# 230. Kth Smallest Element in a BST

[Link](https://leetcode.com/problems/kth-smallest-element-in-a-bst/)

Given a binary search tree, write a function `kthSmallest` to find the **k**th smallest element in it.

**Note:**\
You may assume k is always valid, 1 ≤ k ≤ BST's total elements.

**Example 1:**

```
Input: root = [3,1,4,null,2], k = 1
   3
  / \
 1   4
  \
   2
Output: 1
```

**Example 2:**

```
Input: root = [5,3,6,2,4,null,null,1], k = 3
       5
      / \
     3   6
    / \
   2   4
  /
 1
Output: 3
```

**Follow up:**\
What if the BST is modified (insert/delete operations) often and you need to find the kth smallest frequently? How would you optimize the kthSmallest routine?

**Solution**

這題是Inorder travelsal的應用只要在travel的時透過count去計算就知道哪個是第k小的

T:O(N), DFS binary inoder travelsal

```
 public int kthSmallest(TreeNode root, int k) {
        
        Stack<TreeNode> stack = new Stack<>();
        while(root != null || !stack.isEmpty()){
            TreeNode temp;
            while(root != null){
                stack.push(root);
                root = root.left;
            }
            root = stack.pop();
            if(--k == 0) break;
            root = root.right;
        }
        return root.val;
    }
```

**Follow ups question**
