Sum of all vertical levels of a Binary Tree Last Updated : 23 Jul, 2025 Comments Improve Suggest changes Like Article Like Report Given a binary tree consisting of either 1 or 0 as its node values, the task is to find the sum of all vertical levels of the Binary Tree, considering each value to be a binary representation. Examples: Input: 1 / \ 1 0 / \ / \ 1 0 1 0Output: 7Explanation: Taking vertical levels from left to right:For vertical level 1: (1)2 = 1For vertical level 2: (1)2 = 1For vertical level 3: (101)2 = 5For vertical level 4: (0)2 = 0For vertical level 5: (0)2 = 0Total sum = 1+1+5+0+0 = 7 Input: 0 / \ 1 0 / \ \ 1 1 0 / \ \ / \ 1 1 1 0 0Output: 8Explanation: Taking vertical levels from left to right: For vertical level 1: (1)2 = 1For vertical level 2: (1)2 = 1For vertical level 3: (11)2 = 3For vertical level 4: (01)2 = 1For vertical level 5: (010)2 = 2For vertical level 6: (0)2 = 0For vertical level 7: (0)2 = 0Total sum = 1+1+3+1+2+0+0 = 8 Approach: Follow the steps below to solve the problem: Perform a tree traversal while keeping track of the horizontal and vertical distance from the root nodeStore the node value corresponding to its horizontal distance in a Hashmap.Initialize a variable, say ans, to store the required result.Create a Hashmap, say M, to store horizontal distance as key and an array of pairs {node value, distance of the node from the root}.The height for each node is also stored as the vertical level is needed to be in a sorted order (from top to bottom), to get the correct decimal value of its binary representation.Perform preorder tree traversal and also pass vertical height and horizontal distances as parameters.If the root is not NULL, perform the following operations:Append the pair {node value, vertical height in the horizontal distance} in M.Traverse the left subtree, decrementing the horizontal distance by 1.Traverse the right subtree, incrementing the horizontal distance by 1.Increment the vertical height by 1 for both of the recursive calls.Now, traverse the Hashmap, say M and for every key, perform the following steps:Sort the values on the basis of their height from the root node and then convert the binary number obtained to its decimal equivalent and store it in a variable, say B.Add the value of B to ans.Print the value of ans Below is the implementation of the above approach: C++ // C++ program for super ugly number #include<bits/stdc++.h> using namespace std; // Structure of a Tree node struct TreeNode { int val = 0; TreeNode *left; TreeNode *right; TreeNode(int x) { val = x; left = right = NULL; } }; // Function to convert // binary number to decimal int getDecimal(vector<pair<int, int> > arr) { // Sort the array on // the basis of the // first index i.e, height sort(arr.begin(), arr.end()); // Store the required // decimal equivalent // of the number int ans = 0; // Traverse the array for (int i = 0; i < arr.size(); i++) { ans <<= 1; ans |= arr[i].second; } // Return the answer return ans; } // Function to traverse the tree void Traverse(TreeNode *root, int hd, int ht, map<int, vector<pair<int, int> > > &mp) { // If root is NULL, return if (!root) return; mp[hd].push_back({ht, root->val}); // Make recursive calls to the left and // right subtree Traverse(root->left, hd - 1, ht + 1, mp); Traverse(root->right, hd + 1, ht + 1, mp); } // Function to calculate // sum of vertical levels // of a Binary Tree void getSum(TreeNode *root) { // Dictionary to store the // vertical level as key and // its corresponding // binary number as value map<int,vector<pair<int,int> > > mp; // Function Call to perform traverse the tree Traverse(root, 0, 0, mp); // Store the required answer int ans = 0; // Get decimal values for each vertical level // and add it to ans for (auto i:mp) ans += getDecimal(i.second); // Print the answer cout<<(ans); } /* Driver program to test above functions */ int main() { TreeNode *root = new TreeNode(1); root->left = new TreeNode(1); root->right = new TreeNode(0); root->left->left = new TreeNode(1); root->left->right = new TreeNode(0); root->right->left = new TreeNode(1); root->right->right = new TreeNode(0); // Function call to get the // sum of vertical level // of the tree getSum(root); return 0; } // This code is contributed by mohit kumar 29. Java // Java program for super ugly number import java.io.*; import java.util.*; // Structure of a Tree node class TreeNode { int val = 0; TreeNode left; TreeNode right; TreeNode(int x) { val = x; left = right = null; } } class GFG { static Map<Integer, ArrayList<ArrayList<Integer>>> mp = new HashMap<Integer, ArrayList<ArrayList<Integer>>>(); // Function to convert // binary number to decimal static int getDecimal(ArrayList<ArrayList<Integer> > arr) { // Sort the array on // the basis of the // first index i.e, height Collections.sort(arr, new Comparator<ArrayList<Integer>>() { @Override public int compare(ArrayList<Integer> o1, ArrayList<Integer> o2) { return o1.get(0).compareTo(o2.get(0)); } }); // Store the required // decimal equivalent // of the number int ans = 0; // Traverse the array for (int i = 0; i < arr.size(); i++) { ans <<= 1; ans |= arr.get(i).get(1); } // Return the answer return ans; } // Function to traverse the tree static void Traverse(TreeNode root, int hd, int ht) { // If root is NULL, return if (root == null) return; if(mp.containsKey(hd)) { mp.get(hd).add(new ArrayList<Integer>(Arrays.asList(ht, root.val))); } else { mp.put(hd,new ArrayList<ArrayList<Integer>>()); mp.get(hd).add(new ArrayList<Integer>(Arrays.asList(ht, root.val))); } // Make recursive calls to the left and // right subtree Traverse(root.left, hd - 1, ht + 1); Traverse(root.right, hd + 1, ht + 1); } // Function to calculate // sum of vertical levels // of a Binary Tree static void getSum(TreeNode root) { // Function Call to perform traverse the tree Traverse(root, 0, 0); // Store the required answer int ans = 0; // Get decimal values for each vertical level // and add it to ans for(Integer key : mp.keySet()) { ans += getDecimal(mp.get(key)); } // Print the answer System.out.print(ans); } // Driver code public static void main (String[] args) { TreeNode root = new TreeNode(1); root.left = new TreeNode(1); root.right = new TreeNode(0); root.left.left = new TreeNode(1); root.left.right = new TreeNode(0); root.right.left = new TreeNode(1); root.right.right = new TreeNode(0); // Function call to get the // sum of vertical level // of the tree getSum(root); } } // This code is contributed by avanitrachhadiya2155 Python3 # Python program # for the above approach # Structure of a Tree node class TreeNode: def __init__(self, val ='', left = None, right = None): self.val = val self.left = left self.right = right # Function to convert # binary number to decimal def getDecimal(arr): # Sort the array on # the basis of the # first index i.e, height arr.sort() # Store the required # decimal equivalent # of the number ans = 0 # Traverse the array for i in range(len(arr)): ans <<= 1 ans |= arr[i][1] # Return the answer return ans # Function to calculate # sum of vertical levels # of a Binary Tree def getSum(root): # Dictionary to store the # vertical level as key and # its corresponding # binary number as value mp = {} # Function to traverse the tree def Traverse(root, hd, ht): # If root is NULL, return if not root: return # Store the value in the map if hd not in mp: mp[hd] = [[ht, root.val]] else: mp[hd].append([ht, root.val]) # Make recursive calls to the left and # right subtree Traverse(root.left, hd - 1, ht + 1) Traverse(root.right, hd + 1, ht + 1) # Function Call to perform traverse the tree Traverse(root, 0, 0) # Store the required answer ans = 0 # Get decimal values for each vertical level # and add it to ans for i in mp: ans += getDecimal(mp[i]) # Print the answer print(ans) # Driver Code # Given Tree root = TreeNode(1) root.left = TreeNode(1) root.right = TreeNode(0) root.left.left = TreeNode(1) root.left.right = TreeNode(0) root.right.left = TreeNode(1) root.right.right = TreeNode(0) # Function call to get the # sum of vertical level # of the tree getSum(root) C# // C# program for super ugly number using System; using System.Linq; using System.Collections.Generic; // Structure of a Tree node public class TreeNode { public int val = 0; public TreeNode left, right; public TreeNode(int x) { val = x; left = right = null; } } public class GFG { static Dictionary<int,List<List<int>>> mp = new Dictionary<int,List<List<int>>>(); // Function to convert // binary number to decimal static int getDecimal(List<List<int> > arr) { // Sort the array on // the basis of the // first index i.e, height arr.OrderBy( l => l[0]); // Store the required // decimal equivalent // of the number int ans = 0; // Traverse the array for (int i = 0; i < arr.Count; i++) { ans <<= 1; ans |= arr[i][1]; } // Return the answer return ans; } // Function to traverse the tree static void Traverse(TreeNode root, int hd, int ht) { // If root is NULL, return if (root == null) return; if(mp.ContainsKey(hd)) { mp[hd].Add(new List<int>(){ht, root.val}); } else { mp.Add(hd,new List<List<int>>()); mp[hd].Add(new List<int>(){ht, root.val}); } // Make recursive calls to the left and // right subtree Traverse(root.left, hd - 1, ht + 1); Traverse(root.right, hd + 1, ht + 1); } // Function to calculate // sum of vertical levels // of a Binary Tree static void getSum(TreeNode root) { // Function Call to perform traverse the tree Traverse(root, 0, 0); // Store the required answer int ans = 0; // Get decimal values for each vertical level // and add it to ans foreach(int key in mp.Keys) { ans += getDecimal(mp[key]); } // Print the answer Console.Write(ans); } // Driver code static public void Main () { TreeNode root = new TreeNode(1); root.left = new TreeNode(1); root.right = new TreeNode(0); root.left.left = new TreeNode(1); root.left.right = new TreeNode(0); root.right.left = new TreeNode(1); root.right.right = new TreeNode(0); // Function call to get the // sum of vertical level // of the tree getSum(root); } } // This code is contributed by rag2127 JavaScript <script> // Javascript program for super ugly number // Structure of a Tree node class TreeNode { constructor(x) { this.val = x; this.left = this.right = null; } } let mp = new Map(); // Function to convert // binary number to decimal function getDecimal(arr) { arr.sort(function(a,b){return a[0]-b[0]}); // Store the required // decimal equivalent // of the number let ans = 0; // Traverse the array for (let i = 0; i < arr.length; i++) { ans <<= 1; ans |= arr[i][1]; } // Return the answer return ans; } // Function to traverse the tree function Traverse(root, hd, ht) { // If root is NULL, return if (root == null) return; if(mp.has(hd)) { mp.get(hd).push([ht, root.val]); } else { mp.set(hd,[]); mp.get(hd).push([ht, root.val]); } // Make recursive calls to the left and // right subtree Traverse(root.left, hd - 1, ht + 1); Traverse(root.right, hd + 1, ht + 1); } // Function to calculate // sum of vertical levels // of a Binary Tree function getSum(root) { // Function Call to perform traverse the tree Traverse(root, 0, 0); // Store the required answer let ans = 0; // Get decimal values for each vertical level // and add it to ans for(let [key, value] of mp.entries()) { ans += getDecimal(value); } // Print the answer document.write(ans); } // Driver code let root = new TreeNode(1); root.left = new TreeNode(1); root.right = new TreeNode(0); root.left.left = new TreeNode(1); root.left.right = new TreeNode(0); root.right.left = new TreeNode(1); root.right.right = new TreeNode(0); // Function call to get the // sum of vertical level // of the tree getSum(root); // This code is contributed by unknown2108 </script> Output: 7 Time Complexity: O(N * log(N))Auxiliary Space: O(N) Comment More infoAdvertise with us Next Article Analysis of Algorithms R rohitsingh07052 Follow Improve Article Tags : Tree Sorting Hash Recursion DSA Binary Tree Tree Traversals cpp-map +4 More Practice Tags : HashRecursionSortingTree Similar Reads Basics & PrerequisitesLogic Building ProblemsLogic building is about creating clear, step-by-step methods to solve problems using simple rules and principles. 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