Binary Tree:

A Binary tree is represented by a pointer to the topmost node (commonly known as the “root”) of the tree. If the tree is empty, then the value of the root is NULL. Each node of a Binary Tree contains the following parts: (1) Data. (2) Pointer to left child. (3) Pointer to right child.

Properties of Binary Tree:

1. The maximum number of nodes at level ‘l’ of a binary tree is 2l:
2. The Maximum number of nodes in a binary tree of height ‘h’ is 2h – 1:
3. In a Binary Tree with N nodes, the minimum possible height or the minimum number of levels is Log2(N+1):
4. A Binary Tree with L leaves has at least | Log2L |+ 1 levels:
5. In a Binary tree where every node has 0 or 2 children, the number of leaf nodes is always one more than nodes with two children:
6. In a non-empty binary tree, if n is the total number of nodes and e is the total number of edges, then e = n-1:

Lets create a binary tree with new class .

//creating trees class 


#include<bits/stdc++.h>
using namespace std;

class node{
public:
    int data;
    node* left;
    node* right;
    
    node(int d)
    {
        this->data=d;
        this->left=NULL;
        this->right=NULL;
    }
};

node* buildtree(node* root)
{
    int data;
    cout<<"enter val"<<endl ;
    cin>>data;
    root=new node(data);
    if(data ==-1)
    {
        return NULL;
    }
    
    cout<<"left of"<<data<<endl; 
    root->left=buildtree(root->left);
    cout<<"right of"<<data<<endl; 
    root->right=buildtree(root->right);
    return root;
}

int main(){
    node* root=NULL;
    //creating tree;
    root=buildtree(root);
    return 0 ;
}

To Create a new Tree the complexities are :

Time complexity : O(N) . Space Complexity : O(N) . ,where N is the number of nodes in a binary tree