#include<iostream>
#include<conio.h>
#include<stdlib.h>
#include<math.h>
using namespace std;
struct Node{
float coef;
int exp;
};
typedef Node polynomial;
struct LNode{
polynomial data;
LNode *next;
};
typedef LNode* Link;
void CreateLink(Link &L,int n);
void PrintList(Link L);
void PolyAdd(Link &pc,Link pa,Link pb);
void PolyStract(Link &pc,Link pa,Link pb);
void CopyLink(Link &pc,Link pa);
void PolyMultiply(Link &pc,Link pa,Link pb);
int JudgeIfExpSame(Link pa,Link e);
void DestroyLink(Link &L)
{Link p;
p=L->next;
while(p)
{ L->next=p->next;
delete p;
p=L->next;
}
delete L ;
L=NULL;
}
void CreateLink(Link &L,int n)
{if(L!=NULL)
{DestroyLink(L);}
Link p,newp;
L=new LNode;
L->next=NULL;
(L->data).exp=-1;
p=L;
for(int i=1;i<=n;i++)
{ newp=new LNode;
cout<<"请输入第"<<i<<"项的系数和指数:"<<endl;
cout<<"系数:";
cin>>(newp->data).coef;
cout<<"指数:";
cin>>(newp->data).exp;
if(newp->data.exp<0)
{cout<<"您的输入有误,指数不允许为负值!"<<endl;
delete newp;
i--;
continue;
}
newp->next=NULL;
p=L;
if(newp->data.coef==0)
{cout<<"系数为零,重新输入!"<<endl;
delete newp;
i--;
continue;
}
while((p->next!=NULL)&&((p->next->data).exp<(newp->data).exp))
{ p=p->next;
//p指向指数最小的那一个
}
if(!JudgeIfExpSame(L,newp))
{newp->next=p->next;
p->next=newp;
}
else
{
cout<<"输入的该项指数与多项式中已存在的某项相同,请重新创建一个正确的多项式"<<endl;
delete newp;
DestroyLink(L);
CreateLink(L,n);
break;
}
}
JudgeIf(L);
}
void JudgeIf(Link L)
{Link p;
int flag=0;
p=L->next;
while(p->next!=NULL)
{
if(abs(p->next->data.exp-p->data.exp)>1)
flag=1;
else
flag=0;
p=p->next;
}
if(flag)
cout<<"该多项式是稀疏的"<<endl;
else
cout<<"该多项式是连续的"<<endl;
}
int JudgeIfSame(Link L,Link e)
{Link p;
p=L->next;
while(p!=NULL&&(e->data.exp!=p->data.exp))
p=p->next;
if(p==NULL)
return 0;
else return 1;
}
void PrintList(Link L)
{Link p;
if(L==NULL||L->next==NULL)
cout<<"该一元多项式不空!"<<endl;
else
{p=L->next;
if((p->data).coef>0)
{if((p->data).exp==0)
cout<<(p->data).coef;//如果指数为0则直接输出系数
else if((p->data).coef==1&&(p->data).exp!=1)
cout<<"x";
else if((p->data).coef==1&&(p->data).coef!=1)
cout<<"x^"<<(p->data).exp;
else if((p->data).exp==1&&(p->data).coef!=1)
cout<<(p->data).coef<<"x";
else cout<<(p->data).coef<<"x^"<<(p->data).exp;
}
if((p->data).coef<0)
{
if((p->data).exp==0)
cout<<(p->data).coef;
else if(p->data.coef==-1&&p->data.exp==1)
cout<<"-x";
else if(p->data.coef==-1&&p->data.exp!=1)
cout<<"-x^"<<p->data.exp;
else if(p->data.exp==1)
cout<<p->data.coef<<"x";//如果指数为1,则输出系数倍经
else cout<<(p->data).coef<<"x^"<<(p->data).exp;
}
p=p->next;
while(p!=NULL)
{
if((p->data).coef>0)
{
if((p->data).exp==0)
cout<<"+"<<(p->data).coef;
else if((p->data).exp==1&&(p->data).coef!=1)
cout<<"+"<<(p->data).coef<<"x";
else if((p->data).exp==1&&(p->data).coef==1)
cout<<"+"<<"x";
else if((p->data).coef==1&&(p->data).exp!=1)
cout<<"+"<<"x^"<<(p->data).exp;
else
cout<<"+"<<(p->data).coef<<"x^"<<(p->data).exp;
}
if((p->data).coef<0)//系数小于0时输出情况
{
if((p->data).exp==0)
cout<<(p->data).coef;
else if(p->data.coef==-1&&p->data.exp==1)
cout<<"-x";
else if(p->data.coef==-1&&p->data.exp!=1)
cout<<"-x^"<<p->data.exp;
else if(p->data.exp==1)
cout<<p->data.coef<<"x";
else cout<<(p->data).coef<<"x^"<<(p->data).exp;
}
p=p->next;
}
}
cout<<endl;
}
void CopyLink(Link &pc,Link pa)
{Link p,q,r;
pc=new LNode;
pc->next=NULL;
r=pc;
p=pa;
while(p->next!=NULL)
{
q=new LNode;
q->data.coef=p->next->data.coef;
q->data.exp=p->next->data.exp;
r->next=q;
q->next=NULL;
r=q;
p=p->next;
}
}
//加法模块
void PolyAdd(Link &pc,Link pa,Link pb)
{
Link p1,p2,p,pd;
CopyLink(p1,pa);
CopyLink(p2,pb);
pc=new LNode;
pc->next=NULL;
p=pc;
p1=p1->next;
p2=p2->next;
while(p1!=NULL&&p2!=NULL)
{
if(p1->data.exp<p2->data.exp)
{
p->next=p1;
p=p->next;
p1=p1->next;
}
else if(p1->data.exp>p2->data.exp)
{
p->next=p2;
p=p->next;
p2=p2->next;
}
else
{
p1->data.coef=p1->data.coef+p2->data.coef;
if(p1->data.coef!=0)
{
p->next=p1;
p=p->next;
p1=p1->next;
p2=p2->next;
}
else
{
pd=p1;
p1=p1->next;
p2=p2->next;
delete pd;
}
}
}
if(p1!=NULL)
{
p->next=p1;
}
if(p2!=NULL)
{
P->next=p2;
}
}
void PolySubstract(Link &pc,Link pa,Link pb)
{
Link p,pt;
CopyLink(pt,pb);
p=pt;
while(p!=NULL)
{
(p->data).coef=(-(p->data).coef);
p=p->next;
}
PolyAdd(pc,pa,pt);
DestroyLink(pt);
}
void Clear()
{
system("pause");
system("cls");
}//让用户重新选择
void PolyMultiply(Link &pc,Link pa,Link pb)
{
Link p1,p2,p,pd,newp,t;
pc=new LNode;
pc->next=NULL;
p1=pa->next;
p2=pb->next;
while(p1!=NULL)
{
pd=new LNode;
pd->next=NULL;
p=new LNode;
p->next=NULL;
t=p;
while(p2)
{
newp=new LNode;
newp->next=NULL;
newp->data.coef=p1->data.coef*p2->data.coef;
newp->data.exp=p1->data.exp+p2->data.exp;
t->next=newp;
t=t->next;
p2=p2->next;
}
PolyAdd(pd,pc,p);
CopyLink(pc,pd);
p1=p1->next;
p2=pb->next;
DestroyLink(p);
DestroyLink(pd);
}
}
void Menu()
{
cout<<""<<endl;
cout<<endl;
cout<<"***************************一元多项式的加、减、乘运算***************************"<<endl;
cout<<"\t\t\t\t\t\t\t\t "<<endl;
cout<<"[1] 创建要运算的两个一元多项式\t\t "<<endl;
cout<<"[2] 将两个一元多项式相加\t\t\t "<<endl;
cout<<"[3] 将两个一元多项式相减\t\t\t "<<endl;
cout<<"[4] 将两个一元多项式相乘\t\t\t "<<endl;
cout<<"[5] 显示两个一元多项式\t\t\t "<<endl;
cout<<"[6] 销毁所创建的两个一元多项式\t\t\t "<<endl;
cout<<"[7] 退出\t\t\t\t\t "<<endl;
cout<<"\t\t\t\t\t\t\t\t "<<endl;
cout<<"请选择:";
}
int CompareIfNum(int i)
{
if(i>0&&i<8)
return 0;
else return 1;//返回1时出错,因为菜单中只有1-7
}
void main()
{
int n;
Link L,La=NULL,Lb=NULL;//la,lb分别为创建的两个多项式
int choose;
while(1)
{
Menu();
cin>>choose;
switch(choose)
{
case 1:
cout<<"请输入你要运算的第一个一元多项式的项数:"<<endl;
cin>>n;
if(CompareIfNum(n)==1)
{
cout<<"您的输入有误,请重新输入......"<<endl;
Clear();
break;
}
CreateLink(Lb,n);
Clear();
break;
case 2:
if(La==NULL||Lb==NULL)
{
cout<<"您的多项式创建有误,请重新选择......"<<endl;
Clear();
break;
}
PolyAdd(L,La,Lb);
cout<<""<<endl;
cout<<"设相加的两个一元多项式为A和B则:"<<endl;
cout<<""<<endl;
cout<<"A的多项式为:"<<endl;
PrintList(La);
cout<<""<<endl;
cout<<"B的多项式为:"<<endl;
PrintList(Lb);
cout<<""<<endl;
cout<<"相加后的结果为:"<<endl;
PrintList(L);
cout<<""<<endl;
Clear();
DestroyLink(L);
break;
case 3:
if(La==NULL||Lb==NULL)
{
cout<<"您的多项式创建有误,请重新选择......"<<endl;
Clear();
break;
}
PolySubstract(L,La,Lb);
cout<<"设相减的两个一元多项式为A和B则:"<<endl;
cout<<""<<endl;
cout<<"A的多项式为:"<<endl;
PrintList(La);
cout<<""<<endl;
cout<<"B的多项式为:"<<endl;
PrintList(Lb);
cout<<""<<endl;
cout<<"相减后的结果为:"<<endl;
PrintList(L);
cout<<""<<endl;
Clear();
DestroyLink(L);
break;
case 4:
if(La==NULL||Lb==NULL)
{
cout<<"您的多项式创建有误,请重新选择......"<<endl;
Clear();
break;
}
PolyMultiply(L,La,Lb);
cout<<"设相乘的两个一元多项式为A和B则:"<<endl;
cout<<""<<endl;
cout<<"A的多项式为:"<<endl;
PrintList(La);
cout<<""<<endl;
cout<<"B的多项式为:"<<endl;
PrintList(Lb);
cout<<""<<endl;
cout<<"相乘后的结果为:"<<endl;
PrintList(L);
DestroyLink(L);
cout<<""<<endl;
Clear();
break;
case 5:
if(La==NULL||Lb==NULL)
{
cout<<"您的多项式创建有误,请重新选择......"<<endl;
Clear();
break;
}
cout<<"一元多项式A为:"<<endl;
PrintList(La);
cout<<""<<endl;
cout<<"一元多项式B为:"<<endl;
PrintList(Lb);
cout<<""<<endl;
Clear();
break;
case 6:
if(La&&Lb)
{
DestroyLink(La);
DestroyLink(Lb);
cout<<"多项式销毁成功!"<<endl;
Clear();
}
break;
case 7:
exit(0);//exit(0)强制终止程序,返回状态码0表示正常结束
default:
cout<<"您的输入有误,请重新选择操作......"<<endl;
Clear();
break;
}
}
}