LeetCode Q98: 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.

Solution 1:

Inorder traverse the tree and check whether all nodes visited are sorted in an ascending order.

	/**
	* 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 InOrder(TreeNode* node, long& num){
	if(node==NULL)
	return true;
	bool r0=InOrder(node->left, num);
	bool r = node->val > num;
	num = node->val;
	bool r1=InOrder(node->right, num);
	return r0&&r&&r1;
	}
	bool isValidBST(TreeNode* root) {
	if(root==NULL)
	return true;
	long num=long(INT_MIN)*2;
	return InOrder(root, num);
	}
	};

view raw Q98-1.cpp hosted with ❤ by GitHub

Solution 2:

Recursively check whether the BST properties are hold in left and right subtrees. In the meantime, we need to keep tracking the low and high bound of each side. 

	/**
	* 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 helper(TreeNode* root, long lowBound, long highBound){
	if(root==NULL)
	return true;
	int left=root->left==NULL? true:(root->left->val < root->val) && (root->left->val > lowBound);
	int right=root->right==NULL? true:( root->right->val > root->val) && (root->right->val < highBound);
	bool leftForest=helper(root->left, long(lowBound), min(long(highBound), long(root->val)));
	bool rightForest=helper(root->right, max(long(lowBound), long(root->val)), long(highBound));
	return left && right && leftForest && rightForest;
	}
	bool isValidBST(TreeNode* root) {
	if(root==NULL)
	return true;
	return helper(root, long(INT_MIN)*2, long(INT_MAX)*2); // To tackle to corner case, multiply with 2.
	}
	};

view raw Q98-2.cpp hosted with ❤ by GitHub