一元稀疏多项式加减

小咪咪 2022-08-19 02:10 180阅读 0赞

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//一元稀疏多项式加减
    #include<stdio.h>
    #include<stdlib.h>
    #include<math.h>
    #define OK	1
    #define ERROR	0
    
    typedef int status;
    typedef struct PNode{
    	float coef;
    	int expn;
    	struct PNode *next;
    }PNode,*PolyNomial;
    /*  建立一个多项式链表  */
    status CreatPolyNnomial(PolyNomial &L)
    {//建立一元稀疏多项式，按照指数递减排列，不包含指数重复项
    	int n;//n表示一元多项式的项数，如果输入为小于0的数，则继续输入，直到n合法为止，接下来输入n项的稀疏和指数，若指数小于0，返回ERROR
    	PolyNomial p, pre, r;
    	L = (PolyNomial)malloc(sizeof(PNode));
    	L->coef = NULL; 
    	L->expn = -1;
    	L->next = NULL; 
    	printf("请输入项数：\n");
    	scanf("%d", &n); 
    	while(n == 0){
    		printf("输入的项数有误：\n");
    		scanf("%d", &n); 
    	} //根据合法的系数和指数，生成结点，按照指数从大到小的顺序插入链表，若已存在指数相同的项，则放弃当前项
    	for(int i = 1; i <= n; i++){
    		p = (PolyNomial)malloc(sizeof(PNode)); 
    		printf("请输入%d项系数",i);
    		scanf("%f", &p->coef); 
    		printf("请输入%d项指数",i);
    		scanf("%d", &p->expn);
    		p->next = NULL;
    		pre = L;
    		r = L->next;
    		while(r && r->expn > p->expn){
    			pre = r;
    			r = r->next;
    		}
    		if(r == NULL || r->expn < p->expn){
    			p->next = r;
    			pre->next = p;
    		}else if(r->expn == p->expn){
    			free(p);
    		}
    	} 
    	return OK;
    }
    
    void add(PolyNomial &La,PolyNomial &Lb,PolyNomial &Lc)
    {//求Lc=La+Lb，利用原表空间实现
    	PolyNomial p1, p2, p3, r;
    	int sum;
    	p1 = La->next;
    	p2 = Lb->next;
    	p3 =  La;
    	while(p1 && p2){
    		if(p1->expn == p2->expn){
    			sum = p1->coef + p2->coef;
    			if(sum != 0){
    				p1->expn = sum;
    				p3->next = p1;
    				p3 = p1;
    				p1 = p1->next;
    				r = p2;
    				p2 = p2->next;
    				free(r);
    			}else{
    				r = p1; 
    				p1 = p1->next;
    				free(r);
    				r = p2; 
    				p2 = p2->next;
    				free(r);	
    			}
    		}else if(p1->expn > p2->expn){
    			p3->next = p1;
    			p3 = p1;
    			p1 = p1->next;
    		}else{
    			p3->next = p2;
    			p3 = p2;
    			p2 = p2->next;
    		}
    	}
    	p3->next = p1 ? p1 : p2;
    	free(Lb);
    }
    
    void print(PolyNomial L)
    {//输出多项式L
    	PolyNomial p;
    	p = L->next;
    	while(p){
    		printf("%fX^%d+", p->coef,p->expn);
    		p = p->next;
    	}
    }
    
    int main()
    {
    	PolyNomial La = NULL,Lb = NULL,Lc = NULL;
    	int ch;
    	printf("*****************一元稀疏多项式相加*****************\n");
    	printf("1、建立多项式La   2、建立多项式Lb   3、输出多项式La   4、输出多项式Lb   5、多项式相加   6、输出和多项式   7、退出\n");
    	printf("请选择：");
    	scanf("%d",&ch);
    	while(ch!=7)
    	{
    		switch(ch)
    		{
    		case 1:	
    				CreatPolyNnomial(La);
    				break;
    		case 2:	
    				CreatPolyNnomial(Lb);
    				break;
    		case 3:	
    				print(La);
    				break;
    		case 4:	
    				print(Lb);
    				break;
    		case 5:	
    				add(La, Lb, Lc); 
    				break;
    		case 6:	
    				print(La);
    				break;
    		default: printf("输入错误，请重新输入！\n");
    		}
    		printf("请选择：");
    		scanf("%d",&ch);
    	}
    	
    	return 0;
    }

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