Count Nodes in Complete Binary Tree - Google Top Interview Questions

Problem Statement :

Given a complete binary tree root, return the number of nodes in the tree.

This should be done in \mathcal{O}((\log n)^2)O((logn) 


n ≤ 100,000 where n is the number of nodes in root

Example 1


root = [1, [2, [4, null, null], [5, null, null]], [3, null, null]]



Example 2


root = [1, [2, [4, null, null], [5, null, null]], [3, [6, null, null], [7, null, null]]]



Solution :


                        Solution in C++ :

int solve(Tree* tree) {
    int right_h = 0, left_h = 0;
    auto* curr = tree;
    while (curr) right_h++, curr = curr->right;
    curr = tree;
    while (curr) left_h++, curr = curr->left;
    if (right_h ==
        left_h) {  // if left_height and right_height is same, then the tree has (2**h - 1) nodes
        return (1 << right_h) - 1;
    // If not same, then again make a recursive call on the left and right subtree
    return solve(tree->left) + solve(tree->right) + 1;

                        Solution in Java :

import java.util.*;

 * public class Tree {
 *   int val;
 *   Tree left;
 *   Tree right;
 * }
class Solution {
    public int solve(Tree tree) {
        int lo = 1;
        int hi = 100000;
        while (lo < hi) {
            int m = (lo + hi + 1) / 2;
            boolean exists = check(tree, m);
            if (exists)
                lo = m;
                hi = m - 1;
        return lo;

    public boolean check(Tree t, int m) {
        boolean active = false;
        for (int i = 17; i >= 0; i--) {
            int cur = m & (1 << i);
            if (!active) {
                if (cur > 0)
                    active = true;
            } else {
                if (cur == 0)
                    t = t.left;
                    t = t.right;
                if (t == null)
                    return false;
        return true;

                        Solution in Python : 
class Solution:
    def solve(self, tree):

        # function to find the left most depth or  the right most depth
        def extreme(root, left):
            height = 1
            if left:
                while root:
                    root = root.left
                    height += 1
                while root:
                    root = root.right
                    height += 1
            return height

        # main function to solve the problem

        def traverse(root):
            if not root:
                return 0
            l = extreme(root.left, True)
            r = extreme(root.right, False)
            if l == r:  # encountered a full binary tree
                return 2 ** l - 1
                return traverse(root.left) + traverse(root.right) + 1

        ans = traverse(tree)
        return ans

View More Similar Problems

The Strange Function

One of the most important skills a programmer needs to learn early on is the ability to pose a problem in an abstract way. This skill is important not just for researchers but also in applied fields like software engineering and web development. You are able to solve most of a problem, except for one last subproblem, which you have posed in an abstract way as follows: Given an array consisting

View Solution →

Self-Driving Bus

Treeland is a country with n cities and n - 1 roads. There is exactly one path between any two cities. The ruler of Treeland wants to implement a self-driving bus system and asks tree-loving Alex to plan the bus routes. Alex decides that each route must contain a subset of connected cities; a subset of cities is connected if the following two conditions are true: There is a path between ever

View Solution →

Unique Colors

You are given an unrooted tree of n nodes numbered from 1 to n . Each node i has a color, ci. Let d( i , j ) be the number of different colors in the path between node i and node j. For each node i, calculate the value of sum, defined as follows: Your task is to print the value of sumi for each node 1 <= i <= n. Input Format The first line contains a single integer, n, denoti

View Solution →

Fibonacci Numbers Tree

Shashank loves trees and math. He has a rooted tree, T , consisting of N nodes uniquely labeled with integers in the inclusive range [1 , N ]. The node labeled as 1 is the root node of tree , and each node in is associated with some positive integer value (all values are initially ). Let's define Fk as the Kth Fibonacci number. Shashank wants to perform 22 types of operations over his tree, T

View Solution →

Pair Sums

Given an array, we define its value to be the value obtained by following these instructions: Write down all pairs of numbers from this array. Compute the product of each pair. Find the sum of all the products. For example, for a given array, for a given array [7,2 ,-1 ,2 ] Note that ( 7 , 2 ) is listed twice, one for each occurrence of 2. Given an array of integers, find the largest v

View Solution →

Lazy White Falcon

White Falcon just solved the data structure problem below using heavy-light decomposition. Can you help her find a new solution that doesn't require implementing any fancy techniques? There are 2 types of query operations that can be performed on a tree: 1 u x: Assign x as the value of node u. 2 u v: Print the sum of the node values in the unique path from node u to node v. Given a tree wi

View Solution →