Java program to determine whether two trees are identical

In this program, we need to check whether two trees are identical or not. For two trees to be identical, they have to satisfy two conditions:

Structure of both the trees should be the same.
Nodes present in one tree should be present in another tree.

Java program to determine whether two trees are identical

Above diagram contains three trees namely A, B, and C. Trees A and B are the identical as they are structurally same and values of all nodes are the same. However, trees A and C are structurally same but not identical as nodes are different in both the trees.

Algorithm

Define Node class which has three attributes namely: data left and right. Here, left represents the left child of the node and right represents the right child of the node.
When a node is created, data will pass to data attribute of the node and both left and right will be set to null.
Define another class which has an attribute root.
- Root represents the root node of the tree and initializes it to null.
areIdenticalTrees() will check whether two trees are identical or not:
- If root nodes of both the trees are null then, they are identical.
- If the root node of only one tree is null then, trees are not identical, return false.
- If root node of none of the tree is null, then check whether data of both the nodes are equal and then recursively check the left subtree and right subtree of one tree is identical to another or not.

Program:

public class IdenticalTrees {

      //Represent the node of the binary tree
      public static class Node{
        int data;
        Node left;
        Node right;

        //Assign data to the new node, set left and right children to null
        public Node(int data){
          this.data = data;
          this.left = null;
          this.right = null;
        }
      }

      //Represent the root of the binary tree
      public Node root;

      public IdenticalTrees(){
        root = null;
      }

      //areIdenticalTrees() finds whether two trees are identical or not
      public static boolean areIdenticalTrees(Node root1, Node root2) {

          //Checks if both the trees are empty
          if(root1 == null && root2 == null)
              return true;

          //Trees are not identical if root of only one tree is null thus, return false
          if(root1 == null && root2 == null)
              return true;

          //If both trees are not empty, check whether the data of the nodes is equal
          //Repeat the steps for left subtree and right subtree
          if(root1 != null  && root2 != null) {

              return ((root1.data == root2.data) &&
                      (areIdenticalTrees(root1.left, root2.left)) &&
                      (areIdenticalTrees(root1.right, root2.right)));
          }
          return false;
      }


      public static void main(String[] args) {

        //Adding nodes to the first binary tree
        IdenticalTrees bt1 = new IdenticalTrees();
        bt1.root = new Node(1);
        bt1.root.left = new Node(2);
        bt1.root.right = new Node(3);
        bt1.root.left.left = new Node(4);
        bt1.root.right.left = new Node(5);
        bt1.root.right.right = new Node(6);

        //Adding nodes to the second binary tree
          IdenticalTrees bt2 = new IdenticalTrees();
          bt2.root = new Node(1);
          bt2.root.left = new Node(2);
          bt2.root.right = new Node(3);
          bt2.root.left.left = new Node(4);
          bt2.root.right.left = new Node(5);
          bt2.root.right.right = new Node(6);

          //Displays whether both the trees are identical or not
           if(areIdenticalTrees(bt1.root, bt2.root))
             System.out.println("Both the binary trees are identical");
         else
             System.out.println("Both the binary trees are not identical");
        }
}

Output: