#define N 100
float X[N],Y[N],M[N],a,b;
double f(int i,int j)
{
  double sum1=0;
  if(j-i==1) return (Y[j]-Y[i])/(X[j]-X[i]);
  else return (f(i+1,j)-f(i,j-1))/(X[j]-X[i]);
}

void main()
{

  ifstream istrm("E:\\data.txt");//这里是文件的输入，请相应改成普通键盘输入
  int n=3;
  for(int i=0;i<=n;i++)
   istrm>>X[i]>>Y[i];
  istrm>>a>>b;
  float h[N],u[N],q[N],d[N];
  for(i=0;i<n;i++)
   h[i]=X[i+1]-X[i];
  q[0]=1;q[n]=0;
  for(i=1;i<n;i++)
      q[i]=h[i]/(h[i-1]+h[i]);
  for(i=0;i<=n;i++)
   u[i]=1-q[i];
  d[0]=(6*(f(0,1)-a))/h[0];
  d[n]=(6*(b-f(n-1,n)))/h[n-1];
  for(i=1;i<n;i++)
     d[i]=6*f(i-1,i+1);
  float m[N];
  for(i=0;i<=n;i++) m[i]=2;
  for(i=1;i<=n;i++)
  {
    m[i]=m[i]-(u[i]/m[i-1])*q[i-1];
 d[i]=d[i]-(u[i]/m[i-1])*d[i-1];
  }
  M[n]=d[n]/m[n];
  cout<<M[n]<<endl;
  for(i=n-1;i>=0;i--)
  {
    M[i]=(d[i]-q[i]*M[i+1])/m[i];
 cout<<M[i]<<endl;
  }
}

 void main()
{
  cout<<"输入你想进行的X次多项试计算:";
  cin>>n;
  for(int i=0;i<=n;i++)
  {
    cout<<"输入第"<<i+1<<"个点的坐标:";
 cin>>X[i]>>Y[i];
  }
  sum=Y[0];
  cout<<"输入你想进行计算的x值:";
  cin>>x;
  s=(x-X[0]);
  f(0,n);
  cout<<sum;
}

typedef char TElemType;
typedef struct BiTNode{
  TElemType data;
  struct BiTNode *lchild,*rchild;
}BiTNode,*BiTree;

Status CreateBiTree(BiTree &T)
{
  TElemType ch;
  cout<<"输入你想要的数据：";
  cin>>ch;
  if(ch=='@') T=NULL;
  else
  {
    T=new BiTNode;
 if(!T) return ERROR;
 T->data=ch;
 CreateBiTree(T->lchild);
 CreateBiTree(T->rchild);
  }
  return OK;
}
Status PreOrderTraverse(BiTree T)
{
 if(T)
 {
   cout<<T->data;
   PreOrderTraverse(T->lchild);
   PreOrderTraverse(T->rchild);
 }
 return OK;
}
Status InOrderTraverse(BiTree T)
{
  if(T)
  {
    InOrderTraverse(T->lchild);
 cout<<T->data;
 InOrderTraverse(T->rchild);
  }
  return OK;
}
Status PostOrderTraverse(BiTree T)
{
  if(T)
  {
    PostOrderTraverse(T->lchild);
 PostOrderTraverse(T->rchild);
 cout<<T->data;
 }
  return OK;
}
int BiTreeDepth(BiTree T)
{
  int m=0;

  return m;
}

double f(double x)
{
   return pow(x,3.0/2.0);
}
double T(double n,double a,double b)
{
  double sum=0;
  for(int i=0;2*i+1<=n;i++)
  {
    sum+=f(a+double(2*i+1)/n);
  }
  if(n==1) return 0.5*(f(a)+f(b));
  return 0.5*T(n/2,a,b)+sum*(1.0/n);
}
void Romberg(double a,double b,double e)
{
  double Old[10]={0.0},New[10]={0.0};
  double h=b-a;
  New[0]=h*(f(a)+f(b))/2.0;
  int j;
  for(int i=1;;i++)
  {
    for(j=0;j<i;j++) Old[j]=New[j];
 New[0]=T(pow(2,i),a,b);
 for(j=1;j<=i;j++)
  New[j]=(pow(4,j)*New[j-1]/(pow(4,j)-1)-Old[j-1]/(pow(4,j)-1));
 if(fabs(New[i]-Old[i-1])<e) break;
  }
  cout<<New[i];
}

void main()
{
  double a,b; 
  double e;
  cout<<"请输入积分的下、上限：";
  cin>>a>>b;
  cout<<"输入你要的精度：";
  cin>>e;
  Romberg(a,b,e);
}

double c[10][10];

double f(double x)
{
  double sum=0;
  if(x==0) return 1;
  sum=sin(x)/x;
  return sum;
}
void initcotes(double c[][10])
{
  c[1][0]=c[1][1]=0.5;
  c[2][0]=c[2][2]=1.0/6.0;c[2][1]=2.0/3.0;
  c[3][0]=c[3][3]=1.0/8.0;c[3][1]=c[3][2]=3.0/8.0;
  c[4][0]=c[4][4]=7.0/90.0;c[4][1]=c[4][3]=16.0/45.0;c[4][2]=2.0/15.0;
  c[5][0]=c[4][5]=19.0/288.0;c[5][1]=c[5][4]=25.0/96.0;c[5][2]=c[5][3]=25.0/144.0;
}
void Trapezoid(double a,double b)
{
  cout<<"梯形公式的结果："<<(b-a)*(f(a)+f(b))/2<<endl;
}
void MidRect(double a,double b)
{
  cout<<"中矩形公式的结果："<<(b-a)*f((b+a)/2)<<endl;
}
void NewtonCotes(double a,double b)
{
  int n,k;double h;
  cout<<"请输入n的值：";
  cin>>n;
  h=(b-a)/double(n);
  double sum=0;
  for(k=0;k<=n;k++)
   sum+=c[n][k]*f(a+k*h);
  cout<<"牛顿-柯特斯公式的结果："<<(b-a)*sum<<endl;
}
int STrapezoid(double a,double b)
{ 
  int n,k,q;double h;
  cout<<"1--复化梯形公式"<<endl;
  cout<<"2--复化辛普森求积公式"<<endl;
  cout<<"输入你想进行的操作：";
  cin>>q; 
  cout<<"请输入n的值：";
  cin>>n;
  h=(b-a)/double(n);
  double sum=0;
  sum+=(f(a)+f(b));
  for(k=1;k<=n-1;k++)  sum+=2*f(a+k*h);
 if(q==1)
 {
  cout<<"复化梯形公式的结果："<<(h/2)*sum<<endl;
  return 1;
 }

  for(k=0;k<n;k++)
   sum+=4*f(a+(k+0.5)*h);
  cout<<"复化辛普森求积公式的结果："<<(h/6)*sum<<endl;
  return 1;

}

void main()
{
  double a,b;
  int p;
  cout<<"请输入积分的下、上限：";
  cin>>a>>b;
  initcotes(c);
  while(1)
  {
    cout<<"0--退出"<<endl;
 cout<<"1--梯形公式"<<endl;
 cout<<"2--中矩形公式"<<endl;
 cout<<"3--牛顿柯特斯公式:"<<endl;
 cout<<"4--复化公式"<<endl;
 cout<<"输入你想进行的操作:";
 cin>>p;
 
 switch(p)
 {
 case 1:Trapezoid(a,b);
 case 2:MidRect(a,b);
 case 3:NewtonCotes(a,b);
    case 4:STrapezoid(a,b);
 }
 if(p==0)  break;
  }
}

typedef char ElemType;

typedef struct LNode{
  ElemType data;
  struct LNode *next;
}LNode,*Link;

class LinkList
{
private:
 Link head;
public:
 LinkList(){}
 LinkList(ElemType a[]);
 void CreateLinkList();
 void inver();
 ElemType get(int i);
 Status insert(int loc,ElemType e);
 ElemType del(int i);
 void print();
 void MergeList(LinkList la,LinkList lb);
};
LinkList::LinkList(ElemType a[])
{
  int n=strlen(a),i;
  Link p;
  head=new LNode;
  head->next=NULL;
  for(i=n-1;i>=0;i--)
  {
    p=new LNode;
 p->data=a[i];
 p->next=head->next;
 head->next=p;
  }
};
void LinkList::print()
{
  Link p=head->next;
 while(p)
 {
   cout<<p->data<<"->";
   p=p->next;
 }
 cout<<"NULL"<<endl;
};
void LinkList::CreateLinkList()
{
  int n;
  cout<<"请输入你要构建的表的长度:";
  cin>>n;
  ElemType *e;
  e=new ElemType[n];
  cin>>e;
  int i;
  Link p;
  head=new LNode;
  head->next=NULL;
  for(i=n-1;i>=0;i--)
  {
    p=new LNode;
 p->data=e[i];
 p->next=head->next;
 head->next=p;
  }
 
}
ElemType LinkList::get(int i)
{
  int cnt=1;
  Link p=head->next;
  while(cnt!=i)
   p=p->next;
  return p->data;

}
Status LinkList::insert(int loc,ElemType e)
{
  Link p=head;
  int j=0;
  while(p&&j++<loc-1) p=p->next;
  if(!p||j>loc-1) return ERROR;
  Link s=new LNode;
  s->data=e;
  s->next=p->next;
  p->next=s;
  return OK;
}

#define LIST_INIT_SIZE 100

template <class ElemType>
class SqList
{
  private:
   ElemType *elem;
   int length;
      int listsize;
  public:
   SqList(int max=LIST_INIT_SIZE);
   ~SqList(){delete[] elem;}
      void ClearList();
      Status input(int n);
      Status output();
      Status ListEmpty();
      int    ListLength();
      ElemType GetElem(int i);
      Status NextElem(ElemType i,ElemType &next_e);
      Status ListInsert(int i,ElemType e);
      Status ListDelete(int i,ElemType &e);
   Status inver();// 逆置
      //Status MergeList(SqList La,SqList Lb);
};
template <class ElemType> SqList<ElemType>::SqList(int max)
{
  listsize=max;
  length=0;
  elem=new ElemType[listsize];
};
template <class ElemType> void SqList<ElemType>::ClearList()
{
  delete[] elem;
  elem=new ElemType[listsize];
  length=0;
};
template <class ElemType> Status SqList<ElemType>::input(int n)
{
  if(n<=0) return ERROR;
  for(int i=0;i<n;i++)
  {
    cout<<"输入第"<<i+1<<"个数:";
 cin>>elem[i];
  }
  length=n;
  return OK;
};
template <class ElemType> Status SqList<ElemType>::output()
{
  if(length==0) return ERROR;
  else
  {
    for(int i=0;i<length;i++)
 {
   cout<<elem[i]<<"->";
 }
 cout<<"NULL"<<endl;
  }
  return OK;
};
template <class ElemType> Status SqList<ElemType>::ListEmpty()
{
  if(length==0) return TRUE;
   else return FALSE;
};
template <class ElemType> int SqList<ElemType>::ListLength()
{
  return length;
};
template <class ElemType> ElemType SqList<ElemType>::GetElem(int n)
{
 ElemType e;
  if(length==0) return ERROR;
  if(n<1||n>ListLength()) return OVERFLOW;
  e=elem[n-1];
  return e;
};
template <class ElemType> Status SqList<ElemType>::NextElem(ElemType loc_e,ElemType &next_e)
{
  if(length==0) return ERROR;
  for(int i=1;loc_e!=elem[i-1];i++);
  if(i==length) return OVERFLOW;
  next_e=elem[i];
  return OK;
};
template <class ElemType> Status SqList<ElemType>::ListInsert(int i,ElemType e)
{
  if(i<1||i>length)  return ERROR;
  if(listsize==length) return OVERFLOW;
  for(int n=length-1;n>=i-1;n--)
   elem[n+1]=elem[n];
  elem[i-1]=e;
  length++;
  return OK;
};
template <class ElemType> Status SqList<ElemType>::ListDelete(int i,ElemType &e)
{
  if(i<1||i>length)  return ERROR;
  e=elem[i-1];
  for(int n=i-1;n<length-1;n++)
   elem[n]=elem[n+1];
  length--;
  return OK;
};
template <class ElemType> Status SqList<ElemType>::inver()
{
  int i,m,n;
  ElemType temp;
  n=length;
  m=n/2;
  for(i=0;i<m;i++)
  {
    temp=elem[i];elem[i]=elem[n-i-1];elem[n-i-1]=temp;
  }
  return OK;
};