# Find maximum (or minimum) in Binary Tree

Given a Binary Tree, find maximum(or minimum) element in it. For example, maximum in the following Binary Tree is 9.

In Binary Search Tree, we can find maximum by traversing right pointers until we reach rightmost node. But in Binary Tree, we must visit every node to figure out maximum. So the idea is to traverse the given tree and for every node return maximum of 3 values.
1) Node’s data.
2) Maximum in node’s left subtree.
3) Maximum in node’s right subtree.

Below is the implementation of above approach.

## CPP

// C++ program to find maximum and
// minimum in a Bianry Tree
#include
#include
using namespace std;

// A tree node
class Node
{
public:
int data;
Node* left, *right;

/* Constructor that allocates a new
node with the given data and NULL
left and right pointers. */
Node(int data)
{
this->data = data;
this->left = NULL;
this->right = NULL;
}
};

// Returns maximum value in a given
// Binary Tree
int findMax(Node* root)
{
// Base case
if (root == NULL)
return INT_MIN;

// Return maximum of 3 values:
// 1) Root’s data 2) Max in Left Subtree
// 3) Max in right subtree
int res = root->data;
int lres = findMax(root->left);
int rres = findMax(root->right);
if (lres > res)
res = lres;
if (rres > res)
res = rres;
return res;
}

// Driver Code
int main()
{
Node*NewRoot = NULL;
Node *root = new Node(2);
root->left = new Node(7);
root->right = new Node(5);
root->left->right = new Node(6);
root->left->right->left = new Node(1);
root->left->right->right = new Node(11);
root->right->right = new Node(9);
root->right->right->left = new Node(4);

cout << "Maximum element is " << findMax(root) << endl; return 0; } // This code is contributed by // rathbhupendra [tabby title="C"]

 `// C program to find maximum and minimum in a Bianry Tree ` `#include ` `#include ` `#include ` ` `  `// A tree node ` `struct` `Node ` `{ ` `    ``int` `data; ` `    ``struct` `Node* left, *right; ` `}; ` ` `  `// A utility function to create a new node ` `struct` `Node* newNode(``int` `data) ` `{ ` `    ``struct` `Node* node = (``struct` `Node*) ` `                        ``malloc``(``sizeof``(``struct` `Node)); ` `    ``node->data = data; ` `    ``node->left = node->right = NULL; ` `    ``return``(node); ` `} ` ` `  `// Returns maximum value in a given Binary Tree ` `int` `findMax(``struct` `Node* root) ` `{ ` `    ``// Base case ` `    ``if` `(root == NULL) ` `      ``return` `INT_MIN; ` ` `  `    ``// Return maximum of 3 values: ` `    ``// 1) Root's data 2) Max in Left Subtree ` `    ``// 3) Max in right subtree ` `    ``int` `res = root->data; ` `    ``int` `lres = findMax(root->left); ` `    ``int` `rres = findMax(root->right); ` `    ``if` `(lres > res) ` `      ``res = lres; ` `    ``if` `(rres > res) ` `      ``res = rres; ` `    ``return` `res; ` `} ` ` `  `// Driver program ` `int` `main(``void``) ` `{ ` `    ``struct` `Node*NewRoot=NULL; ` `    ``struct` `Node *root = newNode(2); ` `    ``root->left        = newNode(7); ` `    ``root->right       = newNode(5); ` `    ``root->left->right = newNode(6); ` `    ``root->left->right->left=newNode(1); ` `    ``root->left->right->right=newNode(11); ` `    ``root->right->right=newNode(9); ` `    ``root->right->right->left=newNode(4); ` ` `  `    ``printf` `(````"Maximum element is %d "````, findMax(root)); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java code to Find maximum (or minimum) in  ` `// Binary Tree ` ` `  `// A binary tree node ` `class` `Node { ` `    ``int` `data; ` `    ``Node left, right; ` ` `  `public` `Node(``int` `data) ` `    ``{ ` `        ``this``.data = data; ` `        ``left = right = ``null``; ` `    ``} ` `} ` ` `  `class` `BinaryTree { ` `    ``Node root; ` ` `  `    ``// Returns the max value in a binary tree ` `    ``static` `int` `findMax(Node node) ` `    ``{ ` `        ``if` `(node == ``null``) ` `            ``return` `Integer.MIN_VALUE; ` ` `  `        ``int` `res = node.data; ` `        ``int` `lres = findMax(node.left); ` `        ``int` `rres = findMax(node.right); ` ` `  `        ``if` `(lres > res) ` `            ``res = lres; ` `        ``if` `(rres > res) ` `            ``res = rres; ` `        ``return` `res; ` `    ``} ` ` `  `    ``/* Driver program to test above functions */` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``BinaryTree tree = ``new` `BinaryTree(); ` `        ``tree.root = ``new` `Node(``2``); ` `        ``tree.root.left = ``new` `Node(``7``); ` `        ``tree.root.right = ``new` `Node(``5``); ` `        ``tree.root.left.right = ``new` `Node(``6``); ` `        ``tree.root.left.right.left = ``new` `Node(``1``); ` `        ``tree.root.left.right.right = ``new` `Node(``11``); ` `        ``tree.root.right.right = ``new` `Node(``9``); ` `        ``tree.root.right.right.left = ``new` `Node(``4``); ` ` `  `        ``System.out.println(``"Maximum element is "` `+ ` `                         ``tree.findMax(tree.root)); ` `    ``} ` `} ` ` `  `// This code is contributed by Kamal Rawal `

## Python3

 `# Python3 program to find maximum ` `# and minimum in a Bianry Tree ` ` `  `# A class to create a new node  ` `class` `newNode: ` `    ``def` `__init__(``self``, data): ` `        ``self``.data ``=` `data  ` `        ``self``.left ``=` `self``.right ``=` `None` `     `  `# Returns maximum value in a  ` `# given Binary Tree  ` `def` `findMax(root): ` `     `  `    ``# Base case  ` `    ``if` `(root ``=``=` `None``):  ` `        ``return` `-``999999999999` ` `  `    ``# Return maximum of 3 values:  ` `    ``# 1) Root's data 2) Max in Left Subtree  ` `    ``# 3) Max in right subtree  ` `    ``res ``=` `root.data ` `    ``lres ``=` `findMax(root.left)  ` `    ``rres ``=` `findMax(root.right)  ` `    ``if` `(lres > res): ` `        ``res ``=` `lres  ` `    ``if` `(rres > res):  ` `        ``res ``=` `rres  ` `    ``return` `res ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``root ``=` `newNode(``2``)  ` `    ``root.left     ``=` `newNode(``7``)  ` `    ``root.right     ``=` `newNode(``5``)  ` `    ``root.left.right ``=` `newNode(``6``)  ` `    ``root.left.right.left``=``newNode(``1``)  ` `    ``root.left.right.right``=``newNode(``11``)  ` `    ``root.right.right``=``newNode(``9``)  ` `    ``root.right.right.left``=``newNode(``4``)  ` ` `  `    ``print``(``"Maximum element is"``,  ` `                 ``findMax(root))  ` ` `  `# This code is contributed by PranchalK `

## C#

 `using` `System; ` ` `  `// C# code to Find maximum (or minimum) in   ` `// Binary Tree  ` ` `  `// A binary tree node  ` `public` `class` `Node ` `{ ` `    ``public` `int` `data; ` `    ``public` `Node left, right; ` ` `  `public` `Node(``int` `data) ` `{ ` `        ``this``.data = data; ` `        ``left = right = ``null``; ` `} ` `} ` ` `  `public` `class` `BinaryTree ` `{ ` `    ``public` `Node root; ` ` `  `    ``// Returns the max value in a binary tree  ` `    ``public` `static` `int` `findMax(Node node) ` `    ``{ ` `        ``if` `(node == ``null``) ` `        ``{ ` `            ``return` `int``.MinValue; ` `        ``} ` ` `  `        ``int` `res = node.data; ` `        ``int` `lres = findMax(node.left); ` `        ``int` `rres = findMax(node.right); ` ` `  `        ``if` `(lres > res) ` `        ``{ ` `            ``res = lres; ` `        ``} ` `        ``if` `(rres > res) ` `        ``{ ` `            ``res = rres; ` `        ``} ` `        ``return` `res; ` `    ``} ` ` `  `    ``/* Driver program to test above functions */` `    ``public` `static` `void` `Main(``string``[] args) ` `    ``{ ` `        ``BinaryTree tree = ``new` `BinaryTree(); ` `        ``tree.root = ``new` `Node(2); ` `        ``tree.root.left = ``new` `Node(7); ` `        ``tree.root.right = ``new` `Node(5); ` `        ``tree.root.left.right = ``new` `Node(6); ` `        ``tree.root.left.right.left = ``new` `Node(1); ` `        ``tree.root.left.right.right = ``new` `Node(11); ` `        ``tree.root.right.right = ``new` `Node(9); ` `        ``tree.root.right.right.left = ``new` `Node(4); ` ` `  `        ``Console.WriteLine(``"Maximum element is "` `+ BinaryTree.findMax(tree.root)); ` `    ``} ` `} ` ` `  `  ``// This code is contributed by Shrikant13 `

Output:

`Maximum element is 11`

Similarly, we can find minimum element in Binary tree by comparing three values. Below is the function to find minimum in Binary Tree.

## C

 `// Returns minimum value in a given Binary Tree ` `int` `findMin(``struct` `Node* root) ` `{ ` `    ``// Base case ` `    ``if` `(root == NULL) ` `      ``return` `INT_MAX; ` ` `  `    ``// Return minimum of 3 values: ` `    ``// 1) Root's data 2) Max in Left Subtree ` `    ``// 3) Max in right subtree ` `    ``int` `res = root->data; ` `    ``int` `lres = findMin(root->left); ` `    ``int` `rres = findMin(root->right); ` `    ``if` `(lres < res) ` `      ``res = lres; ` `    ``if` `(rres < res) ` `      ``res = rres; ` `    ``return` `res; ` `} `

## Java

 `// Returns the min value in a binary tree ` `static` `int` `findMin(Node node) ` `{ ` `    ``if` `(node == ``null``) ` `        ``return` `Integer.MAX_VALUE; ` ` `  `    ``int` `res = node.data; ` `    ``int` `lres = findMin(node.left); ` `    ``int` `rres = findMin(node.right); ` ` `  `    ``if` `(lres < res) ` `        ``res = lres; ` `    ``if` `(rres < res) ` `        ``res = rres; ` `    ``return` `res; ` `} `

## C#

 `// Returns the min value in a binary tree ` `public` `static` `int` `findMin(Node node) ` `{ ` `    ``if` `(node == ``null``) ` `        ``return` `int``.MaxValue; ` ` `  `    ``int` `res = node.data; ` `    ``int` `lres = findMin(node.left); ` `    ``int` `rres = findMin(node.right); ` ` `  `    ``if` `(lres < res) ` `        ``res = lres; ` `    ``if` `(rres < res) ` `        ``res = rres; ` `    ``return` `res; ` `} ` ` `  `// This code is contributed by Code_Mech `

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