669 Trim a Binary Search Tree 修剪二叉搜索树
Description:
Given a binary search tree and the lowest and highest boundaries as L and R, trim the tree so that all its elements lies in [L, R] (R >= L). You might need to change the root of the tree, so the result should return the new root of the trimmed binary search tree.
Example:
Example 1:
Input:
1
/ \
0 2
L = 1
R = 2
Output:
1
\
2
Example 2:
Input:
3
/ \
0 4
\
2
/
1
L = 1
R = 3
Output:
3
/
2
/
1
题目描述:
给定一个二叉搜索树，同时给定最小边界L 和最大边界 R。通过修剪二叉搜索树，使得所有节点的值在[L, R]中 (R>=L) 。你可能需要改变树的根节点，所以结果应当返回修剪好的二叉搜索树的新的根节点。
示例 :
示例 1:
输入:
1
/ \
0 2
L = 1
R = 2
输出:
1
\
2
示例 2:
输入:
3
/ \
0 4
\
2
/
1
L = 1
R = 3
输出:
3
/
2
/
1
思路:
注意给的树是 BST, 要利用其性质
- 迭代, 先搜索根节点的值, 满足 root -> val在 (L, R)之间, 然后分别修改左子树和右子树即可
- 递归, 思路与迭代类似
时间复杂度O(n), 空间复杂度O(1)
代码:
C++:
/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/
class Solution
{
public:
TreeNode* trimBST(TreeNode* root, int L, int R)
{
if (root)
{
while (root and (root -> val < L or root -> val > R))
{
if (root -> val < L) root = root -> right;
else root = root -> left;
}
TreeNode* cur = root;
// 修剪左子树
while (cur)
{
while (cur -> left and cur -> left -> val < L) cur -> left = cur -> left -> right;
cur = cur -> left;
}
cur = root;
// 修剪右子树
while (cur)
{
while (cur -> right and cur -> right -> val > R) cur -> right = cur -> right -> left;
cur = cur -> right;
}
}
return root;
}
};
Java:
/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
class Solution {
public TreeNode trimBST(TreeNode root, int L, int R) {
if (root == null) return root;
if (root.val < L) return trimBST(root.right, L, R);
if (root.val > R) return trimBST(root.left, L, R);
root.left = trimBST(root.left, L, R);
root.right = trimBST(root.right, L, R);
return root;
}
}
Python:
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def trimBST(self, root: TreeNode, L: int, R: int) -> TreeNode:
if not root:
return root
if root.val < L:
return self.trimBST(root.right, L, R)
if root.val > R:
return self.trimBST(root.left, L, R)
root.left, root.right = self.trimBST(root.left, L, R), self.trimBST(root.right, L, R)
return root
