Subtree with Maximum Average- Amazon Top Interview Questions


Problem Statement :


Given a binary tree root, return the maximum average value of a subtree. A subtree is defined to be some node in root including all of its descendants. A subtree average is the sum of the node values divided by the number of nodes.

Constraints

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

Example 1

Input

root = [1, [3, null, null], [7, [4, null, null], null]]

Output

5.5

Explanation

The subtree rooted at 7 has the highest average with (7 + 4) / 2.

Example 2

Input

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

Output

4

Explanation

The subtree rooted at 4 has the highest average with 4 / 1.



Solution :



title-img




                        Solution in C++ :

void maxAvg(Tree* root, int& c, int& sum, double& big) {
    if (!root) return;
    sum += root->val;
    c += 1;
    int lCount = 0, rCount = 0, lsum = 0, rsum = 0;
    maxAvg(root->left, lCount, lsum, big);
    maxAvg(root->right, rCount, rsum, big);
    c += lCount + rCount;
    sum += lsum + rsum;
    double avg = (double)sum / (1.0 * c);
    if (avg > big) big = avg;
}
double solve(Tree* root) {
    if (!root) return 0.0;
    double res = 0;
    int c = 0;
    int sum = 0;
    maxAvg(root, c, sum, res);
    return res;
}
                    


                        Solution in Java :

import java.util.*;

/**
 * public class Tree {
 *   int val;
 *   Tree left;
 *   Tree right;
 * }
 */
class Solution {
    public double solve(Tree root) {
        return rec(root).maxAvg;
    }

    public ReturnType rec(Tree node) {
        if (node == null)
            return new ReturnType(0, 0, 0);
        ReturnType l = rec(node.left);
        ReturnType r = rec(node.right);
        int curSum = (l.sum + r.sum + node.val);
        int curCnt = (l.cnt + r.cnt + 1);
        double curAvg = (double) curSum / curCnt;
        double maxAvg = Math.max(Math.max(l.maxAvg, r.maxAvg), curAvg);
        return new ReturnType(curCnt, curSum, maxAvg);
    }

    public class ReturnType {
        int cnt;
        int sum;
        double maxAvg;

        public ReturnType(int cnt, int sum, double maxAvg) {
            this.cnt = cnt;
            this.sum = sum;
            this.maxAvg = maxAvg;
        }
    }
}
                    


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

        ans = 0

        def dfs(root):
            nonlocal ans
            if not root:
                return (0, 0)

            left_sum, nl = dfs(root.left)
            right_sum, nr = dfs(root.right)

            cur_sum = left_sum + right_sum + root.val
            no_of_nodes = nl + nr + 1

            avg = cur_sum / no_of_nodes

            # update ans
            ans = max(avg, ans)

            return (cur_sum, no_of_nodes)

        dfs(root)
        return ans
                    


View More Similar Problems

Subsequence Weighting

A subsequence of a sequence is a sequence which is obtained by deleting zero or more elements from the sequence. You are given a sequence A in which every element is a pair of integers i.e A = [(a1, w1), (a2, w2),..., (aN, wN)]. For a subseqence B = [(b1, v1), (b2, v2), ...., (bM, vM)] of the given sequence : We call it increasing if for every i (1 <= i < M ) , bi < bi+1. Weight(B) =

View Solution →

Kindergarten Adventures

Meera teaches a class of n students, and every day in her classroom is an adventure. Today is drawing day! The students are sitting around a round table, and they are numbered from 1 to n in the clockwise direction. This means that the students are numbered 1, 2, 3, . . . , n-1, n, and students 1 and n are sitting next to each other. After letting the students draw for a certain period of ti

View Solution →

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 →