Iterative method to check if two trees are mirror of each other

Given two binary trees. The problem is to check whether the two binary trees are mirrors of each other or not. 
Mirror of a Binary Tree: Mirror of a Binary Tree T is another Binary Tree M(T) with left and right children of all non-leaf nodes interchanged.

Trees in the above figure are mirrors of each other.

We have discussed a recursive solution to check if two trees are mirror. In this post iterative solution is discussed.
Prerequisite: Iterative inorder tree traversal using stack

Approach:

The following steps are: 

1. Perform iterative inorder traversal of one tree and iterative reverse inorder traversal of the other tree in parallel.
2. During these two iterative traversals check that the corresponding nodes have the same value or not. If not same then they are not mirrors of each other.
3. If values are same, then check whether at any point in the iterative inorder traversal one of the root becomes null and the other is not null. If this happens then they are not mirrors of each other. This check ensures whether they have the corresponding mirror structures or not.
4. Otherwise, both the trees are mirror of each other.

Reverse inorder traversal is the opposite of inorder traversal. In this, the right subtree is traversed first, then root, and then the left subtree.  

Implementation:

C++

// C++ implementation to check whether the two
// binary trees are mirrors of each other or not
#include <bits/stdc++.h>
using namespace std;

// structure of a node in binary tree
struct Node
{
    int data;
    struct Node *left, *right;
};

// Utility function to create and return
// a new node for a binary tree
struct Node* newNode(int data)
{
    struct Node *temp = new Node();
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}

// function to check whether the two binary trees
// are mirrors of each other or not
string areMirrors(Node *root1, Node *root2)
{
    stack<Node*> st1, st2;
    while (1)
    {
        // iterative inorder traversal of 1st tree and
        // reverse inorder traversal of 2nd tree
        while (root1 && root2)
        {
            // if the corresponding nodes in the two traversal
            // have different data values, then they are not
            // mirrors of each other.
            if (root1->data != root2->data)
                return "No";

            st1.push(root1);
            st2.push(root2);
            root1 = root1->left;
            root2 = root2->right;
        }

        // if at any point one root becomes null and
        // the other root is not null, then they are
        // not mirrors. This condition verifies that
        // structures of tree are mirrors of each other.
        if (!(root1 == NULL && root2 == NULL))
            return "No";

        if (!st1.empty() && !st2.empty())
        {
            root1 = st1.top();
            root2 = st2.top();
            st1.pop();
            st2.pop();

            /* we have visited the node and its left subtree.
               Now, it's right subtree's turn */
            root1 = root1->right;

            /* we have visited the node and its right subtree.
               Now, it's left subtree's turn */
            root2 = root2->left;
        }

        // both the trees have been completely traversed
        else
            break;
    }

    // trees are mirrors of each other
    return "Yes";
}

// Driver program to test above
int main()
{
    // 1st binary tree formation
    Node *root1 = newNode(1);            /*         1          */
    root1->left = newNode(3);            /*       /   \        */
    root1->right = newNode(2);           /*      3     2       */
    root1->right->left = newNode(5);     /*          /   \     */
    root1->right->right = newNode(4);    /*         5     4    */

    // 2nd binary tree formation
    Node *root2 = newNode(1);            /*         1          */
    root2->left = newNode(2);            /*       /   \        */
    root2->right = newNode(3);           /*      2     3       */
    root2->left->left = newNode(4);      /*    /   \           */
    root2->left->right = newNode(5);     /*   4    5           */

    cout << areMirrors(root1, root2);
    return 0;
}

Java

// Java implementation to check whether the two
// binary trees are mirrors of each other or not
import java.util.*;
class GfG {

// structure of a node in binary tree
static class Node
{
    int data;
    Node left, right;
}

// Utility function to create and return
// a new node for a binary tree
static Node newNode(int data)
{
    Node temp = new Node();
    temp.data = data;
    temp.left = null;
    temp.right = null;
    return temp;
}

// function to check whether the two binary trees
// are mirrors of each other or not
static String areMirrors(Node root1, Node root2)
{
    Stack<Node> st1 = new Stack<Node> ();
    Stack<Node> st2  = new Stack<Node> ();
    while (true)
    {
        // iterative inorder traversal of 1st tree and
        // reverse inorder traversal of 2nd tree
        while (root1 != null && root2 != null)
        {
            // if the corresponding nodes in the two traversal
            // have different data values, then they are not
            // mirrors of each other.
            if (root1.data != root2.data)
                return "No";

            st1.push(root1);
            st2.push(root2);
            root1 = root1.left;
            root2 = root2.right;
        }

        // if at any point one root becomes null and
        // the other root is not null, then they are
        // not mirrors. This condition verifies that
        // structures of tree are mirrors of each other.
        if (!(root1 == null && root2 == null))
            return "No";

        if (!st1.isEmpty() && !st2.isEmpty())
        {
            root1 = st1.peek();
            root2 = st2.peek();
            st1.pop();
            st2.pop();

            /* we have visited the node and its left subtree.
            Now, it's right subtree's turn */
            root1 = root1.right;

            /* we have visited the node and its right subtree.
            Now, it's left subtree's turn */
            root2 = root2.left;
        }

        // both the trees have been completely traversed
        else
            break;
    }

    // trees are mirrors of each other
    return "Yes";
}

// Driver program to test above
public static void main(String[] args)
{
    // 1st binary tree formation
    Node root1 = newNode(1);         /*         1         */
    root1.left = newNode(3);         /*     / \     */
    root1.right = newNode(2);         /*     3     2     */
    root1.right.left = newNode(5);     /*         / \     */
    root1.right.right = newNode(4); /*         5     4 */

    // 2nd binary tree formation
    Node root2 = newNode(1);         /*         1         */
    root2.left = newNode(2);         /*     / \     */
    root2.right = newNode(3);         /*     2     3     */
    root2.left.left = newNode(4);     /* / \         */
    root2.left.right = newNode(5);     /* 4 5         */

    System.out.println(areMirrors(root1, root2));
}
}

Python3

# Python3 implementation to check whether
# the two binary trees are mirrors of each
# other or not

# Utility function to create and return
# a new node for a binary tree
class newNode:
    def __init__(self, data):
        self.data = data
        self.left = self.right = None

# function to check whether the two binary
# trees are mirrors of each other or not
def areMirrors(root1, root2):
    st1 = []
    st2 = []
    while (1):

        # iterative inorder traversal of 1st tree
        # and reverse inorder traversal of 2nd tree
        while (root1 and root2):

            # if the corresponding nodes in the
            # two traversal have different data
            # values, then they are not mirrors
            # of each other.
            if (root1.data != root2.data):
                return "No"

            st1.append(root1)
            st2.append(root2)
            root1 = root1.left
            root2 = root2.right

        # if at any point one root becomes None and
        # the other root is not None, then they are
        # not mirrors. This condition verifies that
        # structures of tree are mirrors of each other.
        if (not (root1 == None and root2 == None)):
            return "No"

        if (not len(st1) == 0 and not len(st2) == 0):
            root1 = st1[-1]
            root2 = st2[-1]
            st1.pop(-1)
            st2.pop(-1)

            # we have visited the node and its left
            # subtree. Now, it's right subtree's turn
            root1 = root1.right

            # we have visited the node and its right
            # subtree. Now, it's left subtree's turn
            root2 = root2.left

        # both the trees have been
        # completely traversed
        else:
            break

    # trees are mirrors of each other
    return "Yes"

# Driver Code
if __name__ == '__main__':

    # 1st binary tree formation
    root1 = newNode(1)         #          1
    root1.left = newNode(3)         #     / \
    root1.right = newNode(2)  #        3    2
    root1.right.left = newNode(5)#       / \
    root1.right.right = newNode(4) #  5      4

    # 2nd binary tree formation
    root2 = newNode(1)        #          1
    root2.left = newNode(2)         #     / \
    root2.right = newNode(3) #        2     3
    root2.left.left = newNode(4)#  / \
    root2.left.right = newNode(5)# 4  5

    print(areMirrors(root1, root2))

# This code is contributed by pranchalK

C#

// C# implementation to check whether the two
// binary trees are mirrors of each other or not
using System;
using System.Collections.Generic;

class GfG
{

    // structure of a node in binary tree
    public class Node
    {
        public int data;
        public Node left, right;
    }

    // Utility function to create and return
    // a new node for a binary tree
    static Node newNode(int data)
    {
        Node temp = new Node();
        temp.data = data;
        temp.left = null;
        temp.right = null;
        return temp;
    }

    // function to check whether the two binary trees
    // are mirrors of each other or not
    static String areMirrors(Node root1, Node root2)
    {
        Stack<Node> st1 = new Stack<Node> ();
        Stack<Node> st2 = new Stack<Node> ();
        while (true)
        {
            // iterative inorder traversal of 1st tree and
            // reverse inorder traversal of 2nd tree
            while (root1 != null && root2 != null)
            {
                // if the corresponding nodes in the two traversal
                // have different data values, then they are not
                // mirrors of each other.
                if (root1.data != root2.data)
                    return "No";

                st1.Push(root1);
                st2.Push(root2);
                root1 = root1.left;
                root2 = root2.right;
            }

            // if at any point one root becomes null and
            // the other root is not null, then they are
            // not mirrors. This condition verifies that
            // structures of tree are mirrors of each other.
            if (!(root1 == null && root2 == null))
                return "No";

            if (st1.Count != 0 && st2.Count != 0)
            {
                root1 = st1.Peek();
                root2 = st2.Peek();
                st1.Pop();
                st2.Pop();

                /* we have visited the node and its left subtree.
                Now, it's right subtree's turn */
                root1 = root1.right;

                /* we have visited the node and its right subtree.
                Now, it's left subtree's turn */
                root2 = root2.left;
            }

            // both the trees have been completely traversed
            else
                break;
        }

        // trees are mirrors of each other
        return "Yes";
    }

    // Driver program to test above
    public static void Main(String[] args)
    {
        // 1st binary tree formation
        Node root1 = newNode(1);         /*         1         */
        root1.left = newNode(3);         /*     / \     */
        root1.right = newNode(2);         /*     3     2     */
        root1.right.left = newNode(5);     /*         / \     */
        root1.right.right = newNode(4); /*         5     4 */

        // 2nd binary tree formation
        Node root2 = newNode(1);         /*         1         */
        root2.left = newNode(2);         /*     / \     */
        root2.right = newNode(3);         /*     2     3     */
        root2.left.left = newNode(4);     /* / \         */
        root2.left.right = newNode(5);     /* 4 5         */

        Console.WriteLine(areMirrors(root1, root2));
    }
}

// This code has been contributed by 29AjayKumar

Javascript

<script>

// Javascript implementation to check whether
// the two binary trees are mirrors of each
// other or not structure of a node in binary tree
class Node
{
    constructor()
    {
        this.data = 0;
        this.left = null;
        this.right = null;
    }
}

// Utility function to create and return
// a new node for a binary tree
function newNode(data)
{
    var temp = new Node();
    temp.data = data;
    temp.left = null;
    temp.right = null;
    return temp;
}

// Function to check whether the two binary trees
// are mirrors of each other or not
function areMirrors(root1, root2)
{
    var st1 = [];
    var st2 = [];

    while (true)
    {

        // Iterative inorder traversal of 1st tree and
        // reverse inorder traversal of 2nd tree
        while (root1 != null && root2 != null)
        {
            // if the corresponding nodes in the
            // two traversal have different data
            // values, then they are not mirrors
            // of each other.
            if (root1.data != root2.data)
                return "No";

            st1.push(root1);
            st2.push(root2);
            root1 = root1.left;
            root2 = root2.right;
        }

        // If at any point one root becomes null and
        // the other root is not null, then they are
        // not mirrors. This condition verifies that
        // structures of tree are mirrors of each other.
        if (!(root1 == null && root2 == null))
            return "No";

        if (st1.length != 0 && st2.length != 0)
        {
            root1 = st1[st1.length - 1];
            root2 = st2[st2.length - 1];
            st1.pop();
            st2.pop();

            /* We have visited the node and
            its left subtree. Now, it's right
            subtree's turn */
            root1 = root1.right;

            /* We have visited the node and
            its right subtree. Now, it's left
            subtree's turn */
            root2 = root2.left;
        }

        // Both the trees have been
        // completely traversed
        else
            break;
    }

    // Trees are mirrors of each other
    return "Yes";
}

// Driver code
// 1st binary tree formation
var root1 = newNode(1);         /*       1         */
root1.left = newNode(3);         /*     / \     */
root1.right = newNode(2);         /*   3   2     */
root1.right.left = newNode(5);     /*      / \     */
root1.right.right = newNode(4); /*        5   4 */

// 2nd binary tree formation
var root2 = newNode(1);         /*       1         */
root2.left = newNode(2);         /*     / \     */
root2.right = newNode(3);         /*   2   3     */
root2.left.left = newNode(4);     /*  / \         */
root2.left.right = newNode(5);     /* 4  5         */

document.write(areMirrors(root1, root2));

// This code is contributed by noob2000

</script>

Output

Yes

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

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