# Find the maximum node at a given level in a binary tree

Given a Binary Tree and a Level. The task is to find the node with the maximum value at that given level.

The idea is to traverse the tree along depth recursively and return the nodes once the required level is reached and then return the maximum of left and right subtrees for each subsequent call. So that the last call will return the node with maximum value among all nodes at the given level.
Below is the step by step algorithm:

1. Perform DFS traversal and every time decrease the value of level by 1 and keep traversing to the left and right subtrees recursively.
2. When value of level becomes 0, it means we are on the given level, then return root->data.
3. Find the maximum between the two values returned by left and right subtrees and return the maximum.

Below is the implementation of above approach:

 `// CPP program to find the node with` `// maximum value at a given level`   `#include `   `using` `namespace` `std;`   `// Tree node` `struct` `Node {` `    ``int` `data;` `    ``struct` `Node *left, *right;` `};`   `// Utility function to create a new Node` `struct` `Node* newNode(``int` `val)` `{` `    ``struct` `Node* temp = ``new` `Node;` `    ``temp->left = NULL;` `    ``temp->right = NULL;` `    ``temp->data = val;` `    ``return` `temp;` `}`   `// function to find the maximum value` `// at given level` `int` `maxAtLevel(``struct` `Node* root, ``int` `level)` `{` `    ``// If the tree is empty` `    ``if` `(root == NULL)` `        ``return` `0;`   `    ``// if level becomes 0, it means we are on` `    ``// any node at the given level` `    ``if` `(level == 0)` `        ``return` `root->data;`   `    ``int` `x = maxAtLevel(root->left, level - 1);` `    ``int` `y = maxAtLevel(root->right, level - 1);`   `    ``// return maximum of two` `    ``return` `max(x, y);` `}`   `// Driver code` `int` `main()` `{` `    ``// Creating the tree` `    ``struct` `Node* root = NULL;` `    ``root = newNode(45);` `    ``root->left = newNode(46);` `    ``root->left->left = newNode(18);` `    ``root->left->left->left = newNode(16);` `    ``root->left->left->right = newNode(23);` `    ``root->left->right = newNode(17);` `    ``root->left->right->left = newNode(24);` `    ``root->left->right->right = newNode(21);` `    ``root->right = newNode(15);` `    ``root->right->left = newNode(22);` `    ``root->right->left->left = newNode(37);` `    ``root->right->left->right = newNode(41);` `    ``root->right->right = newNode(19);` `    ``root->right->right->left = newNode(49);` `    ``root->right->right->right = newNode(29);`   `    ``int` `level = 3;`   `    ``cout << maxAtLevel(root, level);`   `    ``return` `0;` `}`

 `// Java program to find the ` `// node with maximum value ` `// at a given level` `import` `java.util.*;` `class` `GFG` `{`   `// Tree node` `static` `class` `Node ` `{` `    ``int` `data;` `    ``Node left, right;` `}`   `// Utility function to` `// create a new Node` `static` `Node newNode(``int` `val)` `{` `    ``Node temp = ``new` `Node();` `    ``temp.left = ``null``;` `    ``temp.right = ``null``;` `    ``temp.data = val;` `    ``return` `temp;` `}`   `// function to find ` `// the maximum value` `// at given level` `static` `int` `maxAtLevel(Node root, ``int` `level)` `{` `    ``// If the tree is empty` `    ``if` `(root == ``null``)` `        ``return` `0``;`   `    ``// if level becomes 0, ` `    ``// it means we are on` `    ``// any node at the given level` `    ``if` `(level == ``0``)` `        ``return` `root.data;`   `    ``int` `x = maxAtLevel(root.left, level - ``1``);` `    ``int` `y = maxAtLevel(root.right, level - ``1``);`   `    ``// return maximum of two` `    ``return` `Math.max(x, y);` `}`   `// Driver code` `public` `static` `void` `main(String args[])` `{` `    ``// Creating the tree` `    ``Node root = ``null``;` `    ``root = newNode(``45``);` `    ``root.left = newNode(``46``);` `    ``root.left.left = newNode(``18``);` `    ``root.left.left.left = newNode(``16``);` `    ``root.left.left.right = newNode(``23``);` `    ``root.left.right = newNode(``17``);` `    ``root.left.right.left = newNode(``24``);` `    ``root.left.right.right = newNode(``21``);` `    ``root.right = newNode(``15``);` `    ``root.right.left = newNode(``22``);` `    ``root.right.left.left = newNode(``37``);` `    ``root.right.left.right = newNode(``41``);` `    ``root.right.right = newNode(``19``);` `    ``root.right.right.left = newNode(``49``);` `    ``root.right.right.right = newNode(``29``);`   `    ``int` `level = ``3``;`   `    ``System.out.println(maxAtLevel(root, level));` `}` `}`   `// This code is contributed` `// by Arnab Kundu`

 `# Python3 program to find the node  ` `# with maximum value at a given level `   `# Helper function that allocates a new ` `# node with the given data and None ` `# left and right poers.                                     ` `class` `newNode: `   `    ``# Constructor to create a new node ` `    ``def` `__init__(``self``, data): ` `        ``self``.data ``=` `data` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None`   `# function to find the maximum  ` `# value at given level ` `def` `maxAtLevel(root, level): `   `    ``# If the tree is empty ` `    ``if` `(root ``=``=` `None``) :` `        ``return` `0`   `    ``# if level becomes 0, it means we ` `    ``# are on any node at the given level ` `    ``if` `(level ``=``=` `0``) :` `        ``return` `root.data `   `    ``x ``=` `maxAtLevel(root.left, level ``-` `1``) ` `    ``y ``=` `maxAtLevel(root.right, level ``-` `1``) `   `    ``# return maximum of two ` `    ``return` `max``(x, y)` `    `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``:`   `    ``""" ` `    ``Let us create Binary Tree shown` `    ``in above example """` `    ``root ``=` `newNode(``45``) ` `    ``root.left ``=` `newNode(``46``) ` `    ``root.left.left ``=` `newNode(``18``) ` `    ``root.left.left.left ``=` `newNode(``16``) ` `    ``root.left.left.right ``=` `newNode(``23``) ` `    ``root.left.right ``=` `newNode(``17``) ` `    ``root.left.right.left ``=` `newNode(``24``) ` `    ``root.left.right.right ``=` `newNode(``21``) ` `    ``root.right ``=` `newNode(``15``) ` `    ``root.right.left ``=` `newNode(``22``) ` `    ``root.right.left.left ``=` `newNode(``37``) ` `    ``root.right.left.right ``=` `newNode(``41``) ` `    ``root.right.right ``=` `newNode(``19``) ` `    ``root.right.right.left ``=` `newNode(``49``) ` `    ``root.right.right.right ``=` `newNode(``29``)` `    ``level ``=` `3` `    ``print``(maxAtLevel(root, level))`   `# This code is contributed by` `# Shubham Singh(SHUBHAMSINGH10)`

 `// C# program to find the ` `// node with maximum value ` `// at a given level` `using` `System;`   `class` `GFG` `{`   `    ``// Tree node` `    ``class` `Node ` `    ``{` `        ``public` `int` `data;` `        ``public` `Node left, right;` `    ``}`   `    ``// Utility function to` `    ``// create a new Node` `    ``static` `Node newNode(``int` `val)` `    ``{` `        ``Node temp = ``new` `Node();` `        ``temp.left = ``null``;` `        ``temp.right = ``null``;` `        ``temp.data = val;` `        ``return` `temp;` `    ``}`   `    ``// function to find ` `    ``// the maximum value` `    ``// at given level` `    ``static` `int` `maxAtLevel(Node root, ``int` `level)` `    ``{` `        ``// If the tree is empty` `        ``if` `(root == ``null``)` `            ``return` `0;`   `        ``// if level becomes 0, ` `        ``// it means we are on` `        ``// any node at the given level` `        ``if` `(level == 0)` `            ``return` `root.data;`   `        ``int` `x = maxAtLevel(root.left, level - 1);` `        ``int` `y = maxAtLevel(root.right, level - 1);`   `        ``// return maximum of two` `        ``return` `Math.Max(x, y);` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main(String []args)` `    ``{` `        ``// Creating the tree` `        ``Node root = ``null``;` `        ``root = newNode(45);` `        ``root.left = newNode(46);` `        ``root.left.left = newNode(18);` `        ``root.left.left.left = newNode(16);` `        ``root.left.left.right = newNode(23);` `        ``root.left.right = newNode(17);` `        ``root.left.right.left = newNode(24);` `        ``root.left.right.right = newNode(21);` `        ``root.right = newNode(15);` `        ``root.right.left = newNode(22);` `        ``root.right.left.left = newNode(37);` `        ``root.right.left.right = newNode(41);` `        ``root.right.right = newNode(19);` `        ``root.right.right.left = newNode(49);` `        ``root.right.right.right = newNode(29);`   `        ``int` `level = 3;`   `        ``Console.WriteLine(maxAtLevel(root, level));` `    ``}` `}`   `// This code is contributed by 29AjayKumar`

Output

`49`

Iterative Approach
It can also be done by using Queue, which uses level order traversal and it basically checks for the maximum node when the given level is equal to our count variable. (variable k).

Below is the implementation of the above approach:

 `// C++ prgram for above approach` `#include` `using` `namespace` `std;`   `// Tree Node` `class` `TreeNode` `{` `      ``public``:` `          ``TreeNode *left, *right;` `          ``int` `data;` `};`   `TreeNode* newNode(``int` `item)` `{` ` ``TreeNode* temp = ``new` `TreeNode;` ` ``temp->data = item;` ` ``temp->left = temp->right = NULL;` ` ``return` `temp;` `}`   `// Function to calculate maximum node` `int` `bfs_maximumNode(TreeNode* root, ``int` `level)` `{` `    `  `    ``// Check if root is NULL` `    ``if``(root == NULL)` `        ``return` `0;` `        `  `    ``// Queue of type TreeNode*` `    ``queue mq;` `  `  `    ``// Push root in queue` `    ``mq.push(root);` `  `  `    ``int` `ans = 0, maxm = INT_MIN, k = 0 ;`   `    ``// While queue is not empty` `    ``while``( !mq.empty() )` `    ``{` `        ``int` `size = mq.size();` `        `  `        ``// While size if not 0` `        ``while``(size--)` `        ``{` `           `  `            ``// Accessing front element` `            ``// in queue` `            ``TreeNode* temp = mq.front();` `            ``mq.pop();` `        `  `            ``if``(level == k && maxm < temp->data)` `                ``maxm = temp->data;` `            `  `            ``if``(temp->left)` `                ``mq.push(temp->left);` `                `  `            ``if``(temp->right)` `                ``mq.push(temp->right);` `        ``}` `        ``k++;` `        ``ans = max(maxm, ans);` `    ``}` `  `  `    ``// Return answer` `    ``return` `ans;` `}`   `// Driver Code` `int` `main()` `{` `    ``TreeNode* root = NULL; ` `    ``root = newNode(45); ` `    ``root->left = newNode(46); ` `    ``root->left->left = newNode(18); ` `    ``root->left->left->left = newNode(16);` `    ``root->left->left->right = newNode(23); ` `    ``root->left->right = newNode(17); ` `    ``root->left->right->left = newNode(24); ` `    ``root->left->right->right = newNode(21); ` `    ``root->right = newNode(15); ` `    ``root->right->left = newNode(22); ` `    `  `    ``root->right->left->left = newNode(37); ` `    ``root->right->left->right = newNode(41); ` `    ``root->right->right = newNode(19); ` `    ``root->right->right->left = newNode(49); ` `    ``root->right->right->right = newNode(29); ` `    `  `    `  `    ``int` `level = 3;` `  `  `    ``// Function Call` `    ``cout << bfs_maximumNode(root, level);` `    ``return` `0;` `}`   `//This code is written  done by Anurag Mishra.`

 `# Python3 prgram for above approach` `import` `sys`   `# Tree Node` `class` `TreeNode:` `    `  `    ``def` `__init__(``self``, data):` `        `  `        ``self``.data ``=` `data` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` `      `  `def` `newNode(item):` `    `  `    ``temp ``=` `TreeNode(item)` `    `  `    ``return` `temp` ` `  `# Function to calculate maximum node` `def` `bfs_maximumNode(root, level):` `    `  `    ``# Check if root is NULL` `    ``if``(root ``=``=` `None``):` `        ``return` `0` `         `  `    ``# Queue of type TreeNode*` `    ``mq ``=` `[]` `   `  `    ``# Append root in queue` `    ``mq.append(root)` `   `  `    ``ans ``=` `0` `    ``maxm ``=` `-``sys.maxsize ``-` `1` `    ``k ``=` `0` ` `  `    ``# While queue is not empty` `    ``while``(``len``(mq) !``=` `0``):` `        ``size ``=` `len``(mq)` `         `  `        ``# While size if not 0` `        ``while``(size):` `            ``size ``-``=` `1` `            `  `            ``# Accessing front element` `            ``# in queue` `            ``temp ``=` `mq[``0``]` `            ``mq.pop(``0``)` `         `  `            ``if` `(level ``=``=` `k ``and` `maxm < temp.data):` `                ``maxm ``=` `temp.data` `             `  `            ``if` `(temp.left):` `                ``mq.append(temp.left)` `                 `  `            ``if` `(temp.right):` `                ``mq.append(temp.right)` `        `  `        ``k ``+``=` `1` `        ``ans ``=` `max``(maxm, ans)` `    `  `    ``# Return answer` `    ``return` `ans` `    `  `# Driver Code` `if` `__name__``=``=``"__main__"``:` `    `  `    ``root ``=` `None` `    ``root ``=` `newNode(``45``)` `    ``root.left ``=` `newNode(``46``) ` `    ``root.left.left ``=` `newNode(``18``) ` `    ``root.left.left.left ``=` `newNode(``16``)` `    ``root.left.left.right ``=` `newNode(``23``) ` `    ``root.left.right ``=` `newNode(``17``)` `    ``root.left.right.left ``=` `newNode(``24``) ` `    ``root.left.right.right ``=` `newNode(``21``) ` `    ``root.right ``=` `newNode(``15``)` `    ``root.right.left ``=` `newNode(``22``) ` `     `  `    ``root.right.left.left ``=` `newNode(``37``)` `    ``root.right.left.right ``=` `newNode(``41``) ` `    ``root.right.right ``=` `newNode(``19``)` `    ``root.right.right.left ``=` `newNode(``49``) ` `    ``root.right.right.right ``=` `newNode(``29``) ` `     `  `    ``level ``=` `3` `   `  `    ``# Function Call` `    ``print``(bfs_maximumNode(root, level))` `    `  `# This code is contributed by rutvik_56`

Output
`49`

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