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 the root node down to the nearest leaf node. A leaf node is a node with no children. This problem is fundamental for understanding tree traversal and optimization.

Problem Description

Your task is to implement a function that calculates the minimum depth of a given binary tree. The depth is defined as the number of nodes from the root to a leaf. You need to find the path with the fewest nodes that ends at a leaf.

Requirements:

• Traverse the binary tree.
• Identify leaf nodes.
• Determine the shortest path from the root to any leaf node.
• Return the length of this shortest path (number of nodes).

Edge Cases:

• An empty tree (root is null).
• A tree with only a root node.
• A tree where one branch is significantly shorter than others.

Examples

Example 1:

Input:
    3
   / \
  9  20
    /  \
   15   7

Output: 2
Explanation: The shortest path from the root to a leaf is 3 -> 9, which has a length of 2 nodes.

Example 2:

Input:
    2
     \
      3
       \
        4
         \
          5
           \
            6

Output: 5
Explanation: The shortest path from the root to a leaf is 2 -> 3 -> 4 -> 5 -> 6, which has a length of 5 nodes.

Example 3:

Input:
    1
   /
  2

Output: 2
Explanation: The shortest path from the root to a leaf is 1 -> 2, which has a length of 2 nodes.

Constraints

• The number of nodes in the tree will be between 0 and 10^5.
• Node values are integers.
• Your solution should aim for an efficient time complexity, ideally O(N) where N is the number of nodes in the tree.

Notes

• A null tree should have a minimum depth of 0.
• Consider how you might handle nodes that have only one child.
• Think about different traversal strategies (e.g., Breadth-First Search vs. Depth-First Search) and which might be more suitable for finding the minimum depth.