Symmetric Binary Tree

April 8, 2023

Tree is Symmetric or Not?

Here, in this page we will discuss a Java program to check whether a tree is Symmetric (mirror of itself) or not.

We need to write a recursive function isSymmetrical() that takes two trees as argument and returns true if trees are Symmetrical and false if trees are not Symmetrical.

Check Whether Tree is Symmetric in C Language

Define a recursive function called isMirror() that takes in two binary trees as arguments and returns true if the trees are mirrored and false otherwise.
Within isMirror(), compare the left and right subtrees of each tree by recursively calling isMirror() with their corresponding subtrees.
The base case of isMirror() is when both subtrees are null, in which case they are considered mirrored and true is returned.
Define another function called isSymmetric() that takes in the root of a binary tree as an argument and returns true if the tree is symmetric, and false otherwise.
Within isSymmetric(), call isMirror() with the left and right subtrees of the root and return the result.
If isMirror() returns true, the tree is symmetric, so return true. Otherwise, return false.
Use isSymmetric() to determine whether a binary tree is symmetric or not. If isSymmetric() returns true, the tree is symmetric, otherwise it is not.

Check whether two tree are identical

Spiral Order traversal of Tree

Check If binary tree if Foldable or not

Sum of all nodes in Binary Tree

Check for Children-Sum in Binary Tree

Code in Java to check Symmetry of Binary Tree

Run

class Node {
    int data;
    Node left, right;

    public Node(int item) {
        data = item;
        left = right = null;
    }
    public Node() {
        data = 0;
        left = right = null;
    }
}

// Binary tree Class
class BTree {

    static Node root;
    static boolean isSymmetryTree(Node node) {
        if (node == null) {
            return true;
        }
        return isSymmetry(node.left, node.right);
    }

    static boolean isSymmetry(Node nodeLeft, Node nodeRight) {

        //Check both left and right node is null, if yes then that is fine, return true.
        if (nodeLeft == null && nodeRight == null) {
            return true;
        }
        //If one is present and other is null, return false.
        if (nodeLeft == null || nodeRight == null) {
            return false;
        }
        if (nodeLeft.data != nodeRight.data)
            return false;
        // The most Important step is -> when you are Checking if it is symmetric , 
        // Send the left child of left subtree and right child of right subtree together. Similarly,
        // send the right child of left subtree and left child of right subtree. 
        boolean left = isSymmetry(nodeLeft.left, nodeRight.right);
        boolean right = isSymmetry(nodeLeft.right, nodeRight.left);

        return (left && right);
    }
}
public class Main{

    public static void main(String[] args) {
        BTree tree = new BTree();
        tree.root = new Node(1);
        tree.root.left = new Node(5);
        tree.root.right = new Node(4);
        tree.root.left.left = new Node(9);
        tree.root.left.right = new Node(7);
        tree.root.right.left = new Node(10);
        tree.root.right.right = new Node(13);
        System.out.println(" The Symmetry of tree is " + tree.isSymmetryTree(tree.root));

    }
}

Output:

The Symmetry of tree is false

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