Maximum absolute difference between any two level sum in a Binary Tree

Given a Binary Tree having positive and negative nodes, the task is to find the maximum absolute difference of level sum in it.

Examples:

Input:                     
       4
     /   \
    2    -5
  /  \   / \
-1    3 -2  6
Output: 9
Explanation: 
Sum of all nodes of 0 level is 4
Sum of all nodes of 1 level is -3
Sum of all nodes of 2 level is 6
Hence maximum absolute difference
of level sum = 9 (6 - (-3))

Input: 
        1
      /   \
     2     3
   /  \     \
  4    5     8
            / \
           6   7
Output: 16

Approach: To find the maximum absolute difference of level sum, we only need to find Maximum level sum and Minimum level sum because the absolute difference of maximum and minimum level sum always gives us Maximum absolute difference, i.e.

Maximum absolute difference = abs(Maximum level sum – Minimum level sum)

 Below are the steps for the algorithm of the above observation: 

1. The idea is to do level order traversal of the tree.
2. While doing traversal, process nodes of different levels separately.
3. For every level being processed, compute the sum of nodes in the level and keep track of maximum and minimum level sum.
4. Then return the absolute difference of maximum and minimum level sum.

Below is the implementation of the above approach:

C++

// C++ program to find the maximum
// absolute difference of level
// sum in Binary Tree
#include <bits/stdc++.h>
using namespace std;

// Class containing left and
// right child of current
// node and key value
struct Node
{
    int data;
    Node *left, *right;
};

Node *newNode(int data)
{
    Node *node = new Node();
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    return node;
}

// Function to find the maximum
// absolute difference of level
// sum in binary tree
// using level order traversal
int maxAbsDiffLevelSum(Node *root)
{

    // Initialize value of maximum
    // and minimum level sum
    int maxsum = INT_MIN;
    int minsum = INT_MAX;

    queue<Node *> qu;
    qu.push(root);

    // Do Level order traversal
    // keeping track of number
    // of nodes at every level.
    while (!qu.empty())
    {

        // Get the size of queue when
        // the level order traversal
        // for one level finishes
        int sz = qu.size();

        // Iterate for all the nodes in
        // the queue currently
        int sum = 0;

        for(int i = 0; i < sz; i++)
        {

            // Dequeue an node from queue
            Node *t = qu.front();
            qu.pop();

            // Add this node's value to
            // the current sum.
            sum += t->data;

            // Enqueue left and
            // right children of
            // dequeued node
            if (t->left != NULL)
                qu.push(t->left);

            if (t->right != NULL)
                qu.push(t->right);
        }

        // Update the maximum
        // level sum value
        maxsum = max(maxsum, sum);

        // Update the minimum
        // level sum value
        minsum = min(minsum, sum);
    }

    // return the maximum absolute
    // difference of level sum
    return abs(maxsum - minsum);
}

// Driver code
int main()
{
    Node *root = new Node();

    root = newNode(4);
    root->left = newNode(2);
    root->right = newNode(-5);
    root->left->left = newNode(-1);
    root->left->right = newNode(3);
    root->right->left = newNode(-2);
    root->right->right = newNode(6);

    /*   Constructed Binary tree is:
        4
      /   \
    2      -5
    /  \     / \
    -1    3  -2   6 */

    cout << maxAbsDiffLevelSum(root) << endl;
}

// This code is contributed by sanjeev2552

Java

// Java program to find the maximum
// absolute difference of level
// sum in Binary Tree

import java.util.*;

// Class containing left and
// right child of current
// node and key value
class Node {

    int data;
    Node left, right;

    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}

class BinaryTree {

    // Root of the Binary Tree
    Node root;

    public BinaryTree()
    {
        root = null;
    }

    // Function to find
    // the maximum absolute
    // difference of level
    // sum in binary tree
    // using level order traversal
    public int maxAbsDiffLevelSum()
    {

        // Initialize value of maximum
        // and minimum level sum
        int maxsum = Integer.MIN_VALUE;
        int minsum = Integer.MAX_VALUE;

        Queue<Node> qu = new LinkedList<>();
        qu.offer(root);

        // Do Level order traversal
        // keeping track of number
        // of nodes at every level.
        while (!qu.isEmpty()) {

            // Get the size of queue when
            // the level order traversal
            // for one level finishes
            int sz = qu.size();

            // Iterate for all the nodes in
            // the queue currently
            int sum = 0;

            for (int i = 0; i < sz; i++) {

                // Dequeue an node from queue
                Node t = qu.poll();

                // Add this node's value to
                // the current sum.
                sum += t.data;

                // Enqueue left and
                // right children of
                // dequeued node
                if (t.left != null)
                    qu.offer(t.left);

                if (t.right != null)
                    qu.offer(t.right);
            }

            // Update the maximum
            // level sum value
            maxsum = Math.max(maxsum, sum);

            // Update the minimum
            // level sum value
            minsum = Math.min(minsum, sum);
        }
        // return the maximum absolute
        // difference of level sum
        return Math.abs(maxsum - minsum);
    }

    // Driver code
    public static void main(String[] args)
    {
        BinaryTree tree = new BinaryTree();
        tree.root = new Node(4);
        tree.root.left = new Node(2);
        tree.root.right = new Node(-5);
        tree.root.left.left = new Node(-1);
        tree.root.left.right = new Node(3);
        tree.root.right.left = new Node(-2);
        tree.root.right.right = new Node(6);

        /*   Constructed Binary tree is:
              4
            /   \
          2      -5
        /  \     / \
      -1    3  -2   6 */

        System.out.println(
            tree.maxAbsDiffLevelSum());
    }
}

Python3

# Python 3 program to find
# the maximum absolute difference
# of level sum in Binary Tree

import sys
# Class containing left and
# right child of current
# node and key value

class newNode:

    def __init__(self, data):

        self.data = data
        self.left = None
        self.right = None

# Function to find the maximum
# absolute difference of level
# sum in binary tree
# using level order traversal
def maxAbsDiffLevelSum(root):

    # Initialize value of maximum
    # and minimum level sum
    maxsum = -sys.maxsize - 1
    minsum = sys.maxsize

    qu = []
    qu.append(root)

    # Do Level order traversal
    # keeping track of number
    # of nodes at every level.
    while (len(qu) > 0):

        # Get the size of queue when
        # the level order traversal
        # for one level finishes
        sz = len(qu)

        # Iterate for all the nodes in
        # the queue currently
        sum = 0

        for i in range(sz):

            # Dequeue an node from
            # queue
            t = qu[0]
            qu.remove(qu[0])

            # Add this node's value
            # to the current sum.
            sum += t.data

            # Enqueue left and
            # right children of
            # dequeued node
            if (t.left != None):
                qu.append(t.left)

            if (t.right != None):
                qu.append(t.right)

        # Update the maximum
        # level sum value
        maxsum = max(maxsum, sum)

        # Update the minimum
        # level sum value
        minsum = min(minsum, sum)

    # return the maximum absolute
    # difference of level sum
    return abs(maxsum - minsum)

# Driver code
if __name__ == '__main__':

    root = newNode(4)
    root.left = newNode(2)
    root.right = newNode(-5)
    root.left.left = newNode(-1)
    root.left.right = newNode(3)
    root.right.left = newNode(-2)
    root.right.right = newNode(6)

    '''/*   Constructed Binary tree is:
        4
      /   \
    2      -5
    / /     / \
    -1    3  -2   6 */
    '''

    print(maxAbsDiffLevelSum(root))

# This code is contributed by SURENDRA_GANGWAR

C#

// C# program to find the maximum
// absolute difference of level
// sum in Binary Tree
using System;
using System.Collections.Generic;

// Class to represent Tree node
public class Node
{
    public int data;
    public Node left, right;

    public Node(int item)
    {
        data = item;
        left = null;
        right = null;
    }
}

class BinaryTree{

Node root;

// Function to find the maximum
// absolute difference of level
// sum in binary tree
// using level order traversal
public int maxAbsDiffLevelSum()
{

    // Initialize value of maximum
    // and minimum level sum
    int maxsum = Int32.MinValue;
    int minsum = Int32.MaxValue;

    Queue<Node> qu = new Queue<Node>();
    qu.Enqueue(root);

    // Do Level order traversal
    // keeping track of number
    // of nodes at every level.
    while (qu.Count != 0)
    {

        // Get the size of queue when
        // the level order traversal
        // for one level finishes
        int sz = qu.Count;

        // Iterate for all the nodes in
        // the queue currently
        int sum = 0;

        for(int i = 0; i < sz; i++)
        {

            // Dequeue an node from queue
            Node t = qu.Dequeue();

            // Add this node's value to
            // the current sum.
            sum += t.data;

            // Enqueue left and
            // right children of
            // dequeued node
            if (t.left != null)
                qu.Enqueue(t.left);

            if (t.right != null)
                qu.Enqueue(t.right);
        }

        // Update the maximum
        // level sum value
        maxsum = Math.Max(maxsum, sum);

        // Update the minimum
        // level sum value
        minsum = Math.Min(minsum, sum);
    }

    // Return the maximum absolute
    // difference of level sum
    return Math.Abs(maxsum - minsum);
}

// Driver code
static public void Main ()
{
    BinaryTree tree = new BinaryTree();

    tree.root = new Node(4);
    tree.root.left = new Node(2);
    tree.root.right = new Node(-5);
    tree.root.left.left = new Node(-1);
    tree.root.left.right = new Node(3);
    tree.root.right.left = new Node(-2);
    tree.root.right.right = new Node(6);

    /*   Constructed Binary tree is:
          4
        /   \
      2      -5
    /  \     / \
  -1    3  -2   6 */

   Console.WriteLine(tree.maxAbsDiffLevelSum());
}
}

// This code is contributed by offbeat

Javascript

<script>
    // Javascript program to find the maximum
    // absolute difference of level
    // sum in Binary Tree

    // Class to represent Tree node
    class Node
    {
        constructor(item) {
           this.left = null;
           this.right = null;
           this.data = item;
        }
    }

    let root;

    // Function to find the maximum
    // absolute difference of level
    // sum in binary tree
    // using level order traversal
    function maxAbsDiffLevelSum()
    {

        // Initialize value of maximum
        // and minimum level sum
        let maxsum = Number.MIN_VALUE;
        let minsum = Number.MAX_VALUE;

        let qu = [];
        qu.push(root);

        // Do Level order traversal
        // keeping track of number
        // of nodes at every level.
        while (qu.length != 0)
        {

            // Get the size of queue when
            // the level order traversal
            // for one level finishes
            let sz = qu.length;

            // Iterate for all the nodes in
            // the queue currently
            let sum = 0;

            for(let i = 0; i < sz; i++)
            {

                // Dequeue an node from queue
                let t = qu.shift();

                // Add this node's value to
                // the current sum.
                sum += t.data;

                // Enqueue left and
                // right children of
                // dequeued node
                if (t.left != null)
                    qu.push(t.left);

                if (t.right != null)
                    qu.push(t.right);
            }

            // Update the maximum
            // level sum value
            maxsum = Math.max(maxsum, sum);

            // Update the minimum
            // level sum value
            minsum = Math.min(minsum, sum);
        }

        // Return the maximum absolute
        // difference of level sum
        return Math.abs(maxsum - minsum);
    }

    root = new Node(4);
    root.left = new Node(2);
    root.right = new Node(-5);
    root.left.left = new Node(-1);
    root.left.right = new Node(3);
    root.right.left = new Node(-2);
    root.right.right = new Node(6);

    /*   Constructed Binary tree is:
            4
          /   \
        2      -5
      /  \     / \
    -1    3  -2   6 */

      document.write(maxAbsDiffLevelSum());

// This code is contributed by divyeshrabadiya07.
</script>

Output:

9

Time Complexity: O(N) 
Auxiliary Space: O(N)