#include <iostream>
#include <cmath>
using namespace std;
struct node
{
int ele[4];
int child[4];
node *next;
};
class bptree
{
public:
node *tree[10][10];
int count[10];
int leaf;
int path[10];
node *head;
bptree();
node* create_node();
void insert(int);
void main_search(int);
void display_tree();
void insert_node(node*,int);
void search(int);
int search_node (node*,int);
int nodefull(node*);
void split(node*);
void display_seqset();
};
bptree::bptree()
{
leaf=-1;
for (int i=0;i<10;i++)
{count[i]=-1;path[i]=-1;}
}
node* bptree::create_node()
{
node *n;
n = new node;
for (int i=0;i<4;i++) {n->ele[i]=-1;n->child[i]=-1;}
n->next=NULL;
return n;
}
void bptree::insert(int key)
{
int n, parent;
node *first_node;
if (leaf==-1)
{
first_node=create_node();
tree[0][0]=first_node;
leaf++;count[0]++;
first_node->ele[0]=key;
head=first_node; //header node of seq set
}
else if (leaf==0)
{
if (nodefull(tree[0][0])) {path[leaf]=0;split(tree[0][0]);insert(key);}
else insert_node(tree[0][0],key);
}
else{
search(key);
n=path[leaf];
parent=path[leaf-1];
if ( (nodefull(tree[leaf][n])) )
{
split(tree[leaf][n]);
insert(key);
}
else
insert_node(tree[leaf][n],key);
}
}
void bptree::main_search(int key)
{
int flag=0, i;
node *node1;
search(key);
node1=tree[leaf][path[leaf]];
for (i=0;node1->ele[i]!=-1;i++)
if (node1->ele[i]==key) {flag=1; break;}
cout<<"\nThe path traversed is: ";
for (i=0;path[i]!=-1;i++)
cout<<path[i]<<" -> ";
if (flag) cout <<"\nElement Found";
else cout<<"\nNot Found";
}
void bptree::display_tree()
{
int i,j,k;
for (i=0;i<=leaf;i++)
{
cout<<"\n\nLevel------ " <<i<<"\n";
for (j=0;j<=count[i];j++)
{
if (i!=leaf) k=1; else k=0; //print first element only at leaf level
for (;tree[i][j]->ele[k]!=-1;k++)
cout<<" "<<tree[i][j]->ele[k];
cout<<"\t";
}
}
}
void bptree::search(int key)
{
int i,j,temp;
path[0]=0; //always start the path from root
if (leaf){ // search only if there are more than 1 level
j=0;
for (i=0;i<leaf;i++)
{
temp=search_node(tree[i][j],key);
path[i+1]=temp;
j=temp;
}}
}
int bptree::search_node(node *node1, int key)
{
if (key<=node1->ele[0]) return node1->child[0];
for (int i=1;i<4;i++)
{
if ((key >= node1->ele[i]) && (key < node1->ele[i+1])) return node1->child[i];
else if (node1->ele[i+1]==-1) return node1->child[i];
}
}
int bptree::nodefull(node *node1)
{
if (node1->ele[3]!=-1) return 1;
else return 0;
}
void bptree::insert_node(node *node1, int key)
{
int flag=0, count=-1,i,j, x, y, l;
node *newnode, *parent;
for (i=0;i<4;i++) if (node1->ele[i]!=-1) ++count;
i=0;
while (!flag && node1->ele[i]!=-1)
{
if (node1->ele[i] > key) //not considering duplicate entries
{
flag=1;
for (int j=count;j>=i;j--)
node1->ele[j+1]=node1->ele[j];
node1->ele[i]=key;
}
i++;
}
if (!flag) node1->ele[count+1]=key; //highest element added at end
if (node1->ele[0]==key) //new element is the lowest, hence propogate this till root
{
for (i=leaf-1;i>=0;i--)
{
x=path[i+1];
if (tree[i][path[i]]->ele[x] > key) tree[i][path[i]]->ele[x]=key;
else insert_node(tree[i][x],key);
} }
for (i=0;i<=count+1;i++)
cout<<"\t\t"<<node1->ele[i];
}
void bptree::split(node *oldnode)
{
node *newnode, *parent, *n1, *n2;
int i,j,k,n,t,x,y,pos;
newnode = create_node();
newnode->ele[0]=oldnode->ele[2]; //copy elements to new node
newnode->ele[1]=oldnode->ele[3];
oldnode->ele[2]=-1; //delete entries in old node
oldnode->ele[3]=-1;
t=count[leaf];
n=path[leaf];
for (i=t,j=t+1;i>n;i--,j--) //move the elements in leaf level one place right
tree[leaf][j]=tree[leaf][i];
newnode->next=tree[leaf][n]->next; //updating the next pointers
tree[leaf][n]->next=newnode;
tree[leaf][n+1] = newnode; //insert new node to the tree
count[leaf]++;
x=leaf;
if (count[leaf]+1==1) t=1; else t=log(count[leaf]+1)/log(2); //how many levels does the tree need?
if (t!=leaf) //increase the level of the tree
{
++leaf;
count[leaf]=count[x];
for (i=0;i<=count[leaf];i++) //copy the leaf nodes to the new level
std::swap(tree[leaf][i],tree[x][i]);
}
for (i=leaf-1;i>=0;i--) count[i]=-1; //make the tree empty
for (i=t,j=i-1;i>0;i--,j--)
{
for (k=0;k<=count[i]/3;k++)
{
n1=tree[i][2*k];
n2=tree[i][(2*k)+1];
//for (x=0;n1->ele[x]!=-1;x++); //find last element in the nodes
//for (y=0;n2->ele[y]!=-1;y++);
newnode=create_node();
count[j]++;
tree[j][count[j]]=newnode;
newnode->ele[0]=n1->ele[0];
newnode->child[0]=2*k;
newnode->ele[1]=n2->ele[0];
newnode->child[1]=(2*k)+1;
}
if (count[i]!=1 && count[i]%2==0) //one node is remaining
{
n2=tree[i][count[i]];
//for (y=0;n2->ele[y]!=-1;y++);
newnode->ele[2]=n2->ele[0];
newnode->child[2]=count[i];
}
}
}
void bptree::display_seqset()
{
node *t;
int k;
t=head;
cout<<"\n\nThe sequence set is:";
while (t)
{
for (k=0;t->ele[k]!=-1;k++)
cout<<" "<<t->ele[k];
cout<<"\t";
t=t->next;
}
}
int main()
{
bptree bt;
int choice, key;
while(1)
{
cout<<"\n\n\nMain Menu\n-------------------\n1.Insert\n2.Search\n3.Display Tree\n4.Display Sequence Set\n5.Exit\n\nEnter your choice:";
cin>>choice;
switch(choice)
{
case 1: cout<<"\nEnter the element:";
cin>>key;
bt.insert(key);
break;
case 2:cout<<"Enter the key:";
cin>>key;
bt.main_search(key);
break;
case 3: bt.display_tree();
break;
case 4: bt.display_seqset();
break;
case 5: return 0;
default: cout<<"\nEnter valid choice";
}
}
}
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