Happy Coding: [LeetCode] 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: For each sub-tree, we maintain its lower bound and upper bound. The tricky part is to deal with the maximum integer and the minimum integer. In the following Java code, I used two additional flags to denote whether the lower bound is -infty and whether the upper bound is +infty, respectively.

/**
 * Definition for binary tree
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public boolean isValidBST(
        TreeNode root, 
        int lower_bound, 
        int upper_bound, 
        boolean neg_infty, 
        boolean pos_infty
    ) {
        if (root == null) return true;
        if (root.val <= lower_bound && !neg_infty) return false;
        if (root.val >= upper_bound && !pos_infty) return false;
        return isValidBST(root.left, lower_bound, root.val, neg_infty, false) &&
               isValidBST(root.right, root.val, upper_bound, false, pos_infty);
    }

    public boolean isValidBST(TreeNode root) {
        return isValidBST(root, Integer.MIN_VALUE, Integer.MAX_VALUE, true, true);
    }
}

Solution 2: In-order traversal. The resulting list should be in the increasing order. Simple, yet it uses additional space.

/**
 * Definition for binary tree
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public ArrayList<Integer> inorderTraversal(TreeNode root) {
        ArrayList<Integer> list = new ArrayList<Integer>();
        if (root == null) return list;
        list.addAll(inorderTraversal(root.left));
        list.add(root.val);
        list.addAll(inorderTraversal(root.right));
        return list;
    }

    public boolean isValidBST(TreeNode root) {
        if (root == null) return true;
        ArrayList<Integer> list = inorderTraversal(root);
        for (int i = 1; i < list.size(); i++) {
            if (list.get(i-1) >= list.get(i)) {
                return false;
            }
        }
        return true;
    }
}

Happy Coding

Tuesday, April 28, 2015

[LeetCode] Validate Binary Search Tree

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