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# Vertical order traversal of Binary Tree using Map

Given a binary tree, print it vertically. The following examples illustrate the vertical order traversal.

Examples:

Input:         1
/    \
2      3
/ \   /   \
4   5  6   7
/  \
8    9

Output:

4
2
1 5 6
3 8
7
9

## Vertical order traversal of the binary tree using Self Balancing BSTs:

To solve the problem follow the below idea:

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.

Follow the below steps to solve the problem:

• Do a preorder traversal of the given Binary Tree.
• While traversing the tree, we can recursively calculate HDs. We initially pass the horizontal distance as 0 for the root.
• For the left subtree, we pass the Horizontal Distance as the Horizontal distance of the root minus 1.
• For the right subtree, we pass the Horizontal Distance as the Horizontal Distance of the root plus 1.
• For every HD value, we maintain a list of nodes in a hash map. Whenever we see a node in traversal, we go to the hash map entry and add the node to the hash map using HD as a key in a map.

Below is the implementation of the above approach, thanks to Chirag for providing the below C++ implementation:

## C++

 // C++ program for printing vertical order of a given binary // tree #include using namespace std;   // Structure for a binary tree node struct Node {     int key;     Node *left, *right; };   // A utility function to create a new node struct Node* newNode(int key) {     struct Node* node = new Node;     node->key = key;     node->left = node->right = NULL;     return node; }   // Utility function to store vertical order in map 'm' // 'hd' is horizontal distance of current node from root. // 'hd' is initially passed as 0 void getVerticalOrder(Node* root, int hd,                       map >& m) {     // Base case     if (root == NULL)         return;       // Store current node in map 'm'     m[hd].push_back(root->key);       // Store nodes in left subtree     getVerticalOrder(root->left, hd - 1, m);       // Store nodes in right subtree     getVerticalOrder(root->right, hd + 1, m); }   // The main function to print vertical order of a binary // tree with the given root void printVerticalOrder(Node* root) {     // Create a map and store vertical order in map using     // function getVerticalOrder()     map > m;     int hd = 0;     getVerticalOrder(root, hd, m);       // Traverse the map and print nodes at every horizontal     // distance (hd)     map >::iterator it;     for (it = m.begin(); it != m.end(); it++) {         for (int i = 0; i < it->second.size(); ++i)             cout << it->second[i] << " ";         cout << endl;     } }   // Driver code int main() {     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 << "Vertical order traversal is \n";       // Function call     printVerticalOrder(root);     return 0; }

## Java

 // Java program for printing vertical order of a given // binary tree import java.util.Map.Entry; import java.util.TreeMap; import java.util.Vector;   public class VerticalOrderBtree {     // Tree node     static class Node {         int key;         Node left;         Node right;           // Constructor         Node(int data)         {             key = data;             left = null;             right = null;         }     }       // Utility function to store vertical order in map 'm'     // 'hd' is horizontal distance of current node from     // root. 'hd' is initially passed as 0     static void     getVerticalOrder(Node root, int hd,                      TreeMap > m)     {         // Base case         if (root == null)             return;           // get the vector list at 'hd'         Vector get = m.get(hd);           // Store current node in map 'm'         if (get == null) {             get = new Vector<>();             get.add(root.key);         }         else             get.add(root.key);           m.put(hd, get);           // Store nodes in left subtree         getVerticalOrder(root.left, hd - 1, m);           // Store nodes in right subtree         getVerticalOrder(root.right, hd + 1, m);     }       // The main function to print vertical order of a binary     // tree with the given root     static void printVerticalOrder(Node root)     {         // Create a map and store vertical order in map         // using function getVerticalOrder()         TreeMap > m             = new TreeMap<>();         int hd = 0;         getVerticalOrder(root, hd, m);           // Traverse the map and print nodes at every         // horizontal distance (hd)         for (Entry > entry :              m.entrySet()) {             System.out.println(entry.getValue());         }     }       // Driver code     public static void main(String[] args)     {           // TO DO Auto-generated method stub         Node root = new Node(1);         root.left = new Node(2);         root.right = new Node(3);         root.left.left = new Node(4);         root.left.right = new Node(5);         root.right.left = new Node(6);         root.right.right = new Node(7);         root.right.left.right = new Node(8);         root.right.right.right = new Node(9);         System.out.println("Vertical Order traversal is");         printVerticalOrder(root);     } } // This code is contributed by Sumit Ghosh

## Python3

 # Python3 program for printing vertical order of a given # binary tree   # A binary tree node     class Node:     # Constructor to create a new node     def __init__(self, key):         self.key = key         self.left = None         self.right = None   # Utility function to store vertical order in map 'm' # 'hd' is horizontal distance of current node from root # 'hd' is initially passed as 0     def getVerticalOrder(root, hd, m):       # Base Case     if root is None:         return       # Store current node in map 'm'     try:         m[hd].append(root.key)     except:         m[hd] = [root.key]       # Store nodes in left subtree     getVerticalOrder(root.left, hd-1, m)       # Store nodes in right subtree     getVerticalOrder(root.right, hd+1, m)   # The main function to print vertical order of a binary # tree ith given root     def printVerticalOrder(root):       # Create a map and store vertical order in map using     # function getVerticalORder()     m = dict()     hd = 0     getVerticalOrder(root, hd, m)       # Traverse the map and print nodes at every horizontal     # distance (hd)     for index, value in enumerate(sorted(m)):         for i in m[value]:             print(i, end=" ")         print()     # Driver program to test above function if __name__ == '__main__':     root = Node(1)     root.left = Node(2)     root.right = Node(3)     root.left.left = Node(4)     root.left.right = Node(5)     root.right.left = Node(6)     root.right.right = Node(7)     root.right.left.right = Node(8)     root.right.right.right = Node(9)     print("Vertical order traversal is")     printVerticalOrder(root)   # This code is contributed by Nikhil Kumar Singh(nickzuck_007)

## C#

 // C# program for printing vertical order of a given binary // tree using System; using System.Collections.Generic;   public class VerticalOrderBtree {       // Tree node     public class Node {         public int key;         public Node left;         public Node right;           // Constructor         public Node(int data)         {             key = data;             left = null;             right = null;         }     }       // Utility function to store vertical order in map 'm'     // 'hd' is horizontal distance of current node from     // root. 'hd' is initially passed as 0     static void     getVerticalOrder(Node root, int hd,                      SortedDictionary > m)     {         // Base case         if (root == null)             return;           // get the vector list at 'hd'         List get = new List(); // m[hd];         if (m.ContainsKey(hd))             get.AddRange(m[hd]);           // Store current node in map 'm'         if (get == null) {             get = new List();             get.Add(root.key);         }         else             get.Add(root.key);           m[hd] = get;           // Store nodes in left subtree         getVerticalOrder(root.left, hd - 1, m);           // Store nodes in right subtree         getVerticalOrder(root.right, hd + 1, m);     }       // The main function to print vertical order of a binary     // tree with the given root     static void printVerticalOrder(Node root)     {           // Create a map and store vertical order in map         // using function getVerticalOrder()         SortedDictionary > m             = new SortedDictionary >();         int hd = 0;         getVerticalOrder(root, hd, m);           // Traverse the map and print nodes at every         // horizontal distance (hd)         foreach(KeyValuePair > entry in m)         {             foreach(int v in entry.Value)                 Console.Write(v + " ");             Console.WriteLine();         }     }       // Driver code     public static void Main(String[] args)     {           // TO DO Auto-generated method stub         Node root = new Node(1);         root.left = new Node(2);         root.right = new Node(3);         root.left.left = new Node(4);         root.left.right = new Node(5);         root.right.left = new Node(6);         root.right.right = new Node(7);         root.right.left.right = new Node(8);         root.right.right.right = new Node(9);         Console.WriteLine("Vertical Order traversal is");         printVerticalOrder(root);     } }   // This code is contributed by Rajput-Ji

## Javascript

 // javascript program for printing vertical order of a given binary // tree     // Structure for a binary tree node class Node {           constructor(val){         this.key = val;         this.left = null;         this.right = null;     } }     // Utility function to store vertical order in map 'm' // 'hd' is horizontal distance of current node from root. // 'hd' is initially passed as 0 function getVerticalOrder(root, hd, m) {     // Base case     if (root == null)         return;       // Store current node in map 'm'     if((hd in m) == false){         m[hd] = new Array();     }     m[hd].push(root.key);       // Store nodes in left subtree     getVerticalOrder(root.left, hd - 1, m);       // Store nodes in right subtree     getVerticalOrder(root.right, hd + 1, m); }   //  custom sort function. function sortFunction(a, b) {     if (a[0] === b[0]) {         return 0;     }     else {         return (a[0] < b[0]) ? -1 : 1;     } }   // The main function to print vertical order of a binary // tree with the given root function printVerticalOrder(root) {     // Create a map and store vertical order in map using     // function getVerticalOrder()     let m = {};     let hd = 0;     getVerticalOrder(root, hd, m);       // Traverse the map and print nodes at every horizontal     // distance (hd)     // store the map in the array, as keys act as characters, and cannot be sorted numerically.     let x = new Array();           for (const key in m) {         let y = new Array();         y.push(parseInt(key));         for(let i = 0; i < m[key].length; i++){             y.push(m[key][i]);         }         x.push(y);     }           // sort in ascending order.     x.sort(sortFunction);           // print then.     for(let i = 0; i < x.length; i++){         for(let j = 0; j < x[i].length; j++){             if(j == 0) continue;                           document.write(x[i][j] + " ");         }         document.write("\n");     }       }   // Driver code let root = new Node(1); root.left = new Node(2); root.right = new Node(3); root.left.left = new Node(4); root.left.right = new Node(5); root.right.left = new Node(6); root.right.right = new Node(7); root.right.left.right = new Node(8); root.right.right.right = new Node(9); console.log("Vertical order traversal is \n");   // Function call printVerticalOrder(root);   // The code is contributed by Nidhi goel.

Output

Vertical order traversal is
4
2
1 5 6
3 8
7
9

Time Complexity: O(N log N). The hashing based solution can be considered as O(N) under the assumption that we have a good hashing function that allows insertion and retrieval operations in O(1) time. In the above C++ implementation, map of STL is used. map in STL is typically implemented using a Self-Balancing Binary Search Tree where all operations take O(Log N) time.
Auxiliary Space: O(N)

Note: The above solution may not print nodes in the same vertical order as they appear in the tree.
For example, the above program prints 12 before 9. See this for a sample run.

1
/    \
2       3
/  \     /  \
4    5  6    7
/  \
8     9
/   \
10     11
\
12

Refer below post for a level order traversal-based solution. The below post makes sure that nodes of a vertical line are printed in the same order as they appear in the tree: Print a Binary Tree in Vertical Order | Set 3 (Using Level Order Traversal)

## Print vertical order traversal of the binary tree in the same order as they appear:

To solve the problem follow the below idea:

We can also maintain the order of nodes in the same vertical order as they appear in the tree. Nodes having the same horizontal distance will print according to level order.
For example, In below diagram 9 and 12 have the same horizontal distance. We can make sure that  if a node like 12 comes below in the same vertical line, it is printed after a node like 9

Idea: Instead of using horizontal distance as a key in the map, we will use horizontal distance + vertical distance as the key. We know that the number of nodes can’t be more than the integer range in a binary tree.
We will use the first 30 bits of the key for horizontal distance [MSB to LSB] and will use the 30 next bits for vertical distance. Thus keys will be stored in the map as per our requirement.

Follow the below steps to solve the problem:

• Declare a map to store the value of nodes at each level
• If the root is null then return from the function(Base case)
• Create an integer val and set its value to horizontal distance << 30 OR vertical distance
• Push root->data in the map using val as the key
• Recur for root->left and root->right with horizontal distance – 1, vertical distance + 1 and horizontal distance + 1, vertical distance -1 respectively
• Print the solution using map

Below is the implementation of the above approach:

## C++14

 // C++ program for printing // vertical order of a given binary // tree #include using namespace std;   struct Node {     int data;     Node *left, *right; };   struct Node* newNode(int data) {     struct Node* node = new Node;     node->data = data;     node->left = node->right = NULL;     return node; }   // Store vertical order // in map "m", hd = horizontal // distance, vd = vertical distance void preOrderTraversal(Node* root, long long int hd,                        long long int vd,                        map >& m) {     if (!root)         return;     // key = horizontal     // distance (30 bits) + vertical     // distance (30 bits) map     // will store key in sorted     // order. Thus nodes having same     // horizontal distance     // will sort according to     // vertical distance.     long long val = hd << 30 | vd;       // insert in map     m[val].push_back(root->data);       preOrderTraversal(root->left, hd - 1, vd + 1, m);     preOrderTraversal(root->right, hd + 1, vd + 1, m); }   void verticalOrder(Node* root) {     // map to store all nodes in vertical order.     // keys will be horizontal + vertical distance.     map > mp;       preOrderTraversal(root, 0, 1, mp);       // print map     int prekey = INT_MAX;     map >::iterator it;     for (it = mp.begin(); it != mp.end(); it++) {         if (prekey != INT_MAX             && (it->first >> 30) != prekey) {             cout << endl;         }         prekey = it->first >> 30;         for (int j = 0; j < it->second.size(); j++)             cout << it->second[j] << " ";     } }   // Driver code int main() {     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 << "Vertical order traversal :- " << endl;     verticalOrder(root);     return 0; }

## Java

 // Java program for printing vertical order of a given // binary tree   import java.util.Map.Entry; import java.util.TreeMap; import java.util.Vector;   public class VerticalOrderBtree {     // Tree node     static class Node {         int data;         Node left;         Node right;           // Constructor         Node(int key)         {             data = key;             left = null;             right = null;         }     }     // Store vertical order     // in map "m", hd = horizontal     // distance, vd = vertical distance     static void     preOrderTraversal(Node root, long hd, long vd,                       TreeMap > m)     {         if (root == null)             return;         // key = horizontal         // distance (30 bits) + vertical         // distance (30 bits) map         // will store key in sorted         // order. Thus nodes having same         // horizontal distance         // will sort according to         // vertical distance.         long val = hd << 30 | vd;           // insert in map         if (m.get(val) != null)             m.get(val).add(root.data);         else {             Vector v = new Vector();             v.add(root.data);             m.put(val, v);         }         preOrderTraversal(root.left, hd - 1, vd + 1, m);         preOrderTraversal(root.right, hd + 1, vd + 1, m);     }       static void verticalOrder(Node root)     {         // map to store all nodes in vertical order.         // keys will be horizontal + vertical distance.         TreeMap > mp             = new TreeMap<>();           preOrderTraversal(root, 0, 1, mp);           // print map         int prekey = Integer.MAX_VALUE;         for (Entry > entry :              mp.entrySet()) {             if (prekey != Integer.MAX_VALUE                 && (entry.getKey() >> 30) != prekey) {                 System.out.println();             }             prekey = (int)(entry.getKey() >> 30);             for (int x : entry.getValue())                 System.out.print(x + " ");         }     }       // Driver code     public static void main(String[] args)     {           Node root = new Node(1);         root.left = new Node(2);         root.right = new Node(3);         root.left.left = new Node(4);         root.left.right = new Node(5);         root.right.left = new Node(6);         root.right.right = new Node(7);         root.right.left.right = new Node(8);         root.right.right.right = new Node(9);         System.out.println("Vertical Order traversal :- ");         verticalOrder(root);     } } // This code is contributed by Abhijeet Kumar(abhijeet19403)

## Python3

 import sys   # Python program for printing # vertical order of a given binary # tree     class Node:     def __init__(self, data):         self.data = data         self.left = None         self.right = None   # Store vertical order # in map "m", hd = horizontal # distance, vd = vertical distance     def preOrderTraversal(root, hd, vd, m):     if not root:         return     # key = horizontal     # distance (30 bits) + vertical     # distance (30 bits) map     # will store key in sorted     # order. Thus nodes having same     # horizontal distance     # will sort according to     # vertical distance.     val = hd << 30 | vd       # insert in map     if val in m:         m[val].append(root.data)     else:         m[val] = [root.data]     preOrderTraversal(root.left, hd-1, vd+1, m)     preOrderTraversal(root.right, hd+1, vd+1, m)     def verticalOrder(root):       mp = dict()       preOrderTraversal(root, 0, 0, mp)       # print dictionary     prekey = sys.maxsize       for i in sorted(mp.keys()):         if (prekey != sys.maxsize) and (i >> 30 != prekey):             print()         prekey = i >> 30         for j in mp[i]:             print(j, end=" ")     # Driver code root = Node(1) root.left = Node(2) root.right = Node(3) root.left.left = Node(4) root.left.right = Node(5) root.right.left = Node(6) root.right.right = Node(7) root.right.left.right = Node(8) root.right.right.right = Node(9) print("Vertical order traversal :- ") verticalOrder(root)   # This code is contributed by prashantchandelme.

## C#

 // C# program for printing vertical order of a given binary // tree using System; using System.Collections.Generic;   public class VerticalOrderBtree {       // Tree node     public class Node {         public int data;         public Node left;         public Node right;           // Constructor         public Node(int val)         {             data = val;             left = null;             right = null;         }     }     // Store vertical order     // in map "m", hd = horizontal     // distance, vd = vertical distance     static void     preOrderTraversal(Node root, long hd, long vd,                       SortedDictionary > m)     {         if (root == null)             return;         // key = horizontal         // distance (30 bits) + vertical         // distance (30 bits) map         // will store key in sorted         // order. Thus nodes having same         // horizontal distance         // will sort according to         // vertical distance.         long val = hd << 30 | vd;           // insert in map         if (m.ContainsKey(val) == true)             m[val].Add(root.data);         else {             List v = new List();             v.Add(root.data);             m.Add(val, v);         }         preOrderTraversal(root.left, hd - 1, vd + 1, m);         preOrderTraversal(root.right, hd + 1, vd + 1, m);     }       static void verticalOrder(Node root)     {         // map to store all nodes in vertical order.         // keys will be horizontal + vertical distance.         SortedDictionary > mp             = new SortedDictionary >();           preOrderTraversal(root, 0, 1, mp);           // print map         int prekey = Int32.MaxValue;         foreach(KeyValuePair > entry in mp)         {             if (prekey != Int32.MaxValue                 && (entry.Key >> 30) != prekey) {                 Console.WriteLine();             }             prekey = (int)entry.Key >> 30;             foreach(int v in entry.Value)                 Console.Write(v + " ");         }     }       // Driver program to test above functions     public static void Main(String[] args)     {           Node root = new Node(1);         root.left = new Node(2);         root.right = new Node(3);         root.left.left = new Node(4);         root.left.right = new Node(5);         root.right.left = new Node(6);         root.right.right = new Node(7);         root.right.left.right = new Node(8);         root.right.right.right = new Node(9);         Console.WriteLine("Vertical Order traversal :- ");         verticalOrder(root);     } }   // This code is contributed by Abhijeet Kumar(abhijeet19403)

## Javascript

 class Node {   constructor(data) {     this.data = data;     this.left = null;     this.right = null;   } }   function preOrderTraversal(root, hd, vd, m) {   if (!root) return;     // key = horizontal distance (30 bits) + vertical distance (30 bits)   // map will store key in sorted order. Thus nodes having same   // horizontal distance will sort according to vertical distance.   const val = BigInt(hd << 30n | vd);     // insert in map   if (!m.has(val)) {     m.set(val, []);   }   m.get(val).push(root.data);     preOrderTraversal(root.left, hd - 1n, vd + 1n, m);   preOrderTraversal(root.right, hd + 1n, vd + 1n, m); }   function verticalOrder(root) {   // map to store all nodes in vertical order.   // keys will be horizontal + vertical distance.   const mp = new Map();     preOrderTraversal(root, 0n, 1n, mp);     // print map   let prekey = BigInt(Number.MAX_SAFE_INTEGER);   for (const [key, value] of [...mp.entries()].sort((a, b) => {     // sort map entries by key     if (a[0] < b[0]) return -1;     if (a[0] > b[0]) return 1;     return 0;   })) {     if (prekey !== (key >> 30n)) {       console.log();     }     prekey = key >> 30n;     process.stdout.write(value.join(" ") + " ");   } }   // Driver code const root = new Node(1); root.left = new Node(2); root.right = new Node(3); root.left.left = new Node(4); root.left.right = new Node(5); root.right.left = new Node(6); root.right.right = new Node(7); root.right.left.right = new Node(8); root.right.right.right = new Node(9);   process.stdout.write("Vertical order traversal :- "); verticalOrder(root);

Output

Vertical order traversal :-
4
2
1 5 6
3 8
7
9

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

## Vertical order traversal of the binary tree using computeIfAbsent method in Java:

We can write the code in a more concise way, by using computeIfAbsent method of the map in java and by using a treemap for natural sorting based upon keys.

Below is the implementation of the above approach:

## C++

 #include using namespace std;   // structure of the tree node class Node { public:     int data;     Node* left;     Node* right;     Node(int item)     {         data = item;         left = right = NULL;     } };   class BinaryTree { public:     Node* root;       // Values class     class Values {     public:         int max, min;     };       // Program to find vertical Order     void verticalOrder(Node* node)     {         Values val;           // Create TreeMap         map > mp;           // Function Call to findHorizontalDistance         findHorizontalDistance(node, &val, &val, 0, mp);           // Iterate over map.values()         for (auto list : mp) {             for (auto element : list.second) {                 cout << element << " ";             }             cout << endl;         }     }       // Program to find Horizontal Distance     void findHorizontalDistance(Node* node, Values* min,                                 Values* max, int hd,                                 map >& mp)     {         // If node is null         if (node == NULL)             return;           // if hd is less than min.min         if (hd < min->min)             min->min = hd;           // if hd is greater than min.min         if (hd > max->max)             max->max = hd;           // Using computeIfAbsent         mp[hd].push_back(node->data);           // Function Call with hd equal to hd - 1         findHorizontalDistance(node->left, min, max, hd - 1,                                mp);           // Function Call with hd equal to hd + 1         findHorizontalDistance(node->right, min, max,                                hd + 1, mp);     } };   int main() {     BinaryTree tree;       // Let us construct the tree shown in above diagram     tree.root = new Node(1);     tree.root->left = new Node(2);     tree.root->right = new Node(3);     tree.root->left->left = new Node(4);     tree.root->left->right = new Node(5);     tree.root->right->left = new Node(6);     tree.root->right->right = new Node(7);     tree.root->right->left->right = new Node(8);     tree.root->right->right->right = new Node(9);       cout << "vertical order traversal is :\n";       // Function Call     tree.verticalOrder(tree.root);     return 0; }

## Java

 // Java Program for above approach import java.util.ArrayList; import java.util.List; import java.util.Map; import java.util.TreeMap;   class Node {     int data;     Node left, right;       Node(int item)     {         data = item;         left = right = null;     } }   public class BinaryTree {       Node root;       // Values class     class Values {         int max, min;     }       // Program to find vertical Order     public void verticalOrder(Node node)     {         Values val = new Values();           // Create TreeMap         Map > map             = new TreeMap >();           // Function Call to findHorizontalDistance         findHorizontalDistance(node, val, val, 0, map);           // Iterate over map.values()         for (List list : map.values()) {             System.out.println(list);         }     }       // Program to find Horizontal Distance     public void     findHorizontalDistance(Node node, Values min,                            Values max, int hd,                            Map > map)     {           // If node is null         if (node == null)             return;           // if hd is less than min.min         if (hd < min.min)             min.min = hd;           // if hd is greater than min.min         if (hd > max.max)             max.max = hd;           // Using computeIfAbsent         map.computeIfAbsent(hd,                             k -> new ArrayList())             .add(node.data);           // Function Call with hd equal to hd - 1         findHorizontalDistance(node.left, min, max, hd - 1,                                map);           // Function Call with hd equal to hd + 1         findHorizontalDistance(node.right, min, max, hd + 1,                                map);     }       // Driver Code     public static void main(String[] args)     {           BinaryTree tree = new BinaryTree();           /* Let us construct the tree shown                              in above diagram */         tree.root = new Node(1);         tree.root.left = new Node(2);         tree.root.right = new Node(3);         tree.root.left.left = new Node(4);         tree.root.left.right = new Node(5);         tree.root.right.left = new Node(6);         tree.root.right.right = new Node(7);         tree.root.right.left.right = new Node(8);         tree.root.right.right.right = new Node(9);           System.out.println("vertical order traversal is :");           // Function Call         tree.verticalOrder(tree.root);     } }

## C#

 // C# Program for above approach using System; using System.Collections.Generic;   public class Node {     public int data;     public Node left, right;     public Node(int item)     {         data = item;         left = right = null;     } }   public class BinaryTree {       public Node root;       // Values class     public class Values {         public int max, min;     }       // Program to find vertical Order     public void verticalOrder(Node node)     {         Values val = new Values();           // Create TreeMap         SortedDictionary > map             = new SortedDictionary >();           // Function Call to findHorizontalDistance         findHorizontalDistance(node, val, val, 0, map);           // Iterate over map.values()         foreach(List list in map.Values)         {             Console.WriteLine(String.Join(" ", list));         }     }       // Program to find Horizontal Distance     public static void findHorizontalDistance(         Node node, Values min, Values max, int hd,         SortedDictionary > map)     {           // If node is null         if (node == null)             return;           // if hd is less than min.min         if (hd < min.min)             min.min = hd;           // if hd is greater than min.min         if (hd > max.max)             max.max = hd;           // Using TryGetValue and Add methods         if (!map.TryGetValue(hd, out List value)) {             value = new List();             map.Add(hd, value);         }         value.Add(node.data);           // Function Call with hd equal to hd - 1         findHorizontalDistance(node.left, min, max, hd - 1,                                map);           // Function Call with hd equal to hd + 1         findHorizontalDistance(node.right, min, max, hd + 1,                                map);     }       // Driver Code     public static void Main(string[] args)     {           BinaryTree tree = new BinaryTree();           /* Let us construct the tree shown                              in above diagram */         tree.root = new Node(1);         tree.root.left = new Node(2);         tree.root.right = new Node(3);         tree.root.left.left = new Node(4);         tree.root.left.right = new Node(5);         tree.root.right.left = new Node(6);         tree.root.right.right = new Node(7);         tree.root.right.left.right = new Node(8);         tree.root.right.right.right = new Node(9);           Console.WriteLine("vertical order traversal is :");           // Function Call         tree.verticalOrder(tree.root);     } }   // The code is contributed by Arushi Goel.

## Python3

 class Node:     def __init__(self, item):         self.data = item         self.left = None         self.right = None     class BinaryTree:     def __init__(self):         self.root = None       class Values:         def __init__(self):             self.max = float('-inf')             self.min = float('inf')       def verticalOrder(self, node):         val = self.Values()           # Create dictionary to store vertical order         mp = {}           # Function call to findHorizontalDistance         self.findHorizontalDistance(node, val, val, 0, mp)           # Iterate over dictionary values         for hd, lst in sorted(mp.items()):             for element in lst:                 print(element, end=" ")             print()       def findHorizontalDistance(self, node, minVal, maxVal, hd, mp):         # If node is None         if node is None:             return           # if hd is less than min.min         if hd < minVal.min:             minVal.min = hd           # if hd is greater than min.min         if hd > maxVal.max:             maxVal.max = hd           # Using setdefault         mp.setdefault(hd, []).append(node.data)           # Function Call with hd equal to hd - 1         self.findHorizontalDistance(node.left, minVal, maxVal, hd - 1, mp)           # Function Call with hd equal to hd + 1         self.findHorizontalDistance(node.right, minVal, maxVal, hd + 1, mp)     if __name__ == '__main__':     tree = BinaryTree()       # Let us construct the tree shown in above diagram     tree.root = Node(1)     tree.root.left = Node(2)     tree.root.right = Node(3)     tree.root.left.left = Node(4)     tree.root.left.right = Node(5)     tree.root.right.left = Node(6)     tree.root.right.right = Node(7)     tree.root.right.left.right = Node(8)     tree.root.right.right.right = Node(9)       print("Vertical order traversal is:\n")       # Function Call     tree.verticalOrder(tree.root)

## Javascript

 // Javascript code addition   class Node {   constructor(item) {     this.data = item;     this.left = null;     this.right = null;   } }   class BinaryTree {   constructor() {     this.root = null;   }     verticalOrder(node) {     let val = new Values();       // Create dictionary to store vertical order     let mp = {};       // Function call to findHorizontalDistance     this.findHorizontalDistance(node, val, val, 0, mp);       // Iterate over dictionary values     for (let hd of Object.keys(mp).sort((a, b) => a - b)) {       let lst = mp[hd];       for (let element of lst) {         process.stdout.write(element + " ");       }       process.stdout.write("\n");     }   }     findHorizontalDistance(node, minVal, maxVal, hd, mp) {     // If node is null     if (!node) {       return;     }       // if hd is less than min.min     if (hd < minVal.min) {       minVal.min = hd;     }       // if hd is greater than min.min     if (hd > maxVal.max) {       maxVal.max = hd;     }       // Using setdefault     if (!mp[hd]) {       mp[hd] = [];     }     mp[hd].push(node.data);       // Function Call with hd equal to hd - 1     this.findHorizontalDistance(node.left, minVal, maxVal, hd - 1, mp);       // Function Call with hd equal to hd + 1     this.findHorizontalDistance(node.right, minVal, maxVal, hd + 1, mp);   } }   class Values {   constructor() {     this.max = -Infinity;     this.min = Infinity;   } }   let tree = new BinaryTree();   // Let us construct the tree shown in above diagram tree.root = new Node(1); tree.root.left = new Node(2); tree.root.right = new Node(3); tree.root.left.left = new Node(4); tree.root.left.right = new Node(5); tree.root.right.left = new Node(6); tree.root.right.right = new Node(7); tree.root.right.left.right = new Node(8); tree.root.right.right.right = new Node(9);   process.stdout.write("Vertical order traversal is:\n");   // Function Call tree.verticalOrder(tree.root);   // The code is contributed by Arushi Goel.

Output

vertical order traversal is :
[4]
[2]
[1, 5, 6]
[3, 8]
[7]
[9]

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

## Vertical order traversal of the binary tree using the Unordered Map method:

Note: We have seen the ordered map above but, its complexity is O(N log N), and also it does not print the vertical nodes of the same horizontal distance in the correct order.

Here we implement this using an unordered map, as the unordered map is implemented using a hash table its complexity is O(n), better than using an ordered map which is implemented using a BST.

Follow the below steps to solve the problem:

• Create a queue of pair to store the node and its horizontal distance in the tree
• Create a map to store the value of nodes at each horizontal distance
• Now perform a BFS on the tree
• At each iteration store the nodes with a particular horizontal distance in the map
• Push the left and the right child of the tree with horizontal distance – 1 and horizontal distance + 1 into the queue
• Print the answer using map

Note: Here for printing all nodes of the same horizontal distance from the root we use mn and mx two variables that store the minimum and maximum horizontal distance from the root:

## C++

 // C++ program for printing vertical // order of a given binary tree using BFS #include   using namespace std;   // Structure for a binary tree node struct Node {     int key;     Node *left, *right; };   // A function to create a new node Node* newNode(int key) {     Node* node = new Node;     node->key = key;     node->left = node->right = NULL;     return node; }   // The main function to print vertical // order of a binary tree with given root void printVerticalOrder(Node* root) {     // Base case     if (!root)         return;       // Create a map and store vertical     // order in map using     // function getVerticalOrder()     unordered_map > m;     int hd = 0;       // Create queue to do level order     // traversal Every item of queue contains     // node and horizontal distance     queue > q;     q.push({ root, hd });       // mn and mx contain the minimum and     // maximum horizontal distance from root     int mn = 0, mx = 0;     while (q.size() > 0) {           // pop from queue front         pair temp = q.front();         q.pop();         hd = temp.second;         Node* node = temp.first;           // insert this node's data         // in vector of hash         m[hd].push_back(node->key);           if (node->left)             q.push({ node->left, hd - 1 });         if (node->right)             q.push({ node->right, hd + 1 });           // Update mn and mx         if (mn > hd)             mn = hd;         else if (mx < hd)             mx = hd;     }       // run the loop from minimum to maximum     // every horizontal distance hd     for (int i = mn; i <= mx; i++) {         vector tmp = m[i];         for (int j = 0; j < tmp.size(); j++)             cout << tmp[j] << " ";         cout << endl;     } }   // Driver code int main() {     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 << "Vertical order traversal is \n";     printVerticalOrder(root);     return 0; }

## Java

 // Java program for printing vertical // order of a given binary tree using BFS import java.io.*; import java.util.*;   class GFG {     // Structure for a binary tree node     static class Node {         int key;         Node left, right;         Node(int key)         {             this.key = key;             left = null;             right = null;         }     }       static class pair {         Node first;         int second;         pair(Node first, int second)         {             this.first = first;             this.second = second;         }     }       // The main function to print vertical     // order of a binary tree with given root     static void printVerticalOrder(Node root)     {         // Base case         if (root == null)             return;           // Create a map and store vertical         // order in map using         // function getVerticalOrder()         HashMap > m             = new HashMap<>();         int hd = 0;           // Create queue to do level order         // traversal Every item of queue contains         // node and horizontal distance         Queue q = new ArrayDeque<>();         q.add(new pair(root, hd));           // mn and mx contain the minimum and         // maximum horizontal distance from root         int mn = 0, mx = 0;         while (q.size() > 0) {               // pop from queue front             pair temp = q.remove();               hd = temp.second;             Node node = temp.first;               // insert this node's data             // in vector of hash             if (!m.containsKey(hd))                 m.put(hd, new ArrayList<>());             m.get(hd).add(node.key);               if (node.left != null)                 q.add(new pair(node.left, hd - 1));             if (node.right != null)                 q.add(new pair(node.right, hd + 1));               // Update mn and mx             if (mn > hd)                 mn = hd;             else if (mx < hd)                 mx = hd;         }           // run the loop from minimum to maximum         // every horizontal distance hd         for (int i = mn; i <= mx; i++) {             ArrayList tmp = m.get(i);             for (int j = 0; j < tmp.size(); j++)                 System.out.print(tmp.get(j) + " ");               System.out.println();         }     }       // Driver code     public static void main(String[] args)     {         Node root = new Node(1);         root.left = new Node(2);         root.right = new Node(3);         root.left.left = new Node(4);         root.left.right = new Node(5);         root.right.left = new Node(6);         root.right.right = new Node(7);         root.right.left.right = new Node(8);         root.right.right.right = new Node(9);         System.out.println("Vertical order traversal is ");         printVerticalOrder(root);     } }   // This code is contributed by karandeep1234

## C#

 // C# program for printing vertical // order of a given binary tree using BFS   using System; using System.Collections.Generic;     // Driver code class GFG {     // Structure for a binary tree node   class Node   {     public int key;     public Node left, right;     public Node (int key)     {       this.key = key;       left = null;       right = null;     }   }     class pair   {     public Node first;     public int second;     public pair (Node first, int second)     {       this.first = first;       this.second = second;     }   }     // The main function to print vertical   // order of a binary tree with given root   static void printVerticalOrder (Node root)   {     // Base case     if (root == null)       return;       // Create a map and store vertical     // order in map using     // function getVerticalOrder()     Dictionary < int, List < int >>m = new Dictionary < int, List < int >>();     int hd = 0;       // Create queue to do level order     // traversal Every item of queue contains     // node and horizontal distance     Queue < pair > q = new Queue < pair > ();     q.Enqueue (new pair (root, hd));       // mn and mx contain the minimum and     // maximum horizontal distance from root     int mn = 0, mx = 0;     while (q.Count > 0)       {       // pop from queue front     pair temp = q.Dequeue ();       hd = temp.second;     Node node = temp.first;       // insert this node's data     // in vector of hash     if (!m.ContainsKey (hd))       m.Add (hd, new List < int >());     m[hd].Add (node.key);       if (node.left != null)       q.Enqueue (new pair (node.left, hd - 1));     if (node.right != null)       q.Enqueue (new pair (node.right, hd + 1));       // Update mn and mx     if (mn > hd)       mn = hd;     else if (mx < hd)       mx = hd;       }       // run the loop from minimum to maximum     // every horizontal distance hd     for (int i = mn; i <= mx; i++)       {     List < int >tmp = m[i];     for (int j = 0; j < tmp.Count; j++)       Console.Write (tmp[j] + " ");       Console.WriteLine ();       }   }       static void Main ()   {     Node root = new Node (1);     root.left = new Node (2);     root.right = new Node (3);     root.left.left = new Node (4);     root.left.right = new Node (5);     root.right.left = new Node (6);     root.right.right = new Node (7);     root.right.left.right = new Node (8);     root.right.right.right = new Node (9);     Console.WriteLine ("Vertical order traversal is ");     printVerticalOrder (root);   } }

## Javascript

 // Javascript program for printing vertical // order of a given binary tree using BFS         // program to implement queue data structure       class Queue {         constructor() {           this.items = Array.from(Array(), () => new Array());         }           // add element to the queue         push(element) {           return this.items.push(element);         }           // remove element from the queue         pop() {           if (this.items.length > 0) {             return this.items.shift();           }         }           // view the first element         front() {           return this.items[0];         }           // check if the queue is empty         empty() {           return this.items.length == 0;         }           // the size of the queue         size() {           return this.items.length;         }       }         // Structure for a binary tree node       class Node {         constructor(key) {           this.key = key;           this.left = null;           this.right = null;         }       }         // The main function to print vertical       // order of a binary tree with given root       function printVerticalOrder(root) {         // Base case         if (!root) return;           // Create a map and store vertical         // order in map using         // function getVerticalOrder()         let m = new Map();         let hd = 0;           // Create queue to do level order         // traversal Every item of queue contains         // node and horizontal distance         let q = new Queue();         q.push([root, hd]);           // mn and mx contain the minimum and         // maximum horizontal distance from root         let mn = 0,           mx = 0;         while (q.size() > 0) {           // pop from queue front           temp = q.front();           q.pop();           hd = temp[1];           node = temp[0];             //insert this node's data           //in string of hash           if (m.get(hd) === undefined) {             m.set(hd, "" + node.key);           } else {             m.set(hd, m.get(hd) + " " + node.key);           }             if (node.left) q.push([node.left, hd - 1]);           if (node.right) q.push([node.right, hd + 1]);             // Update mn and mx           if (mn > hd) mn = hd;           else if (mx < hd) mx = hd;         }           // run the loop from minimum to maximum         // every horizontal distance hd         for (let i = mn; i <= mx; i++) {           tmp = m.get(i);           console.log(tmp);         }       }         // Driver code         let root = new Node(1);       root.left = new Node(2);       root.right = new Node(3);       root.left.left = new Node(4);       root.left.right = new Node(5);       root.right.left = new Node(6);       root.right.right = new Node(7);       root.right.left.right = new Node(8);       root.right.right.right = new Node(9);       console.log("Vertical order traversal is ");       printVerticalOrder(root);

## Python3

 # Python program for printing vertical order of a given binary tree using BFS   # Structure for a binary tree node class Node:     def __init__(self, key):         self.key = key         self.left = None         self.right = None   # A function to create a new node def newNode(key):     node = Node(key)     return node   # The main function to print vertical # order of a binary tree with given root def printVerticalOrder(root):     # Base case     if not root:         return       # Create a dictionary and store vertical     # order in dictionary using     # function getVerticalOrder()     m = {}     hd = 0       # Create queue to do level order     # traversal Every item of queue contains     # node and horizontal distance     q = []     q.append((root, hd))       # mn and mx contain the minimum and     # maximum horizontal distance from root     mn, mx = 0, 0     while q:         # pop from queue front         temp = q.pop(0)         hd = temp[1]         node = temp[0]           # insert this node's data         # in vector of hash         if hd in m:             m[hd].append(node.key)         else:             m[hd] = [node.key]           if node.left:             q.append((node.left, hd - 1))         if node.right:             q.append((node.right, hd + 1))           # Update mn and mx         if mn > hd:             mn = hd         elif mx < hd:             mx = hd       # run the loop from minimum to maximum     # every horizontal distance hd     for i in range(mn, mx+1):         if i in m:             tmp = m[i]             for j in range(len(tmp)):                 print(tmp[j], end=' ')             print()   # Driver code if __name__ == '__main__':     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)     print("Vertical order traversal is")     printVerticalOrder(root)

Output

Vertical order traversal is
4
2
1 5 6
3 8
7
9

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

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