编程实现若干个多项式相乘
时间: 2024-05-04 08:21:40 浏览: 10
可以使用Python语言实现多项式相乘。以下是一个简单的例子,假设有两个多项式A和B,每个多项式用一个列表表示,列表中存储了多项式中各项的系数,例如A=[1,2,3]表示多项式A为3x^2+2x+1。
```python
def poly_mul(A, B):
m, n = len(A), len(B)
res = [0] * (m + n - 1)
for i in range(m):
for j in range(n):
res[i + j] += A[i] * B[j]
return res
```
在这个函数中,我们首先计算出两个多项式的长度m和n,并将结果存储在一个长度为m+n-1的列表res中。然后使用两个嵌套的循环,遍历A和B中的所有项,并将它们的乘积加到res中相应的位置。最后返回res即可得到相乘后的多项式。
例如,如果我们想计算多项式A=[1,2,3]和B=[4,5,6]的乘积,可以调用poly_mul(A,B)函数,得到结果[4, 13, 28, 27, 18],表示多项式A*B为18x^4+27x^3+28x^2+13x+4。
相关问题
编程实现若干个多项式相乘。多项式的输入输出格式为:系数在前,指数在后,各项按指数递增排列,每个多项式输入时以两个0结束。系数为0的项不输出。
以下为C++的实现示例,具体思路是将每个多项式的系数与指数存储在一个数组中,然后对多项式进行相乘并输出结果。
```cpp
#include <iostream>
using namespace std;
const int MAXN = 1005; // 多项式最大项数
int a[MAXN], b[MAXN], c[MAXN]; // 存储多项式的系数与指数
void multiply(int n, int m) {
for (int i = 0; i <= n; i++) {
for (int j = 0; j <= m; j++) {
c[i+j] += a[i] * b[j]; // 将多项式相乘的结果存储在数组c中
}
}
}
int main() {
int n, m;
cin >> n >> m;
while (n != 0 || m != 0) {
for (int i = 0; i <= n; i++) {
cin >> a[i];
}
for (int i = 0; i <= m; i++) {
cin >> b[i];
}
multiply(n, m); // 相乘
int flag = 0; // 判断输出格式
for (int i = 0; i <= n + m; i++) {
if (c[i] != 0) { // 系数不为0
if (flag == 1) {
cout << " ";
}
cout << c[i];
flag = 1;
}
c[i] = 0; // 清空数组c
}
cout << endl;
cin >> n >> m;
}
return 0;
}
```
注意,多项式的输入格式为:系数在前,指数在后,各项按指数递增排列,每个多项式输入时以两个0结束。系数为0的项不输出。
链表实现两个多项式相乘c语言
链表是一种常用的数据结构,可以用来实现多项式的存储和操作。在C语言中,可以通过定义一个结构体来表示多项式的每一项,然后使用链表将这些项连接起来。
首先,我们可以定义一个结构体来表示多项式的每一项,包括系数和指数:
```c
struct Node {
int coefficient; // 系数
int exponent; // 指数
struct Node* next; // 指向下一个节点的指针
};
```
然后,我们可以定义一个函数来创建一个空的多项式链表:
```c
struct Node* createPolynomial() {
return NULL;
}
```
接下来,我们可以定义一个函数来向多项式链表中插入一项:
```c
void insertTerm(struct Node** polynomial, int coefficient, int exponent) {
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
newNode->coefficient = coefficient;
newNode->exponent = exponent;
newNode->next = NULL;
if (*polynomial == NULL) {
*polynomial = newNode;
} else {
struct Node* current = *polynomial;
while (current->next != NULL) {
current = current->next;
}
current->next = newNode;
}
}
```
然后,我们可以定义一个函数来打印多项式链表:
```c
void printPolynomial(struct Node* polynomial) {
struct Node* current = polynomial;
while (current != NULL) {
printf("%dx^%d ", current->coefficient, current->exponent);
current = current->next;
}
printf("\n");
}
```
最后,我们可以定义一个函数来实现两个多项式的相乘:
```c
struct Node* multiplyPolynomials(struct Node* poly1, struct Node* poly2) {
struct Node* result = createPolynomial();
struct Node* current1 = poly1;
while (current1 != NULL) {
struct Node* current2 = poly2;
while (current2 != NULL) {
int coefficient = current1->coefficient * current2->coefficient;
int exponent = current1->exponent + current2->exponent;
insertTerm(&result, coefficient, exponent);
current2 = current2->next;
}
current1 = current1->next;
}
return result;
}
```
使用上述定义的函数,我们可以实现两个多项式的相乘。以下是一个示例程序:
```c
#include <stdio.h>
#include <stdlib.h>
struct Node {
int coefficient;
int exponent;
struct Node* next;
};
struct Node* createPolynomial() {
return NULL;
}
void insertTerm(struct Node** polynomial, int coefficient, int exponent) {
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
newNode->coefficient = coefficient;
newNode->exponent = exponent;
newNode->next = NULL;
if (*polynomial == NULL) {
*polynomial = newNode;
} else {
struct Node* current = *polynomial;
while (current->next != NULL) {
current = current->next;
}
current->next = newNode;
}
}
void printPolynomial(struct Node* polynomial) {
struct Node* current = polynomial;
while (current != NULL) {
printf("%dx^%d ", current->coefficient, current->exponent);
current = current->next;
}
printf("\n");
}
struct Node* multiplyPolynomials(struct Node* poly1, struct Node* poly2) {
struct Node* result = createPolynomial();
struct Node* current1 = poly1;
while (current1 != NULL) {
struct Node* current2 = poly2;
while (current2 != NULL) {
int coefficient = current1->coefficient * current2->coefficient;
int exponent = current1->exponent + current2->exponent;
insertTerm(&result, coefficient, exponent);
current2 = current2->next;
}
current1 = current1->next;
}
return result;
}
int main() {
struct Node* poly1 = createPolynomial();
insertTerm(&poly1, 2, 2);
insertTerm(&poly1, 3, 1);
insertTerm(&poly1, 4, 0);
struct Node* poly2 = createPolynomial();
insertTerm(&poly2, 5, 1);
insertTerm(&poly2, 6, 0);
printf("多项式1:");
printPolynomial(poly1);
printf("多项式2:");
printPolynomial(poly2);
struct Node* result = multiplyPolynomials(poly1, poly2);
printf("相乘结果:");
printPolynomial(result);
return 0;
}
```
希望以上代码能够帮助你理解如何使用链表来实现两个多项式的相乘。如果有任何疑问,请随时提出。