> For the complete documentation index, see [llms.txt](https://zedive.gitbook.io/project-l/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://zedive.gitbook.io/project-l/part-1/basic_data_structure/binary_tree/divide_and_conquer/maxmin-depth-of-binary-tree.md).

# Max Depth of Binary Tree

## Maximum Depth of Binary Tree ([LC.104](https://leetcode.com/problems/maximum-depth-of-binary-tree/))

> Given a binary tree, find its maximum depth.

## Example

```
+    1
   /   \
  2     3
 / \
4   5
Max depth: 3
```

## Analysis

If you can do D\&C, always try D\&C first. Traverse is longer to write.

## Code

```java
public int maxDepth(TreeNode root) {
    // base case
    if (root == null)
        return 0;

    // divide
    int leftSubtree = maxDepth(root.left);
    int rightSubtree = maxDepth(root.right);

    // conquer
    return 1 + Math.max(leftSubtree, rightSubtree);
}
```

## Minimum Depth of Binary Tree ([LC.111](https://leetcode.com/problems/minimum-depth-of-binary-tree/))

> Given a binary tree, find its minimum depth.

## Example

```
+    1
   /   \
  2     3
 /     /
4     5
Min depth: 3 (not 2)
```

## Analysis

Divide and conquer again. But this time need to handle a special case where a subtree has a left child but no right child. Math.min(leftSubtree, rightSubtree) will give 0 but in truth we have 1.

## Code

```java
public int minDepth(TreeNode root) {
    // base case
    if (root == null)
        return 0;

    // divide
    int leftSubtree = minDepth(root.left);
    int rightSubtree = minDepth(root.right);

    // conquer
    if (Math.min(leftSubtree, rightSubtree) > 0) {
        return 1 + Math.min(leftSubtree, rightSubtree);
    } else {
        return 1 + Math.max(leftSubtree, rightSubtree);
    }
    // return 1 + (Math.min(L, R) > 0 ? Math.min(L, R) : Math.max(L, R));
}
```