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# Minimum Depth of Binary Tree

## [Minimum Depth of Binary Tree](https://leetcode.com/problems/minimum-depth-of-binary-tree)

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 1:** ![](https://assets.leetcode.com/uploads/2020/10/12/ex_depth.jpg)

```

Input: root = [3,9,20,null,null,15,7]
Output: 2
```

**Example 2:**

```

Input: root = [2,null,3,null,4,null,5,null,6]
Output: 5
```

**Constraints:**

* The number of nodes in the tree is in the range `[0, 105]`.
* `-1000 <= Node.val <= 1000`

## Solutions

### 🧠 Cpp

```cpp
/**
 * Definition for a binary tree node.
 * struct TreeNode
 * {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */

class Solution
{
public:
    //O(2^n) solution
    int minDepth(TreeNode* root)
    {
        if(!root)
            return 0;
        //if both leafs are null, we have the last leaf
        else if(!root->left && !root->right)
            return 1;

        //pre-order traversal
        return 1 + std::min(minDepth(root->left), minDepth(root->right), 
                            [](int a , int b)
                            {
                                if(!a) return false;
                                if(!b) return true;
                                return a < b;
                            });
    }
};
```