线性结构2 一元多项式的乘法与加法运算

02-线性结构2 一元多项式的乘法与加法运算（20 分）

设计函数分别求两个一元多项式的乘积与和。

输入格式:

输入分2行，每行分别先给出多项式非零项的个数，再以指数递降方式输入一个多项式非零项系数和指数（绝对值均为不超过1000的整数）。数字间以空格分隔。

输出格式:

输出分2行，分别以指数递降方式输出乘积多项式以及和多项式非零项的系数和指数。数字间以空格分隔，但结尾不能有多余空格。零多项式应输出0 0。

输入样例:

4 3 4 -5 2  6 1  -2 0
3 5 20  -7 4  3 1

输出样例:

15 24 -25 22 30 21 -10 20 -21 8 35 6 -33 5 14 4 -15 3 18 2 -6 1
5 20 -4 4 -5 2 9 1 -2 0

此题对我来说太难了，我只是把PPT里的代码自己打了一遍，仅能做到理解的程度。

#include<stdio.h>
#include<stdlib.h>
typedef struct PolyNode *Polynomial;
struct PolyNode{
	int coef;
	int expon;
	Polynomial link;
};

Polynomial ReadPoly();
void Attach(int c, int e,Polynomial *pRear );
Polynomial Add(Polynomial P1, Polynomial P2);
Polynomial Mult(Polynomial P1, Polynomial P2);
void PrintPoly(Polynomial P);

int main(){
	Polynomial P1,P2,PP,PS;
	P1=ReadPoly();    //读入
	P2=ReadPoly();
	PP = Mult(P1,P2);   //乘法运算并输出
	PrintPoly(PP);
	PS = Add(P1,P2);    //加法运算并输出
	PrintPoly(PS);
	return 0;
}
Polynomial ReadPoly(){
	Polynomial P,Rear,t;
	int N,c,e;
	scanf("%d",&N);
	P=(Polynomial)malloc(sizeof(struct PolyNode));     //空结点
	P->link = NULL;                           //初始指向空结点，再连接
	Rear=P;
	while(N--){
		scanf("%d %d",&c,&e);
		Attach(c,e,&Rear);             //将当前项插入多项式尾部
	}
	t = P; P= P->link; free(t);               //删除临时结点

	return P;
}

void Attach(int c, int e,Polynomial *pRear ){      //因为要对pRear进行修改，所以传进*pRear
	Polynomial P;

	P=(Polynomial)malloc(sizeof(struct PolyNode));
	P->coef=c;
	P->expon=e;
	P->link=NULL;
	(*pRear)->link = P;
	*pRear = P;                   //修改pRear
}

Polynomial Add(Polynomial P1, Polynomial P2)
{
	Polynomial Rear,t1,t2,P,tmp;
	t1 = P1; t2 = P2;
	P=(Polynomial)malloc(sizeof(struct PolyNode));           //先产生一个空结点
	P->link = NULL;
	Rear=P;
	while( t1 && t2){
		if(t1->expon == t2->expon){
			int sum = t1->coef+t2->coef;
			if( sum ) Attach(sum,t1->expon,&Rear);   //注意判断系数和是否为零
			t1=t1->link;
			t2=t2->link;
		}
		else if (t1->expon > t2->expon){
			Attach(t1->coef,t1->expon,&Rear);
			t1 = t1->link;
		}
		else {
			Attach(t2->coef,t2->expon,&Rear);
			t2 = t2->link;
		}
	}
	while( t1 ){
			Attach(t1->coef,t1->expon,&Rear);
			t1 = t1->link;
	}
	while( t2 ){
			Attach(t2->coef,t2->expon,&Rear);
			t2 = t2->link;
	}
	Rear->link = NULL;
	tmp = P;
	P = P->link;    //令P指向第一个非零项
	free(tmp);
	return P;
}

Polynomial Mult(Polynomial P1, Polynomial P2)
{
	Polynomial Rear,t1,t2,P,t;   // 
	int c,e;
	
	if( !P1 || !P2) return NULL;

	t1 = P1; t2 = P2;
	P=(Polynomial)malloc(sizeof(struct PolyNode));
	P->link = NULL;
	Rear=P;

	while(t2){                            //P1当前项乘P2，再加到结果多项式里
		Attach(t1->coef * t2->coef, t1->expon + t2->expon, &Rear);
		t2= t2->link;    
	}
	t1 = t1->link;  
	while(t1){                            //当前项乘当前项，并插入，注意插入位置       
		t2 = P2; Rear = P;            //回归到链表头
		while(t2){
			e = t1->expon + t2->expon;
			c = t1->coef*t2->coef;   //????,????
			while(Rear->link && Rear->link->expon > e) //当系数过大，后移（e要插在前一位）
			{Rear = Rear->link;}	
			if(Rear->link && Rear->link->expon == e)	// 当指数相等
			{
				if(Rear->link->coef+c)     // 判断系数和是否为零
					Rear->link->coef += c;    // 系数不为零，系数相加
				else{                        // 系数为零，处理方法？？不懂？？
					t =Rear->link;
					Rear->link=t->link;
					free(t);
				}
			}
			else{                                       //接在后面
					t=(Polynomial)malloc(sizeof(struct PolyNode));
					t->coef = c; t->expon = e;
					t->link = Rear->link;
					Rear->link = t;
					Rear = Rear->link;                     
					
			}
			t2=t2->link;
		}
		t1=t1->link;
	}
	t2 = P; P=P->link; free(t2);          //释放

	return P;    
}

void PrintPoly(Polynomial P)
{
	int flag = 0; //判断是否为第一位

	if (!P) {printf("0 0\n");return;}  //P是否为零

	while( P ){
		if(!flag) flag = 1;
		else printf(" "); 
		printf("%d %d",P->coef,P->expon);
		P = P->link;
	}
	printf("\n");    
}