用C语言实现一元多项式加减法与乘法完整代码

在C语言中，可以使用结构体和指针来实现一元多项式的加减法与乘法。这里是一个简化的例子，我们首先定义一个结构体`Polynomial`表示一个多项式项：

#include <stdio.h>
typedef struct {
    double coefficient; // 系数
    int exponent;       // 指数
} Term;

// 单个项的加法
Term addTerms(Term a, Term b) {
    if (a.exponent == b.exponent)
        return (Term){a.coefficient + b.coefficient, a.exponent};
    else if (a.exponent > b.exponent)
        return a;
    else
        return b;
}

// 单个项的减法
Term subtractTerms(Term a, Term b) {
    if (a.exponent == b.exponent)
        return (Term){a.coefficient - b.coefficient, a.exponent};
    else if (a.exponent > b.exponent)
        return a;
    else
        return (Term){b.coefficient, b.exponent};
}

// 两个多项式的加法
void addPolynomials(Term* result, Term* poly1, Term* poly2, int size1, int size2) {
    for (int i = 0; i < size1; ++i) {
        *result++ = addTerms(poly1[i], (size2 <= i) ? poly2[i] : (Term){0, 0});
    }
    while (size2--) {
        *result++ = poly2[size2];
    }
}

// 两个多项式的减法
void subtractPolynomials(Term* result, Term* poly1, Term* poly2, int size1, int size2) {
    for (int i = 0; i < size1 && i < size2; ++i) {
        *result++ = subtractTerms(poly1[i], poly2[i]);
    }
    for (int i = size1; i < size2; ++i) {
        *result++ = poly2[i];
    }
}

// 两个多项式的乘法（笛卡尔积）
void multiplyPolynomials(Term** result, Term* poly1, Term* poly2, int size1, int size2) {
    int newSize = size1 + size2 - 1;
    Term* tempResult = malloc(newSize * sizeof(Term));
    for (int i = 0; i < size1; ++i) {
        for (int j = 0; j < size2; ++j) {
            Term product = {poly1[i].coefficient * poly2[j].coefficient,
                            poly1[i].exponent + poly2[j].exponent};
            tempResult[newSize - 1 - (i + j)] = product;
        }
    }
    *result = tempResult;
}

int main() {
    Term poly1[] = {{2, 1}, {1, 2}, {0, 3}};
    Term poly2[] = {{3, 0}, {-1, 1}};
    int size1 = sizeof(poly1) / sizeof(poly1[0]);
    int size2 = sizeof(poly2) / sizeof(poly2[0]);

    Term* sum = malloc(size1 + size2 * sizeof(Term)); // 加法结果预留空间
    addPolynomials(sum, poly1, poly2, size1, size2);
    printf("Sum: ");
    for (int i = 0; i < size1 + size2; ++i) {
        printf("%.2f*x^%d ", sum[i].coefficient, sum[i].exponent);
    }
    printf("\n");

    Term* diff = malloc(size1 + size2 * sizeof(Term)); // 减法结果预留空间
    subtractPolynomials(diff, poly1, poly2, size1, size2);
    printf("Difference: ");
    for (int i = 0; i < size1 + size2; ++i) {
        printf("%.2f*x^%d ", diff[i].coefficient, diff[i].exponent);
    }
    printf("\n");

    Term** prod = malloc(size1 * size2 * sizeof(Term*)); // 乘法结果需要动态分配数组
    multiplyPolynomials(prod, poly1, poly2, size1, size2);
    printf("Product: ");
    for (int i = 0; i < newSize; ++i) {
        printf("%.2f*x^%d ", prod[i]->coefficient, prod[i]->exponent);
    }
    printf("\n");

    free(sum);
    free(diff);
    if (prod != NULL) {
        free(*prod);
        free(prod);
    }

    return 0;
}

这段代码实现了多项式的一维数组形式，并完成了基本的加、减、乘操作。注意，乘法的结果需要额外的空间存储，所以返回的是指向新生成多项式的指针。