C语言实现一元多项式的表示和实现

一元多项式可以用如下结构体表示：

typedef struct node {
    float coef;             // 系数
    int expo;               // 指数
    struct node *next;      // 下一个节点的指针
} node;

其中，`coef` 表示系数，`expo` 表示指数，`next` 表示下一个节点的指针。

下面是一元多项式的基本操作函数实现：

1. 创建一个新的节点：

node *create_node(float coef, int expo) {
    node *new_node = (node *)malloc(sizeof(node));
    if (new_node == NULL) {
        printf("Memory allocation failed.");
        exit(1);
    }
    new_node->coef = coef;
    new_node->expo = expo;
    new_node->next = NULL;
    return new_node;
}

2. 插入一个节点到多项式中：

void insert_node(node **head, float coef, int expo) {
    node *new_node = create_node(coef, expo);
    if (*head == NULL) {
        *head = new_node;
    } else {
        node *cur = *head;
        while (cur->next != NULL && cur->next->expo > expo) {
            cur = cur->next;
        }
        if (cur->expo == expo) {
            cur->coef += coef;
            free(new_node);
        } else if (cur->next == NULL) {
            cur->next = new_node;
        } else {
            new_node->next = cur->next;
            cur->next = new_node;
        }
    }
}

3. 删除一个节点：

void delete_node(node **head, int expo) {
    if (*head == NULL) {
        printf("The polynomial is empty.\n");
        return;
    }
    node *cur = *head;
    node *pre = NULL;
    while (cur != NULL && cur->expo != expo) {
        pre = cur;
        cur = cur->next;
    }
    if (cur == NULL) {
        printf("The node with exponent %d does not exist.\n", expo);
        return;
    }
    if (pre == NULL) {
        *head = cur->next;
    } else {
        pre->next = cur->next;
    }
    free(cur);
}

4. 两个多项式相加：

node *add_poly(node *p1, node *p2) {
    node *head = NULL;
    while (p1 != NULL && p2 != NULL) {
        if (p1->expo > p2->expo) {
            insert_node(&head, p1->coef, p1->expo);
            p1 = p1->next;
        } else if (p1->expo < p2->expo) {
            insert_node(&head, p2->coef, p2->expo);
            p2 = p2->next;
        } else {
            insert_node(&head, p1->coef + p2->coef, p1->expo);
            p1 = p1->next;
            p2 = p2->next;
        }
    }
    while (p1 != NULL) {
        insert_node(&head, p1->coef, p1->expo);
        p1 = p1->next;
    }
    while (p2 != NULL) {
        insert_node(&head, p2->coef, p2->expo);
        p2 = p2->next;
    }
    return head;
}

5. 两个多项式相减：

node *sub_poly(node *p1, node *p2) {
    node *head = NULL;
    while (p1 != NULL && p2 != NULL) {
        if (p1->expo > p2->expo) {
            insert_node(&head, p1->coef, p1->expo);
            p1 = p1->next;
        } else if (p1->expo < p2->expo) {
            insert_node(&head, -p2->coef, p2->expo);
            p2 = p2->next;
        } else {
            insert_node(&head, p1->coef - p2->coef, p1->expo);
            p1 = p1->next;
            p2 = p2->next;
        }
    }
    while (p1 != NULL) {
        insert_node(&head, p1->coef, p1->expo);
        p1 = p1->next;
    }
    while (p2 != NULL) {
        insert_node(&head, -p2->coef, p2->expo);
        p2 = p2->next;
    }
    return head;
}

6. 两个多项式相乘：

node *mul_poly(node *p1, node *p2) {
    node *head = NULL;
    while (p1 != NULL) {
        node *p = p2;
        while (p != NULL) {
            insert_node(&head, p1->coef * p->coef, p1->expo + p->expo);
            p = p->next;
        }
        p1 = p1->next;
    }
    return head;
}

以上是一元多项式的基本操作函数实现，可以根据需要进行调用。