# Maximum value of Bitwise AND from root to leaf in a Binary tree

Given a Binary Tree, the task is to find the maximum value of Bitwise AND from any path from the root node to the leaf node.

Examples:

Input: Below is the given graph: Output: 7
Explanation:
path 1: 15->3->5 = (15 & 3 & 5) = 1
path 2: 15->3->1 =(15 & 3 & 1) = 1
path 3: 15->7->31=(15 & 7 & 31)= 7 (maximum)
path 4: 15->7->9 = (15 & 7 & 9) =1, out of these 7 is the maximum.

Input: Below is the given graph: Output: 6
Explanation:
Path 1: 31->3->7  =  (31 & 3 & 7)  = 3
Path 2: 31->3->1 =  (31 & 3 & 1)  = 1
Path 3: 31->15->5 =  (31 & 15 & 5)  5
Path 4: 31->15->22 =  (31 & 15 & 22)  = 6, out of these 6 is the maximum.

Approach: The idea is to traverse all the path from the root node to the leaf node and calculate the Bitwise AND of all the nodes that occurred in that path. Keep a global variable to update the maximum Bitwise AND value from all the paths.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach`   `#include ` `using` `namespace` `std;`   `// Initialise to update the maximum` `// AND value from all the path` `int` `maxm = 0;`   `// Node structure` `struct` `Node {` `    ``int` `val;`   `    ``// Left & right child of the node` `    ``Node *left, *right;`   `    ``// Intialize consutructor` `    ``Node(``int` `x)` `    ``{` `        ``val = x;` `        ``left = NULL;` `        ``right = NULL;` `    ``}` `};`   `// Function to find the maximum value` `// of Bitwise AND from root to leaf` `// in a Binary tree` `void` `maxm_Anding(Node* root, ``int` `ans)` `{` `    ``// Check if root is not null` `    ``if` `(!root)` `        ``return``;`   `    ``if` `(root->left == NULL` `        ``and root->right == NULL) {` `        ``ans &= root->val;`   `        ``// Find the maxmimum AND value and` `        ``// store in global maxm varibale` `        ``maxm = max(ans, maxm);`   `        ``return``;` `    ``}`   `    ``// Traverse left of binary tree` `    ``maxm_Anding(root->left,` `                ``ans & root->val);`   `    ``// Traverse right of the binary tree` `    ``maxm_Anding(root->right,` `                ``ans & root->val);` `}`   `// Driver Code` `int` `main()` `{` `    ``// Given Tree` `    ``Node* root = ``new` `Node(15);` `    ``root->left = ``new` `Node(3);` `    ``root->right = ``new` `Node(7);` `    ``root->left->left = ``new` `Node(5);` `    ``root->left->right = ``new` `Node(1);` `    ``root->right->left = ``new` `Node(31);` `    ``root->right->right = ``new` `Node(9);`   `    ``// Function Call` `    ``maxm_Anding(root, root->val);`   `    ``// Print the maximum AND value` `    ``cout << maxm << endl;`   `    ``return` `0;` `}`

## Java

 `// Java program for the above approach` `class` `GFG{`   `// Initialise to update the maximum` `// AND value from all the path` `static` `int` `maxm = ``0``;`   `// Node structure` `static` `class` `Node ` `{` `    ``int` `val;`   `    ``// Left & right child of the node` `    ``Node left, right;`   `    ``// Intialize consutructor` `    ``Node(``int` `x)` `    ``{` `        ``val = x;` `        ``left = ``null``;` `        ``right = ``null``;` `    ``}` `};`   `// Function to find the maximum value` `// of Bitwise AND from root to leaf` `// in a Binary tree` `static` `void` `maxm_Anding(Node root, ``int` `ans)` `{` `    ``// Check if root is not null` `    ``if` `(root == ``null``)` `        ``return``;`   `    ``if` `(root.left == ``null` `&& root.right == ``null``) ` `    ``{` `        ``ans &= root.val;`   `        ``// Find the maxmimum AND value and` `        ``// store in global maxm varibale` `        ``maxm = Math.max(ans, maxm);`   `        ``return``;` `    ``}`   `    ``// Traverse left of binary tree` `    ``maxm_Anding(root.left,` `                ``ans & root.val);`   `    ``// Traverse right of the binary tree` `    ``maxm_Anding(root.right,` `                ``ans & root.val);` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``// Given Tree` `    ``Node root = ``new` `Node(``15``);` `    ``root.left = ``new` `Node(``3``);` `    ``root.right = ``new` `Node(``7``);` `    ``root.left.left = ``new` `Node(``5``);` `    ``root.left.right = ``new` `Node(``1``);` `    ``root.right.left = ``new` `Node(``31``);` `    ``root.right.right = ``new` `Node(``9``);`   `    ``// Function Call` `    ``maxm_Anding(root, root.val);`   `    ``// Print the maximum AND value` `    ``System.out.print(maxm + ``"\n"``);` `}` `}`   `// This code is contributed by sapnasingh4991`

## C#

 `// C# program for the above approach` `using` `System;` `class` `GFG{`   `// Initialise to update the maximum` `// AND value from all the path` `static` `int` `maxm = 0;`   `// Node structure` `class` `Node ` `{` `    ``public` `int` `val;`   `    ``// Left & right child of the node` `    ``public` `Node left, right;`   `    ``// Intialize consutructor` `    ``public` `Node(``int` `x)` `    ``{` `        ``val = x;` `        ``left = ``null``;` `        ``right = ``null``;` `    ``}` `};`   `// Function to find the maximum value` `// of Bitwise AND from root to leaf` `// in a Binary tree` `static` `void` `maxm_Anding(Node root, ``int` `ans)` `{` `    ``// Check if root is not null` `    ``if` `(root == ``null``)` `        ``return``;`   `    ``if` `(root.left == ``null` `&& root.right == ``null``) ` `    ``{` `        ``ans &= root.val;`   `        ``// Find the maxmimum AND value and` `        ``// store in global maxm varibale` `        ``maxm = Math.Max(ans, maxm);`   `        ``return``;` `    ``}`   `    ``// Traverse left of binary tree` `    ``maxm_Anding(root.left,` `                ``ans & root.val);`   `    ``// Traverse right of the binary tree` `    ``maxm_Anding(root.right,` `                ``ans & root.val);` `}`   `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` `    ``// Given Tree` `    ``Node root = ``new` `Node(15);` `    ``root.left = ``new` `Node(3);` `    ``root.right = ``new` `Node(7);` `    ``root.left.left = ``new` `Node(5);` `    ``root.left.right = ``new` `Node(1);` `    ``root.right.left = ``new` `Node(31);` `    ``root.right.right = ``new` `Node(9);`   `    ``// Function Call` `    ``maxm_Anding(root, root.val);`   `    ``// Print the maximum AND value` `    ``Console.Write(maxm + ``"\n"``);` `}` `}`   `// This code is contributed by sapnasingh4991`

Output:

```7

```

Time Complexity: O(N2)
Auxiliary Space: O(1)

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Improved By : sapnasingh4991