BFS solution

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def minDepth(self, root: TreeNode) -> int:
        if not root:
            return 0
        q = collections.deque([(root,1)])
        while q:
            node, level = q.popleft()
            if not node.left and not node.right:
                return level
            if node.left:
                q.append((node.left,level+1))
            if node.right:
                q.append((node.right,level+1))

DFS

class Solution:
    def minDepth(self, root: TreeNode) -> int:
        def dfs(node,level):
            l= r = float('inf')
            if not node:
                return level - 1
            if not node.left and not node.right:
                return level
            if node.left:
                l = dfs(node.left,level+1)
            if node.right :
                r = dfs(node.right,level+1)
            return min(l,r)
        return dfs(root,1)

without helper function

class Solution:
    def minDepth(self, root: TreeNode) -> int:
        if not root:
            return 0
        if None in [root.left,root.right]:
            return max(self.minDepth(root.left),self.minDepth(root.right)) +1 
        return min(self.minDepth(root.left),self.minDepth(root.right)) +1