Check given binary tree is mirror or symmetric tree (Java/ recursive /example)

• Given two binary trees, check whether one binary tree is mirror/symmetric of another binary tree.
  • Traverse the binary trees using depth first search (DFS)  recursive algorithm.
• Binary tree and corresponding mirror (image) binary tree are shown in Fig 1.

Algorithm – check one binary tree is mirror of another tree (recursive).

1. Check If both input trees (tree1 & tree2) are null
   • Successfully traversed binary trees, return true.
2. If any of the input trees is null
   • tree1 is not mirror of other tree2, return false.
3. Evaluate the Current Node
4. Compare the data of binary trees, tree1 & tree2
   • If Data is same for both nodes [Success condition]
     • Traverse Left child of tree1 and right child of tree2.
     • Traverse right child of tree1 and left child of tree2.
   • else, data of both nodes are not same
     • Trees are not mirror trees, return false.
5. At end of traversal, we will know whether one tree is mirror of another tree.

Program : check binary trees are mirror image of each other using java

1.) IsMirrorTree Class:

• IsMirrorTree class is used to check one binary tree is mirror of another binary tree.
• Traverse the binary tree using recursive algorithm.

package org.learn.Question;

import java.util.LinkedList;
import java.util.Queue;

public class IsMirrorTree {
	public static boolean isMirrorTree(Node tree, Node mirrorTree) {
		if( null == tree && null == mirrorTree) 
			return true;
		
		if( null == tree || null == mirrorTree) 
			return false;
		
		if(tree.data != mirrorTree.data)
			return false;
		
		if(false == isMirrorTree(tree.left,mirrorTree.right))
			return false;
		
		if(false ==  isMirrorTree(tree.right,mirrorTree.left))
			return false;
		
		return true;
	}
	
	public static void printTree(Node root) {
		if (root == null) {
			System.out.println("Tree is empty");
			return ;
		}
		Queue<Node> queue = new LinkedList<Node>();
		queue.offer(root);
		while (!queue.isEmpty()) {
			Node node = queue.poll();			
			System.out.printf("%d ",node.data);		
			if (node.left != null) {
				queue.offer(node.left);
			}
			if (node.right != null) {
				queue.offer(node.right);
			}
		}
		System.out.println("");	
		return;
	}
}

2.) Node:

• Node class representing the nodes in a binary tree.

package org.learn.Question;

public class Node {
	public int data;
	public Node left;
	public Node right;

	public Node(int num) {
		this.data = num;
		this.left = null;
		this.right = null;
	}

	public Node() {
		this.left = null;
		this.right = null;
	}
	
	public static Node createNode(int number) {
		return new Node(number);
	}
}

3.) App Class:

• We are the creating binary tree in main method.
• We are calling IsMirrorTree class, to check one binary tree is mirror  of another binary tree.

package org.learn.Client;

import org.learn.Question.IsMirrorTree;
import org.learn.Question.Node;

public class App {
	public static void main(String[] args) {
		// Binary Tree 1:
		// root level 0
		Node A = Node.createNode(70);
		// Level 1
		Node B = Node.createNode(50);
		Node C = Node.createNode(55);
		// Level 2
		Node D = Node.createNode(25);
		Node E = Node.createNode(80);
		Node F = Node.createNode(37);
		Node G = Node.createNode(45);

		// connect Level 0 and 1
		A.left = B;
		A.right = C;
		// connect level 1 and level 2
		B.left = D;
		B.right = E;
		C.left = F;
		C.right = G;

		//Binary Tree 2:
		
		// root level 0
		Node P = Node.createNode(70);
		// Level 1
		Node Q = Node.createNode(55);
		Node R = Node.createNode(50);
		// Level 2
		Node S = Node.createNode(45);
		Node T = Node.createNode(37);
		Node U = Node.createNode(80);
		Node V = Node.createNode(25);

		// connect Level 0 and 1
		P.left = Q;
		P.right = R;
		// connect level 1 and level 2
		Q.left  = S;
		Q.right = T;
		R.left  = U;
		R.right = V;

		System.out.println("Binary Tree 1 :");
		IsMirrorTree.printTree(A);
		System.out.println("Binary Tree 2 :");
		boolean isMirrorBinaryTrees = IsMirrorTree.isMirrorTree(A,P);
		System.out.printf("Check Trees are mirror binary tree : %b",isMirrorBinaryTrees);
	}
}

Output : check binary tree is symmetric of another binary tree using java

Binary Tree 1 :
70 50 55 25 80 37 45 
Binary Tree 2 :
70 55 50 45 37 80 25 
Check Trees are mirror binary tree : true

Download code – check trees are mirror binary tree using java