Question Link:

https://leetcode.com/problems/minimum-depth-of-binary-tree/

To find the minimum depth, we BFS from the root and record the depth. For each level we add 1 to the depth and return the depth value when we reach a leaf.

The python code is as follows.

[-] Python code accepted by LeetCode OJ 
# Definition for a  binary tree node
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
    # @param root, a tree node
    # @return an integer
    def minDepth(self, root):
        """
        BFS the tree and record the depth,
        return this value for the first time that a leaf is reached.
        """
        if not root:
            return 0
        depth = 1
        q = [root]
        while q:
            new_q = []
            for n in q:
                if n.left == n.right == None:
                    return depth
                if n.left:
                    new_q.append(n.left)
                if n.right:
                    new_q.append(n.right)
            q = new_q
            depth += 1