**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 :

` ````
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

## Mr. X and His Shots

A cricket match is going to be held. The field is represented by a 1D plane. A cricketer, Mr. X has N favorite shots. Each shot has a particular range. The range of the ith shot is from Ai to Bi. That means his favorite shot can be anywhere in this range. Each player on the opposite team can field only in a particular range. Player i can field from Ci to Di. You are given the N favorite shots of M

View Solution →## Jim and the Skyscrapers

Jim has invented a new flying object called HZ42. HZ42 is like a broom and can only fly horizontally, independent of the environment. One day, Jim started his flight from Dubai's highest skyscraper, traveled some distance and landed on another skyscraper of same height! So much fun! But unfortunately, new skyscrapers have been built recently. Let us describe the problem in one dimensional space

View Solution →## Palindromic Subsets

Consider a lowercase English alphabetic letter character denoted by c. A shift operation on some c turns it into the next letter in the alphabet. For example, and ,shift(a) = b , shift(e) = f, shift(z) = a . Given a zero-indexed string, s, of n lowercase letters, perform q queries on s where each query takes one of the following two forms: 1 i j t: All letters in the inclusive range from i t

View Solution →## Counting On a Tree

Taylor loves trees, and this new challenge has him stumped! Consider a tree, t, consisting of n nodes. Each node is numbered from 1 to n, and each node i has an integer, ci, attached to it. A query on tree t takes the form w x y z. To process a query, you must print the count of ordered pairs of integers ( i , j ) such that the following four conditions are all satisfied: the path from n

View Solution →## Polynomial Division

Consider a sequence, c0, c1, . . . , cn-1 , and a polynomial of degree 1 defined as Q(x ) = a * x + b. You must perform q queries on the sequence, where each query is one of the following two types: 1 i x: Replace ci with x. 2 l r: Consider the polynomial and determine whether is divisible by over the field , where . In other words, check if there exists a polynomial with integer coefficie

View Solution →## Costly Intervals

Given an array, your goal is to find, for each element, the largest subarray containing it whose cost is at least k. Specifically, let A = [A1, A2, . . . , An ] be an array of length n, and let be the subarray from index l to index r. Also, Let MAX( l, r ) be the largest number in Al. . . r. Let MIN( l, r ) be the smallest number in Al . . .r . Let OR( l , r ) be the bitwise OR of the

View Solution →