链表实现多项式的加法和乘法

#include<stdio.h>
#include<stdlib.h>
#define LEN sizeof(PolyNode)

typedef struct node{      //声明多项式节点的结构体表示
	float coef;       //系数
	int exp;          //指数
	struct node* next;
}PolyNode;           //多项式节点
typedef PolyNode* Polynomial;   

Polynomial create(){            //输入并创建链表的函数
	Polynomial p,q,head=(Polynomial)malloc(LEN);
	float coef;
	int exp;
	head->next=NULL;
	printf("Please enter the coef and exp,ending with '0 0':");
	while(scanf("%f %d",&coef,&exp)&&coef){
		if(head->next){
			p=head;
			while(p->next&&exp<p->next->exp)      //找到要插入的位置，插在p节点的后面
				p=p->next;
			if(p->next){
				if(p->next->exp==exp){                 //有相同指数时直接加到原来的节点上
					p->next->coef+=coef;
					if(p->next->coef>-0.000001&&p->next->coef<0.000001){  //若系数之和为零，则舍去该点,浮点运算存在误差
						q=p->next;
						p->next=q->next;
						free(q);
					}
				}
				else{
					q=(Polynomial)malloc(LEN);
					q->coef=coef;
					q->exp=exp;
					q->next=p->next;
					p->next=q;
				}
			}
			else{           //若要插入的系数最小，插在最末
				p->next=(Polynomial)malloc(LEN);
				p->next->coef=coef;
				p->next->exp=exp;
				p->next->next=NULL;
			}
		}
		else{           //插入第一个节点时
			head->next=(Polynomial)malloc(LEN);
			head->next->coef=coef;
			head->next->exp=exp;
			head->next->next=NULL;
		}
	}
	return head;
}

Polynomial add(Polynomial poly1,Polynomial poly2){             //将poly1,poly2相加得到一个新多项式链表poly3
	Polynomial p,q,r,poly=(Polynomial)malloc(LEN);    //poly为和多项式链表的头节点
	poly->next=NULL;
	r=poly;                 //r指向poly的最后一个节点
	p=poly1->next;
	q=poly2->next;
	while(p&&q){
		if(p->exp>q->exp){   
			r->next=(Polynomial)malloc(LEN);
			r=r->next;
			r->coef=p->coef;
			r->exp=p->exp;
			p=p->next;
		}
		else if(p->exp<q->exp){
			r->next=(Polynomial)malloc(LEN);
			r=r->next;
			r->coef=q->coef;
			r->exp=q->exp;
			q=q->next;
		}
		else{
			float m=p->coef+q->coef;
			if(!(m>-0.000001&&m<0.000001)){
				r->next=(Polynomial)malloc(LEN);
				r=r->next;
				r->coef=m;
				r->exp=p->exp;
			}
			p=p->next;
			q=q->next;
		}
	}
	while(p){        //若p中有剩余
		r->next=(Polynomial)malloc(LEN);
		r=r->next;
		r->coef=p->coef;
		r->exp=p->exp;
		p=p->next;
	}	
	while(q){       //若q中有剩余
		r->next=(Polynomial)malloc(LEN);
		r=r->next;
		r->coef=q->coef;
		r->exp=q->exp;
		q=q->next;
	}	
	r->next=NULL;
	return poly;
}

void polyAdd(Polynomial poly1,Polynomial poly2){          //把poly2加到poly1上，加完之后poly1为和多项式，poly2将被释放
	Polynomial p,q,t;
	q=poly2->next;
	while(q){
		p=poly1;
		while(p->next&&q->exp<p->next->exp)            //找到要插入poly1的位置，插在p与p->next之间
			p=p->next;
		if(p->next){            //插在poly1中间
			if(q->exp==p->next->exp){        //若要插入节点的系数等于p->next的系数
				float m=q->coef+p->next->coef;
				if(m>-0.000001&&m<0.000001){
					Polynomial tmp1=p->next;
					p->next=tmp1->next;
					free(tmp1);
				}
				else{
					p->next->coef=m;
				}
			}
			else{
				Polynomial tmp2=(Polynomial)malloc(LEN);
				tmp2->coef=q->coef;
				tmp2->exp=q->exp;
				tmp2->next=p->next;
				p->next=tmp2;
			}
		}
		else{                 //插在poly1末端
			p->next=(Polynomial)malloc(LEN);
			p->next->coef=q->coef;
			p->next->exp=q->exp;
			p->next->next=NULL;
		}
		t=q;
		q=q->next;
		free(t);
	}
	free(poly2);          //释放poly2的头节点
}

Polynomial multiply(Polynomial poly,float coef,int exp){    //多项式poly与单项coef^exp相乘，返回乘法之后的多项式链表
	Polynomial p,r,head=(Polynomial)malloc(LEN);
	head->next=NULL;
	r=head;
	p=poly->next;
	while(p){
		r->next=(Polynomial)malloc(LEN);
		r=r->next;
		r->coef=p->coef*coef;
		r->exp=p->exp+exp;
		p=p->next;
	}
	return head;
}

Polynomial polyMultiply(Polynomial poly1,Polynomial poly2){    //返回poly1*poly2的多项式链表
	Polynomial p,poly=(Polynomial)malloc(LEN);     //乘积多项式的头指针
	poly->next=NULL;
	p=poly2->next;
	while(p){
		polyAdd(poly,multiply(poly1,p->coef,p->exp));   //把poly1和poly2中的每一项相乘后求和
		p=p->next;
	}
	return poly;
}

void print(Polynomial poly){     //输出链表的函数
	if(poly&&poly->next){
		Polynomial p=poly->next;
		while(p){
			if(p->next==NULL){   //当p为最后一个节点时
				if(p->exp!=0) printf("%fx^%d",p->coef,p->exp);
				else printf("%f",p->coef);
			}
			else{
				printf("%fx^%d",p->coef,p->exp);
				if(p->next->coef>0) printf("+");
			}
			p=p->next;
		}
		printf("
");
	}
	else 
		printf("0.000000
");
}

void clear(Polynomial poly){    //释放内存
	if(poly&&poly->next){
		Polynomial p,q;
		p=poly;
		while(p){
			q=p->next;
			free(p);
			p=q;
		}
	}
	poly=NULL;
}

int main(){
	Polynomial p1,p2,p3,p4;
	printf("Please input p1:
");
	p1=create();
	printf("Please input p2:
");
	p2=create();
	printf("p1=");
	print(p1);
	printf("p2=");
	print(p2);
	p3=add(p1,p2);          //p3=p1+p2
	printf("p3=p1+p2=");
	print(p3);
	p4=polyMultiply(p1,p2);  //p4=p1*p2
	printf("p4=p1*p2=");
	print(p4);
	clear(p1);        //释放内存
	clear(p2);
	clear(p3);
	clear(p4);
	return 0;
}