230. Kth Smallest Element in a BST

Given a binary search tree, write a function kthSmallest to find the kth smallest element in it.

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

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?

Hint:

1. Try to utilize the property of a BST.
2. What if you could modify the BST node's structure?
3. The optimal runtime complexity is O(height of BST).

直接中序遍历，第K个访问到的即是所求。

 int cnt;int ret=0;public int kthSmallest(TreeNode root, int k){if(root!=null)inorder(root, k);return ret;}private void inorder(TreeNode t,int k){if(t.left!=null)inorder(t.left, k);cnt++;if(cnt==k){ret=t.val;return ;}if(t.right!=null)inorder(t.right, k);}

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O(height of BST).的方法

https://leetcode.com/discuss/43771/implemented-java-binary-search-order-iterative-recursive

  public int kthSmallest(TreeNode root, int k) {        int count = countNodes(root.left);        if (k <= count) {            return kthSmallest(root.left, k);        } else if (k > count + 1) {            return kthSmallest(root.right, k-1-count); // 1 is counted as current node        }        return root.val;    }    public int countNodes(TreeNode n) {        if (n == null) return 0;        return 1 + countNodes(n.left) + countNodes(n.right);    }