//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");
		}
	}
}