数据结构习题---单链表---一元多项式的加减

【问题描述】

设计一个一元稀疏多项式简单计算器。

【基本要求】

一元稀疏多项式简单计算器的基本功能是：
（1）输入并建立多项式；
（2）输出多项式，输出形式为整数序列：n，c1，e1，c2，e2，…，cn，en，其中ｎ是多项式的项数，ci和ei分别是第i项的系数和指数，序列按指数降序排列；
（3）实现多项式相加：C=A＋B；
（4）实现多项式相减：C=A－B。

ps.用带表头结点的单链表存储多项式，多项式的项数存放在头结点。

//异地相加减 

#include<stdio.h>
#include<stdlib.h>
#include<math.h>

typedef struct PolyNode{
	float coef;
	int expn;
	struct PolyNode *next;
}PolyNode;
typedef PolyNode* PolyLinkList;

void CreatPolyn(PolyLinkList *L, int n);
void DestroyPloyn(PolyLinkList *L);
void AddPolyn(PolyLinkList La, PolyLinkList Lb, PolyLinkList *Lc);
void SubtractPolyn(PolyLinkList La, PolyLinkList Lb, PolyLinkList *Lc);
void PrintPolyn(PolyLinkList L);

 
//1.创建一元多项式，n为项数
void CreatPolyn(PolyLinkList *L, int n){
	PolyNode *newNode, *r;
	float x;
	int y,i;
	
	*L = (PolyNode *)malloc(sizeof(PolyNode));
	if(!(*L)){
		printf("分配内存失败!\n"); 
		exit(OVERFLOW);
	}
	(*L)->next = NULL;	//初始化，建立一个头结点
	
	r = *L;		//尾指针，始终指向当前链表的尾结点
	printf("请升幂输入各项：");
	for(i = 0; i < n; i++){
		scanf("%f%d", &x, &y);
		newNode = (PolyNode *)malloc(sizeof(PolyNode));
		if(!newNode)	exit(OVERFLOW);
		newNode->coef = x;
		newNode->expn = y;
		r->next = newNode;
		r = newNode;
	}
	r->next = NULL;
}

//2.销毁多项式 
void DestroyPloyn(PolyLinkList *L){
	PolyNode *pre = *L, *p = pre->next;
	while(p!=NULL){
		free(pre);
		pre = p;
		p = pre->next;
	}
	free(pre);
	*L = NULL;
}

//3.多项式相加，即Lc = La + Lb 
void AddPolyn(PolyLinkList La, PolyLinkList Lb, PolyLinkList *Lc){
	PolyNode *pa, *pb, *pc, *s;
	pc = *Lc = (PolyNode *)malloc(sizeof(PolyNode));
	pc->next = NULL;
	pa = La->next;
	pb = Lb->next; 
	while(pa!=NULL&&pb!=NULL){
		if(pa->expn < pb->expn){
			s = (PolyNode *)malloc(sizeof(PolyNode));
			s->coef = pa->coef; 
			s->expn = pa->expn;
			s->next = NULL;
			pc->next = s;
			pc = s;
			pa = pa->next;
		}
		else if(pa->expn > pb->expn){
			s = (PolyNode *)malloc(sizeof(PolyNode));
			s->coef = pb->coef; 
			s->expn = pb->expn;
			s->next = NULL;
			pc->next = s;
			pc = s;
			pb = pb->next;
		}
		else{
			float x = pa->coef + pb->coef;
			if(abs(x)<=1.0e-6){
				pa = pa->next;
				pb = pb->next;
			}
			else{
				s = (PolyNode *)malloc(sizeof(PolyNode));
				s->coef = x; 
				s->expn = pb->expn;
				s->next = NULL;
				pc->next = s;
				pc = s;
				pa = pa->next;	
				pb = pb->next;
			}
		}
	}
	
	while(pa!=NULL){   //pb==NULL时 将a的剩余部分连到c后面 
		s = (PolyNode *)malloc(sizeof(PolyNode));
		s->coef = pa->coef; 
		s->expn = pa->expn;
		s->next = NULL;
		pc->next = s;
		pc = s;
		pa = pa->next;
	}
	
	while(pb!=NULL){
		s = (PolyNode *)malloc(sizeof(PolyNode));
		s->coef = pb->coef; 
		s->expn = pb->expn;
		s->next = NULL;
		pc->next = s;
		pc = s;
		pb = pb->next;
	}
}

//4.多项式相减，即Lc = La - Lb 利用Lb取反实现 
void SubtractPolyn(PolyLinkList La, PolyLinkList Lb, PolyLinkList *Lc){
	PolyNode *p = Lb->next;
	while(p!=NULL){
		p->coef = -p->coef;//Lb系数逐项取反 
		p = p->next;
	}
	AddPolyn(La, Lb, Lc);
}

//5.输出多项式 
void PrintPolyn(PolyLinkList L){
	if(L->next==NULL){
		printf("0");
		return;
	}
	PolyNode *p = L->next;
	int i = 0;
	while(p!=NULL){
		if(i==0){         	//第一项单独处理 
			if(p->expn==0)	//指数等于0，系数原样输出 
				printf("%.1f", p->coef);
			else if(p->expn==1){ //指数等于1
				if(p->coef==1)	//系数为1
					printf("x");
				else if(p->coef==-1)	//系数为-1
					printf("-x");
				else 
					printf("%.1fx", p->coef);
			}
			else{  	//其他指数
				if(p->coef==1)	//系数为1
					printf("x^%d", p->expn);
				else if(p->coef==-1)	//系数为-1
					printf("-x^%d", p->expn);
				else 
					printf("%.1fx^%d", p->coef, p->expn);
			}
		}
		else{  	//其余项
			if(p->expn==1){  		//指数等于1 
				if(p->coef==1)	//系数为1
					printf(" + x");
				else if(p->coef==-1)	//系数为-1
					printf(" - x");
				else
					if(p->coef>0)	printf(" + %.1fx", p->coef);
					else	printf(" - %.1fx", -p->coef);
			}
			else{ 	//其他指数
				if(p->coef==1)	//系数为1
					printf(" + x^%d", p->expn);
				else if(p->coef==-1)	//系数为-1
					printf(" - x^%d", p->expn);
				else
					if(p->coef>0)	printf(" + %.1fx^%d", p->coef, p->expn);
					else	printf(" - %.1fx^%d", -p->coef, p->expn);
			}
		}
		p = p->next;
		i++;
	}
	printf("\n\n");
}


int main(){
	PolyLinkList La, Lb, Lc;
	int n, m;
	
	printf("----------一元多项式的计算-----------\n\n");
	printf("多项式若为ax+bx^2,请输入a 1 b 2(系数和幂次都要输)\n");
	printf("请输入第一个多项式的项数：");
	scanf("%d", &n);
	CreatPolyn(&La, n);
	printf("第一个多项式为：");
	PrintPolyn(La);
	
	printf("请输入第二个多项式的项数：");
	scanf("%d", &m);
	CreatPolyn(&Lb, m);
	printf("第二个多项式为：");
	PrintPolyn(Lb);
	
	AddPolyn(La, Lb, &Lc);
	printf("两者相加：");
	PrintPolyn(Lc);
	
	SubtractPolyn(La, Lb, &Lc);
	printf("两者相减：");
	PrintPolyn(Lc);
	
	return 0; 
}