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Check if a Binary Tree is an Even-Odd Tree or not

  • Difficulty Level : Medium
  • Last Updated : 03 Aug, 2021

Given a Binary Tree, the task is to check if the binary tree is an Even-Odd binary tree or not. 

A Binary Tree is called an Even-Odd Tree when all the nodes which are at even levels have even values (assuming root to be at level 0) and all the nodes which are at odd levels have odd values.

 Examples:

Input: 

             2
            / \
           3   9
          / \   \
         4   10  6

Output: YES 
Explanation: 
Only node on level 0 (even) is 2 (even). 
Nodes present in level 1 are 3 and 9 (both odd). 
Nodes present in level 2 are 4, 10 and 6 (all even). 
Therefore, the Binary tree is an odd-even binary tree.

Input:  

             4
            / \
           3   7
          / \   \
         4   10  5

Output: NO 
 

Approach: Follow the steps below to solve the problem: 

  1. The idea is to perform level-order traversal and check if the nodes present on even levels are even valued or not and nodes present on odd levels are odd valued or not.
  2. If any node at an odd level is found to have odd value or vice-versa, then print “NO“.
  3. Otherwise, after complete traversal of the tree, print “YES“.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
#include<bits/stdc++.h>
using namespace std;
 
struct Node
{
    int val;
    Node *left, *right;
};
 
struct Node* newNode(int data)
{
    struct Node* temp = (struct Node*)malloc(sizeof(struct Node));
    temp->val = data;
    temp->left = NULL;
    temp->right = NULL;
    return temp;
}
 
// Function to check if the
// tree is even-odd tree
bool isEvenOddBinaryTree(Node *root)
{
    if (root == NULL)
        return true;
 
    // Stores nodes of each level
    queue<Node*> q;
    q.push(root);
 
    // Store the current level
    // of the binary tree
    int level = 0;
 
    // Traverse until the
    // queue is empty
    while (!q.empty())
    {
         
        // Stores the number of nodes
        // present in the current level
        int size = q.size();
 
        for(int i = 0; i < size; i++)
        {
            Node *node = q.front();
             
            // Check if the level
            // is even or odd
            if (level % 2 == 0)
            {
                if (node->val % 2 == 1)
                    return false;
            }
            else if (level % 2 == 1)
            {
                if (node->val % 2 == 0)
                    return true;
            }
 
            // Add the nodes of the next
            // level into the queue
            if (node->left != NULL)
            {
                q.push(node->left);
            }
            if (node->right != NULL)
            {
                q.push(node->right);
            }
        }
 
        // Increment the level count
        level++;
    }
    return true;
}
 
// Driver Code
int main()
{
     
    // Construct a Binary Tree
    Node *root = NULL;
    root = newNode(2);
    root->left = newNode(3);
    root->right = newNode(9);
    root->left->left = newNode(4);
    root->left->right = newNode(10);
    root->right->right = newNode(6);
 
    // Check if the binary tree
    // is even-odd tree or not
    if (isEvenOddBinaryTree(root))
        cout << "YES";
    else
        cout << "NO";
}
 
// This code is contributed by ipg2016107

Java




// Java Program for the above approach
import java.util.*;
 
class GfG {
 
    // Tree node
    static class Node {
        int val;
        Node left, right;
    }
 
    // Function to return new tree node
    static Node newNode(int data)
    {
        Node temp = new Node();
        temp.val = data;
        temp.left = null;
        temp.right = null;
        return temp;
    }
 
    // Function to check if the
    // tree is even-odd tree
    public static boolean
    isEvenOddBinaryTree(Node root)
    {
        if (root == null)
            return true;
 
        // Stores nodes of each level
        Queue<Node> q
            = new LinkedList<>();
        q.add(root);
 
        // Store the current level
        // of the binary tree
        int level = 0;
 
        // Traverse until the
        // queue is empty
        while (!q.isEmpty()) {
 
            // Stores the number of nodes
            // present in the current level
            int size = q.size();
 
            for (int i = 0; i < size; i++) {
                Node node = q.poll();
 
                // Check if the level
                // is even or odd
                if (level % 2 == 0) {
 
                    if (node.val % 2 == 1)
                        return false;
                }
                else if (level % 2 == 1) {
 
                    if (node.val % 2 == 0)
                        return false;
                }
 
                // Add the nodes of the next
                // level into the queue
                if (node.left != null) {
 
                    q.add(node.left);
                }
                if (node.right != null) {
 
                    q.add(node.right);
                }
            }
 
            // Increment the level count
            level++;
        }
 
        return true;
    }
 
    // Driver Code
    public static void main(String[] args)
    {
 
        // Construct a Binary Tree
        Node root = null;
        root = newNode(2);
        root.left = newNode(3);
        root.right = newNode(9);
        root.left.left = newNode(4);
        root.left.right = newNode(10);
        root.right.right = newNode(6);
 
        // Check if the binary tree
        // is even-odd tree or not
        if (isEvenOddBinaryTree(root)) {
 
            System.out.println("YES");
        }
        else {
 
            System.out.println("NO");
        }
    }
}

Python3




# Python3 program for the above approach
 
# Tree node
class Node:
     
    def __init__(self, data):
         
        self.left = None
        self.right = None
        self.val = data
         
# Function to return new tree node
def newNode(data):
 
    temp = Node(data)
     
    return temp
 
# Function to check if the
# tree is even-odd tree
def isEvenOddBinaryTree(root):
     
    if (root == None):
        return True
  
    q = []
     
    # Stores nodes of each level
    q.append(root)
  
    # Store the current level
    # of the binary tree
    level = 0
  
    # Traverse until the
    # queue is empty
    while (len(q) != 0):
  
        # Stores the number of nodes
        # present in the current level
        size = len(q)
         
        for i in range(size):
            node = q[0]
            q.pop(0)
  
            # Check if the level
            # is even or odd
            if (level % 2 == 0):
  
                if (node.val % 2 == 1):
                    return False
                 
                elif (level % 2 == 1):
                    if (node.val % 2 == 0):
                        return False
                 
                # Add the nodes of the next
                # level into the queue
                if (node.left != None):
                    q.append(node.left)
                 
                if (node.right != None):
                    q.append(node.right)
                 
            # Increment the level count
            level += 1
         
        return True
     
# Driver code
if __name__=="__main__":
     
    # Construct a Binary Tree
    root = None
    root = newNode(2)
    root.left = newNode(3)
    root.right = newNode(9)
    root.left.left = newNode(4)
    root.left.right = newNode(10)
    root.right.right = newNode(6)
  
    # Check if the binary tree
    # is even-odd tree or not
    if (isEvenOddBinaryTree(root)):
        print("YES")
    else:
        print("NO")
        
# This code is contributed by rutvik_56

C#




// C# Program for the
// above approach
using System;
using System.Collections.Generic;
class GfG{
 
// Tree node
class Node
{
  public int val;
  public Node left, right;
}
 
// Function to return new
// tree node
static Node newNode(int data)
{
  Node temp = new Node();
  temp.val = data;
  temp.left = null;
  temp.right = null;
  return temp;
}
 
// Function to check if the
// tree is even-odd tree
static bool isEvenOddBinaryTree(Node root)
{
  if (root == null)
    return true;
 
  // Stores nodes of each level
  Queue<Node> q = new Queue<Node>();
  q.Enqueue(root);
 
  // Store the current level
  // of the binary tree
  int level = 0;
 
  // Traverse until the
  // queue is empty
  while (q.Count != 0)
  {
    // Stores the number of nodes
    // present in the current level
    int size = q.Count;
 
    for (int i = 0; i < size; i++)
    {
      Node node = q.Dequeue();
 
      // Check if the level
      // is even or odd
      if (level % 2 == 0)
      {
        if (node.val % 2 == 1)
          return false;
      }
      else if (level % 2 == 1)
      {
        if (node.val % 2 == 0)
          return false;
      }
 
      // Add the nodes of the next
      // level into the queue
      if (node.left != null)
      {
        q.Enqueue(node.left);
      }
      if (node.right != null)
      {
        q.Enqueue(node.right);
      }
    }
 
    // Increment the level count
    level++;
  }
 
  return true;
}
 
// Driver Code
public static void Main(String[] args)
{
  // Construct a Binary Tree
  Node root = null;
  root = newNode(2);
  root.left = newNode(3);
  root.right = newNode(9);
  root.left.left = newNode(4);
  root.left.right = newNode(10);
  root.right.right = newNode(6);
 
  // Check if the binary tree
  // is even-odd tree or not
  if (isEvenOddBinaryTree(root))
  {
    Console.WriteLine("YES");
  }
  else
  {
    Console.WriteLine("NO");
  }
}
}
 
// This code is contributed by Princi Singh

Javascript




<script>
 
// Javascript program for the above approach
 
// Tree node
class Node
{
    constructor(data)
    {
        this.left = null;
        this.right = null;
        this.val = data;
    }
}
 
// Function to return new tree node
function newNode(data)
{
    let temp = new Node(data);
    return temp;
}
 
// Function to check if the
// tree is even-odd tree
function isEvenOddBinaryTree(root)
{
    if (root == null)
        return true;
 
    // Stores nodes of each level
    let q = [];
    q.push(root);
 
    // Store the current level
    // of the binary tree
    let level = 0;
 
    // Traverse until the
    // queue is empty
    while (q.length > 0)
    {
         
        // Stores the number of nodes
        // present in the current level
        let size = q.length;
 
        for(let i = 0; i < size; i++)
        {
            let node = q[0];
            q.shift();
 
            // Check if the level
            // is even or odd
            if (level % 2 == 0)
            {
                if (node.val % 2 == 1)
                    return false;
            }
            else if (level % 2 == 1)
            {
                if (node.val % 2 == 0)
                    return false;
            }
 
            // Add the nodes of the next
            // level into the queue
            if (node.left != null)
            {
                q.push(node.left);
            }
            if (node.right != null)
            {
                q.push(node.right);
            }
        }
 
        // Increment the level count
        level++;
    }
    return true;
}
 
// Driver code
 
// Construct a Binary Tree
let root = null;
root = newNode(2);
root.left = newNode(3);
root.right = newNode(9);
root.left.left = newNode(4);
root.left.right = newNode(10);
root.right.right = newNode(6);
 
// Check if the binary tree
// is even-odd tree or not
if (isEvenOddBinaryTree(root))
{
    document.write("YES");
}
else
{
    document.write("NO");
}
 
// This code is contributed by suresh07
 
</script>
Output: 
YES

 

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

Method 2 (Using parent child difference)

Approach:
The idea is to check for the absolute difference between the child and parent node. 

1.  If the root node is odd, return “NO“.

2. If root node is even, then the child nodes should be odd, so difference should always come as odd. In true case return “YES“, else return “NO“.

Below is the implementation of the above approach:

C++




#include <bits/stdc++.h>
using namespace std;
   
// tree node
struct Node
{
    int data;
    Node *left, *right;
};
   
// returns a new
// tree Node
Node* newNode(int data)
{
    Node* temp = new Node();
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}
   
// Utility function to recursively traverse tree and check the diff between child nodes
bool BSTUtil(Node * root){
    if(root==NULL)
        return true;
     
    //if left nodes exist and absolute difference between left child and parent is divisible by 2, then return false       
    if(root->left!=NULL && abs(root->data - root->left->data)%2==0)
        return false;
     //if right nodes exist and absolute difference between right child and parent is divisible by 2, then return false
    if(root->right!=NULL && abs(root->data - root->right->data)%2==0)
        return false;
     
    //recursively traverse left and right subtree
    return BSTUtil(root->left) && BSTUtil(root->right);
}
 
// Utility function to check if binary tree is even-odd binary tree
bool isEvenOddBinaryTree(Node * root){
    if(root==NULL)
        return true;
     
    // if root node is odd, return false
    if(root->data%2 != 0)
        return false;
     
    return BSTUtil(root);  
}
   
// driver program
int main()
{
    // construct a tree
    Node* root = newNode(5);
    root->left = newNode(2);
    root->right = newNode(6);
    root->left->left = newNode(1);
    root->left->right = newNode(5);
    root->right->right = newNode(7);
    root->left->right->left = newNode(12);
 
    root->right->right->right = newNode(14);
    root->right->right->left = newNode(16);
     
    if(BSTUtil(root))
      cout<<"YES";
    else
      cout<<"NO";
    return 0;
}
Output
YES

Time Complexity: O(N)

Auxiliary Space: O(1)


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