构造两个按指数递增的有序链表，实现两个一元多项式相加。c语言

在 C 语言中，我们可以构建两个结构体分别表示两个一元多项式的项，每个项包含系数和指数。然后，我们创建两个这样的链表，每个链表的节点按照指数递增顺序存储。对于多项式的加法，我们需要遍历这两个链表，并将相应位置的系数相加。

首先，定义链表节点结构体 `Node`：

typedef struct Node {
    double coefficient; // 系数
    int exponent;       // 指数
    struct Node* next;   // 指向下一个节点的指针
} Node;

接着，创建函数来构造指数递增的链表：

// 构建指数递增链表
void buildIndexedList(Node** head, double* coefficients, int* exponents, int n) {
    Node* current = *head;
    for (int i = 0; i < n; ++i) {
        if (current->exponent != exponents[i]) { // 如果新节点的指数比当前节点大
            current = (*head)->next;
        }
        current->coefficient = coefficients[i];
        current->exponent = exponents[i];
        if (!current->next) break; // 遇到最后一个元素，设置 next 为 NULL
        current = current->next;
    }
}

接下来，实现多项式的加法：

// 相加两个一元多项式
void addPolynomials(Node** sumHead, Node** poly1Head, Node** poly2Head) {
    Node* current1 = *poly1Head;
    Node* current2 = *poly2Head;
    Node* sumCurrent = *sumHead;

    while (current1 || current2) {
        double coeff1 = (current1) ? current1->coefficient : 0;
        double coeff2 = (current2) ? current2->coefficient : 0;
        
        double result = coeff1 + coeff2;
        sumCurrent->coefficient = result;
        sumCurrent->exponent = current1 ? current1->exponent : current2->exponent;

        if (current1 && current1->next) {
            current1 = current1->next;
        } else if (current2 && current2->next) {
            current2 = current2->next;
        } else {
            if (current1) current1 = NULL; // 如果还有剩余的poly1，则移动指针
            if (current2) current2 = NULL; // 同理，处理poly2
        }

        if (sumCurrent->next == NULL) {
            sumCurrent->next = NULL; // 初始化 sumHead 的末尾
        } else {
            sumCurrent = sumCurrent->next;
        }
    }
}

最后，你可以像这样使用上述函数：

// 示例
double coefficients[] = {1.0, 2.0, 3.0};
int exponents[] = {0, 1, 2};
buildIndexedList(&poly1Head, coefficients, exponents, 3);
double otherCoefficients[] = {4.0, 5.0};
int otherExponents[] = {0, 1};
buildIndexedList(&poly2Head, otherCoefficients, otherExponents, 2);

Node* sumHead = NULL;
addPolynomials(&sumHead, poly1Head, poly2Head);