用C语言实现多项式的相加

在C语言中，你可以使用结构体来表示一个多项式，并通过链表的方式来存储多项式的系数和对应的次数。下面是一个简单的多项式相加的实现示例：

#include <stdio.h>
#include <stdlib.h>

typedef struct Term {
    int coefficient; // 系数
    int exponent;     // 次数
} Term;

typedef struct Polynomial {
    Term* terms;
    int count;
} Polynomial;

// 创建一个新的多项式项
Term* create_term(int coefficient, int exponent) {
    Term* new_term = (Term*)malloc(sizeof(Term));
    if (new_term != NULL) {
        new_term->coefficient = coefficient;
        new_term->exponent = exponent;
    }
    return new_term;
}

// 初始化多项式
Polynomial* create_polynomial() {
    Polynomial* poly = (Polynomial*)malloc(sizeof(Polynomial));
    if (poly != NULL) {
        poly->terms = NULL;
        poly->count = 0;
    }
    return poly;
}

// 添加多项式项到链表
void add_term(Polynomial* poly, int coefficient, int exponent) {
    if (poly == NULL || poly->count == 0) {
        poly->terms = create_term(coefficient, exponent);
        poly->count++;
    } else {
        Term* last = poly->terms;
        while (last->next != NULL && last->exponent > exponent) {
            last = last->next;
        }
        if (last->exponent == exponent) {
            last->coefficient += coefficient;
        } else {
            last->next = create_term(coefficient, exponent);
            poly->count++;
        }
    }
}

// 相加两个多项式
Polynomial* add_poly(Polynomial* poly1, Polynomial* poly2) {
    Polynomial* result = create_polynomial();
    if (poly1 != NULL && poly2 != NULL) {
        for (int i = 0; i < poly1->count; i++) {
            add_term(result, poly1->terms[i].coefficient, poly1->terms[i].exponent);
        }
        for (int i = 0; i < poly2->count; i++) {
            add_term(result, poly2->terms[i].coefficient, poly2->terms[i].exponent);
        }
    }
    return result;
}

// 打印多项式
void print_polynomial(Polynomial* poly) {
    printf("Polynomial:\n");
    if (poly->terms == NULL) {
        printf("Constant term: %d\n", poly->terms[0].coefficient); // 如果只有一个常数项
    } else {
        for (Term* term = poly->terms; term != NULL; term = term->next) {
            printf("%d * x^%d + ", term->coefficient, term->exponent);
        }
        printf("\n"); // 最后打印换行
    }
}

int main() {
    Polynomial* p1 = create_polynomial();
    Polynomial* p2 = create_polynomial();

    // 添加多项式项
    add_term(p1, 2, 1);
    add_term(p1, -1, 2);
    add_term(p2, 3, 0);

    Polynomial* sum = add_poly(p1, p2);
    print_polynomial(sum);

    free(p1->terms);
    free(p1);
    free(p2->terms);
    free(p2);
    free(sum->terms);
    free(sum);

    return 0;
}

在这个例子中，我们首先创建了两个`Polynomial`结构体实例，并分别添加了一些项。然后通过`add_poly`函数将它们相加，最后打印出结果。