Question

You need to find the number of pairs ( ) possible such that if you swap the subtrees rooted at nodes and and relabel all the vertices in the tree according to your choice then the new tree and the original tree are same.

Answer 1

// Java program to find maximum sum from a subset of 

// nodes of binary tree 

import java.util.HashMap;

public class FindSumOfNotAdjacentNodes {

  

    // method returns maximum sum possible from subtrees rooted 

    // at grandChildrens of node 'node' 

    public static int sumOfGrandChildren(Node node, HashMap<Node,Integer> mp) 

    { 

        int sum = 0; 

        //  call for children of left child only if it is not NULL 

        if (node.left!=null) 

            sum += getMaxSumUtil(node.left.left, mp) + 

                   getMaxSumUtil(node.left.right, mp); 

    

        //  call for children of right child only if it is not NULL 

        if (node.right!=null) 

            sum += getMaxSumUtil(node.right.left, mp) + 

                   getMaxSumUtil(node.right.right, mp); 

        return sum; 

    }

  

    //  Utility method to return maximum sum rooted at node 'node' 

    public static int getMaxSumUtil(Node node, HashMap<Node,Integer> mp) 

    { 

        if (node == null) 

            return 0; 

    

        // If node is already processed then return calculated 

        // value from map 

        if(mp.containsKey(node))

            return mp.get(node);

    

        //  take current node value and call for all grand children 

        int incl = node.data + sumOfGrandChildren(node, mp); 

    

        //  don't take current node value and call for all children 

        int excl = getMaxSumUtil(node.left, mp) + 

                   getMaxSumUtil(node.right, mp); 

    

        //  choose maximum from both above calls and store that in map 

        mp.put(node,Math.max(incl, excl)); 

    

        return mp.get(node); 

    } 

  

    // Returns maximum sum from subset of nodes 

    // of binary tree under given constraints 

    public static int getMaxSum(Node node) 

    { 

        if (node == null) 

            return 0; 

        HashMap<Node,Integer> mp=new HashMap<>();

        return getMaxSumUtil(node, mp); 

    }

  

    public static void main(String args[]) 

    {

        Node root = new Node(1); 

        root.left = new Node(2); 

        root.right = new Node(3); 

        root.right.left = new Node(4); 

        root.right.right = new Node(5); 

        root.left.left = new Node(1);     

        System.out.print(getMaxSum(root));

    }

}

  

/* A binary tree node structure */

class Node 

{ 

    int data; 

    Node left, right; 

    Node(int data)

    {

        this.data=data;

        left=right=null;

    }

};