# [Minimum Depth of Binary Tree][title]

## Description

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.

**Note:** A leaf is a node with no children.

**Example:**

Given binary tree `[3,9,20,null,null,15,7]`,

```
    3
   / \
  9  20
    /  \
   15   7
```

return its minimum depth = 2.

**Tags:** Tree, Depth-first Search, Breadth-first Search


## 思路 0

题意是查找二叉树的最小深度，也就是找到从根结点到叶子节点的最小深度，最容易想到的当然是深搜，如果节点的左右深度都不是 0 的话，说明该节点含有左右子树，所以它的最小高度就是 1 加上其左右子树高度较小者，否则如果左子树为空或者右子树为空或者两者都为空，那么就是 1 加上非空子树高度。

```java
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int minDepth(TreeNode root) {
        if (root == null) return 0;
        int l = minDepth(root.left);
        int r = minDepth(root.right);
        if (l != 0 && r != 0) return 1 + Math.min(l, r);
        return l + r + 1;
    }
}
```

## 思路 1

第二种思路就是利用宽搜了，搜索到该层有叶子节点，那就返回该层宽度即可。

```java
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int minDepth(TreeNode root) {
        if (root == null) return 0;
        LinkedList<TreeNode> q = new LinkedList<>();
        q.add(root);
        int ans = 1;
        while (!q.isEmpty()) {
            int size = q.size();
            for (int i = 0; i < size; ++i) {
                TreeNode node = q.remove();
                if (node.left == null && node.right == null) {
                    return ans;
                }
                if (node.left != null) q.add(node.left);
                if (node.right != null) q.add(node.right);
            }
            ++ans;
        }
        return 520;
    }
}
```


## 结语

如果你同我一样热爱数据结构、算法、LeetCode，可以关注我 GitHub 上的 LeetCode 题解：[awesome-java-leetcode][ajl]



[title]: https://leetcode.com/problems/minimum-depth-of-binary-tree
[ajl]: https://github.com/Blankj/awesome-java-leetcode