用C语言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，用

在C语言中，我们可以使用结构体来表示一个多项式的项，包括系数和指数，并使用链表数据结构存储这些项。为了构建两个按指数递增的有序链表，我们需要创建一个节点结构，然后分别维护两个链表。当需要添加一元多项式时，我们只需按照指数排序链表并合并。

首先，定义一个节点结构：

typedef struct {
    int coefficient; // 系数
    int exponent;     // 指数
    struct Node* next; // 下一个节点指针
} Term;

接着，实现链表相关的操作，如插入、比较和合并：
1. 插入函数用于在链表中插入新的项（按指数递增）：

void insert(Term** head, int coefficient, int exponent) {
    if (*head == NULL || exponent > (*head)->exponent) {
        Term* newNode = (Term*)malloc(sizeof(Term));
        newNode->coefficient = coefficient;
        newNode->exponent = exponent;
        newNode->next = *head;
        *head = newNode;
    } else {
        Term* current = *head;
        while (current->next != NULL && current->next->exponent < exponent) {
            current = current->next;
        }
        if (current->next == NULL) {
            Term* newNode = (Term*)malloc(sizeof(Term));
            newNode->coefficient = coefficient;
            newNode->exponent = exponent;
            newNode->next = current->next;
            current->next = newNode;
        } else {
            newNode = current->next;
            current->next = newNode;
            newNode->coefficient += coefficient;
        }
    }
}

2. 合并两个有序链表：

Term* mergeLists(Term* list1, Term* list2) {
    Term* mergedHead = NULL;
    Term* temp;

    if (list1 == NULL) return list2;
    else if (list2 == NULL) return list1;

    if (list1->exponent < list2->exponent) {
        mergedHead = list1;
        temp = list1->next;
        list1->next = list2;
    } else {
        mergedHead = list2;
        temp = list2->next;
        list2->next = list1;
    }

    while (temp != NULL) {
        if (temp->exponent < mergedHead->exponent || (temp->exponent == mergedHead->exponent && temp->coefficient <= mergedHead->coefficient)) {
            Term* newNode = (Term*)malloc(sizeof(Term));
            newNode->coefficient = temp->coefficient;
            newNode->exponent = temp->exponent;
            newNode->next = mergedHead->next;
            mergedHead->next = newNode;
            temp = mergedHead->next;
        } else {
            temp = temp->next;
        }
    }

    return mergedHead;
}

最后，你可以通过这两个函数来实现两个一元多项式的相加：

Term* addPolynomials(Term* poly1, Term* poly2) {
    return mergeLists(poly1, poly2);
}

// 示例
Term* list1 = NULL;
insert(&list1, 1, 0); // x^0 + 1
insert(&list1, 2, 2); // x^2 + 2x^0

Term* list2 = NULL;
insert(&list2, 3, 1); // x^1 + 3x^0

Term* result = addPolynomials(list1, list2);

// 输出结果
while (result != NULL) {
    printf("%.0fx^%d + ", result->coefficient, result->exponent);
    result = result->next;
}
printf("\n");