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# 111 Minimum Depth of Binary Tree

## 111. Minimum Depth of Binary Tree

## 1. Question

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.

## 2. Implementation

**(1) DFS recursion**

```java
class Solution {
    public int minDepth(TreeNode root) {
        if (root == null) return 0;
        if (root.left == null) return 1 + minDepth(root.right);
        if (root.right == null) return 1 + minDepth(root.left);
        return Math.min(minDepth(root.left), minDepth(root.right)) + 1;
    }
}
```

**(2) BFS**

```java
class Solution {
    public int minDepth(TreeNode root) {
        if (root == null) {
            return 0;
        }

        Queue<TreeNode> queue = new LinkedList<>();
        queue.add(root);
        int depth = 0;

        while (!queue.isEmpty()) {
            int size = queue.size();
            ++depth;

            for (int i = 0; i < size; i++) {
                TreeNode curNode = queue.remove();

                if (curNode.left == null && curNode.right == null) {
                    return depth;
                }

                if (curNode.left != null) {
                    queue.add(curNode.left);
                }

                if (curNode.right != null) {
                    queue.add(curNode.right);
                }
            }
        }
        return depth;
    }
}
```

## 3. Time & Space Complexity

DFS recursion: 时间复杂度: O(h), 空间复杂度: O(h)

BFS:时间复杂度O(n), 空间复杂度: O(w), w为树一层中有最多node的个数