98. Validate Binary Search Tree
Given a binary tree, determine if it is a valid binary search tree (BST).
Assume a BST is defined as follows:
- The left subtree of a node contains only nodes with keys less than the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- Both the left and right subtrees must also be binary search trees.
Example 1:
2
/ \
1 3
Input: [2,1,3]
Output: true
Example 2:
5
/ \
1 4
/ \
3 6
Input: [5,1,4,null,null,3,6]
Output: false
Explanation: The root node's value is 5 but its right child's value is 4.
題目鏈接:https://leetcode-cn.com/problems/validate-binary-search-tree/
法一:遞歸
遞歸的寫法也有多種,除了這裏寫到的可以繼續思考有沒有更優美的寫法。
坑:
1)上下邊界都要記錄,因爲還在節點有左有右,判定邊界有區別。
2)如果把上下邊界初始化爲INT_MAX和INT_MIN,要考慮元素值等於邊界的情況,以及更新後的元素值又等於INT_MAX和INT_MIN的情況。
/**
* 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:
bool isValidBST(TreeNode* root) {
return validate(root, LONG_MAX, LONG_MIN);
}
bool validate(TreeNode* root, long high, long low){
if(!root || (!root->left && !root->right)) return true;
auto l = root->left, r = root->right;
int mid = root->val;
if(l && (l->val>=mid || l->val<=low)) return false;
if(r && (r->val<=mid || r->val>=high)) return false;
return validate(l, mid, low) && validate(r, high, mid);
}
};
法二:中序遍歷
將樹中序遍歷輸出,如果輸出的不是嚴格遞增數列,則false。