Print the elements of given two Binary Trees in sorted order

Given two binary trees, the task is to print the elements of both the binary trees in non-decreasing order.

Examples:

Input: Trees in the image below

Output: 1 2 3 4 5 6
Explanation: The nodes in the 1st and 2nd binary tree are {3, 1, 5} and {4, 2, 6} respectively. Upon merging and sorting the two arrays, the required array becomes {1, 2, 3, 4, 5, 6} which is the required answer.

Input: Trees in the image below

Output: 0 1 2 3 5 8 10

Approach: The given problem can be solved using the following steps:

• Create a map to store each element present in both trees along with their frequencies.
• Traverse the first tree and insert each element with its frequency in the map.
• Similarly, traverse the first tree and insert each element with its frequency in the map.
• Traverse the map and print all elements, their frequency times.

Below is the implementation of the above approach:

C++

// C++ program of the above approach
#include <bits/stdc++.h>
using namespace std;

// Structure of a binary tree node
class node {
public:
    int data;
    node* left;
    node* right;
};

// Helper function that allocates
// a new node with the given data
node* newNode(int data)
{
    node* Node = new node();
    Node->data = data;
    Node->left = NULL;
    Node->right = NULL;

    return (Node);
}

// Map to store all elements
// from given two trees
map<int, int> m;

// Recursive function to perform
// inorder traversal on tree
void traverse(node* root)
{
    // Base Case
    if (root == NULL)
        return;
    else {
        // Update map
        m[root->data]++;
    }

    // Recursive call for left subtree
    traverse(root->left);

    // Recursive call for right subtree
    traverse(root->right);
}

// Function to print all the elements of
// two given binary trees in sorted order
void printAllElements(node* root1, node* root2)
{
    // Traverse the 1st tree
    traverse(root1);

    // Traverse the 2nd tree
    traverse(root2);

    // Traverse the map
    for (auto it : m) {
        // Print current element
        // its frequency times
        for (int i = 0; i < it.second; i++) {
            cout << it.first << " ";
        }
    }
}

// Driver code
int main()
{
    node* root1 = newNode(8);
    root1->left = newNode(2);
    root1->right = newNode(10);
    root1->left->left = newNode(1);

    node* root2 = newNode(5);
    root2->left = newNode(3);
    root2->right = newNode(0);

    printAllElements(root1, root2);

    return 0;
}

Java

// Java program of the above approach
import java.io.*;
import java.lang.*;
import java.util.*;

// Structure of a binary tree node
public class GFG{
public static class Node {
    int data;
    Node left, right;
    Node(int data)
    {
        left=right=null;
        this.data=data;
    }
}
// Map to store all elements
// from given two trees
public static Map<Integer, Integer> m = new HashMap<>();

// Recursive function to perform
// inorder traversal on tree
public static void traverse(Node root)
{
    // Base Case
    if (root == null)
        return;
    else {
        // Update map
        if(m.containsKey(root.data))
        m.put(root.data,m.get(root.data)+1);
        else
        m.put(root.data,1);
    }

    // Recursive call for left subtree
    traverse(root.left);

    // Recursive call for right subtree
    traverse(root.right);
}

// Function to print all the elements of
// two given binary trees in sorted order
public static void printAllElements(Node root1, Node root2)
{
    // Traverse the 1st tree
    traverse(root1);

    // Traverse the 2nd tree
    traverse(root2);

    // Traverse the map
    for (Map.Entry<Integer,Integer> it : m.entrySet()) {
        // Print current element
        // its frequency times
        for (int i = 0; i < it.getValue(); i++) {
             System.out.print(it.getKey()+" ");
        }
    }
}

// Driver code
public static void main(String[] args)
{
    Node root1 = new Node(8);
    root1.left = new Node(2);
    root1.right = new Node(10);
    root1.left.left = new Node(1);

    Node root2 = new Node(5);
    root2.left = new Node(3);
    root2.right = new Node(0);

    printAllElements(root1, root2);

}
}

// This code is contributed by Pushpesh raj.

Python3

# Python code for the above approach

# Structure of a binary tree node
class node:
    def __init__(self, d):
        self.data = d
        self.left = None
        self.right = None

# Map to store all elements
# from given two trees
m = {}

# Recursive function to perform
# inorder traversal on tree
def traverse(root):

    # Base Case
    if (root == None):
        return
    else:

        # Update map
        if (root.data in m):
            m[root.data] += 1
        else:
            m[root.data] = 1

    # Recursive call for left subtree
    traverse(root.left)

    # Recursive call for right subtree
    traverse(root.right)

# Function to print all the elements of
# two given binary trees in sorted order
def printAllElements(root1, root2):

    # Traverse the 1st tree
    traverse(root1)

    # Traverse the 2nd tree
    traverse(root2)
    v = []

    # Traverse the map
    for key in m:

        # Print current element
        # its frequency times
        for i in range(m[key]):
            v.append(key)

    v.sort()
    for i in range(len(v)):
        print(v[i], end=" ")

# Driver code
root1 = node(8)
root1.left = node(2)
root1.right = node(10)
root1.left.left = node(1)

root2 = node(5)
root2.left = node(3)
root2.right = node(0)

printAllElements(root1, root2)

# This code is contributed by Saurabh Jaiswal

C#

// C# program of the above approach

using System;
using System.Collections;
using System.Collections.Generic;

public class GFG {

    // Structure of a binary tree node
    public class Node {
        public int data;
        public Node left, right;
        public Node(int data)
        {
            left = right = null;
            this.data = data;
        }
    }

    // Dictionary to store all elements from given two trees
    static Dictionary<int, int> m
        = new Dictionary<int, int>();

    // Recursive function to perform inorder traversal on
    // tree
    public static void traverse(Node root)
    {
        // Base Case
        if (root == null)
            return;
        else {
            // Update map
            if (m.ContainsKey(root.data))
                m[root.data] += 1;
            else
                m.Add(root.data, 1);
        }

        // Recursive call for left subtree
        traverse(root.left);

        // Recursive call for right subtree
        traverse(root.right);
    }

    // Function to print all the elements of two given
    // binary trees in sorted order
    public static void printAllElements(Node root1,
                                        Node root2)
    {
        // Traverse the 1st tree
        traverse(root1);

        // Traverse the 2nd tree
        traverse(root2);

        ArrayList v = new ArrayList();

        // Traverse the map.
        foreach(KeyValuePair<int, int> it in m)
        {
            for (int i = 0; i < it.Value; i++) {
                v.Add(it.Key);
            }
        }

        v.Sort();

        foreach(var i in v) { Console.Write(i + " "); }
    }

    static public void Main()
    {

        // Code
        Node root1 = new Node(8);
        root1.left = new Node(2);
        root1.right = new Node(10);
        root1.left.left = new Node(1);

        Node root2 = new Node(5);
        root2.left = new Node(3);
        root2.right = new Node(0);

        printAllElements(root1, root2);
    }
}

// This code is contributed by lokesh (lokeshmvs21).

Javascript

<script>
       // JavaScript code for the above approach

       // Structure of a binary tree node
       class node {
           constructor(d) {
               this.data = d;
               this.left = null;
               this.right = null;
           }
       };

       // Map to store all elements
       // from given two trees
       let m = new Map();

       // Recursive function to perform
       // inorder traversal on tree
       function traverse(root)
       {

           // Base Case
           if (root == null)
               return;
           else
           {

               // Update map
               if (m.has(root.data))
               {
                   m.set(root.data, m.get(root.data) + 1);
               }
               else {
                   m.set(root.data, 1)
               }
           }

           // Recursive call for left subtree
           traverse(root.left);

           // Recursive call for right subtree
           traverse(root.right);
       }

       // Function to print all the elements of
       // two given binary trees in sorted order
       function printAllElements(root1, root2)
       {

           // Traverse the 1st tree
           traverse(root1);

           // Traverse the 2nd tree
           traverse(root2);
           let v = []

           // Traverse the map
           for (let [key, val] of m)
           {

               // Print current element
               // its frequency times
               for (let i = 0; i < val; i++) {
                   v.push(key);
               }
           }
           v.sort(function (a, b) { return a - b })
           for (let i = 0; i < v.length; i++) {
               document.write(v[i] + " ")
           }
       }

       // Driver code
       let root1 = new node(8);
       root1.left = new node(2);
       root1.right = new node(10);
       root1.left.left = new node(1);

       let root2 = new node(5);
       root2.left = new node(3);
       root2.right = new node(0);

       printAllElements(root1, root2);

      // This code is contributed by Potta Lokesh
   </script>

Output

0 1 2 3 5 8 10 

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

Method 2 ( merge sort algorithm)

 The way to solve this problem is to use a modified version of the merge step of the merge sort algorithm.

Algorithm

1. Initialize an empty dictionary called `freq_map` to store the frequency of each node's value.
2. Traverse the first binary tree in inorder and update the frequency map with each node's value.
3. Traverse the second binary tree in inorder and update the frequency map with each node's value.
4. Initialize an empty list called `merged` to hold the merged values.
5. Iterate through the keys of the frequency map in sorted order.
6. For each key, append the key to the `merged` list the number of times it appears in the frequency map.
7. Return the `merged` list.

C++

//C++ code for the above approach
#include <iostream>
#include <vector>
#include <map>

// Define a binary tree node class with a value, left child,
// and right child
struct TreeNode {
    int val;
    TreeNode* left;
    TreeNode* right;

    TreeNode(int val) {
        this->val = val;
        this->left = nullptr;
        this->right = nullptr;
    }
};

// Forward declarations
void inorderTraversal(TreeNode* root, std::map<int, int>& freqMap);
std::vector<int> mergeTrees(TreeNode* root1, TreeNode* root2);

// Define a function to merge two binary trees into a
// sorted list of their values
std::vector<int> mergeTrees(TreeNode* root1, TreeNode* root2) {
    // Create a map to store the frequency of each
    // node's value (automatically sorted by key)
    std::map<int, int> freqMap;

    // Traverse the first tree in inorder and update the
    // frequency map
    inorderTraversal(root1, freqMap);

    // Traverse the second tree in inorder and update
    // the frequency map
    inorderTraversal(root2, freqMap);

    // Create an empty vector to hold the merged values
    std::vector<int> merged;

    // Iterate through the keys of the frequency map
    // (sorted order)
    for (const auto& entry : freqMap) {
        // Append the value to the merged vector the
        // number of times it appears in the frequency
        // map
        int key = entry.first;
        int freq = entry.second;
        for (int i = 0; i < freq; i++) {
            merged.push_back(key);
        }
    }

    // Return the merged vector
    return merged;
}

// Define a function to traverse a binary tree in
// inorder and update the frequency map
void inorderTraversal(TreeNode* root, std::map<int, int>& freqMap) {
    // If the root is null, return
    if (root == nullptr) {
        return;
    }

    // Traverse the left subtree
    inorderTraversal(root->left, freqMap);

    // Update the frequency of the current node's value
    // in the frequency map
    freqMap[root->val]++;

    // Traverse the right subtree
    inorderTraversal(root->right, freqMap);
}

// Main function to test the code
int main() {
    // Example usage:
    // Create two binary trees
    TreeNode* root1 = new TreeNode(8);
    root1->left = new TreeNode(2);
    root1->right = new TreeNode(10);
    root1->left->left = new TreeNode(1);

    TreeNode* root2 = new TreeNode(5);
    root2->left = new TreeNode(3);
    root2->right = new TreeNode(0);

    // Merge the trees and store the result
    std::vector<int> merged = mergeTrees(root1, root2);

    // Print the result in the specified format
    std::cout << "[";
    for (size_t i = 0; i < merged.size(); i++) {
        std::cout << merged[i];
        if (i < merged.size() - 1) {
            std::cout << ", ";
        }
    }
    std::cout << "]" << std::endl;
    // Output: [0, 1, 2, 3, 5, 8, 10]

    // Don't forget to free the dynamically allocated memory
    // ReleaseMemory(root1);
    // ReleaseMemory(root2);

    return 0;
}

Java

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.TreeMap;

// Define a binary tree node class with a value, left child,
// and right child
class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;

    TreeNode(int val)
    {
        this.val = val;
        this.left = null;
        this.right = null;
    }
}

public class GFG {

    // Define a function to merge two binary trees into a
    // sorted list of their values
    public static List<Integer> mergeTrees(TreeNode root1,
                                           TreeNode root2)
    {
        // Create a TreeMap to store the frequency of each
        // node's value (automatically sorted by key)
        Map<Integer, Integer> freqMap = new TreeMap<>();
        // Traverse the first tree in inorder and update the
        // frequency map
        inorderTraversal(root1, freqMap);
        // Traverse the second tree in inorder and update
        // the frequency map
        inorderTraversal(root2, freqMap);
        // Create an empty list to hold the merged values
        List<Integer> merged = new ArrayList<>();
        // Iterate through the keys of the frequency map
        // (sorted order)
        for (int key : freqMap.keySet()) {
            // Append the value to the merged list the
            // number of times it appears in the frequency
            // map
            int freq = freqMap.get(key);
            for (int i = 0; i < freq; i++) {
                merged.add(key);
            }
        }
        // Return the merged list
        return merged;
    }

    // Define a function to traverse a binary tree in
    // inorder and update the frequency map
    private static void
    inorderTraversal(TreeNode root,
                     Map<Integer, Integer> freqMap)
    {
        // If the root is null, return
        if (root == null) {
            return;
        }
        // Traverse the left subtree
        inorderTraversal(root.left, freqMap);
        // Update the frequency of the current node's value
        // in the frequency map
        freqMap.put(root.val,
                    freqMap.getOrDefault(root.val, 0) + 1);
        // Traverse the right subtree
        inorderTraversal(root.right, freqMap);
    }

    // Main function to test the code
    public static void main(String[] args)
    {
        // Example usage:
        // Create two binary trees
        TreeNode root1 = new TreeNode(8);
        root1.left = new TreeNode(2);
        root1.right = new TreeNode(10);
        root1.left.left = new TreeNode(1);
        TreeNode root2 = new TreeNode(5);
        root2.left = new TreeNode(3);
        root2.right = new TreeNode(0);

        // Merge the trees and print the result
        List<Integer> merged = mergeTrees(root1, root2);
        System.out.println(
            merged); // Output: [0, 1, 2, 3, 5, 8, 10]
    }
}

Python

# Define a binary tree node class with a value, left child, and right child
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

# Define a function to merge two binary trees into a sorted list of their values
def merge_trees(root1, root2):
    # Create a dictionary to store the frequency of each node's value
    freq_map = {}
    # Traverse the first tree in inorder and update the frequency map
    inorder_traversal(root1, freq_map)
    # Traverse the second tree in inorder and update the frequency map
    inorder_traversal(root2, freq_map)
    # Create an empty list to hold the merged values
    merged = []
    # Iterate through the keys of the frequency map in sorted order
    for key in sorted(freq_map.keys()):
        # Append the value to the merged list the number of times it appears in the frequency map
        merged.extend([key] * freq_map[key])
    # Return the merged list
    return merged

# Define a function to traverse a binary tree in inorder and update the frequency map
def inorder_traversal(root, freq_map):
    # If the root is None, return
    if root is None:
        return
    # Traverse the left subtree
    inorder_traversal(root.left, freq_map)
    # Update the frequency of the current node's value in the frequency map
    freq_map[root.val] = freq_map.get(root.val, 0) + 1
    # Traverse the right subtree
    inorder_traversal(root.right, freq_map)

# Example usage:
# Create two binary trees
root1 = TreeNode(8)
root1.left = TreeNode(2)
root1.right = TreeNode(10)
root1.left.left = TreeNode(1)
root2 = TreeNode(5)
root2.left = TreeNode(3)
root2.right = TreeNode(0)

 # Merge the trees and print the result
merged = merge_trees(root1, root2)
print(merged) # Output: [1, 2, 3, 4, 5, 6]

C#

using System;
using System.Collections.Generic;
using System.Linq;
using System.Collections;

// Define a binary tree node class with a value, left child,
// and right child
public class TreeNode
{
    public int val;
    public TreeNode left;
    public TreeNode right;

    public TreeNode(int val)
    {
        this.val = val;
        this.left = null;
        this.right = null;
    }
}

public class GFG
{
    // Define a function to merge two binary trees into a
    // sorted list of their values
    public static List<int> MergeTrees(TreeNode root1,
                                       TreeNode root2)
    {
        // Create a TreeMap to store the frequency of each
        // node's value (automatically sorted by key)
        SortedDictionary<int, int> freqMap = new SortedDictionary<int, int>();
        // Traverse the first tree in inorder and update the
        // frequency map
        InorderTraversal(root1, freqMap);
        // Traverse the second tree in inorder and update
        // the frequency map
        InorderTraversal(root2, freqMap);
        // Create an empty list to hold the merged values
        List<int> merged = new List<int>();
        // Iterate through the keys of the frequency map
        // (sorted order)
        foreach (int key in freqMap.Keys)
        {
            // Append the value to the merged list the
            // number of times it appears in the frequency
            // map
            int freq = freqMap[key];
            for (int i = 0; i < freq; i++)
            {
                merged.Add(key);
            }
        }
        // Return the merged list
        return merged;
    }

    // Define a function to traverse a binary tree in
    // inorder and update the frequency map
    private static void InorderTraversal(TreeNode root,
                                         SortedDictionary<int, int> freqMap)
    {
        // If the root is null, return
        if (root == null)
        {
            return;
        }
        // Traverse the left subtree
        InorderTraversal(root.left, freqMap);
        // Update the frequency of the current node's value
        // in the frequency map
        if (freqMap.ContainsKey(root.val))
        {
            freqMap[root.val]++;
        }
        else
        {
            freqMap[root.val] = 1;
        }
        // Traverse the right subtree
        InorderTraversal(root.right, freqMap);
    }

    // Main function to test the code
    public static void Main(string[] args)
    {
        // Example usage:
        // Create two binary trees
        TreeNode root1 = new TreeNode(8);
        root1.left = new TreeNode(2);
        root1.right = new TreeNode(10);
        root1.left.left = new TreeNode(1);
        TreeNode root2 = new TreeNode(5);
        root2.left = new TreeNode(3);
        root2.right = new TreeNode(0);

        // Merge the trees and print the result
        List<int> merged = MergeTrees(root1, root2);
        Console.WriteLine("{"+string.Join(", ", merged)+"}"); // Output: 0, 1, 2, 3, 5, 8, 10
    }
}

// This code is contributed by Dwaipayan Bandyopadhyay

Javascript

// Define a binary tree node class with a value, left child,
// and right child
class TreeNode {
    constructor(val) {
        this.val = val;
        this.left = null;
        this.right = null;
    }
}

// Forward declarations
function inorderTraversal(root, freqMap) {
    if (root === null) {
        return;
    }

    inorderTraversal(root.left, freqMap);
    freqMap[root.val] = (freqMap[root.val] || 0) + 1;
    inorderTraversal(root.right, freqMap);
}

function mergeTrees(root1, root2) {
    // Create a map to store the frequency of each
    // node's value (automatically sorted by key)
    const freqMap = {};

    // Traverse the first tree in inorder and update the
    // frequency map
    inorderTraversal(root1, freqMap);

    // Traverse the second tree in inorder and update
    // the frequency map
    inorderTraversal(root2, freqMap);

    // Create an empty array to hold the merged values
    const merged = [];

    // Iterate through the keys of the frequency map
    // (sorted order)
    Object.keys(freqMap).forEach((key) => {
        const freq = freqMap[key];
        for (let i = 0; i < freq; i++) {
            merged.push(parseInt(key));
        }
    });

    // Return the merged array
    return merged;
}

// Main function to test the code
function main() {
    // Example usage:
    // Create two binary trees
    const root1 = new TreeNode(8);
    root1.left = new TreeNode(2);
    root1.right = new TreeNode(10);
    root1.left.left = new TreeNode(1);

    const root2 = new TreeNode(5);
    root2.left = new TreeNode(3);
    root2.right = new TreeNode(0);

    // Merge the trees and store the result
    const merged = mergeTrees(root1, root2);

    // Print the result in the specified format
    console.log("[" + merged.join(", ") + "]");
    // Output: [0, 1, 2, 3, 5, 8, 10]

    // Don't forget to free the dynamically allocated memory
    // (JavaScript handles memory management automatically)
}

// Call the main function
main();

Output

[0, 1, 2, 3, 5, 8, 10]

Time complexity: O(nlogn), where n is the total number of elements in both trees.
Space complexity: O(n), where n is the total number of nodes in the input binary trees.