//头文件
#include<>
#include<>
#include<>

//定义多项式的项
typedef struct Polynomial{
    float coef;
    int expn;
    struct Polynomial *next;
}*Polyn,Polynomial;

void Insert(Polyn p,Polyn h){     
    if(p->coef==0) free(p);//系数为0的话释放结点
    else
    {
        Polyn q1,q2;
        q1=h;
        q2=h->next;
        while(q2&&p->expn<q2->expn)
        {//查找插入位置
            q1=q2;
            q2=q2->next;
        }
        if(q2&&p->expn==q2->expn)
        {//将指数相同相合并
            q2->coef+=p->coef;
            free(p);
            if(!q2->coef)
            {//系数为0的话释放结点
                q1->next=q2->next;
                free(q2);
            }
        }
        else
        {//指数为新时将结点插入
            p->next=q2;
            q1->next=p;
        }
    }
}

Polyn CreatePolyn(Polyn head,int m){
    //建立一个头指针为head、项数为m的一元多项式
    int i;
    Polyn p;
    p=head=(Polyn)malloc(sizeof(struct Polynomial));
    head->next=NULL;
    for(i=0;i<m;i++)
    {
        p=(Polyn)malloc(sizeof(struct Polynomial));//建立新结点以接收数据
        printf("请输入第%d项的系数与指数:",i+1);
        scanf("%f %d",&p->coef,&p->expn);
        Insert(p,head);   //调用Insert函数插入结点
    }
    return head;
}

void DestroyPolyn(Polyn p){
    //销毁多项式p
    Polyn q1,q2;
    q1=p->next;
    q2=q1->next;
    while(q1->next)
    {
        free(q1);
        q1=q2;
        q2=q2->next;
    }
}

void PrintPolyn(Polyn P){
    Polyn q=P->next;
    int flag=1;//项数计数器
    if(!q)
    { //若多项式为空，输出0
        putchar('0');
        printf("\n");
        return;
    }   
    while(q)
    {
        if(q->coef>0&&flag!=1) putchar('+'); //系数大于0且不是第一项
        if(q->coef!=1&&q->coef!=-1)
        {//系数非1或-1的普通情况
            printf("%g",q->coef);
            if(q->expn==1) putchar('X');
            else if(q->expn) printf("X^%d",q->expn);
        }
        else
        {
            if(q->coef==1)
            {
                if(!q->expn) putchar('1');
                else if(q->expn==1) putchar('X');
                else printf("X^%d",q->expn);
            }
            if(q->coef==-1)
            {
                if(!q->expn) printf("-1");
                else if(q->expn==1) printf("-X");
                else printf("-X^%d",q->expn);
            }
        }
        q=q->next;
        flag++;
    }
    printf("\n");
}

int compare(Polyn a,Polyn b){
    if(a&&b)
    {
        if(!b||a->expn>b->expn) return 1;
        else if(!a||a->expn<b->expn) return -1;
        else return 0;
    }
    else if(!a&&b) return -1;//a多项式已空，但b多项式非空
    else return 1;//b多项式已空，但a多项式非空
}

Polyn AddPolyn(Polyn pa,Polyn pb){//求解并建立多项式a+b，返回其头指针
    Polyn qa=pa->next;
    Polyn qb=pb->next;
    Polyn headc,hc,qc;
    hc=(Polyn)malloc(sizeof(struct Polynomial));//建立头结点
    hc->next=NULL;
    headc=hc;
    while(qa||qb)
    {
        qc=(Polyn)malloc(sizeof(struct Polynomial));
        switch(compare(qa,qb)){
        case 1:
            {
                qc->coef=qa->coef;
                qc->expn=qa->expn;
                qa=qa->next;
                break;
            }
        case 0:
            {
                qc->coef=qa->coef+qb->coef;
                qc->expn=qa->expn;
                qa=qa->next;
                qb=qb->next;
                break;
            }
        case -1:
            {
                qc->coef=qb->coef;
                qc->expn=qb->expn;
                qb=qb->next;
                break;
            }
        }
        if(qc->coef!=0)
        {
            qc->next=hc->next;
            hc->next=qc;
            hc=qc;
        }
    else free(qc);//当相加系数为0时，释放该结点
    }
    return headc;
}

Polyn SubtractPolyn(Polyn pa,Polyn pb){//求解并建立多项式a-b，返回其头指针
    Polyn h=pb;
    Polyn p=pb->next;
    Polyn pd;
    while(p)
    {           //将pb的系数取反
        p->coef*=-1;
        p=p->next;
    }
    pd=AddPolyn(pa,h);
    for(p=h->next;p;p=p->next)    //恢复pb的系数
        p->coef*=-1;
    return pd;
}

int ValuePolyn(Polyn head,int x){
    //输入x值，计算并返回多项式的值
    Polyn p;
    int i;
    int sum=0,t;
    for(p=head->next;p;p=p->next)
    {
        t=1;
        for(i=p->expn;i!=0;)
        {
            if(i<0){t/=x;i++;}//指数小于0，进行除法
            else{t*=x;i--;}//指数大于0，进行乘法
        }
        sum+=p->coef*t;
    }
    return sum;
}

Polyn Derivative(Polyn head){
    //求解并建立导函数多项式，并返回其头指针
    Polyn q=head->next,p1,p2,hd;
    hd=p1=(Polyn)malloc(sizeof(struct Polynomial));//建立头结点
    hd->next=NULL;
    while(q)
    {
        if(q->expn!=0)
        {               //该项不是常数项时
            p2=(Polyn)malloc(sizeof(struct Polynomial));
            p2->coef=q->coef*q->expn;
            p2->expn=q->expn-1;
            p2->next=p1->next;//连接结点
            p1->next=p2;
            p1=p2;
        }
        q=q->next;
    }
    return hd;
}

Polyn MultiplyPolyn(Polyn pa,Polyn pb){
    //求解并建立多项式a*b，返回其头指针
    Polyn hf,pf;
    Polyn qa=pa->next;
    Polyn qb=pb->next;
    hf=(Polyn)malloc(sizeof(struct Polynomial));//建立头结点
    hf->next=NULL;
    for(;qa;qa=qa->next)
    {
        for(qb=pb->next;qb;qb=qb->next)
        {
            pf=(Polyn)malloc(sizeof(struct Polynomial));
            pf->coef=qa->coef*qb->coef;
            pf->expn=qa->expn+qb->expn;
            Insert(pf,hf);//调用Insert函数以合并指数相同的项
        }
    }
    return hf;
}

void main()
{
    int m,n,a,x;
    char flag;
    Polyn pa=0,pb=0,pc;

    printf("         欢迎使用多项式操作程序\n\n");
    printf("请输入a的项数:");
    scanf("%d",&m);
    pa=CreatePolyn(pa,m);//建立多项式a
    printf("请输入b的项数:");
    scanf("%d",&n);
    pb=CreatePolyn(pb,n);//建立多项式b

    //输出菜单
    printf("   *******************************************************\n");
    printf("   *                   多项式操作程序                    *\n");
    printf("   *                                                     *\n");
    printf("   *       A:输出多项式             B:输出多项式b        *\n");
    printf("   *                                                     *\n");
    printf("   *       C:输出a的导数            D:输出b的导数        *\n");
    printf("   *                                                     *\n");
    printf("   *       E:代入x的值计算a         F:代入x的值计算b     *\n");
    printf("   *                                                     *\n");
    printf("   *       G:输出a+b                H:输出a-b            *\n");
    printf("   *                                                     *\n");
    printf("   *       I:输出a*b                J:退出程序           *\n");
    printf("   *                                                     *\n");
    printf("   *******************************************************\n");

    while(a)
    {
        printf("\n请选择操作：");
        scanf(" %c",&flag);//空格符号一定要注意
        switch(flag)
        {

            case'A':
            case'a':
                {
                    printf("\n       多项式a=");
                    PrintPolyn(pa);
                    break;
                }
            case'B':
            case'b':
                {
                    printf("\n       多项式b=");
                    PrintPolyn(pb);
                    break;
                }
            case'C':
            case'c':
                {
                      pc=Derivative(pa);
                      printf("\n       多项式a的导函数为：a'=");
                    PrintPolyn(pc);
                    break;
                }
            case'D':
            case'd':
                {
                    pc=Derivative(pb);
                    printf("\n       多项式b的导函数为：b'=");
                    PrintPolyn(pc);
                    break;
                }
            case'E':
            case'e':
                {
                    printf("输入x的值：x=");
                    scanf("%d",&x);
                    printf("\n       x=%d时，a=%d\n",x,ValuePolyn(pa,x));
                    break;
                }
            case'F':
            case'f':
                {
                    printf("输入x的值：x=");
                    scanf("%d",&x);
                    printf("\n       x=%d时，b=%d\n",x,ValuePolyn(pb,x));
                    break;
                }
            case'G':
            case'g':
                {
                    pc=AddPolyn(pa,pb);
                    printf("\n       a+b=");
                    PrintPolyn(pc);
                    break;
                }
            case'H':
            case'h':
                {
                    pc=SubtractPolyn(pa,pb);
                    printf("\n       a-b=");
                    PrintPolyn(pc);
                    break;
                }
            case'I':
            case'i':
                {
                    pc=MultiplyPolyn(pa,pb);
                    printf("\n      a*b=");
                    PrintPolyn(pc);
                    break;
                }
            case'J':
            case'j':
                {
                    printf("\n       感谢使用此程序！\n");
                    DestroyPolyn(pa);
                    DestroyPolyn(pb);
                    a=0;
                    break;
                }
            default:
                printf("\n       您的选择错误，请重新选择!\n");
        }
    }
}