[i] = A[i];
}
// Take ever term of first polynomial
for (int i = 0; i < n; i++) {
sum[i] += B[i];
}
return sum;
}
// A utility function to print a polynomial
static void printPoly(int poly[], int n) {
for (int i = 0; i < n; i++) {
System.out.print(poly[i]);
if (i != 0) {
System.out.print("x^" + i);
}
if (i != n - 1) {
System.out.print(" + ");
}
}
}
// Driver program to test above functions
public static void main(String[] args) {
// The following array represents polynomial 5 + 10x^2 + 6x^3
int A[] = {5, 0, 10, 6};
// The following array represents polynomial 1 + 2x + 4x^2
int B[] = {1, 2, 4};
int m = A.length;
int n = B.length;
System.out.println("First polynomial is");
printPoly(A, m);
System.out.println("\nSecond polynomial is");
printPoly(B, n);
int sum[] = add(A, B, m, n);
int size = max(m, n);
System.out.println("\nsum polynomial is");
printPoly(sum, size);
}
}
Python3
# Simple Python 3 program to add two
# polynomials
# A utility function to return maximum
# of two integers
# A[] represents coefficients of first polynomial
# B[] represents coefficients of second polynomial
# m and n are sizes of A[] and B[] respectively
def add(A, B, m, n):
size = max(m, n);
sum = [0 for i in range(size)]
# Initialize the product polynomial
for i in range(0, m, 1):
sum[i] = A[i]
# Take ever term of first polynomial
for i in range(n):
sum[i] += B[i]
return sum
# A utility function to print a polynomial
def printPoly(poly, n):
for i in range(n):
print(poly[i], end = "")
if (i != 0):
print("x^", i, end = "")
if (i != n - 1):
print(" + ", end = "")
# Driver Code
if __name__ == '__main__':
# The following array represents
# polynomial 5 + 10x^2 + 6x^3
A = [5, 0, 10, 6]
# The following array represents
# polynomial 1 + 2x + 4x^2
B = [1, 2, 4]
m = len(A)
n = len(B)
print("First polynomial is")
printPoly(A, m)
print("\n", end = "")
print("Second polynomial is")
printPoly(B, n)
print("\n", end = "")
sum = add(A, B, m, n)
size = max(m, n)
print("sum polynomial is")
printPoly(sum, size)
# This code is contributed by
# Sahil_Shelangia
C#
// C# program to add two polynomials
using System;
class GFG {
// A utility function to return maximum of two integers
static int max(int m, int n)
{
return (m > n) ? m : n;
}
// A[] represents coefficients of first polynomial
// B[] represents coefficients of second polynomial
// m and n are sizes of A[] and B[] respectively
static int[] add(int[] A, int[] B, int m, int n)
{
int size = max(m, n);
int[] sum = new int[size];
// Initialize the product polynomial
for (int i = 0; i < m; i++)
{
sum[i] = A[i];
}
// Take ever term of first polynomial
for (int i = 0; i < n; i++)
{
sum[i] += B[i];
}
return sum;
}
// A utility function to print a polynomial
static void printPoly(int[] poly, int n)
{
for (int i = 0; i < n; i++)
{
Console.Write(poly[i]);
if (i != 0)
{
Console.Write("x^" + i);
}
if (i != n - 1)
{
Console.Write(" + ");
}
}
}
// Driver code
public static void Main()
{
// The following array represents
// polynomial 5 + 10x^2 + 6x^3
int[] A = {5, 0, 10, 6};
// The following array represents
// polynomial 1 + 2x + 4x^2
int[] B = {1, 2, 4};
int m = A.Length;
int n = B.Length;
Console.WriteLine("First polynomial is");
printPoly(A, m);
Console.WriteLine("\nSecond polynomial is");
printPoly(B, n);
int[] sum = add(A, B, m, n);
int size = max(m, n);
Console.WriteLine("\nsum polynomial is");
printPoly(sum, size);
}
}
//This Code is Contributed
// by Mukul Singh
PHP
<?php
// Simple PHP program to add two polynomials
// A[] represents coefficients of first polynomial
// B[] represents coefficients of second polynomial
// m and n are sizes of A[] and B[] respectively
function add($A, $B, $m, $n)
{
$size = max($m, $n);
$sum = array_fill(0, $size, 0);
// Initialize the product polynomial
for ($i = 0; $i < $m; $i++)
$sum[$i] = $A[$i];
// Take ever term of first polynomial
for ($i = 0; $i < $n; $i++)
$sum[$i] += $B[$i];
return $sum;
}
// A utility function to print a polynomial
function printPoly($poly, $n)
{
for ($i = 0; $i < $n; $i++)
{
echo $poly[$i];
if ($i != 0)
echo "x^" . $i;
if ($i != $n - 1)
echo " + ";
}
}
// Driver Code
// The following array represents
// polynomial 5 + 10x^2 + 6x^3
$A = array(5, 0, 10, 6);
// The following array represents
// polynomial 1 + 2x + 4x^2
$B = array(1, 2, 4);
$m = count($A);
$n = count($B);
echo "First polynomial is \n";
printPoly($A, $m);
echo "\nSecond polynomial is \n";
printPoly($B, $n);
$sum = add($A, $B, $m, $n);
$size = max($m, $n);
echo "\nsum polynomial is \n";
printPoly($sum, $size);
// This code is contributed by chandan_jnu
?>
Javascript
<script>
// Simple JavaScript program to add two
// polynomials
// A utility function to return maximum
// of two integers
// A[] represents coefficients of first polynomial
// B[] represents coefficients of second polynomial
// m and n are sizes of A[] and B[] respectively
function add(A, B, m, n){
let size = Math.max(m, n);
var sum = [];
for (var i = 0; i < 10; i++) sum[i] = 0;
// Initialize the product polynomial
for(let i = 0;i<m;i++){
sum[i] = A[i];
}
// Take ever term of first polynomial
for (let i = 0;i<n;i++){
sum[i] += B[i];
}
return sum;
}
// A utility function to print a polynomial
function printPoly(poly, n){
let ans = '';
for(let i = 0;i<n;i++){
ans += poly[i];
if (i != 0){
ans +="x^ ";
ans +=i;
}
if (i != n - 1){
ans += " + ";
}
}
document.write(ans);
}
// Driver Code
// The following array represents
// polynomial 5 + 10x^2 + 6x^3
let A = [5, 0, 10, 6];
// The following array represents
// polynomial 1 + 2x + 4x^2
let B = [1, 2, 4];
let m = A.length;
let n = B.length;
document.write("First polynomial is" + "</br>");
printPoly(A, m);
document.write("</br>");
document.write("Second polynomial is" + "</br>");
printPoly(B, n);
let sum = add(A, B, m, n);
let size = Math.max(m, n);
document.write("</br>");
document.write("sum polynomial is" + "</br>");
printPoly(sum, size);
</script>
Producción:
First polynomial is 5 + 0x^1 + 10x^2 + 6x^3 Second polynomial is 1 + 2x^1 + 4x^2 Sum polynomial is 6 + 2x^1 + 14x^2 + 6x^3
La complejidad temporal del algoritmo y programa anterior es O(m+n) donde m y n son órdenes de dos polinomios dados.
Espacio auxiliar: O(max(m, n))
Este artículo es una contribución de Harsh. Escriba comentarios si encuentra algo incorrecto o si desea compartir más información sobre el tema tratado anteriormente.
Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA