C语言单链表实现多项式的相乘

此次写该程序的时候费了不少劲，主要是在调试代码上，但是也花费了不少时间在构思代码的方法上，我做该程序时的思路如下：
1.首先构出两个多项式

head1=3 + 4x + 7x^2 +7x^9
head2=1 + 4x^2 + 8x^3 + 4x^6

2. 人为计算的时候是head1中的每一项依次和head2中的每一项进行计算的，所以我用结构体数组存储该新形成的链表

p[0]=3*(1 + 4x^2 + 8x^3 + 4x^6)//用单链表存储
p[1]=4x * (1 + 4x^2 + 8x^3 + 4x^6)
p[2]=7x^2 * (1 + 4x^2 + 8x^3 + 4x^6)
p[3]=7x^9 * (1 + 4x^2 + 8x^3 + 4x^6)

3. 将p[0]->p[3]连接成一个总链表
   函数：void combineAll(NODE arr[], int n)

p=3 + 12x^2 +24x^3 +12x^6 +4x + 16 x^3 +32x^4 +16 x^7 +7x^2 +28x^4 +56x^5 +28x^8 +7x^9 +28x^11 + 56x^12 +28x^15
并将所有的指数存在num[lenth]数组里面

4. 当然不能这样输出要整理下，所以我想了个函数用来处理指数相同的项，并将系数相加
   函数：void SD(int num[],int n)

void SD(int num[],int n)//找到有几种不同的指数
{
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            if ((num[j] == num[i]) && (j != i)&&(num[j]!=-1))
            {
                num[j] = -1;
            }
        }
    }
    
    for (int i = 0; i < n; i++)
    {
        if (num[i] != -1)
        {
            Arr[cnt1] = num[i];
            cnt1++;//cnt1是全局变量因为要计算有几种不同的指数
        }
    }
}

5. 处理指数的排序问题
   函数：void swapData(NODE head)
   只交换数据域不交换链表的指针
6. 完整代码如下

#include
#include 
#define lenth 16
typedef struct node
{
    int index;
    int coef;
    struct node*next;
}node, *NODE;
int Arr[lenth] = { -1 };//全局变量，用来存储指数
int cnt1 = 0;
void initNode(NODE *head)//初始化头结点
{
    (*head) = (NODE)malloc(sizeof(node));
    (*head)->next = NULL;
}
NODE typeData(NODE head, int index[], int coef[], int len)//给相乘的两个单链表输入数据
{
    //head必须在主函数里面申请过空间设置对象
    NODE p;
    p = head;
    for (int i = 0; i < len; i++)
    {
        NODE temp = (NODE)malloc(sizeof(node));
        temp->index = index[i];
        temp->coef = coef[i];
        p->next= temp;
        p = temp;
        temp->next = NULL;
    }
    return head;
}
void mutipleFunc(NODE add[],NODE head1, NODE head2, int len1, int len2)//功能函数
{
    NODE p, begin;
    p = head1;
    p = p->next;
    for (int i = 0; i < len1; i++)
    {
        NODE q = head2->next;
        begin = add[i];
        for (int j = 0; j < len2; j++)
        {
            NODE temp = (NODE)malloc(sizeof(node));
            temp->index = p->index + q->index;//指数相加
            temp->coef = p->coef * q->coef;//系数相乘
            begin->next = temp;
            begin = temp;

            temp->next = NULL;
            q = q->next;
        }
        p = p->next;
    }
}
void showNode(NODE *head)
{
    NODE p;
    p = (*head);
    p = p->next;
    while (p!= NULL)
    {
        printf("系数是%d,指数是%d\n", p->coef, p->index);
        p = p->next;
    }
}
void SD(int num[],int n)//找到有几种不同的指数
{
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            if ((num[j] == num[i]) && (j != i)&&(num[j]!=-1))
            {
                num[j] = -1;
            }
        }
    }
    
    for (int i = 0; i < n; i++)
    {
        if (num[i] != -1)
        {
            Arr[cnt1] = num[i];
            cnt1++;
        }
    }
}
void swap(int *data1, int *data2)
{
    int temp;
    temp = (*data1);
    (*data1) = (*data2);
    (*data2) = temp;
}
void swapData(NODE head)//只交换数据域
{
    NODE p,q;
    p = head;
    p = p->next;
    int i = 0;
    while (p->next != NULL)
    {
        q = head;
        for (int j = 0; j <= i; j++)
        {
            q = q->next;
        }
        while (q->next != NULL)
        {
            q = q->next;
            if (p->index > q->index)
            {
                swap(&p->index, &q->index);
                swap(&p->coef, &q->coef);
            }
        }
        p = p->next;
        i++;
    }
}
NODE combineAll(NODE arr[], int n)//多个多项式相加首先这些多项式都是顺序的
{
    NODE p, q, head;
    head = (NODE)malloc(sizeof(node));
    p = head;//p指针指向head
    for (int i = 0; i < n; i++)//将所有的多项式合并为一个式子
    {
        q = arr[i]->next;
        while (q != NULL)
        {
            p->next = q;
            p = q;
            q = q->next;
        }
    }
}
    //判断有几个不同的指数
void function(NODE head)
{   
        NODE SchIndex;
    SchIndex = head;
    SchIndex = SchIndex->next;
    int cnt = 0;
    int num[lenth] = { 0 };
    while (SchIndex != NULL)//将所有的指数存在数组num[]中
    {
        num[cnt] = SchIndex->index;
        cnt++;
        SchIndex = SchIndex->next;
    }
    SD(num, cnt);
    NODE New, P;
    New = (NODE)malloc(sizeof(node));
    New->next = NULL;
    New->index = -1;
    New->coef = -1;
    P = New;
    int j = 0;
    while (j < cnt1)
    {
        NODE m;
        m = head;
        m = m->next;
        int sumCoef = 0;
        NODE temp = (NODE)malloc(sizeof(node));
        while (m != NULL)
        {
            if (m->index == Arr[j])
            {
                sumCoef = sumCoef + m->coef;
            }
            m = m->next;
        }
        temp->coef = sumCoef;
        temp->index = Arr[j];
        temp->next = NULL;
        P->next = temp;
        P = temp;
        j++;
    }
    swapData(New);
    showNode(&New);
}
int main()
{
    NODE head1, head2,head;
    NODE add[lenth];
    for (int i = 0; i < lenth; i++)
    {
        initNode(&add[i]);
    }
    //初始化多项式
    initNode(&head1);
    initNode(&head2);
        initNode(&head);
    //系数和指数用数组赋值
    int arr_index[4] = { 0,1,2,9};
    int arr_coef[4] = { 3,4,7,7};
    int Arr_index[4] = { 0,2,3,6};
    int Arr_coef[4] = { 1,4,8,4};
    //输入多项式数据
    typeData(head1, arr_index, arr_coef, 4);
    typeData(head2, Arr_index, Arr_coef, 4);
    //功能函数
    mutipleFunc(add,head1, head2, 4, 4);
    //多项式合并成一个式子
    head=combineAll(add, 4);
    function(head);
    system("pause");
    return 0;
}