98. Validate Binary Search Tree

最新推荐文章于 2020-10-18 10:11:10 发布

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最新推荐文章于 2020-10-18 10:11:10 发布

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本文介绍了一种使用递归方法来判断给定的二叉树是否为有效的二叉搜索树（BST）。通过定义每个节点的有效值范围，确保左子树的所有节点小于父节点而右子树的所有节点大于父节点。

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问题描述
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
```
Binary tree [2,1,3], return true.

Example 2:
```
 1
/ \
2   3
```
Binary tree [1,2,3], return false.
解决思路
利用递归，但每次需要传入一个判断区间。
代码

/**
 * 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) {
        if (root == NULL)
            return true;
        if (root->left == NULL && root->right == NULL)
            return true;
        long max = INT_MAX,min = INT_MIN;
        if (root->left == NULL)
            return root->right->val > root->val && helper(root->right,max,root->val,false,true);
        if (root->right == NULL)
            return root->left->val < root->val && helper(root->left,root->val,min,true,false);
        if (root->right->val <= root->val || root->left->val >= root->val)
            return false;
        return helper(root->right,max,root->val,false,true) && helper(root->left,root->val,min,true,false);
    }
    bool helper(TreeNode* root,int left_max, int right_min, bool left, bool right) {
        if (root == NULL)
            return true;
        if (!left&&(root->val > left_max || root->val <= right_min))
            return false;
        if (!right&&(root->val >= left_max || root->val < right_min))
            return false;
        if (left&&right&&(root->val >= left_max || root->val <= right_min))
            return false;
        if (root->left == NULL && root->right == NULL) {
            return true;
        }
        if (root->left == NULL)
            return root->right->val > root->val && helper(root->right,left_max,root->val,left,true);
        if (root->right == NULL)
            return root->left->val < root->val && helper(root->left,root->val,right_min,true,right);
        if (root->right->val <= root->val || root->left->val >= root->val)
            return false;
        return helper(root->left,root->val,right_min,true,right) && helper(root->right,left_max,root->val,left,true);
    }
};