We can find the first leaf using level search.

```
# Definition for a binary tree node.
# class TreeNode(object):
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution(object):
def minDepth(self, root):
"""
:type root: TreeNode
:rtype: int
"""
if root == None: return 0
depth, cur_level = 0, [root]
# level search
while cur_level:
depth += 1
next_level = []
for x in cur_level:
if x.left==None and x.right==None: return depth
if x.left!=None: next_level.append(x.left)
if x.right!=None: next_level.append(x.right)
cur_level = next_level
return depth
```