Minimum Depth of a Binary Tree

Find Minimum Depth of a Binary Tree

Given a binary tree, find its minimum depth. The minimum depth is the number of nodes along the shortest path from root node down to the nearest leaf node. 

For example, minimum height of below Binary Tree is 2.

Note that the path must end on a leaf node. For example, minimum height of below Binary Tree is also 2.

          10
        /    
      5  

We strongly recommend you to minimize your browser and try this yourself first.

The idea is to traverse the given Binary Tree. For every node, check if it is a leaf node. If yes, then return 1. If not leaf node then if left subtree is NULL, then recur for right subtree. And if right subtree is NULL, then recur for left subtree. If both left and right subtrees are not NULL, then take the minimum of two heights.

Below is implementation of the above idea.

• C++
• Java
• Python

# Python program to find minimum depth of a given Binary Tree

# Tree node
class Node:
    def __init__(self , key):
        self.data = key 
        self.left = None
        self.right = None

def minDepth(root):
    # Corner Case.Should never be hit unless the code is 
    # called on root = NULL
    if root is None:
        return 0 
    
    # Base Case : Leaf node.This acoounts for height = 1
    if root.left is None and root.right is None:
        return 1
    
    # If left subtree is Null, recur for right subtree
    if root.left is None:
        return minDepth(root.right)+1
    
    # If right subtree is Null , recur for left subtree
    if root.right is None:
        return minDepth(root.left) +1 
    
    return min(minDepth(root.left), minDepth(root.right))+1

# Driver Program 
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
print minDepth(root)

# This code is contributed by Nikhil Kumar Singh(nickzuck_007)        

Output:

2

Time complexity of above solution is O(n) as it traverses the tree only once.
Thanks to Gaurav Ahirwar for providing above solution.

The above method may end up with complete traversal of Binary Tree even when the topmost leaf is close to root. A Better Solution is to do Level Order Traversal. While doing traversal, returns depth of the first encountered leaf node. Below is implementation of this solution.

• C
• Python

# Python program to find minimum depth of a given Binary Tree

# A Binary Tree node
class Node:
    # Utility to create new node
    def __init__(self , data):
        self.data = data
        self.left = None
        self.right = None

def minDepth(root):
    # Corner Case
    if root is None:
         return 0 

    # Create an empty queue for level order traversal
    q = []
    
    # Enqueue root and initialize depth as 1
    q.append({'node': root , 'depth' : 1})

    # Do level order traversal
    while(len(q)>0):
        # Remove the front queue item
        queueItem = q.pop(0)
    
        # Get details of the removed item
        node = queueItem['node']
        depth = queueItem['depth']
        # If this is the first leaf node seen so far
        # then return its depth as answer
        if node.left is None and node.right is None:    
            return depth 
        
        # If left subtree is not None, add it to queue
        if node.left is not None:
            q.append({'node' : node.left , 'depth' : depth+1})

        # if right subtree is not None, add it to queue
        if node.right is not None:  
            q.append({'node': node.right , 'depth' : depth+1})

# Driver program to test above function
# Lets construct a binary tree shown in above diagram
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
print minDepth(root)

# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

Output:

2

Thanks to Manish Chauhan for suggesting above idea and Ravi for providing implementation.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above