请用c++帮我写一份用链表实现一元多项式求和的代码 ,并对代码进项详细解释。

这里是用链表实现一元多项式求和的C代码：

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

struct Node {
    int coefficient;  // 系数
    int exponent;     // 指数
    struct Node* next;
};

struct Node* createNode(int coefficient, int exponent) {
    struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
    if (newNode == NULL) {
        printf("动态内存分配失败。\n");
        exit(0);
    }
    newNode->coefficient = coefficient;
    newNode->exponent = exponent;
    newNode->next = NULL;
    return newNode;
}


void insert(struct Node** headRef, int coefficient, int exponent) {
    struct Node* newNode = createNode(coefficient, exponent);

    if (*headRef == NULL || exponent >= (*headRef)->exponent) {
        newNode->next = *headRef;
        *headRef = newNode;
    } else {
        struct Node* current = *headRef;
        while (current->next != NULL && current->next->exponent > exponent) {
            current = current->next;
        }
        newNode->next = current->next;
        current->next = newNode;
    }
}


void printList(struct Node* head) {
    if (head == NULL) {
        printf("列表是空的。\n");
    } else {
        struct Node* current = head;
        while (current != NULL) {
            printf("%dx^%d", current->coefficient, current->exponent);
            if (current->next != NULL) {
                printf(" + ");
            }
            current = current->next;
        }
        printf("\n");
    }
}


struct Node* addPolynomials(struct Node* poly1, struct Node* poly2) {
    struct Node* head = NULL;
    struct Node* current1 = poly1;
    struct Node* current2 = poly2;

    while (current1 != NULL && current2 != NULL) {
        if (current1->exponent == current2->exponent) {
            insert(&head, current1->coefficient + current2->coefficient, current1->exponent);
            current1 = current1->next;
            current2 = current2->next;
        } else if (current1->exponent > current2->exponent) {
            insert(&head, current1->coefficient, current1->exponent);
            current1 = current1->next;
        } else {
            insert(&head, current2->coefficient, current2->exponent);
            current2 = current2->next;
        }
    }

    while (current1 != NULL) {
        insert(&head, current1->coefficient, current1->exponent);
        current1 = current1->next;
    }

    while (current2 != NULL) {
        insert(&head, current2->coefficient, current2->exponent);
        current2 = current2->next;
    }

    return head;
}


int main() {
    struct Node* poly1 = NULL;
    struct Node* poly2 = NULL;
    struct Node* poly3 = NULL;

    insert(&poly1, 5, 2);
    insert(&poly1, 4, 1);
    insert(&poly1, 2, 0);

    insert(&poly2, 5, 1);
    insert(&poly2, 5, 0);

    printf("第一个多项式是： ");
    printList(poly1);

    printf("第二个多项式是： ");
    printList(poly2);

    poly3 = addPolynomials(poly1, poly2);

    printf("它们的和是：  ");
    printList(poly3);

    return 0;
}

注释及代码运行流程的详细解释如下：

### 1. 声明链表节点（Node）结构体

struct Node {
    int coefficient;  // 系数
    int exponent;     // 指数
    struct Node* next;
};

这个结构体定义了一个多项式中的每一项的系数和指数。每个Node都指向下一个Node，以构成链表。

### 2. 创建节点函数

struct Node* createNode(int coefficient, int exponent) {
    struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
    if (newNode == NULL) {
        printf("动态内存分配失败。\n");
        exit(0);
    }
    newNode->coefficient = coefficient;
    newNode->exponent = exponent;
    newNode->next = NULL;
    return newNode;
}

这个函数返回一个新的Node，其系数和指数分别为输入参数coefficient和exponent。newNode->next被设置为NULL，因为这是一个新链表的最后一个节点。

### 3. 在链表中插入节点

void insert(struct Node** headRef, int coefficient, int exponent) {
    struct Node* newNode = createNode(coefficient, exponent);

    if (*headRef == NULL || exponent >= (*headRef)->exponent) {
        newNode->next = *headRef;
        *headRef = newNode;
    } else {
        struct Node* current = *headRef;
        while (current->next != NULL && current->next->exponent > exponent) {
            current = current->next;
        }
        newNode->next = current->next;
        current->next = newNode;
    }
}

这个函数把一个新的节点插入到由*headRef指针所指向的链表中。它先调用createNode函数创建一个新Node，并设置其系数和指数。 如果链表是空的，或者新节点的指数大于等于链表中的第一个节点的指数，那么新节点就会插入到链表的开头。否则，函数会在链表中插入新节点，保证链表中的节点按指数大小升序排列。

### 4. 遍历链表并打印

void printList(struct Node* head) {
    if (head == NULL) {
        printf("列表是空的。\n");
    } else {
        struct Node* current = head;
        while (current != NULL) {
            printf("%dx^%d", current->coefficient, current->exponent);
            if (current->next != NULL) {
                printf(" + ");
            }
            current = current->next;
        }
        printf("\n");
    }
}

这个函数遍历链表，并逐个节点输出其系数和指数。

### 5. 多项式相加

struct Node* addPolynomials(struct Node* poly1, struct Node* poly2) {
    struct Node* head = NULL;
    struct Node* current1 = poly1;
    struct Node* current2 = poly2;

    while (current1 != NULL && current2 != NULL) {
        if (current1->exponent == current2->exponent) {
            insert(&head, current1->coefficient + current2->coefficient, current1->exponent);
            current1 = current1->next;
            current2 = current2->next;
        } else if (current1->exponent > current2->exponent) {
            insert(&head, current1->coefficient, current1->exponent);
            current1 = current1->next;
        } else {
            insert(&head, current2->coefficient, current2->exponent);
            current2 = current2->next;
        }
    }

    while (current1 != NULL) {
        insert(&head, current1->coefficient, current1->exponent);
        current1 = current1->next;
    }

    while (current2 != NULL) {
        insert(&head, current2->coefficient, current2->exponent);
        current2 = current2->next;
    }

    return head;
}

这个函数输入两个多项式poly1和poly2，并返回它们的和。它使用指针current1和current2遍历两个多项式，并在每个节点处进行相加。对于每一项，insert函数被调用来向链表中插入新节点。如果在任何一个多项式的末尾，那么这个多项式的当前节点就会为NULL，在这种情况下，剩余的多项式中的所有节点都可以被添加到结果多项式中。

### 6. 主函数

int main() {
    struct Node* poly1 = NULL;
    struct Node* poly2 = NULL;
    struct Node* poly3 = NULL;

    insert(&poly1, 5, 2);
    insert(&poly1, 4, 1);
    insert(&poly1, 2, 0);

    insert(&poly2, 5, 1);
    insert(&poly2, 5, 0);

    printf("第一个多项式是： ");
    printList(poly1);

    printf("第二个多项式是： ");
    printList(poly2);

    poly3 = addPolynomials(poly1, poly2);

    printf("它们的和是：  ");
    printList(poly3);

    return 0;
}

这个函数调用insert函数向链表中插入多项式的每一项。然后调用addPolynomials函数计算两个多项式的和，并将其打印到屏幕上。