利用链表表示一元多项式，并设计算法计算两个一元多项式的和(C语言)

利用链表表示一元多项式可以通过定义一个结构体来实现，结构体中包含两个成员变量，一个是系数coeff，表示多项式的系数，另一个是指数exp，表示多项式的指数。然后通过链表的方式将多个结构体连接起来，形成一个链表表示的一元多项式。

以下是一个示例的C语言代码：

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

// 定义多项式的结构体
typedef struct Polynomial {
    int coeff;  // 系数
    int exp;    // 指数
    struct Polynomial* next;  // 指向下一个节点的指针
} Polynomial;

// 创建一个新的多项式节点
Polynomial* createNode(int coeff, int exp) {
    Polynomial* newNode = (Polynomial*)malloc(sizeof(Polynomial));
    newNode->coeff = coeff;
    newNode->exp = exp;
    newNode->next = NULL;
    return newNode;
}

// 向多项式链表中插入一个节点
void insertNode(Polynomial** poly, int coeff, int exp) {
    Polynomial* newNode = createNode(coeff, exp);
    if (*poly == NULL) {
        *poly = newNode;
    } else {
        Polynomial* temp = *poly;        while (temp->next != NULL) {
            temp = temp->next;
        }
        temp->next = newNode;
    }
}

// 计算两个一元多项式的和
Polynomial* addPolynomials(Polynomial* poly1, Polynomial* poly2) {
    Polynomial* result = NULL;
    while (poly1 != NULL && poly2 != NULL) {
        if (poly1->exp > poly2->exp) {
            insertNode(&result, poly1->coeff, poly1->exp);
            poly1 = poly1->next;
        } else if (poly1->exp < poly2->exp) {
            insertNode(&result, poly2->coeff, poly2->exp);
            poly2 = poly2->next;
        } else {
            int sum = poly1->coeff + poly2->coeff;
            if (sum != 0) {
                insertNode(&result, sum, poly1->exp);
            }
            poly1 = poly1->next;
            poly2 = poly2->next;
        }
    }
    while (poly1 != NULL) {
        insertNode(&result, poly1->coeff, poly1->exp);
        poly1 = poly1->next;
    }
    while (poly2 != NULL) {
        insertNode(&result, poly2->coeff, poly2->exp);
        poly2 = poly2->next;
    }
    return result;
}

// 打印多项式
void printPolynomial(Polynomial* poly) {
    Polynomial* temp = poly;
    while (temp != NULL) {
        printf("%dx^%d ", temp->coeff, temp->exp);
        temp = temp->next;
        if (temp != NULL) {
            printf("+ ");
        }
    }
    printf("\n");
}

int main() {
    Polynomial* poly1 = NULL;
    Polynomial* poly2 = NULL;

    // 插入节点到多项式链表
    insertNode(&poly1, 3, 4);
    insertNode(&poly1, 2, 3);
    insertNode(&poly1, 5, 1);

    insertNode(&poly2, 1, 3);
    insertNode(&poly2, 4, 2);
    insertNode(&poly2, 2, 0);

    // 计算两个多项式的和
    Polynomial* sum = addPolynomials(poly1, poly2);

    // 打印结果
    printf("多项式1：");
    printPolynomial(poly1);
    printf("多项式2：");
    printPolynomial(poly2);
    printf("和：");
    printPolynomial(sum);

    return 0;
}