Vertical Sum in a given Binary Tree | Set 1

Given a Binary Tree, find the vertical sum of the nodes that are in the same vertical line. Print all sums through different vertical lines.

Examples:

      1
    /   \
  2      3
 / \    / \
4   5  6   7

The tree has 5 vertical lines

• Vertical-Line-1 has only one node 4 => vertical sum is 4 
• Vertical-Line-2: has only one node 2=> vertical sum is 2 
• Vertical-Line-3: has three nodes: 1,5,6 => vertical sum is 1+5+6 = 12 
• Vertical-Line-4: has only one node 3 => vertical sum is 3 
• Vertical-Line-5: has only one node 7 => vertical sum is 7
• So expected output is 4, 2, 12, 3 and 7 

We need to check the Horizontal Distances from the root for all nodes. If two nodes have the same Horizontal Distance (HD), then they are on the same vertical line. The idea of HD is simple. HD for root is 0, a right edge (edge connecting to right subtree) is considered as +1 horizontal distance and a left edge is considered as -1 horizontal distance. For example, in the above tree, HD for Node 4 is at -2, HD for Node 2 is -1, HD for 5 and 6 is 0 and HD for node 7 is +2. 

We can do an in-order traversal of the given Binary Tree. While traversing the tree, we can recursively calculate HDs. We initially pass the horizontal distance as 0 for root. For left subtree, we pass the Horizontal Distance as Horizontal distance of root minus 1. For right subtree, we pass the Horizontal Distance as Horizontal Distance of root plus 1.
Following is Java implementation for the same. HashMap is used to store the vertical sums for different horizontal distances. Thanks to Nages for suggesting this method. 

C++

// C++ program to find Vertical Sum in
// a given Binary Tree
#include<bits/stdc++.h>
using namespace std;

struct Node
{
    int data;
    struct Node *left, *right;
};

// A utility function to create a new
// Binary Tree node
Node* newNode(int data)
{
    Node *temp = new Node;
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}

// Traverses the tree in in-order form and
// populates a hashMap that contains the
// vertical sum
void verticalSumUtil(Node *node, int hd,
                     map<int, int> &Map)
{
    // Base case
    if (node == NULL) return;

    // Recur for left subtree
    verticalSumUtil(node->left, hd-1, Map);

    // Add val of current node to
    // map entry of corresponding hd
    Map[hd] += node->data;

    // Recur for right subtree
    verticalSumUtil(node->right, hd+1, Map);
}

// Function to find vertical sum
void verticalSum(Node *root)
{
    // a map to store sum of nodes for each
    // horizontal distance
    map < int, int> Map;
    map < int, int> :: iterator it;

    // populate the map
    verticalSumUtil(root, 0, Map);

    // Prints the values stored by VerticalSumUtil()
    for (it = Map.begin(); it != Map.end(); ++it)
    {
        cout << it->first << ": "
             << it->second << endl;
    }
}

// Driver program to test above functions
int main()
{
    // Create binary tree as shown in above figure
    Node *root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->left = newNode(6);
    root->right->right = newNode(7);
    root->right->left->right = newNode(8);
    root->right->right->right = newNode(9);

    cout << "Following are the values of vertical"
            " sums with the positions of the "
            "columns with respect to root\n";
    verticalSum(root);

    return 0;
}
// This code is contributed by Aditi Sharma

Java

import java.util.TreeMap;

// Class for a tree node
class TreeNode {

    // data members
    private int key;
    private TreeNode left;
    private TreeNode right;

    // Accessor methods
    public int key()        { return key; }
    public TreeNode left()  { return left; }
    public TreeNode right() { return right; }

    // Constructor
    public TreeNode(int key)
   { this.key = key; left = null; right = null; }

    // Methods to set left and right subtrees
    public void setLeft(TreeNode left)   { this.left = left; }
    public void setRight(TreeNode right) { this.right = right; }
}

// Class for a Binary Tree
class Tree {

    private TreeNode root;

    // Constructors
    public Tree() { root = null; }
    public Tree(TreeNode n) { root = n; }

    // Method to be called by the consumer classes
    // like Main class
    public void VerticalSumMain() { VerticalSum(root); }

    // A wrapper over VerticalSumUtil()
    private void VerticalSum(TreeNode root) {

        // base case
        if (root == null) { return; }

        // Creates an empty TreeMap hM
        TreeMap<Integer, Integer> hM =
                   new TreeMap<Integer, Integer>();

        // Calls the VerticalSumUtil() to store the
        // vertical sum values in hM
        VerticalSumUtil(root, 0, hM);

        // Prints the values stored by VerticalSumUtil()
        if (hM != null) {
            System.out.println(hM.entrySet());
        }
    }

    // Traverses the tree in in-order form and builds
    // a hashMap hM that contains the vertical sum
    private void VerticalSumUtil(TreeNode root, int hD,
                         TreeMap<Integer, Integer> hM) {

        // base case
        if (root == null) {  return; }

        // Store the values in hM for left subtree
        VerticalSumUtil(root.left(), hD - 1, hM);

        // Update vertical sum for hD of this node
        int prevSum = (hM.get(hD) == null) ? 0 : hM.get(hD);
        hM.put(hD, prevSum + root.key());

        // Store the values in hM for right subtree
        VerticalSumUtil(root.right(), hD + 1, hM);
    }
}

// Driver class to test the verticalSum methods
public class Main {

    public static void main(String[] args) {
        /* Create the following Binary Tree
              1
            /    \
          2        3
         / \      / \
        4   5    6   7

        */
        TreeNode root = new TreeNode(1);
        root.setLeft(new TreeNode(2));
        root.setRight(new TreeNode(3));
        root.left().setLeft(new TreeNode(4));
        root.left().setRight(new TreeNode(5));
        root.right().setLeft(new TreeNode(6));
        root.right().setRight(new TreeNode(7));
        Tree t = new Tree(root);

        System.out.println("Following are the values of" +
                           " vertical sums with the positions" +
                        " of the columns with respect to root ");
        t.VerticalSumMain();
    }
}

Python3

# Python3 program to find Vertical Sum in
# a given Binary Tree

# Node definition
class newNode:

    def __init__(self, data):

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

# Traverses the tree in in-order form and
# populates a hashMap that contains the
# vertical sum
def verticalSumUtil(root, hd, Map):

    # Base case
    if(root == None):
        return

    # Recur for left subtree
    verticalSumUtil(root.left, hd - 1, Map)

    # Add val of current node to
    # map entry of corresponding hd
    if(hd in Map.keys()):
        Map[hd] = Map[hd] + root.data
    else:
        Map[hd] = root.data

    # Recur for right subtree
    verticalSumUtil(root.right, hd + 1, Map)

# Function to find vertical_sum
def verticalSum(root):

    # a dictionary to store sum of
    # nodes for each horizontal distance
    Map = {}

    # Populate the dictionary
    verticalSumUtil(root, 0, Map);

    # Prints the values stored
    # by VerticalSumUtil()
    for i,j in Map.items():
        print(i, "=", j, end = ", ")

# Driver Code
if __name__ == "__main__":

    '''      Create the following Binary Tree
              1
            /    \
          2        3
         / \      / \
        4   5    6   7
    '''
    root = newNode(1)
    root.left = newNode(2)
    root.right = newNode(3)
    root.left.left = newNode(4)
    root.left.right = newNode(5)
    root.right.left = newNode(6)
    root.right.right = newNode(7)

    print("Following are the values of vertical "
          "sums with the positions of the "
          "columns with respect to root")

    verticalSum(root)

# This code is contributed by vipinyadav15799

C#

// C# program to find Vertical Sum in
// a given Binary Tree
using System;
using System.Collections.Generic;

// Class for a tree node
class TreeNode
{

    // data members
    public int key;
    public TreeNode left;
    public TreeNode right;

    // Accessor methods
    public int Key()
    {
        return key;
    }
    public TreeNode Left() { return left; }
    public TreeNode Right() { return right; }

    // Constructor
    public TreeNode(int key)
    {
        this.key = key;
        left = null;
        right = null;
    }

    // Methods to set left and right subtrees
    public void setLeft(TreeNode left)
    {
        this.left = left;
    }
    public void setRight(TreeNode right)
    {
        this.right = right;
    }
}

// Class for a Binary Tree
class Tree
{
    private TreeNode root;

    // Constructors
    public Tree() { root = null; }
    public Tree(TreeNode n) { root = n; }

    // Method to be called by the consumer classes
    // like Main class
    public void VerticalSumMain()
    {
        VerticalSum(root);
    }

    // A wrapper over VerticalSumUtil()
    private void VerticalSum(TreeNode root)
    {

        // base case
        if (root == null) { return; }

        // Creates an empty hashMap hM
        Dictionary<int,
                   int> hM = new Dictionary<int,
                                            int>();

        // Calls the VerticalSumUtil() to store the
        // vertical sum values in hM
        VerticalSumUtil(root, 0, hM);

        // Prints the values stored by VerticalSumUtil()
        if (hM != null)
        {
            Console.Write("[");
            foreach(KeyValuePair<int, int> entry in hM)
            {
                Console.Write(entry.Key + " = " +
                              entry.Value + ", ");
            }
            Console.Write("]");
        }
    }

    // Traverses the tree in in-order form and builds
    // a hashMap hM that contains the vertical sum
    private void VerticalSumUtil(TreeNode root, int hD,
                                 Dictionary<int, int> hM)
    {

        // base case
        if (root == null) { return; }

        // Store the values in hM for left subtree
        VerticalSumUtil(root.Left(), hD - 1, hM);

        // Update vertical sum for hD of this node
        int prevSum = 0;
        if(hM.ContainsKey(hD))
        {
            prevSum = hM[hD];
            hM[hD] = prevSum + root.Key();
        }
        else
            hM.Add(hD, prevSum + root.Key());

        // Store the values in hM for right subtree
        VerticalSumUtil(root.Right(), hD + 1, hM);
    }
}

// Driver Code
public class GFG
{
    public static void Main(String[] args)
    {
        /* Create the following Binary Tree
            1
            / \
        2     3
        / \     / \
        4 5 6 7

        */
        TreeNode root = new TreeNode(1);
        root.setLeft(new TreeNode(2));
        root.setRight(new TreeNode(3));
        root.Left().setLeft(new TreeNode(4));
        root.Left().setRight(new TreeNode(5));
        root.Right().setLeft(new TreeNode(6));
        root.Right().setRight(new TreeNode(7));
        Tree t = new Tree(root);

        Console.WriteLine("Following are the values of" +
                          " vertical sums with the positions" +
                          " of the columns with respect to root ");
        t.VerticalSumMain();
    }
}

// This code is contributed by Rajput-Ji

Javascript

<script>
// JavaScript program to find Vertical Sum in
// a given Binary Tree

// Node definition
class newNode{

  constructor(data){
    this.left = null
        this.right = null
        this.data = data
  }

}

// Traverses the tree in in-order form and
// populates a hashMap that contains the
// vertical sum
function verticalSumUtil(root, hd, map){

       // Base case
    if(root == null)
    return;

// Recur for left subtree
  verticalSumUtil(root.left, hd - 1, map)

// Add val of current node to
// map entry of corresponding hd
   if(map.has(hd) == true)
     map.set(hd , map.get(hd) + root.data)
   else
     map.set(hd , root.data)

// Recur for right subtree
   verticalSumUtil(root.right, hd + 1, map)

}

// Function to find vertical_sum
function verticalSum(root){

// a dictionary to store sum of
// nodes for each horizontal distance
  let map = new Map()

// Populate the dictionary
  verticalSumUtil(root, 0, map);

// Prints the values stored
// by VerticalSumUtil()
  for(const [i,j] of map.entries())
     document.write(i + ": " + j)

}

// Driver Code

        //  Create the following Binary Tree
        //     1
        //     / \
        // 2     3
        /// \     / \
    // 4   5 6 7

    root = new newNode(1)
    root.left = new newNode(2)
    root.right = new newNode(3)
    root.left.left = new newNode(4)
    root.left.right = new newNode(5)
    root.right.left = new newNode(6)
    root.right.right = new newNode(7)
  root.right.left.right = new newNode(8);
  root.right.right.right = new newNode(9);

    document.write("Following are the values of vertical sums with the positions of the columns with respect to root")

    verticalSum(root)

// This code is contributed by shinjanpatra
</script>

Output

Following are the values of vertical sums with 
the positions of the columns with respect to root
-2: 4
-1: 2
0: 12
1: 11
2: 7
3: 9

Vertical Sum in Binary Tree | Set 2 (Space Optimized)

Time Complexity: O(n log n)
Auxiliary Space: O(n), As we are using extra space for the map and recursion call stack.