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C++ Program to Implement B+ Tree
The B+ tree is a generalization of a binary search tree in that a node can have more than two children. It is basically a self-balancing tree data structure that maintains sorted data and allows sequential access, searches, insertions, and deletions in logarithmic time.
It can be viewed as a B-tree in which each node contains only keys and to which an additional level is added at the bottom with linked leaves.
Algorithm
Begin function insert() to insert the nodes into the tree: Initialize x as root. if x is leaf and having space for one more info then insert a to x. else if x is not leaf, do Find the child of x that is going to to be traversed next. If the child is not full, change x to point to the child. If the child is full, split it and change x to point to one of the two parts of the child. If a is smaller than mid key in the child, then set x as first part of the child. Else second part of the child. End
Example Code
#include<iostream>
using namespace std;
struct BplusTree {
int *d;
BplusTree **child_ptr;
bool l;
int n;
}*r = NULL, *np = NULL, *x = NULL;
BplusTree* init()//to create nodes {
int i;
np = new BplusTree;
np->d = new int[6];//order 6
np->child_ptr = new BplusTree *[7];
np->l = true;
np->n = 0;
for (i = 0; i < 7; i++) {
np->child_ptr[i] = NULL;
}
return np;
}
void traverse(BplusTree *p)//traverse tree {
cout<<endl;
int i;
for (i = 0; i < p->n; i++) {
if (p->l == false) {
traverse(p->child_ptr[i]);
}
cout << " " << p->d[i];
}
if (p->l == false) {
traverse(p->child_ptr[i]);
}
cout<<endl;
}
void sort(int *p, int n)//sort the tree {
int i, j, t;
for (i = 0; i < n; i++) {
for (j = i; j <= n; j++) {
if (p[i] >p[j]) {
t = p[i];
p[i] = p[j];
p[j] = t;
}
}
}
}
int split_child(BplusTree *x, int i) {
int j, mid;
BplusTree *np1, *np3, *y;
np3 = init();
np3->l = true;
if (i == -1) {
mid = x->d[2];
x->d[2] = 0;
x->n--;
np1 = init();
np1->l = false;
x->l = true;
for (j = 3; j < 6; j++) {
np3->d[j - 3] = x->d[j];
np3->child_ptr[j - 3] = x->child_ptr[j];
np3->n++;
x->d[j] = 0;
x->n--;
}
for (j = 0; j < 6; j++) {
x->child_ptr[j] = NULL;
}
np1->d[0] = mid;
np1->child_ptr[np1->n] = x;
np1->child_ptr[np1->n + 1] = np3;
np1->n++;
r = np1;
} else {
y = x->child_ptr[i];
mid = y->d[2];
y->d[2] = 0;
y->n--;
for (j = 3; j <6 ; j++) {
np3->d[j - 3] = y->d[j];
np3->n++;
y->d[j] = 0;
y->n--;
}
x->child_ptr[i + 1] = y;
x->child_ptr[i + 1] = np3;
}
return mid;
}
void insert(int a) {
int i, t;
x = r;
if (x == NULL) {
r = init();
x = r;
} else {
if (x->l== true && x->n == 6) {
t = split_child(x, -1);
x = r;
for (i = 0; i < (x->n); i++) {
if ((a >x->d[i]) && (a < x->d[i + 1])) {
i++;
break;
} else if (a < x->d[0]) {
break;
} else {
continue;
}
}
x = x->child_ptr[i];
} else {
while (x->l == false) {
for (i = 0; i < (x->n); i++) {
if ((a >x->d[i]) && (a < x->d[i + 1])) {
i++;
break;
} else if (a < x->d[0]) {
break;
} else {
continue;
}
}
if ((x->child_ptr[i])->n == 6) {
t = split_child(x, i);
x->d[x->n] = t;
x->n++;
continue;
} else {
x = x->child_ptr[i];
}
}
}
}
x->d[x->n] = a;
sort(x->d, x->n);
x->n++;
}
int main() {
int i, n, t;
cout<<"enter the no of elements to be inserted\n";
cin>>n;
for(i = 0; i < n; i++) {
cout<<"enter the element\n";
cin>>t;
insert(t);
}
cout<<"traversal of constructed B tree\n";
traverse(r);
}Output
enter the no of elements to be inserted 10 enter the element 10 enter the element 20 enter the element 30 enter the element 40 enter the element 50 enter the element 60 enter the element 70 enter the element 80 enter the element 90 enter the element 100 traversal of constructed B tree 10 20 30 40 50 60 70 80 90 100
Updated on: 30-Jul-2019
3K+ Views
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