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:
Try to utilize the property of a BST.
What if you could modify the BST node's structure?
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);
}

-----------------------------------------------------------------

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);
}