浙大数据结构——小白专场：一元多项式的加法与乘法运算

本文链接：https://blog.youkuaiyun.com/qq_33514421/article/details/88605587

本文详细介绍了一种使用链表结构表示和操作多项式的算法实现。包括读取多项式、加法、乘法运算以及输出结果的具体步骤。适用于计算机科学与技术、软件工程等专业的学生和教师，以及对算法设计感兴趣的开发者。

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一、多项式的表示

typedef struct PolyNode *Polynomial;
struct PolyNode{
	int coef;
	int expon;
	Polynomial link;
};

二、程序框架

int main(){
	Polynomial P1,P2,PP,PS;
	
	//读入多项式1
	P1=ReadPoly();
	//读入多项式2
	P2=ReadPoly();
	//加法运算并输出 
	PS=Add(P1,P2);
	PrintPoly(PS);
	//乘法运算并输出 
	PP=Mult(P1,P2);
	PrintPoly(PP);
	
	return 0; 
}

三、如何读入多项式

void Attach(int c,int e,Polynomial *pRear){
	Polynomial P;
	P=(Polynomial)mallco(sizeof(PolyNode));
	P->coef=c;
	P->expon=e;
	P->link=NULL;
	(*pRear)->link=P;
	*pRear=P;
}

Polynomial ReadPoly(){
	Polynomial P,Rear,t;
	int c,e,N;
	scanf("%d",&N);
	P=(Polynomial)mallco(sizeof(struct PolyNode));
	P->link=NULL;
	Rear=P;
	while(N--){
		scanf("%d %d",&c,&e);
		Attach(c,e,&Rear);
	} 
	t=P;P=P->link;free(t);
	return P;
}

四、如何将两个多项式相加

Polynomial Add(Polynomial P1,Polynomial P2){
	Polynomial front,rear,tenp;
	int sum;
	rear=(Polynomial)mallco(sizeof(struct PolyNode));
	front=rear;
	while(P1&&P2){
		switch(Compare(P1->expon,P2->expon)){
			case 1:
				Attach(P1->coef,P1->expon,&rear);
				P1=P1->link;
				break;
			case -1:
				Attach(P2->coef,P2->expon,&rear);
				P2=P1->link;
				break;
			case 0:
				sum=P1->coef+P2->coef;
				if(sum){
					Attach(sum,P1->expon,&rear);
					P1=P1->link;
					P2=P2->link;
					break;
				}
		}
	}
	for(;P1;P1=P1->link){
		Attach(P1->coef,P1->expon,&rear);
	}
	for(;P2;P2=P2->link){
		Attach(P2->coef,P2->expon,&rear);
	}
	rear->link=NULL;
	temp=front;
	front=front->link;
	free(temp);
	return front;
}

五、如何将两个多项式相乘

Polynomial Mult(Polynomial P1,Polynomial P2){
	Polynomial P,Rear,t1,t2;
	int c,e;
	if(!P1 || !P2){
		return NULL;
	}
	t1=P1;t2=P2;
	P=(Polynomial)mallco(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){
				if(Rear->link->coef + c){
					Rear->link->coef += c;
				}else{
					t=Rear->link;
					Rear->link=t->link;
					free(t);
				}
			}else{
				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;
}

六、如何将多项式输出

void PrintPoly(Polynomial P){
	int flag = 0;
	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");
}