# Vertical Sum in a given Binary Tree | Set 1

• Difficulty Level : Medium
• Last Updated : 14 Dec, 2022

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``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 hM =``                   ``new` `TreeMap();`` ` `        ``// 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 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

 ``

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.

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