Binary tree implementation in C++

btree.cpp

#include <iostream>
#include <cmath>

#define p(x) cout << #x << ":" << x << endl;

#define LIMIT (int)pow(2, 3)

using namespace std;

class Node{
    public:
    int t; //total
    int s, e; //start, end
    Node *l;
    Node *r;
    
    void init(int _t, int _s, int _e){
        t = _t;
        s = _s;
        e = _e;
        l = NULL;
        r = NULL;
    }
    
} tree;

int add(Node *n, int s, int e){
    if(s > e) return 0;
    //p(n->s) p(n->e)   
        
    int size = (n->e - n->s)+1;
    
    if(s == n->s && e == n->e){
        n->t = size;
    }else{
        if(n->l == NULL){
            Node *nl = new Node;
            nl->init(0, n->s, n->s+(size/2)-1);
            n->l = nl;
        }
        if(n->r == NULL){
            Node *nr = new Node;
            nr->init(0, n->s+(size/2), n->e);
            n->r = nr;
        }
        n->t = add(n->l, s, min(n->l->e, e)) + add(n->r, max(n->r->s, s), e);
    }
    
    return n->t;
}

int remove(Node *n, int s, int e){
    if(s > e) return n->t;
    //p(n->s) p(n->e)
    
    int size = (n->e - n->s)+1;
    
    if(s == n->s && e == n->e){
        n->t = 0;
    }else{
        int total = 0;
                
        if(n->t == size){
            
            Node *nl = new Node;
            nl->init(size/2, n->s, n->s+(size/2)-1); 
            n->l = nl;
            
            Node *nr = new Node;
            nr->init(size/2, n->s+(size/2), n->e);
            n->r = nr;
        }
        
        if(n->l != NULL){
            total += remove(n->l, s, min(n->l->e, e));
        }
        if(n->r != NULL){
            total += remove(n->r, max(n->r->s, s), e);
        }
        
        
        //p(n->t)
        n->t =  total;
    }
    return n->t;
}

int getCount(){
    return tree.t;
}

int main(){
    tree.init(0, 1, LIMIT);
    
    //p(tree.t) p(tree.s) p(tree.e)
 
    cout << add(&tree, 3, 8) << endl;
    
    cout << remove(&tree, 4, 5) << endl;
    
    return 0;
}