【刷题-LeetCode】230. Kth Smallest Element in a BST

1. Kth Smallest Element in a BST

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

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?

Constraints:

• The number of elements of the BST is between 1 to 10^4.
• You may assume k is always valid, 1 ≤ k ≤ BST's total elements.

解法1 利用BST中序序列有序的特点找第k次访问的节点

class Solution {
public:
    int kthSmallest(TreeNode* root, int k) {
        int order = 0, ans = INT_MAX;
        bool flag = false;
        in_order(root, order, k, flag, ans);
        return ans;
    }
    void in_order(TreeNode* root, int &order, int k, bool &flag, int &ans){
        if(flag)return;
        if(!root)return;
        in_order(root->left, order, k, flag, ans);
        order++;
        if(order == k){
            flag = true;
            ans = root->val;
        }
        in_order(root->right, order, k, flag, ans);
    }
};

解法2 将BST修改成为中序的线索二叉树