C语言实现一元多项式加法：使用链表算法

本题可使用链表实现一元多项式的加法。具体步骤如下：

定义一个结构体，表示多项式中的一项，包含系数和指数。

typedef struct PolyNode {
    int coef;  // 系数
    int expo;  // 指数
    struct PolyNode *next;  // 指向下一项的指针
} PolyNode, *Polynomial;

编写输入函数，用于输入多项式的系数和指数。

Polynomial ReadPoly() {
    Polynomial P, rear, t;
    int coef, expo;

    P = (Polynomial)malloc(sizeof(PolyNode));
    P->next = NULL;
    rear = P;

    int n;
    scanf("%d", &n);

    for (int i = 0; i < n; i++) {
        scanf("%d %d", &coef, &expo);
        t = (Polynomial)malloc(sizeof(PolyNode));
        t->coef = coef;
        t->expo = expo;
        t->next = NULL;
        rear->next = t;
        rear = t;
    }

    return P;
}

编写加法函数，用于将两个多项式相加。

Polynomial Add(Polynomial P1, Polynomial P2) {
    Polynomial P, rear, t;
    P = (Polynomial)malloc(sizeof(PolyNode));
    P->next = NULL;
    rear = P;

    while (P1 && P2) {
        if (P1->expo > P2->expo) {
            t = (Polynomial)malloc(sizeof(PolyNode));
            t->coef = P1->coef;
            t->expo = P1->expo;
            t->next = NULL;
            rear->next = t;
            rear = t;
            P1 = P1->next;
        } else if (P1->expo < P2->expo) {
            t = (Polynomial)malloc(sizeof(PolyNode));
            t->coef = P2->coef;
            t->expo = P2->expo;
            t->next = NULL;
            rear->next = t;
            rear = t;
            P2 = P2->next;
        } else {
            int sum = P1->coef + P2->coef;
            if (sum != 0) {
                t = (Polynomial)malloc(sizeof(PolyNode));
                t->coef = sum;
                t->expo = P1->expo;
                t->next = NULL;
                rear->next = t;
                rear = t;
            }
            P1 = P1->next;
            P2 = P2->next;
        }
    }

    while (P1) {
        t = (Polynomial)malloc(sizeof(PolyNode));
        t->coef = P1->coef;
        t->expo = P1->expo;
        t->next = NULL;
        rear->next = t;
        rear = t;
        P1 = P1->next;
    }

    while (P2) {
        t = (Polynomial)malloc(sizeof(PolyNode));
        t->coef = P2->coef;
        t->expo = P2->expo;
        t->next = NULL;
        rear->next = t;
        rear = t;
        P2 = P2->next;
    }

    return P;
}

编写输出函数，用于输出多项式。

void PrintPoly(Polynomial P) {
    if (!P) {
        printf("0 0\n");
        return;
    }

    printf("%d %d", P->coef, P->expo);
    P = P->next;

    while (P) {
        printf(" %d %d", P->coef, P->expo);
        P = P->next;
    }

    printf("\n");
}

在主函数中调用输入函数和加法函数，输出相加后的多项式。

int main() {
    Polynomial P1, P2, P;

    P1 = ReadPoly();
    P2 = ReadPoly();

    P = Add(P1, P2);

    PrintPoly(P);

    return 0;
}