Largest sub-tree having equal no of 1’s and 0’s

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:

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// 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;
}

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Output:

6


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