用C语言实现一元多项式的表示与相加，数据结构

可以使用链表来实现一元多项式的表示和相加，具体实现如下：

1.定义一个结构体来表示一元多项式中的每一项：

typedef struct Node {
    float coef; // 系数
    int exp; // 指数
    struct Node *next;
} Node, *Polynomial;

2.定义一个函数来创建一元多项式：

Polynomial createPoly() {
    Polynomial p = (Polynomial)malloc(sizeof(Node));
    p->next = NULL;

    float coef;
    int exp;

    printf("请输入一元多项式的系数和指数，以 0 0 结束输入：\n");
    scanf("%f %d", &coef, &exp);
    while (coef != 0 || exp != 0) {
        Node *newNode = (Node *)malloc(sizeof(Node));
        newNode->coef = coef;
        newNode->exp = exp;

        Node *pre = p;
        Node *cur = p->next;
        while (cur != NULL && cur->exp > exp) {
            pre = cur;
            cur = cur->next;
        }
        newNode->next = cur;
        pre->next = newNode;

        scanf("%f %d", &coef, &exp);
    }

    return p;
}

3.定义一个函数来输出一元多项式：

void printPoly(Polynomial p) {
    Node *cur = p->next;
    int first = 1;

    while (cur != NULL) {
        if (first) {
            first = 0;
        } else {
            printf(" + ");
        }

        printf("%.2f", cur->coef);
        if (cur->exp > 0) {
            printf("x^%d", cur->exp);
        }

        cur = cur->next;
    }

    printf("\n");
}

4.定义一个函数来实现一元多项式的相加：

Polynomial addPoly(Polynomial p1, Polynomial p2) {
    Polynomial sum = (Polynomial)malloc(sizeof(Node));
    sum->next = NULL;

    Node *cur1 = p1->next;
    Node *cur2 = p2->next;

    while (cur1 != NULL && cur2 != NULL) {
        Node *newNode = (Node *)malloc(sizeof(Node));

        if (cur1->exp == cur2->exp) {
            newNode->coef = cur1->coef + cur2->coef;
            newNode->exp = cur1->exp;

            cur1 = cur1->next;
            cur2 = cur2->next;
        } else if (cur1->exp > cur2->exp) {
            newNode->coef = cur1->coef;
            newNode->exp = cur1->exp;

            cur1 = cur1->next;
        } else {
            newNode->coef = cur2->coef;
            newNode->exp = cur2->exp;

            cur2 = cur2->next;
        }

        Node *pre = sum;
        Node *cur = sum->next;
        while (cur != NULL && cur->exp > newNode->exp) {
            pre = cur;
            cur = cur->next;
        }
        newNode->next = cur;
        pre->next = newNode;
    }

    while (cur1 != NULL) {
        Node *newNode = (Node *)malloc(sizeof(Node));
        newNode->coef = cur1->coef;
        newNode->exp = cur1->exp;

        Node *pre = sum;
        Node *cur = sum->next;
        while (cur != NULL && cur->exp > newNode->exp) {
            pre = cur;
            cur = cur->next;
        }
        newNode->next = cur;
        pre->next = newNode;

        cur1 = cur1->next;
    }

    while (cur2 != NULL) {
        Node *newNode = (Node *)malloc(sizeof(Node));
        newNode->coef = cur2->coef;
        newNode->exp = cur2->exp;

        Node *pre = sum;
        Node *cur = sum->next;
        while (cur != NULL && cur->exp > newNode->exp) {
            pre = cur;
            cur = cur->next;
        }
        newNode->next = cur;
        pre->next = newNode;

        cur2 = cur2->next;
    }

    return sum;
}

使用示例：

int main() {
    Polynomial p1 = createPoly();
    printf("第一个多项式为：");
    printPoly(p1);

    Polynomial p2 = createPoly();
    printf("第二个多项式为：");
    printPoly(p2);

    Polynomial sum = addPoly(p1, p2);
    printf("相加后的多项式为：");
    printPoly(sum);

    return 0;
}

注意：在使用完链表后，需要手动释放链表的内存空间，否则会造成内存泄漏。