c语言写“. 求两个多项式的和并输出;求两个多项式的差并输出;4. 求两个多项式的积并输出;思考: 如何求两个多项式的商?
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数据结构(C语言)用单链表存储一元多项式并实现两个多项式的相加运算.doc
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在C语言中,处理多项式通常涉及到结构体、数组以及一些基本数学运算。以下是简单的示例,演示如何实现多项式的加法、减法和乘法:
1. **多项式加法**:
```c
typedef struct {
int coef[100]; // 多项式的系数数组
int exp; // 最高指数
} Polynomial;
void add_poly(Polynomial *poly1, Polynomial *poly2) {
Polynomial sum;
int i = min(poly1->exp, poly2->exp);
for (i = 0; i <= poly1->exp && i <= poly2->exp; i++) {
sum.coef[i] = poly1->coef[i] + poly2->coef[i];
}
if (poly1->exp > poly2->exp)
sum.exp = poly1->exp;
else if (poly2->exp > poly1->exp)
sum.exp = poly2->exp;
else
sum.exp++;
*poly1 = sum;
}
// 使用示例
Polynomial p1 = {...}, p2 = {...};
add_poly(&p1, &p2);
```
2. **多项式减法**:
```c
void subtract_poly(Polynomial *poly1, Polynomial *poly2) {
Polynomial diff;
int i = min(poly1->exp, poly2->exp);
for (i = 0; i <= poly1->exp && i <= poly2->exp; i++) {
diff.coef[i] = poly1->coef[i] - poly2->coef[i];
}
if (poly1->exp > poly2->exp)
diff.exp = poly1->exp;
else if (poly2->exp > poly1->exp)
diff.exp = poly2->exp;
else
diff.exp++;
*poly1 = diff;
}
```
3. **多项式乘法**:
```c
void multiply_poly(Polynomial *poly1, Polynomial *poly2, Polynomial *result) {
result->exp = poly1->exp + poly2->exp;
int len = 1 << (poly1->exp + poly2->exp); // 计算结果长度
result->coef = malloc(len * sizeof(result->coef[0]));
for (int i = 0; i < len; ++i) {
result->coef[i] = 0;
for (int j = 0; j <= poly1->exp; ++j) {
for (int k = 0; k <= poly2->exp; ++k) {
if ((i - j - k) >= 0)
result->coef[i] += poly1->coef[j] * poly2->coef[k] * pow(10, (i - j - k));
}
}
}
}
// 示例
Polynomial p3;
multiply_poly(&p1, &p2, &p3);
```
**关于多项式除法**,由于多项式除法涉及到更复杂的算法,比如长除法或拉格朗日插值,直接在C语言基础结构上实现可能会变得复杂。在实际应用中,你可能需要利用库函数或者编写专门的算法来处理这个任务,例如在数值计算库如GMP或MPFR中就有相关的支持。
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