多项式.cpp

可进行多项式加

#define NULL 0
#include <stdio.h>
#include <math.h>
#include <iostream.h>
struct sq{
	double coef;
	int expn;
	struct sq *next;
}*head[11];
int i,j,k;

//去除零项
int purge(int m){
	struct sq *z,*p,*q;

    if (head[m]==NULL)
		return(0);
	p=head[m];
	q=p;
	while(p!=NULL){
		if (p->coef==0){
			z=p;
			if (p==head[m]){
				head[m]=p->next;
				p=p->next;
			}
			else{
			    q->next=p->next;
				p=p->next;
			}
			delete z;
		}
		else {
			q=p;
			p=p->next;
		}
	}
	return (0);
}

//创建
void creat(int m,int n){
	struct sq *z,*p,*q;
	
	if(n==0)
		return ;
	z=new struct sq ;
	cin>>z->coef>>z->expn;
	z->next=NULL;
	head[m]=z;
	for(i=1;i<=n-1;i++){
	    z=new struct sq ;
	    cin>>z->coef>>z->expn;
    	p=head[m];
    	if(z->expn<p->expn){
    	   head[m]=z;
 	       z->next=p; 
           continue;
        }
        for (;(p->next!=NULL)&&(z->expn>p->expn);){
           q=p;
           p=p->next;
        }
		if(z->expn==p->expn){
			p->coef=p->coef+z->coef;
			continue;
		}
        if(p->next==NULL)
           if(z->expn>p->expn){
              p->next=z;
              z->next=NULL;}
           else {
              q->next=z;
              z->next=p;
           }
        else{
           q->next=z;
           z->next=p;
        }
     }
	purge (m);
}

//显示
void print(int m){
    struct sq *p;
    
	p=head[m];
	if (head[m]==NULL){
	   cout<<"多项式不存在"<<endl;
    }
    else{
       for(;p!=NULL;){
          if(p->coef>0&&p->expn>0){
             cout<<p->coef<<"x^"<<p->expn<<"+";
             p=p->next;
          }
          else if(p->coef<0&&p->expn>0){
             cout<<"\b";
             cout<<p->coef<<"x^"<<p->expn<<"+";
             p=p->next;
          }
          else if(p->coef<0&&p->expn<0){
             cout<<"\b";
             cout<<p->coef<<"x^"<<"("<<p->expn<<")"<<"+";
             p=p->next;
          }
          else {
             cout<<p->coef<<"x^"<<"("<<p->expn<<")"<<"+";
             p=p->next;
          }
       }
	   cout<<"\b "<<endl;
	}
}
                                
//复制
int cpy(int m, int mc){
    struct sq *z,*p,*q,*y;
    
	if(head[m]==NULL){
		head[mc]=NULL;
		return 0;
	}
    z=new struct sq ;
    head[mc]=z;
    p=head[m];
    q=head[mc];
	for(;p!=NULL;){
	   z->coef=p->coef;
       z->expn=p->expn;
       z->next=p->next;
       p=p->next;
       y=z;
       z=new struct sq ;
       y->next=z;
    }
    y->next=NULL;
    delete z;
	return 0;
}

//求和(就地运算)
void add(int m1,int m2){                 //存在m1处 
   struct sq *z,*y,*p,*q;
   
   z=p=head[m1];
   q=head[m2];
   for(;p!=NULL&&q!=NULL;){
      if(p->expn<q->expn){
         z=p;
         p=p->next;
      }
      else if(p->expn>q->expn){
		 if(p!=head[m1])
			 z->next=q;
		 else
		    head[m1]=q;
         y=q->next;        
         z=q;
         q->next=p;
         q=y;
      }
      else if(p->expn==q->expn){
         p->coef+=q->coef;
         z=p;
         y=q;
		 if(z==head[m1])
			 head[m1]=p;
         p=p->next;
         q=q->next;
         delete y;
      }
   }
   if(p==NULL)
	  if(p!=head[m1])
         z->next=q;
	  else
		 head[m1]=q;
   head[m2]=NULL;
   purge(m1);
}
                  
//求和(异地运算)  
void add(int m1,int m2,int m3){                           //此处用了函数重载 
   struct sq *z,*y,*p,*q;
   
   z=new struct sq;
   head[m3]=z;
   p=head[m1];
   q=head[m2];
   y=NULL;
   for(;p!=NULL&&q!=NULL;){
      if(p->expn<q->expn){
         z->coef=p->coef;
         z->expn=p->expn;
         p=p->next;
      }
      else if(p->expn>q->expn){
         z->coef=q->coef;
         z->expn=q->expn;
         q=q->next;
      }
      else if(p->expn==q->expn){
         z->coef=p->coef+q->coef;
         z->expn=p->expn;
         p=p->next;
         q=q->next;
      }
      z->next=new struct sq;
      y=z;
      z=z->next;
   }
   if(p==NULL){
      for(;q!=NULL;){
         z->coef=q->coef;
         z->expn=q->expn;
         z->next=new struct sq;
         y=z;
         z=z->next;
         q=q->next;
      }
      if(q==NULL){        
		 if(head[m3]==y)
            y->next=NULL;
		 else
			 head[m3]=NULL;
		 delete z;
      }
   }
   else{
      for(;p!=NULL&&q==NULL;){
         z->coef=p->coef;
         z->expn=p->expn;
         z->next=new struct sq;
         y=z;
         z=z->next;
         p=p->next;
      }
      delete z;
      y->next=NULL;
   }
   purge(m3);
}

//求值
double ans(int m, double x){
   double answer=0.0;
   struct sq *p;
   
   if(head[m]==0)
      return(0);
   p=head[m];
   for(;p!=NULL;){
      answer+=p->coef*pow(x,p->expn);
      p=p->next;
   }
   return answer;
}
 
//求差(就地运算)                                     //存在m1处
void dev(int m1,int m2){
   struct sq *z,*y,*p,*q;
   
   z=p=head[m1];
   q=head[m2];
   for(;p!=NULL&&q!=NULL;){
      if(p->expn<q->expn){
         z=p;
         p=p->next;
      }
      else if(p->expn>q->expn){
         if(p!=head[m1])
            z->next=q;
         else           
            head[m1]=q;
		 y=q->next;
         q->coef=-q->coef;
         q->next=p;
		 z=q;
         q=y;
      }
      else if(p->expn==q->expn){
         p->coef-=q->coef;
         z=p;
         y=q;
		 if(z==head[m1])
			 head[m1]=p;
         p=p->next;
         q=q->next;
         delete y;		 
      }
   }
   if(p==NULL){
	  if(z==head[m1])
	     head[m1]=q;
	  else
         z->next=q;
   }
   for(;q!=NULL;){
	  q->coef=-q->coef;
	  q=q->next;
   }
   head[m2]=NULL;
   purge(m1);
} 

//求差(异地运算)                                      //此处用了函数重载 
void dev(int m1,int m2,int m3){
   struct sq *z,*y,*p,*q;
   
   z=new struct sq;
   head[m3]=z;
   p=head[m1];
   q=head[m2];
   for(;p!=NULL&&q!=NULL;){
      if(p->expn<q->expn){
         z->coef=p->coef;
         z->expn=p->expn;
         p=p->next;
      }
      else if(p->expn>q->expn){
         z->coef=-q->coef;
         z->expn=q->expn;
         q=q->next;
      }
      else if(p->expn==q->expn){
         z->coef=p->coef-q->coef;
         z->expn=p->expn;
         p=p->next;
         q=q->next;
      }
      z->next=new struct sq;
      y=z;
      z=z->next;
   }
   if(p==NULL){
      for(;q!=NULL;){
         z->coef=-q->coef;
         z->expn=q->expn;
         z->next=new struct sq;
         y=z;
         z=z->next;
         q=q->next;
      }
      if(q==NULL){         
		 if(head[m3]==y)
            y->next=NULL;
		 else 
			head[m3]=NULL;
		 delete z;
      }
   }
   else{
      for(;p!=NULL&&q==NULL;){
         z->coef=p->coef;
         z->expn=p->expn;
         z->next=new struct sq;
         y=z;
         z=z->next;
         p=p->next;
      }
      delete z;
      y->next=NULL;
   }
   purge(m3);
}
	
//N阶导数(就地运算) 
int derivative(int m1, int N){                       //存在m1处
   struct sq *p;
   int i;

   if(head[m1]==NULL){
	   cout<<"多项是不存在"<<endl;
	   return(0);
   }
   p=head[m1];
   for(;p!=NULL;){
      for(i=0;i<N;i++)
         p->coef*=(p->expn-i);
      p->expn-=N;