# Maximum in Binary tree

Abhishek Kumar Category: Data StructuresTags: datastructures binary-tree

Find the maximum element in a Binary tree using recursion or iterative solution. For example, a binary tree contains the following elements-
1, 2, 3, 4, 5, 6, 7
Here the maximum element will be 7.

In a Binary Tree, to find the maximum element we have to traverse each element and check if an element higher than the current one is available then assign it as the maximum element. In the same way, we can find the minimum element too.

We can solve this problem in two ways-

### Recursive solution

For recursive solution we have to check each node one by one recursively as we have done in binary tree recursive traversal.

``````class Node:
def __init__(self, data):
self.left = None
self.data = data
self.right = None

def find_max(root):
if root is None:
return float('-inf')
max_val = root.data
left_val = find_max(root.left)
right_val = find_max(root.right)
if left_val > max_val:
max_val = left_val
if right_val > max_val:
max_val = right_val
return max_val

root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
root.right.left = Node(6)
root.right.right = Node(7)
print(find_max(root))``````
``````class Node {
constructor(data) {
this.left = null;
this.data = data;
this.right = null;
}
}

function findMax(root) {
if (root == null) {
return Number.NEGATIVE_INFINITY;
}
let maxVal = root.data;
leftVal = findMax(root.left);
rightVal = findMax(root.right);
if (leftVal > maxVal) {
maxVal = leftVal;
}
if (rightVal > maxVal) {
maxVal = rightVal;
}
return maxVal;
}

const root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);
root.right.left = new Node(6);
root.right.right = new Node(7);
console.log(findMax(root));``````

Output

`7`

### Iterative solution

For iterative solution, we have to traverse each node in level order and find the maximum by comparision.

``````import queue

class Node:
def __init__(self, data):
self.left = None
self.data = data
self.right = None

def find_max(root):
if root:
max_val = root.data
q = queue.Queue()
q.put(root)
while not q.empty():
node = q.get()
if node.data > max_val:
max_val = node.data
if node.left:
q.put(node.left)
if node.right:
q.put(node.right)
return max_val
else:
return None

root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
root.right.left = Node(6)
root.right.right = Node(7)
print(find_max(root))``````
``````class Node {
constructor(data) {
this.left = null;
this.data = data;
this.right = null;
}
}

function findMax(root) {
if (root) {
const q = [];
q.push(root);
node = null;

let maxVal = root.data;
while (q.length > 0) {
node = q.shift();

if (node.data > maxVal) {
maxVal = node.data;
}
if (node.left) {
q.push(node.left);
}
if (node.right) {
q.push(node.right);
}
}
return maxVal;
} else {
return null;
}
}

const root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);
root.right.left = new Node(6);
root.right.right = new Node(7);
console.log(findMax(root));``````

#### Output

Output

`7`

By using similar logic, we can also find the minimum element in a binary tree.

Time complexity: The time complexity of both of these solution will be O(n) because we are just traversing each element of node one by one.

AUTHOR

### Abhishek Kumar

Software engineer | Blogger | Keen learner
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Passionate about learning and experimenting with new things and open to more opportunities and collaborations.