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Find Minimum Depth of a Binary Tree

  • Difficulty Level : Easy
  • Last Updated : 22 Jun, 2021
Geek Week

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

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

Example Tree

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

          10
        /    
      5  
 

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 the left subtree is NULL, then recur for the right subtree. And if the right subtree is NULL, then recur for the 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++




// C++ program to find minimum depth of a given Binary Tree
#include<bits/stdc++.h>
using namespace std;
 
// A BT Node
struct Node
{
    int data;
    struct Node* left, *right;
};
 
int minDepth(Node *root)
{
    // Corner case. Should never be hit unless the code is
    // called on root = NULL
    if (root == NULL)
        return 0;
 
    // Base case : Leaf Node. This accounts for height = 1.
    if (root->left == NULL && root->right == NULL)
    return 1;
   
    int l = INT_MAX, r = INT_MAX;
    // If left subtree is not NULL, recur for left subtree
   
    if (root->left)
    l = minDepth(root->left);
 
    // If right subtree is not NULL, recur for right subtree
    if (root->right)
    r =  minDepth(root->right);
 
  //height will be minimum of left and right height +1
    return min(l , r) + 1;
}
 
// Utility function to create new Node
Node *newNode(int data)
{
    Node *temp = new Node;
    temp->data = data;
    temp->left = temp->right = NULL;
    return (temp);
}
 
// Driver program
int main()
{
    // Let us construct the Tree shown in the above figure
    Node *root     = newNode(1);
    root->left     = newNode(2);
    root->right     = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    cout <<"The minimum depth of binary tree is : "<< minDepth(root);
    return 0;
}

Java




/* Java implementation to find minimum depth
   of a given Binary tree */
 
/* Class containing left and right child of current
node and key value*/
class Node
{
    int data;
    Node left, right;
    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}
public class BinaryTree
{
    //Root of the Binary Tree
    Node root;
 
    int minimumDepth()
    {
        return minimumDepth(root);
    }
 
    /* Function to calculate the minimum depth of the tree */
    int minimumDepth(Node root)
    {
        // Corner case. Should never be hit unless the code is
        // called on root = NULL
        if (root == null)
            return 0;
 
        // Base case : Leaf Node. This accounts for height = 1.
        if (root.left == null && root.right == null)
            return 1;
 
        // If left subtree is NULL, recur for right subtree
        if (root.left == null)
            return minimumDepth(root.right) + 1;
 
        // If right subtree is NULL, recur for left subtree
        if (root.right == null)
            return minimumDepth(root.left) + 1;
 
        return Math.min(minimumDepth(root.left),
                        minimumDepth(root.right)) + 1;
    }
 
    /* Driver program to test above functions */
    public static void main(String args[])
    {
        BinaryTree tree = new BinaryTree();
        tree.root = new Node(1);
        tree.root.left = new Node(2);
        tree.root.right = new Node(3);
        tree.root.left.left = new Node(4);
        tree.root.left.right = new Node(5);
 
        System.out.println("The minimum depth of "+
          "binary tree is : " + tree.minimumDepth());
    }
}

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)       

C#




using System;
 
/* C# implementation to find minimum depth
   of a given Binary tree */
 
/* Class containing left and right child of current
node and key value*/
public class Node
{
    public int data;
    public Node left, right;
    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}
public class BinaryTree
{
    //Root of the Binary Tree
    public Node root;
 
    public virtual int minimumDepth()
    {
        return minimumDepth(root);
    }
 
    /* Function to calculate the minimum depth of the tree */
    public virtual int minimumDepth(Node root)
    {
        // Corner case. Should never be hit unless the code is
        // called on root = NULL
        if (root == null)
        {
            return 0;
        }
 
        // Base case : Leaf Node. This accounts for height = 1.
        if (root.left == null && root.right == null)
        {
            return 1;
        }
 
        // If left subtree is NULL, recur for right subtree
        if (root.left == null)
        {
            return minimumDepth(root.right) + 1;
        }
 
        // If right subtree is NULL, recur for left subtree
        if (root.right == null)
        {
            return minimumDepth(root.left) + 1;
        }
 
        return Math.Min(minimumDepth(root.left), minimumDepth(root.right)) + 1;
    }
 
    /* Driver program to test above functions */
    public static void Main(string[] args)
    {
        BinaryTree tree = new BinaryTree();
        tree.root = new Node(1);
        tree.root.left = new Node(2);
        tree.root.right = new Node(3);
        tree.root.left.left = new Node(4);
        tree.root.left.right = new Node(5);
 
        Console.WriteLine("The minimum depth of binary tree is : " + tree.minimumDepth());
    }
}
 
  // This code is contributed by Shrikant13

Javascript




<script>
/* javascript implementation to find minimum depth
   of a given Binary tree */
 
/* Class containing left and right child of current
node and key value*/
class Node {
    constructor(item) {
        this.data = item;
        this.left = this.right = null;
    }
}
    // Root of the Binary Tree
    let root;
 
    function minimumDepth() {
        return minimumDepth(root);
    }
 
    /* Function to calculate the minimum depth of the tree */
    function minimumDepth( root) {
        // Corner case. Should never be hit unless the code is
        // called on root = NULL
        if (root == null)
            return 0;
 
        // Base case : Leaf Node. This accounts for height = 1.
        if (root.left == null && root.right == null)
            return 1;
 
        // If left subtree is NULL, recur for right subtree
        if (root.left == null)
            return minimumDepth(root.right) + 1;
 
        // If right subtree is NULL, recur for left subtree
        if (root.right == null)
            return minimumDepth(root.left) + 1;
 
        return Math.min(minimumDepth(root.left), minimumDepth(root.right)) + 1;
    }
 
    /* Driver program to test above functions */
     
         
        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);
 
        document.write("The minimum depth of "
        + "binary tree is : " + minimumDepth(root));
 
 
// This code contributed by aashish1995
</script>

Output: 

The minimum depth of binary tree is : 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++




// C++ program to find minimum depth of a given Binary Tree
#include<bits/stdc++.h>
using namespace std;
 
// A Binary Tree Node
struct Node
{
    int data;
    struct Node *left, *right;
};
 
// A queue item (Stores pointer to node and an integer)
struct qItem
{
   Node *node;
   int depth;
};
 
// Iterative method to find minimum depth of Binary Tree
int minDepth(Node *root)
{
    // Corner Case
    if (root == NULL)
        return 0;
 
    // Create an empty queue for level order traversal
    queue<qItem> q;
 
    // Enqueue Root and initialize depth as 1
    qItem qi = {root, 1};
    q.push(qi);
 
    // Do level order traversal
    while (q.empty() == false)
    {
       // Remove the front queue item
       qi = q.front();
       q.pop();
 
       // Get details of the remove item
       Node *node = qi.node;
       int depth = qi.depth;
 
       // If this  is the first leaf node seen so far
       // Then return its depth as answer
       if (node->left == NULL && node->right == NULL)
          return depth;
 
       // If left subtree is not NULL, add it to queue
       if (node->left != NULL)
       {
          qi.node  = node->left;
          qi.depth = depth + 1;
          q.push(qi);
       }
 
       // If right subtree is not NULL, add it to queue
       if (node->right != NULL)
       {
          qi.node  = node->right;
          qi.depth = depth+1;
          q.push(qi);
       }
    }
    return 0;
}
 
// Utility function to create a new tree Node
Node* newNode(int data)
{
    Node *temp = new Node;
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}
 
// Driver program to test above functions
int main()
{
    // Let us create binary tree shown in above diagram
    Node *root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
 
    cout << minDepth(root);
    return 0;
}

Java




// Java program to find minimum depth
// of a given Binary Tree
import java.util.*;
class GFG
{
     
// A binary Tree node
static class Node
{
    int data;
    Node left, right;
}
 
// A queue item (Stores pointer to
// node and an integer)
static class qItem
{
    Node node;
    int depth;
 
    public qItem(Node node, int depth)
    {
        this.node = node;
        this.depth = depth;
    }
}
 
// Iterative method to find
// minimum depth of Binary Tree
static int minDepth(Node root)
{
    // Corner Case
    if (root == null)
        return 0;
 
    // Create an empty queue for level order traversal
    Queue<qItem> q = new LinkedList<>();
 
    // Enqueue Root and initialize depth as 1
    qItem qi = new qItem(root, 1);
    q.add(qi);
 
    // Do level order traversal
    while (q.isEmpty() == false)
    {
        // Remove the front queue item
        qi = q.peek();
        q.remove();
     
        // Get details of the remove item
        Node node = qi.node;
        int depth = qi.depth;
     
        // If this is the first leaf node seen so far
        // Then return its depth as answer
        if (node.left == null && node.right == null)
            return depth;
     
        // If left subtree is not null,
        // add it to queue
        if (node.left != null)
        {
            qi.node = node.left;
            qi.depth = depth + 1;
            q.add(qi);
        }
     
        // If right subtree is not null,
        // add it to queue
        if (node.right != null)
        {
            qi.node = node.right;
            qi.depth = depth + 1;
            q.add(qi);
        }
    }
    return 0;
}
 
// Utility function to create a new tree Node
static Node newNode(int data)
{
    Node temp = new Node();
    temp.data = data;
    temp.left = temp.right = null;
    return temp;
}
 
// Driver Code
public static void main(String[] args)
{
    // Let us create binary tree shown in above diagram
    Node root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.left.right = newNode(5);
 
    System.out.println(minDepth(root));
}
}
 
// This code is contributed by 29AjayKumar

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)

C#




// C# program to find minimum depth
// of a given Binary Tree
using System;
using System.Collections.Generic;
     
class GFG
{
     
// A binary Tree node
public class Node
{
    public int data;
    public Node left, right;
}
 
// A queue item (Stores pointer to
// node and an integer)
public class qItem
{
    public Node node;
    public int depth;
 
    public qItem(Node node, int depth)
    {
        this.node = node;
        this.depth = depth;
    }
}
 
// Iterative method to find
// minimum depth of Binary Tree
static int minDepth(Node root)
{
    // Corner Case
    if (root == null)
        return 0;
 
    // Create an empty queue for
    // level order traversal
    Queue<qItem> q = new Queue<qItem>();
 
    // Enqueue Root and initialize depth as 1
    qItem qi = new qItem(root, 1);
    q.Enqueue(qi);
 
    // Do level order traversal
    while (q.Count != 0)
    {
        // Remove the front queue item
        qi = q.Peek();
        q.Dequeue();
     
        // Get details of the remove item
        Node node = qi.node;
        int depth = qi.depth;
     
        // If this is the first leaf node
        // seen so far.
        // Then return its depth as answer
        if (node.left == null &&
            node.right == null)
            return depth;
     
        // If left subtree is not null,
        // add it to queue
        if (node.left != null)
        {
            qi.node = node.left;
            qi.depth = depth + 1;
            q.Enqueue(qi);
        }
     
        // If right subtree is not null,
        // add it to queue
        if (node.right != null)
        {
            qi.node = node.right;
            qi.depth = depth + 1;
            q.Enqueue(qi);
        }
    }
    return 0;
}
 
// Utility function to create a new tree Node
static Node newNode(int data)
{
    Node temp = new Node();
    temp.data = data;
    temp.left = temp.right = null;
    return temp;
}
 
// Driver Code
public static void Main(String[] args)
{
    // Let us create binary tree
    // shown in above diagram
    Node root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.left.right = newNode(5);
 
    Console.WriteLine(minDepth(root));
}
}
 
// This code is contributed by PrinciRaj1992

Javascript




<script>
 
// Javascript program to find minimum depth
// of a given Binary Tree
class Node
{
     
    // Utility function to create a new tree Node
    constructor(data)
    {
        this.data = data;
        this.left = this.right = null;
    }
}
 
class qItem
{
    constructor(node,depth)
    {
        this.node = node;
        this.depth = depth;
    }
}
 
function minDepth(root)
{
     
    // Corner Case
    if (root == null)
        return 0;
         
    // Create an empty queue for
    // level order traversal
    let q = [];
  
    // Enqueue Root and initialize depth as 1
    let qi = new qItem(root, 1);
    q.push(qi);
  
    // Do level order traversal
    while (q.length != 0)
    {
         
        // Remove the front queue item
        qi = q.shift();
         
        // Get details of the remove item
        let node = qi.node;
        let depth = qi.depth;
      
        // If this is the first leaf node seen so far
        // Then return its depth as answer
        if (node.left == null && node.right == null)
            return depth;
      
        // If left subtree is not null,
        // add it to queue
        if (node.left != null)
        {
            qi.node = node.left;
            qi.depth = depth + 1;
            q.push(qi);
        }
      
        // If right subtree is not null,
        // add it to queue
        if (node.right != null)
        {
            qi.node = node.right;
            qi.depth = depth + 1;
            q.push(qi);
        }
    }
    return 0;
}
 
// Driver Code
 
// Let us create binary tree shown
// in above diagram
let 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);
 
document.write(minDepth(root));
 
// This code is contributed by rag2127
 
</script>

Output: 

2

Another approach: 

C++




/* C++ implementation to find minimum depth
of a given Binary tree */
#include <iostream>
#include<math.h>
using namespace std;
 
struct Node 
{
  int data;
  struct Node *left;
  struct Node *right;
  Node(int k){
      data = k;
      left = right = NULL;
  }
};
 
/* Function to calculate the minimum depth of the tree */
int minimumDepth(Node *root, int level)
{
           
        if (root == NULL)
            return level;
        level++;
   
        return min(minimumDepth(root->left, level),
                minimumDepth(root->right, level));
}
 
/* Driver program to test above functions */
int main()
{
   
    // Let us create binary tree shown in above diagram
    Node *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);
   
    cout << minimumDepth(root, 0);
    return 0;
}
 
// This code is contributed by aafreen1804.

Java




/* Java implementation to find minimum depth
of a given Binary tree */
 
/* Class containing left and right child of current
Node and key value*/
class Node {
    int data;
    Node left, right;
 
    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}
 
public class MinimumTreeHeight {
    // Root of the Binary Tree
    Node root;
 
    int minimumDepth() { return minimumDepth(root, 0); }
 
    /* Function to calculate the minimum depth of the tree
     */
    int minimumDepth(Node root, int level)
    {
 
        if (root == null)
            return level;
        level++;
 
        return Math.min(minimumDepth(root.left, level),
                        minimumDepth(root.right, level));
    }
 
    /* Driver program to test above functions */
    public static void main(String args[])
    {
        MinimumTreeHeight tree = new MinimumTreeHeight();
        tree.root = new Node(1);
        tree.root.left = new Node(2);
        tree.root.right = new Node(3);
        tree.root.left.left = new Node(4);
        tree.root.left.right = new Node(5);
 
        System.out.println("The minimum depth of "
                           + "binary tree is : "
                           + tree.minimumDepth());
    }
}

Python3




# Python implementation to find minimum depth
# of a given Binary tree
  
# Class containing left and right child of current
# Node and key value
class Node:
   
    # Constructor to create a new node
    def __init__(self, d):
        self.data = d
        self.left = None
        self.right = None
 
# Function to calculate the minimum depth of the tree
def minimumDepth(root, level):
    if (root == None):
        return level;
 
    level += 1;
     
    return min(minimumDepth(root.left, level),
                        minimumDepth(root.right, level))
 
# Driver program to test above functions
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
 
print("The minimum depth of ","binary tree is : ", minimumDepth(root, 0))
 
# This code is contributed by ab2127

C#




/* C# implementation to find minimum depth
of a given Binary tree */
using System;
 
/* Class containing left and
right child of current
Node and key value*/
public class Node {
    public int data;
    public Node left, right;
 
    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}
 
public class MinimumTreeHeight {
    // Root of the Binary Tree
    Node root;
 
    int minimumDepth() { return minimumDepth(root, 0); }
 
    /* Function to calculate the
    minimum depth of the tree */
    int minimumDepth(Node root, int level)
    {
 
        if (root == null)
            return level;
        level++;
 
        return Math.Min(minimumDepth(root.left, level),
                        minimumDepth(root.right, level));
    }
 
    /* Driver code */
    public static void Main(String[] args)
    {
        MinimumTreeHeight tree = new MinimumTreeHeight();
        tree.root = new Node(1);
        tree.root.left = new Node(2);
        tree.root.right = new Node(3);
        tree.root.left.left = new Node(4);
        tree.root.left.right = new Node(5);
 
        Console.WriteLine("The minimum depth of "
                          + "binary tree is : "
                          + tree.minimumDepth());
    }
}
 
// This code has been contributed by 29AjayKumar

Javascript




<script>
/* Javascript implementation to find minimum depth
of a given Binary tree */
  
/* Class containing left and right child of current
Node and key value*/
 
class Node
{
    constructor(item)
    {
        this.data=item;
        this.left=this.right=null;
    }
}
// Root of the Binary Tree
let root;
 
/* Function to calculate the minimum depth of the tree
     */
function minimumDepths()
{
    return minimumDepth(root, 0);
}
 
function minimumDepth(root,level)
{
    if (root == null)
            return level;
        level++;
  
        return Math.min(minimumDepth(root.left, level),
                        minimumDepth(root.right, level));
}
 
 
    /* Driver program to test above functions */
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);
 
document.write("The minimum depth of "
                   + "binary tree is : "
                   + minimumDepths());
 
 
// This code is contributed by avanitrachhadiya2155
</script>

Output: 

The minimum depth of binary tree is : 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
 

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