Find maximum (or minimum) in Binary Tree

1.9

Given a Binary Tree, find maximum(or minimum) element in it. For example, maximum in the following Binary Tree is 11.

tree1

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.

C

// C program to find maximum and minimum in a Bianry Tree
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>

// 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 \n", 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


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;
}

This article is contributed by Himanshu Gupta. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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