Find Minimum Depth of a Binary Tree

Last Updated : 25 May, 2023

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 depth of below Binary Tree is 2.

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

          10
        /    
      5

Method 1: 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 depths.

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;
}

C

// C program to find minimum depth of a given Binary Tree
#include <limits.h>
#include <stdio.h>
#include <stdlib.h>
 
// A BT Node
typedef struct Node {
    int data;
    struct Node *left, *right;
} Node;
 
int min(int num1, int num2)
{
    return (num1 > num2) ? num2 : num1;
}
 
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;
    int r = INT_MIN;
    // 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 = (Node*)malloc(sizeof(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);
    printf("The minimum depth of binary tree is : %d",
           minDepth(root));
    return 0;
}
 
// This code is contributed by aditya kumar (adityakumar129)

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());
    }
}

Python3

# 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 accounts 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: O(n), as it traverses the tree only once.
Auxiliary Space: O(h), where h is the height of the tree, this space is due to the recursive call stack.

Method 2: 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 the 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;
    Node(int d = 0)
        : data{ d }
    {
    }
};
 
// 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 = 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 << minDepth(root);
    return 0;
}

Java

// Java program to find minimum depth 
// of a given Binary Tree 
import java.util.*;
public 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

Python3

# 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

Time Complexity: O(n), where n is the number of nodes in the given binary tree. This is due to the fact that we are visiting each node once.
Auxiliary Space: O(n), as we need to store the elements in a queue for level order traversal.

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Height and Depth of a node in a Binary Tree

Given a Binary Tree consisting of N nodes and a integer K, the task is to find the depth and height of the node with value K in the Binary Tree. The depth of a node is the number of edges present in path from the root node of a tree to that node.The height of a node is the number of edges present in the longest path connecting that node to a leaf n

Minimum valued node having maximum depth in an N-ary Tree

Given a tree of N nodes, the task is to find the node having maximum depth starting from the root node, taking the root node at zero depth. If there are more than 1 maximum depth node, then find the one having the smallest value. Examples: Input: 1 / \ 2 3 / \ 4 5 Output: 4 Explanation: For this tree: Height of Node 1 - 0, Height of Node 2 - 1, Hei

Complexity of different operations in Binary tree, Binary Search Tree and AVL tree

In this article, we will discuss the complexity of different operations in binary trees including BST and AVL trees. Before understanding this article, you should have a basic idea about Binary Tree, Binary Search Tree, and AVL Tree. The main operations in a binary tree are: search, insert and delete. We will see the worst-case time complexity of t

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