برنامه ضرب چند جمله ای ها — راهنمای کاربردی

1// Simple C++ program to multiply two polynomials 
2#include <iostream> 
3using namespace std; 
4  
5// A[] represents coefficients of first polynomial 
6// B[] represents coefficients of second polynomial 
7// m and n are sizes of A[] and B[] respectively 
8int *multiply(int A[], int B[], int m, int n) 
9{ 
10   int *prod = new int[m+n-1]; 
11  
12   // Initialize the porduct polynomial 
13   for (int i = 0; i<m+n-1; i++) 
14     prod[i] = 0; 
15  
16   // Multiply two polynomials term by term 
17  
18   // Take ever term of first polynomial 
19   for (int i=0; i<m; i++) 
20   { 
21     // Multiply the current term of first polynomial 
22     // with every term of second polynomial. 
23     for (int j=0; j<n; j++) 
24         prod[i+j] += A[i]*B[j]; 
25   } 
26  
27   return prod; 
28} 
29  
30// A utility function to print a polynomial 
31void printPoly(int poly[], int n) 
32{ 
33    for (int i=0; i<n; i++) 
34    { 
35       cout << poly[i]; 
36       if (i != 0) 
37        cout << "x^" << i ; 
38       if (i != n-1) 
39       cout << " + "; 
40    } 
41} 
42  
43// Driver program to test above functions 
44int main() 
45{ 
46    // The following array represents polynomial 5 + 10x^2 + 6x^3 
47    int A[] = {5, 0, 10, 6}; 
48  
49    // The following array represents polynomial 1 + 2x + 4x^2 
50    int B[] = {1, 2, 4}; 
51    int m = sizeof(A)/sizeof(A[0]); 
52    int n = sizeof(B)/sizeof(B[0]); 
53  
54    cout << "First polynomial is n"; 
55    printPoly(A, m); 
56    cout << "nSecond polynomial is n"; 
57    printPoly(B, n); 
58  
59    int *prod = multiply(A, B, m, n); 
60  
61    cout << "nProduct polynomial is n"; 
62    printPoly(prod, m+n-1); 
63  
64    return 0; 
65}

1// Java program to multiply two polynomials 
2class GFG 
3{ 
4  
5    // A[] represents coefficients  
6    // of first polynomial 
7    // B[] represents coefficients  
8    // of second polynomial 
9    // m and n are sizes of A[] and B[] respectively 
10    static int[] multiply(int A[], int B[],  
11                            int m, int n)  
12    { 
13        int[] prod = new int[m + n - 1]; 
14  
15        // Initialize the porduct polynomial 
16        for (int i = 0; i < m + n - 1; i++)  
17        { 
18            prod[i] = 0; 
19        } 
20  
21        // Multiply two polynomials term by term 
22        // Take ever term of first polynomial 
23        for (int i = 0; i < m; i++)  
24        { 
25            // Multiply the current term of first polynomial 
26            // with every term of second polynomial. 
27            for (int j = 0; j < n; j++)  
28            { 
29                prod[i + j] += A[i] * B[j]; 
30            } 
31        } 
32  
33        return prod; 
34    } 
35  
36    // A utility function to print a polynomial 
37    static void printPoly(int poly[], int n)  
38    { 
39        for (int i = 0; i < n; i++)  
40        { 
41            System.out.print(poly[i]); 
42            if (i != 0)  
43            { 
44                System.out.print("x^" + i); 
45            } 
46            if (i != n - 1)  
47            { 
48                System.out.print(" + "); 
49            } 
50        } 
51    } 
52  
53    // Driver code 
54    public static void main(String[] args) 
55    { 
56        // The following array represents  
57        // polynomial 5 + 10x^2 + 6x^3 
58        int A[] = {5, 0, 10, 6}; 
59  
60        // The following array represents  
61        // polynomial 1 + 2x + 4x^2 
62        int B[] = {1, 2, 4}; 
63        int m = A.length; 
64        int n = B.length; 
65  
66        System.out.println("First polynomial is n"); 
67        printPoly(A, m); 
68        System.out.println("nSecond polynomial is n"); 
69        printPoly(B, n); 
70  
71        int[] prod = multiply(A, B, m, n); 
72  
73        System.out.println("nProduct polynomial is n"); 
74        printPoly(prod, m + n - 1); 
75    } 
76} 
77  
78// This code contributed by Rajput-Ji

1# Simple Python3 program to multiply two polynomials 
2  
3# A[] represents coefficients of first polynomial 
4# B[] represents coefficients of second polynomial 
5# m and n are sizes of A[] and B[] respectively 
6def multiply(A, B, m, n): 
7  
8    prod = [0] * (m + n - 1); 
9      
10    # Multiply two polynomials term by term 
11      
12    # Take ever term of first polynomial 
13    for i in range(m): 
14          
15        # Multiply the current term of first  
16        # polynomial with every term of  
17        # second polynomial. 
18        for j in range(n): 
19            prod[i + j] += A[i] * B[j]; 
20  
21    return prod; 
22  
23# A utility function to print a polynomial 
24def printPoly(poly, n): 
25  
26    for i in range(n): 
27        print(poly[i], end = ""); 
28        if (i != 0): 
29            print("x^", i, end = ""); 
30        if (i != n - 1): 
31            print(" + ", end = ""); 
32  
33# Driver Code 
34  
35# The following array represents 
36# polynomial 5 + 10x^2 + 6x^3 
37A = [5, 0, 10, 6]; 
38  
39# The following array represents  
40# polynomial 1 + 2x + 4x^2 
41B = [1, 2, 4]; 
42m = len(A); 
43n = len(B); 
44  
45print("First polynomial is "); 
46printPoly(A, m); 
47print("\nSecond polynomial is "); 
48printPoly(B, n); 
49  
50prod = multiply(A, B, m, n); 
51  
52print("\nProduct polynomial is "); 
53printPoly(prod, m+n-1); 
54  
55# This code is contributed by chandan_jnu

1// C# program to multiply two polynomials 
2using System; 
3  
4class GFG  
5{ 
6  
7    // A[] represents coefficients  
8    // of first polynomial 
9    // B[] represents coefficients  
10    // of second polynomial 
11    // m and n are sizes of A[]  
12    // and B[] respectively 
13    static int[] multiply(int []A, int []B,  
14                            int m, int n)  
15    { 
16        int[] prod = new int[m + n - 1]; 
17  
18        // Initialize the porduct polynomial 
19        for (int i = 0; i < m + n - 1; i++)  
20        { 
21            prod[i] = 0; 
22        } 
23  
24        // Multiply two polynomials term by term 
25        // Take ever term of first polynomial 
26        for (int i = 0; i < m; i++) 
27        { 
28            // Multiply the current term of first polynomial 
29            // with every term of second polynomial. 
30            for (int j = 0; j < n; j++)  
31            { 
32                prod[i + j] += A[i] * B[j]; 
33            } 
34        } 
35  
36        return prod; 
37    } 
38  
39    // A utility function to print a polynomial 
40    static void printPoly(int []poly, int n) 
41    { 
42        for (int i = 0; i < n; i++) { 
43            Console.Write(poly[i]); 
44            if (i != 0) { 
45                Console.Write("x^" + i); 
46            } 
47            if (i != n - 1) { 
48                Console.Write(" + "); 
49            } 
50        } 
51    } 
52  
53    // Driver code 
54    public static void Main(String[] args) 
55    { 
56          
57        // The following array represents  
58        // polynomial 5 + 10x^2 + 6x^3 
59        int []A = {5, 0, 10, 6}; 
60  
61        // The following array represents 
62        // polynomial 1 + 2x + 4x^2 
63        int []B = {1, 2, 4}; 
64        int m = A.Length; 
65        int n = B.Length; 
66  
67        Console.WriteLine("First polynomial is n"); 
68        printPoly(A, m); 
69        Console.WriteLine("nSecond polynomial is n"); 
70        printPoly(B, n); 
71  
72        int[] prod = multiply(A, B, m, n); 
73  
74        Console.WriteLine("nProduct polynomial is n"); 
75        printPoly(prod, m + n - 1); 
76    } 
77} 
78  
79// This code has been contributed by 29AjayKumar  

1<?php 
2// Simple PHP program to multiply two polynomials 
3  
4// A[] represents coefficients of first polynomial 
5// B[] represents coefficients of second polynomial 
6// m and n are sizes of A[] and B[] respectively 
7function multiply($A, $B, $m, $n) 
8{ 
9    $prod = array_fill(0, $m + $n - 1, 0); 
10      
11    // Multiply two polynomials term by term 
12      
13    // Take ever term of first polynomial 
14    for ($i = 0; $i < $m; $i++) 
15    { 
16        // Multiply the current term of first  
17        // polynomial with every term of  
18        // second polynomial. 
19        for ($j = 0; $j < $n; $j++) 
20            $prod[$i + $j] += $A[$i] * $B[$j]; 
21    } 
22  
23    return $prod; 
24} 
25  
26// A utility function to print a polynomial 
27function printPoly($poly, $n) 
28{ 
29    for ($i = 0; $i < $n; $i++) 
30    { 
31        echo $poly[$i]; 
32        if ($i != 0) 
33            echo "x^" . $i; 
34        if ($i != $n - 1) 
35        echo " + "; 
36    } 
37} 
38  
39// Driver Code 
40  
41// The following array represents 
42// polynomial 5 + 10x^2 + 6x^3 
43$A = array(5, 0, 10, 6); 
44  
45// The following array represents  
46// polynomial 1 + 2x + 4x^2 
47$B = array(1, 2, 4); 
48$m = count($A); 
49$n = count($B); 
50  
51echo "First polynomial is \n"; 
52printPoly($A, $m); 
53echo "\nSecond polynomial is \n"; 
54printPoly($B, $n); 
55  
56$prod = multiply($A, $B, $m, $n); 
57  
58echo "\nProduct polynomial is \n"; 
59printPoly($prod, $m+$n-1); 
60  
61// This code is contributed by chandan_jnu 
62?>

1(a + b)(c + d) = ad + bc + ac + bd

1(ax + b)(cx + d) = acx2 + 
2((a + b)(c + d) , ac , bd )x + bd