7-2 一元多项式的乘法与加法运算 (20 分)

 

 

#include <cstdio>
#include <cstdlib>
// 多项式相乘 相加
// 数据结构设计
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 Compare(int a, int b);

// 程序框架搭建
int main()
{
	Polynomial P1, P2, PP, PS;
	
	P1 = ReadPoly();
	P2 = ReadPoly();
	PP = Mult(P1, P2);
	PrintPoly(PP);
	PS = Add(P1, P2);
	PrintPoly(PS);
	
	return 0;
} 

// 如何读入多项式
Polynomial ReadPoly()
{
	Polynomial P, Rear, t;
	int c, e, N;
	 
	scanf("%d", &N);
	P = (Polynomial)malloc(sizeof(struct PolyNode));	// 链表头空节点 
	P->link = NULL;
	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);	// 删除临时生成的头结点 
	return P;
} 

void Attach(int c, int e, Polynomial *pRear)
{
	Polynomial P;
	
	P = (Polynomial)malloc(sizeof(struct PolyNode));
	P->coef = c;	// 对新结点赋值 
	P->expon = e;
	P->link = NULL;
	(*pRear)->link = P;
	*pRear = P;	// 修改pRear的值 
}

int Compare(int a, int b)
{
	if(a > b)	return 1;
	else if(a < b)	return -1;
	else	return 0;
}

// 多项式相加
Polynomial Add(Polynomial P1, Polynomial P2)
{
	Polynomial P, Rear, t, t1, t2;
	t1 = P1; t2 = P2;
	P = (Polynomial)malloc(sizeof(struct PolyNode));
	P->link = NULL;
	Rear = P;
	while(t1 && t2)
	{
		switch(Compare(t1->expon, t2->expon))
		{
			case 1:
				Attach(t1->coef, t1->expon, &Rear);
				t1 = t1->link;
				break;
			case -1:
				Attach(t2->coef, t2->expon, &Rear);
				t2 = t2->link;
				break;
			case 0:
				if(t1->coef + t2->coef)	Attach(t1->coef + t2->coef, t1->expon, &Rear);
				t1 = t1->link;
				t2 = t2->link;
				break;
		}
	}
	for(; t1; t1 = t1->link)	Attach(t1->coef, t1->expon, &Rear);
	for(; t2; t2 = t2->link)	Attach(t2->coef, t2->expon, &Rear);
	Rear->link = NULL;
	t = P;
	P = P->link;
	free(t);
	return P;
} 

// 多项式相乘
Polynomial Mult(Polynomial P1, Polynomial P2)
{
	Polynomial P, Rear, t1, t2, 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)
	{
		Attach(t1->coef*t2->coef, t1->expon+t2->expon, &Rear);
		t2 = t2->link;
	}
	t1 = t1->link;
	 
	while(t1)
	{
		t2 = P2; Rear = P;
		while(t2)
		{
			e = t1->expon + t2->expon;
			c = t1->coef * t2->coef;
			while(Rear->link && Rear->link->expon > e)
				Rear = Rear->link;
			if(Rear->link && Rear->link->expon == e)
			{	// 指数的系数相等 
				if(Rear->link->coef + c)
					Rear->link->coef += c;
				else {
					t = Rear->link;
					Rear->link = t->link;
					free(t);
				}	
			}
			else	// 指数的系数不相等 
			{
				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);
	
	return P;
} 

// 如何将多项式输出
void PrintPoly(Polynomial P)
{
	int flag = 0;	// 辅助调整输出格式用 
	
	if(!P)	
	{
		printf("0 0\n");
		return ;
	}
	
	while(P)
	{
		if(!flag)	flag = 1;
		else	printf(" ");
		
		printf("%d %d", P->coef, P->expon);
		P = P->link;
	}
	printf("\n");
}