# 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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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 `

Output:

```6
```

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