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) 
2
 ).

Constraints

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


Example 1

Input



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

Output

5

Example 2

Input



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

Output

7


Solution :



title-img 




                        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;
            else
                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;
                else
                    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
            else:
                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
            else:
                return traverse(root.left) + traverse(root.right) + 1

        ans = traverse(tree)
        return ans


View More Similar Problems

Maximum Element

You have an empty sequence, and you will be given N queries. Each query is one of these three types: 1 x -Push the element x into the stack. 2 -Delete the element present at the top of the stack. 3 -Print the maximum element in the stack. Input Format The first line of input contains an integer, N . The next N lines each contain an above mentioned query. (It is guaranteed that each

View Solution →

Balanced Brackets

A bracket is considered to be any one of the following characters: (, ), {, }, [, or ]. Two brackets are considered to be a matched pair if the an opening bracket (i.e., (, [, or {) occurs to the left of a closing bracket (i.e., ), ], or }) of the exact same type. There are three types of matched pairs of brackets: [], {}, and (). A matching pair of brackets is not balanced if the set of bra

View Solution →

Equal Stacks

ou have three stacks of cylinders where each cylinder has the same diameter, but they may vary in height. You can change the height of a stack by removing and discarding its topmost cylinder any number of times. Find the maximum possible height of the stacks such that all of the stacks are exactly the same height. This means you must remove zero or more cylinders from the top of zero or more of

View Solution →

Game of Two Stacks

Alexa has two stacks of non-negative integers, stack A = [a0, a1, . . . , an-1 ] and stack B = [b0, b1, . . . , b m-1] where index 0 denotes the top of the stack. Alexa challenges Nick to play the following game: In each move, Nick can remove one integer from the top of either stack A or stack B. Nick keeps a running sum of the integers he removes from the two stacks. Nick is disqualified f

View Solution →

Largest Rectangle

Skyline Real Estate Developers is planning to demolish a number of old, unoccupied buildings and construct a shopping mall in their place. Your task is to find the largest solid area in which the mall can be constructed. There are a number of buildings in a certain two-dimensional landscape. Each building has a height, given by . If you join adjacent buildings, they will form a solid rectangle

View Solution →

Simple Text Editor

In this challenge, you must implement a simple text editor. Initially, your editor contains an empty string, S. You must perform Q operations of the following 4 types: 1. append(W) - Append W string to the end of S. 2 . delete( k ) - Delete the last k characters of S. 3 .print( k ) - Print the kth character of S. 4 . undo( ) - Undo the last (not previously undone) operation of type 1 or 2,

View Solution →