# B树的插入与删除

//这是一个奇数阶b树
#include<iostream.h>

#define m 5
typedef struct nd
{
int keynum;
int data[m+1];
struct nd *chd[m+1];
struct nd *pr;
}btnode,*pbtnode;

class btree
{
private:
pbtnode root;
public:
btree()
{
root=0;
int i;
cout<<“enter node infor ,0 is the endl/nstart:”;
//  cin>>i;
//  while(i)
//  {
for(i=100;i>0;i–)
// for(i=1;i<9;i++)
{
if(i==12)
call();
InsertBtree(root,i);
}

//   cin>>i;
//  }
}

void call()
{
return;
}

int search(pbtnode &rt,int k)
{
if(rt==0)return 0;
for(int i=1;i<=rt->keynum&&rt->data[i]<k;i++);          //change for me
return i;
}

void searchBtree(pbtnode &rt,int k,pbtnode &q,bool &bl)
{
while(rt)
{
q=rt;
//   int i;
int i=search(rt,k);   //how to change the deled?whow can call me?
//damation hvae in the choose
//      if(i>rt->keynum)
//    i=i-1;
if(i==0)
{
//    cout<<“have a null tear!/n”;
return;
}
if(rt->keynum<i)              //do the change for
{
rt=rt->chd[i-1];
}
else if(rt->data[i]==k)
{
//    cout<<“the node have in the tree!/n”;
bl=true;
return;
}
//*****

//*************
else if(k<rt->data[i])
{
rt=rt->chd[i-1];
}
bl=false;
}
}

//Insert the information in the tree!1

void Insert(pbtnode &rt,int k,pbtnode ap)
{
if(!rt)
{
rt=new btnode;
rt->data[1]=k;
for(int i=0;i<=m;i++)
rt->chd[i]=0;
rt->keynum=1;
rt->pr=0;
//   cout<<“seceess insert!/n”;
}
else
{
int i=search(rt,k);
if(rt->data[i]==k)
{
//    cout<<“the node have in the tree!/n”;
}
else
{
for(int j=rt->keynum;j>=i;j–)
{
rt->data[j+1]=rt->data[j];
}
for(j=rt->keynum;j>=i;j–)
{
rt->chd[j+1]=rt->chd[j];
}
rt->chd[i]=ap;
rt->data[i]=k;
rt->keynum++;
//    cout<<“Insert seccess!!/n”;
if(rt->keynum==m)
{
slpit(rt);
}
}
}
}

void InsertBtree(pbtnode &rt,int k)
{
pbtnode p=rt,q;
bool bl;
if(!rt)
{
Insert(rt,k,0);
return;
}
else
{
searchBtree(p,k,q,bl);
Insert(q,k,0);
}
}

//*****************************************************************************
void slpit(pbtnode &rt)
{
if(!rt->pr)
{
newroot(root);
}
else
{
btnode q=*rt;
int i,j;
pbtnode p=new btnode;

for(j=0, i=m/2+1;i<=m;i++,j++)
{
p->chd[j]=q.chd[i];
if(p->chd[j]!=0)
p->chd[j]->pr=p;
}

for(i=1,j=m/2+2;j<=m;j++,i++)
{
p->data[i]=q.data[j];       //change in the here!!
}
rt->keynum=m/2;
p->keynum=m/2;
p->pr=rt->pr;
int n=rt->data[m/2+1];
Insert(q.pr,n,p);
}
//  cout<<“insert up seccess!/n”;
}
//*****************************************************************************

void newroot(pbtnode &rt)        //change at the night
{
pbtnode root=new btnode;
pbtnode nd=new btnode;
for(int i=0;i<m+1;i++)
{
root->chd[i]=0;
nd->chd[i]=0;
}
int j;
for(i=0,j=m/2+1;j<=m+1;j++,i++)
{     //**
rt->chd[j]->pr=nd;
nd->chd[i]=rt->chd[j];
}

root->pr=0;
root->keynum=1;
root->data[1]=rt->data[m/2+1];
root->chd[0]=rt;
root->chd[1]=nd;
rt->pr=root;
nd->pr=root;

for(i=m/2+2,j=1;i<=m;i++,j++)
{
nd->data[j]=rt->data[i];

}
nd->chd[j]=rt->chd[i];
rt->keynum=m/2;
nd->keynum=m-rt->keynum-1;
rt=root;
//****************************************
}

//delete a key from the tree
void del(int k)                     //do the 2-3 tree ,use this think to do the programm
{
deletebtree(root,k);
}

void deletebtree(pbtnode &rt,int k)
{
bool bl=false;
pbtnode p,q=rt;
searchBtree(q,k,p,bl);
if(!bl)
{
cout<<“the node null in the tree!/n”;
return;
}
else
{
int i=search(p,k);
if(!p->chd[i-1])        //whether have a dubeg for here!!
{
delnode(p,k);
}
else
{
int i=search(p,k);
if(i<=p->keynum&&p->data[i]==k)        //hve dan change 11:12
i=i;
else
i=i-1;
pbtnode q,pp=p;
p=p->chd[i];
while(p)
{
q=p;
p=p->chd[0];
}
int n=q->data[1];
pp->data[i]=n;
delnode(q,n);
}
}
}

void delnode(pbtnode &p,int k)
{
if(p->keynum>m/2)
{
int n=search(p,k);
for(int i=n;i<p->keynum;i++)
{
p->data[i]=p->data[i+1];
p->chd[i]=p->chd[i+1];
}
p->keynum–;
}
else
{
if(p->pr==0)
{
int n=search(p,k);
for(int i=n;i<p->keynum;i++)
{
p->data[i]=p->data[i+1];
p->chd[i]=p->chd[i+1];
}
p->keynum–;
if(p->keynum==0)
{
for(i=0;i<=m;i++)
{
if(p->chd[i])
p->chd[i]->pr=0;
}
// p=p->chd[0];
root=p->chd[0];

}
}
else
{
int j;
pbtnode pr=p->pr,lb,rb;
//    int j=search(pr,k)-1;
//    /*
j=search(pr,k);
if(pr->data[j]!=k)
j=j-1;
//    */
if(j==0)
lb=0;
else
lb=pr->chd[j-1];
if(j==pr->keynum)
rb=0;
else
rb=pr->chd[j+1];
if(lb && (lb->keynum>m/2))
lfbr(lb,pr,p,k);
else if(rb && (rb->keynum>m/2))
rtbr(p,pr,rb,k);
else if(lb)
lfconb(lb,pr,p,k);
else if(rb)
rtconb(p,pr,rb,k);
}
}
}

void lfbr(pbtnode &lb,pbtnode &pr,pbtnode &p ,int k)
{
int loc1=search(p,k);    //the k in the node location
int loc2=search(pr,k)-1;   //the k may in the pr location
//for the node p do the change .let the node have in the
for(int i=loc1;i>=1;i–)
{
if(i>1)
p->data[i]=p->data[i-1];
if(p->chd[i-1])
p->chd[i]=p->chd[i-1];
}
p->data[1]=pr->data[loc2];
pr->data[loc2]=lb->data[lb->keynum];
if(lb->chd[lb->keynum])
lb->chd[lb->keynum]->pr=p;
p->chd[0]=lb->chd[lb->keynum];
lb->keynum–;
}

void lfconb(pbtnode &lb,pbtnode &pr,pbtnode &p ,int k)
{
int j;
int loc1=search(p,k);    //the k in the node location
//  int loc2=search(pr,k)-1;   //the k may in the pr location

//  /*
int loc2=search(pr,k);               //this the change of you will do
if(pr->data[loc2]!=k)
loc2=loc2-1;
//  */
//do the change for the node ,I am put the node’s right child make null,so I will do like:
for(int i=loc1;i<p->keynum;i++)
{
p->data[i]=p->data[i+1];
p->chd[i]=p->chd[i+1];
}
lb->data[lb->keynum+1]=pr->data[loc2];
lb->chd[lb->keynum +1]=p->chd[0];
if(p->chd[0])
p->chd[0]->pr=lb;
pr->chd[loc2]=0;                 //make null
for(i=lb->keynum+2,j=1; i<=lb->keynum+p->keynum;i++,j++)
{
if(p->chd[j])
p->chd[j]->pr=lb;
lb->chd[i]=p->chd[j];
lb->data[i]=p->data[j];
}
lb->keynum+=p->keynum;
delnode(pr,pr->data[loc2]);
}

void rtbr(pbtnode &p,pbtnode &pr,pbtnode &rb,int k)
{
int loc1=search(p,k);    //the k in the node location
int loc2=search(pr,k);   //the k may in the pr location,this is a not like for left change
//change the node to can be insert
for(int i=loc1;i<p->keynum;i++)
{
p->data[i]=p->data[i+1];
p->chd[i]=p->chd[i+1];
}
p->chd[p->keynum]=rb->chd[0];
if(rb->chd[0])
rb->chd[0]->pr=p;
p->data[p->keynum]=pr->data[loc2];
pr->data[loc2]=rb->data[1];
rb->chd[0]=rb->chd[1];
for(i=1;i<rb->keynum;i++)
{
rb->chd[i]=rb->chd[i+1];
rb->data[i]=rb->data[i+1];
}
rb->keynum–;
}

void rtconb(pbtnode &p,pbtnode &pr,pbtnode &rb,int k)
{
int i,j;
int loc1=search(p,k);    //the k in the node location
int loc2=search(pr,k);   //the k may in the pr location,this is a not like for lfconb change
//change the node
for(i=loc1;i<p->keynum;i++)
{
p->chd[i]=p->chd[i+1];
p->data[i]=p->data[i+1];
}
p->data[p->keynum]=pr->data[loc2];
p->chd[p->keynum]=rb->chd[0];
if(rb->chd[0])
rb->chd[0]->pr=p;
pr->chd[loc2]=0;              //make null
for(j=p->keynum+1,i=1;j<=p->keynum+rb->keynum;j++,i++)
{
p->data[j]=rb->data[i];
if(rb->chd[i])
rb->chd[i]->pr=p;
p->chd[j]=rb->chd[i];
}
p->keynum+=rb->keynum;
delnode(pr,pr->data[loc2]);
}

//the node see

void Inorder(pbtnode &rt)
{
if(!rt)return;
for(int i=0;i<=rt->keynum;i++)
{
Inorder(rt->chd[i]);
if(i<rt->keynum&&rt->data[i+1])
cout<<rt->data[i+1]<<”   “;
}
}

void print()
{
Inorder(root);
cout<<“/nthe B_tree/n”;
}

};

void main()
{
int key,key1=0;
key=0;
btree bt;
cout<<endl;
bt.print();

for(;;)
{
cout<<“enter the node with you want to delete/ncin>:”;
cin>>key>>key1;
//for(int i=key;i<=key1;i++)
for(int i=key;i>key1;i–)
{
if(i==8)
bt.call();
// bt.del(key);
bt.del(i);
//  cout<<“the btree delete:”<<key<<endl;
cout<<“the btree delete:”<<i<<endl;
bt.print();
}
}
}

原文作者：B树
原文地址: https://blog.csdn.net/tubierr/article/details/1707544
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