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Largest sub-tree having equal no of 1’s and 0’s
  • Difficulty Level : Medium
  • Last Updated : 02 Jun, 2021

Given a tree having every node’s value as either 0 or 1, the task is to find the maximum size of the sub-tree in the given tree that has equal number of 0’s and 1’s, if no such sub-tree exists then print -1.
Examples: 
 

Input: 
 

Output: 6
Input: 
 



Output: -1 
 

 

Approach: 
 

  1. Change all the nodes of the tree which are 0 to -1. Now the problem gets reduced to finding the maximum size of a sub-tree sum of whose nodes is 0.
  2. Update all the nodes of the tree so that they represent the sum of all nodes in the sub-tree rooted at the current node.
  3. Now find the size of the maximum sub-tree rooted at a node whose value is 0. If no such node is found then print -1

Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <iostream>
using namespace std;
 
// To store the size of the maximum sub-tree
// with equal number of 0's and 1's
int maxSize = -1;
 
// Represents a node of the tree
struct node {
    int data;
    struct node *right, *left;
};
 
// To create a new node
struct node* newnode(int key)
{
    struct node* temp = new node;
    temp->data = key;
    temp->right = NULL;
    temp->left = NULL;
    return temp;
}
 
// Function to perform inorder traversal on
// the tree and print the nodes in that order
void inorder(struct node* root)
{
    if (root == NULL)
        return;
    inorder(root->left);
    cout << root->data << endl;
    inorder(root->right);
}
 
// Function to return the maximum size of
// the sub-tree having equal number of 0's and 1's
int maxsize(struct node* root)
{
    int a = 0, b = 0;
    if (root == NULL)
        return 0;
 
    // Max size in the right sub-tree
    a = maxsize(root->right);
 
    // 1 is added for the parent
    a = a + 1;
 
    // Max size in the left sub-tree
    b = maxsize(root->left);
 
    // Total size of the tree
    // rooted at the current node
    a = b + a;
 
    // If the current tree has equal
    // number of 0's and 1's
    if (root->data == 0)
 
        // If the total size exceeds
        // the current max
        if (a >= maxSize)
            maxSize = a;
 
    return a;
}
 
// Function to update and return the sum
// of all the tree nodes rooted at
// the passed node
int sum_tree(struct node* root)
{
 
    if (root != NULL)
 
        // If current node's value is 0
        // then update it to -1
        if (root->data == 0)
            root->data = -1;
 
    int a = 0, b = 0;
 
    // If left child exists
    if (root->left != NULL)
        a = sum_tree(root->left);
 
    // If right child exists
    if (root->right != NULL)
        b = sum_tree(root->right);
    root->data += (a + b);
 
    return root->data;
}
 
// Driver code
int main()
{
    struct node* root = newnode(1);
    root->right = newnode(0);
    root->right->right = newnode(1);
    root->right->right->right = newnode(1);
    root->left = newnode(0);
    root->left->left = newnode(1);
    root->left->left->left = newnode(1);
    root->left->right = newnode(0);
    root->left->right->left = newnode(1);
    root->left->right->left->left = newnode(1);
    root->left->right->right = newnode(0);
    root->left->right->right->left = newnode(0);
    root->left->right->right->left->left = newnode(1);
 
    sum_tree(root);
 
    maxsize(root);
 
    cout << maxSize;
 
    return 0;
}

Java




// Java implementation of the approach
class GFG
{
 
// To store the size of the maximum sub-tree
// with equal number of 0's and 1's
static int maxSize = -1;
 
// Represents a node of the tree
static class node
{
    int data;
    node right, left;
};
 
// To create a new node
static node newnode(int key)
{
    node temp = new node();
    temp.data = key;
    temp.right = null;
    temp.left = null;
    return temp;
}
 
// Function to perform inorder traversal on
// the tree and print the nodes in that order
static void inorder(node root)
{
    if (root == null)
        return;
    inorder(root.left);
    System.out.print(root.data +"\n");
    inorder(root.right);
}
 
// Function to return the maximum size of
// the sub-tree having equal number of 0's and 1's
static int maxsize(node root)
{
    int a = 0, b = 0;
    if (root == null)
        return 0;
 
    // Max size in the right sub-tree
    a = maxsize(root.right);
 
    // 1 is added for the parent
    a = a + 1;
 
    // Max size in the left sub-tree
    b = maxsize(root.left);
 
    // Total size of the tree
    // rooted at the current node
    a = b + a;
 
    // If the current tree has equal
    // number of 0's and 1's
    if (root.data == 0)
 
        // If the total size exceeds
        // the current max
        if (a >= maxSize)
            maxSize = a;
 
    return a;
}
 
// Function to update and return the sum
// of all the tree nodes rooted at
// the passed node
static int sum_tree(node root)
{
 
    if (root != null)
 
        // If current node's value is 0
        // then update it to -1
        if (root.data == 0)
            root.data = -1;
 
    int a = 0, b = 0;
 
    // If left child exists
    if (root.left != null)
        a = sum_tree(root.left);
 
    // If right child exists
    if (root.right != null)
        b = sum_tree(root.right);
    root.data += (a + b);
 
    return root.data;
}
 
// Driver code
public static void main(String[] args)
{
    node root = newnode(1);
    root.right = newnode(0);
    root.right.right = newnode(1);
    root.right.right.right = newnode(1);
    root.left = newnode(0);
    root.left.left = newnode(1);
    root.left.left.left = newnode(1);
    root.left.right = newnode(0);
    root.left.right.left = newnode(1);
    root.left.right.left.left = newnode(1);
    root.left.right.right = newnode(0);
    root.left.right.right.left = newnode(0);
    root.left.right.right.left.left = newnode(1);
 
    sum_tree(root);
 
    maxsize(root);
 
    System.out.print(maxSize);
}
}
 
// This code is contributed by PrinciRaj1992

C#




// C# implementation of the approach
using System;
 
class GFG
{
 
// To store the size of the maximum sub-tree
// with equal number of 0's and 1's
static int maxSize = -1;
 
// Represents a node of the tree
public class node
{
    public int data;
    public node right, left;
};
 
// To create a new node
static node newnode(int key)
{
    node temp = new node();
    temp.data = key;
    temp.right = null;
    temp.left = null;
    return temp;
}
 
// Function to perform inorder traversal on
// the tree and print the nodes in that order
static void inorder(node root)
{
    if (root == null)
        return;
    inorder(root.left);
    Console.Write(root.data +"\n");
    inorder(root.right);
}
 
// Function to return the maximum size of
// the sub-tree having equal number of 0's and 1's
static int maxsize(node root)
{
    int a = 0, b = 0;
    if (root == null)
        return 0;
 
    // Max size in the right sub-tree
    a = maxsize(root.right);
 
    // 1 is added for the parent
    a = a + 1;
 
    // Max size in the left sub-tree
    b = maxsize(root.left);
 
    // Total size of the tree
    // rooted at the current node
    a = b + a;
 
    // If the current tree has equal
    // number of 0's and 1's
    if (root.data == 0)
 
        // If the total size exceeds
        // the current max
        if (a >= maxSize)
            maxSize = a;
 
    return a;
}
 
// Function to update and return the sum
// of all the tree nodes rooted at
// the passed node
static int sum_tree(node root)
{
 
    if (root != null)
 
        // If current node's value is 0
        // then update it to -1
        if (root.data == 0)
            root.data = -1;
 
    int a = 0, b = 0;
 
    // If left child exists
    if (root.left != null)
        a = sum_tree(root.left);
 
    // If right child exists
    if (root.right != null)
        b = sum_tree(root.right);
    root.data += (a + b);
 
    return root.data;
}
 
// Driver code
public static void Main(String[] args)
{
    node root = newnode(1);
    root.right = newnode(0);
    root.right.right = newnode(1);
    root.right.right.right = newnode(1);
    root.left = newnode(0);
    root.left.left = newnode(1);
    root.left.left.left = newnode(1);
    root.left.right = newnode(0);
    root.left.right.left = newnode(1);
    root.left.right.left.left = newnode(1);
    root.left.right.right = newnode(0);
    root.left.right.right.left = newnode(0);
    root.left.right.right.left.left = newnode(1);
 
    sum_tree(root);
 
    maxsize(root);
 
    Console.Write(maxSize);
}
}
 
// This code is contributed by Rajput-Ji

Javascript




<script>
 
// JavaScript implementation of the approach   
// To store the size of the maximum sub-tree
    // with equal number of 0's and 1's
    var maxSize = -1;
 
    // Represents a node of the tree
    class Node {
        constructor(val) {
            this.data = val;
            this.left = null;
            this.right = null;
        }
    }
  
    // To create a new node
     function newnode(key) {
        var temp = new Node();
        temp.data = key;
        temp.right = null;
        temp.left = null;
        return temp;
    }
 
    // Function to perform inorder traversal on
    // the tree and prvar the nodes in that order
    function inorder( root) {
        if (root == null)
            return;
        inorder(root.left);
        document.write(root.data + "\n");
        inorder(root.right);
    }
 
    // Function to return the maximum size of
    // the sub-tree having equal number of 0's and 1's
    function maxsize( root) {
        var a = 0, b = 0;
        if (root == null)
            return 0;
 
        // Max size in the right sub-tree
        a = maxsize(root.right);
 
        // 1 is added for the parent
        a = a + 1;
 
        // Max size in the left sub-tree
        b = maxsize(root.left);
 
        // Total size of the tree
        // rooted at the current node
        a = b + a;
 
        // If the current tree has equal
        // number of 0's and 1's
        if (root.data == 0)
 
            // If the total size exceeds
            // the current max
            if (a >= maxSize)
                maxSize = a;
 
        return a;
    }
 
    // Function to update and return the sum
    // of all the tree nodes rooted at
    // the passed node
    function sum_tree( root) {
 
        if (root != null)
 
            // If current node's value is 0
            // then update it to -1
            if (root.data == 0)
                root.data = -1;
 
        var a = 0, b = 0;
 
        // If left child exists
        if (root.left != null)
            a = sum_tree(root.left);
 
        // If right child exists
        if (root.right != null)
            b = sum_tree(root.right);
        root.data += (a + b);
 
        return root.data;
    }
 
    // Driver code
     
        var root = newnode(1);
        root.right = newnode(0);
        root.right.right = newnode(1);
        root.right.right.right = newnode(1);
        root.left = newnode(0);
        root.left.left = newnode(1);
        root.left.left.left = newnode(1);
        root.left.right = newnode(0);
        root.left.right.left = newnode(1);
        root.left.right.left.left = newnode(1);
        root.left.right.right = newnode(0);
        root.left.right.right.left = newnode(0);
        root.left.right.right.left.left = newnode(1);
 
        sum_tree(root);
 
        maxsize(root);
 
        document.write(maxSize);
 
// This code contributed by aashish1995
 
</script>
Output: 
6

 

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