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Find maximum vertical sum in binary tree

  • Difficulty Level : Medium
  • Last Updated : 29 Jun, 2021

Given a binary tree, find the maximum vertical level sum in binary tree.

Examples: 

Input : 
                3
              /  \
             4    6
           /  \  /  \
         -1   -2 5   10
                  \
                   8  

Output : 14
Vertical level having nodes 6 and 8 has maximum
vertical sum 14. 

Input :
                1
              /  \
             5    8
           /  \    \
          2   -6    3
           \       /
           -1     -4
             \
              9

Output : 4 

A simple solution is to first find vertical level sum of each level starting from minimum vertical level to maximum vertical level. Finding sum of one vertical level takes O(n) time. In worst case time complexity of this solution is O(n^2).

An efficient solution is to do level order traversal of given binary tree and update vertical level sum of each level while doing the traversal. After finding vertical sum of each level find maximum vertical sum from these values.

Below is the implementation of above approach: 



C++




// C++ program to find maximum vertical
// sum in binary tree.
#include <bits/stdc++.h>
using namespace std;
 
// A Binary Tree Node
struct Node {
    int data;
    struct Node *left, *right;
};
 
// A utility function to create a new
// Binary Tree Node
struct Node* newNode(int item)
{
    struct Node* temp = (struct Node*)malloc(sizeof(struct Node));
    temp->data = item;
    temp->left = temp->right = NULL;
    return temp;
}
 
// Function to find maximum vertical sum
// in binary tree.
int maxVerticalSum(Node* root)
{
    if (root == NULL) {
        return 0;
    }
 
    // To store sum of each vertical level.
    unordered_map<int, int> verSum;
 
    // To store maximum vertical level sum.
    int maxSum = INT_MIN;
 
    // To store vertical level of current node.
    int currLev;
 
    // Queue to perform level order traversal.
    // Each element of queue is a pair of node
    // and its vertical level.
    queue<pair<Node*, int> > q;
    q.push({ root, 0 });
 
    while (!q.empty()) {
 
        // Extract node at front of queue
        // and its vertical level.
        root = q.front().first;
        currLev = q.front().second;
        q.pop();
 
        // Update vertical level sum of
        // vertical level to which
        // current node belongs to.
        verSum[currLev] += root->data;
 
        if (root->left)
            q.push({ root->left, currLev - 1 });
 
        if (root->right)
            q.push({ root->right, currLev + 1 });
    }
 
    // Find maximum vertical level sum.
    for (auto it : verSum)
        maxSum = max(maxSum, it.second);
    
    return maxSum;
}
 
// Driver Program to test above functions
int main()
{
    /*
                3
              /  \
             4    6
           /  \  /  \
         -1   -2 5   10
                  \
                   
    */
 
    struct Node* root = newNode(3);
    root->left = newNode(4);
    root->right = newNode(6);
    root->left->left = newNode(-1);
    root->left->right = newNode(-2);
    root->right->left = newNode(5);
    root->right->right = newNode(10);
    root->right->left->right = newNode(8);
 
    cout << maxVerticalSum(root);
    return 0;
}

Python3




# Python3 program to find maximum
# vertical sum in binary tree.
from sys import maxsize
from collections import deque
 
INT_MIN = -maxsize
 
class Node:
     
    def __init__(self, data):
         
        self.data = data
        self.left = None
        self.right = None
 
# Function to find maximum vertical sum
# in binary tree.
def maxVerticalSum(root: Node) -> int:
     
    if (root is None):
        return 0
 
    # To store sum of each vertical level.
    verSum = dict()
 
    # To store maximum vertical level sum.
    maxSum = INT_MIN
 
    # To store vertical level of current node.
    currLev = 0
 
    # Queue to perform level order traversal.
    # Each element of queue is a pair of node
    # and its vertical level.
    q = deque()
    q.append([root, 0])
 
    while (q):
 
        # Extract node at front of queue
        # and its vertical level.
        root = q[0][0]
        currLev = q[0][1]
        q.popleft()
 
        # Update vertical level sum of
        # vertical level to which
        # current node belongs to.
        if currLev not in verSum:
            verSum[currLev] = 0
             
        verSum[currLev] += root.data
 
        if (root.left):
            q.append([root.left, currLev - 1])
 
        if (root.right):
            q.append([root.right, currLev + 1])
 
    # Find maximum vertical level sum.
    for it in verSum:
        maxSum = max([maxSum, verSum[it]])
 
    return maxSum
 
# Driver code
if __name__ == "__main__":
     
    '''
                3
              /  \
             4    6
           /  \  /  \
         -1   -2 5   10
                  \
                   
    '''
 
    root = Node(3)
    root.left = Node(4)
    root.right = Node(6)
    root.left.left = Node(-1)
    root.left.right = Node(-2)
    root.right.left = Node(5)
    root.right.right = Node(10)
    root.right.left.right = Node(8)
 
    print(maxVerticalSum(root))
 
# This code is contributed by sanjeev2552

Javascript




<script>
 
// Javascript program to find maximum
// vertical sum in binary tree.
 
// A Binary Tree Node
class Node
{
    constructor(item)
    {
        this.left = null;
        this.right = null;
        this.data = item;
    }
}
 
// A utility function to create a new
// Binary Tree Node
function newNode(item)
{
    let temp = new Node(item);
    return temp;
}
 
// Function to find maximum vertical sum
// in binary tree.
function maxVerticalSum(root)
{
    if (root == null)
    {
        return 0;
    }
 
    // To store sum of each vertical level.
    let verSum = new Map();
 
    // To store maximum vertical level sum.
    let maxSum = Number.MIN_VALUE;
 
    // To store vertical level of current node.
    let currLev;
 
    // Queue to perform level order traversal.
    // Each element of queue is a pair of node
    // and its vertical level.
    let q = [];
    q.push([ root, 0 ]);
 
    while (q.length > 0)
    {
         
        // Extract node at front of queue
        // and its vertical level.
        root = q[0][0];
        currLev = q[0][1];
        q.shift();
 
        // Update vertical level sum of
        // vertical level to which
        // current node belongs to.
        if (verSum.has(currLev))
        {
            verSum.set(currLev, verSum.get(currLev) +
                                root.data);
        }
        else
        {
            verSum.set(currLev, root.data);
        }
 
        if (root.left)
            q.push([root.left, currLev - 1]);
 
        if (root.right)
            q.push([root.right, currLev + 1]);
    }
 
    // Find maximum vertical level sum.
      verSum.forEach((values, keys)=>{
          maxSum = Math.max(maxSum, values);
    })
    return maxSum;
}
 
// Driver code
/*
            3
          /  \
         4    6
       /  \  /  \
     -1   -2 5   10
              \
               8
*/
let root = newNode(3);
root.left = newNode(4);
root.right = newNode(6);
root.left.left = newNode(-1);
root.left.right = newNode(-2);
root.right.left = newNode(5);
root.right.right = newNode(10);
root.right.left.right = newNode(8);
 
document.write(maxVerticalSum(root));
 
// This code is contributed by divyesh072019
 
</script>
Output: 
14

 

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

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