利用单链表存储一元多项式，编写函数求解两个多项式相加的运算。用c语言写出此算法

在C语言中，我们可以使用结构体表示多项式的系数及其对应的指数，并利用单链表作为数据结构存储一元多项式。下面是一个简单的算法实现，用于计算两个一元多项式相加：

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

// 定义多项式的节点结构体
typedef struct {
    int coefficient; // 系数
    int exponent;     // 指数
    struct Node* next; // 指向下一个节点的指针
} Node;

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

// 初始化一个空的多项式链表
Node* initPoly() {
    return NULL;
}

// 将多项式转换为链表形式
void polyToList(Node** polyList, int* coefficients, int degree) {
    *polyList = createNode(coefficients[degree], degree);
    for (int i = degree - 1; i >= 0; i--) {
        (*polyList)->next = createNode(coefficients[i], i);
        polyList = &(*polyList)->next;
    }
}

// 合并两个多项式链表
Node* addPolynomials(Node* poly1, Node* poly2) {
    Node* sumList = initPoly();
    while (poly1 && poly2) {
        if (poly1->exponent > poly2->exponent) {
            sumList->coefficient += poly1->coefficient;
            poly1 = poly1->next;
        } else if (poly1->exponent < poly2->exponent) {
            sumList->coefficient += poly2->coefficient;
            poly2 = poly2->next;
        } else {
            sumList->coefficient += poly1->coefficient + poly2->coefficient;
            poly1 = poly1->next;
            poly2 = poly2->next;
        }
    }
    
    // 将剩余部分添加到结果
    while (poly1) {
        sumList->coefficient += poly1->coefficient;
        poly1 = poly1->next;
        sumList = createNode(sumList->coefficient, sumList->exponent);
        sumList->next = NULL;
    }
    
    while (poly2) {
        sumList->coefficient += poly2->coefficient;
        poly2 = poly2->next;
        sumList = createNode(sumList->coefficient, sumList->exponent);
        sumList->next = NULL;
    }

    return sumList;
}

// 打印多项式链表
void printPoly(Node* poly) {
    Node* temp = poly;
    printf("Sum of the polynomials:\n");
    while (temp) {
        printf("%d*x^%d ", temp->coefficient, temp->exponent);
        temp = temp->next;
    }
    printf("\n");
}

int main() {
    int coefficients1[] = {2, 3, 4}; // 第一个多项式
    int coefficients2[] = {1, 0, 5}; // 第二个多项式
    int degree1 = sizeof(coefficients1) / sizeof(coefficients1[0]);
    int degree2 = sizeof(coefficients2) / sizeof(coefficients2[0]);

    Node* poly1 = initPoly();
    Node* poly2 = initPoly();

    polyToList(&poly1, coefficients1, degree1);
    polyToList(&poly2, coefficients2, degree2);

    Node* result = addPolynomials(poly1, poly2);

    printPoly(result);

    return 0;
}

在这个程序中，我们首先定义了表示多项式节点的结构体`Node`，然后实现了创建节点、初始化链表、合并多项式以及打印链表等函数。在`main()`函数里，我们创建了两个多项式，分别存储在`poly1`和`poly2`，通过`addPolynomials`函数将它们相加，并打印出结果。