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.

[解题思路]

1.中序遍历BST得到的是一个有序的结果，遍历该结果如果出现前面数字比后面大的则说明不是BST

/**
 * 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) {
        // Start typing your Java solution below
        // DO NOT write main() function
        if(root == null){
            return true;
        }
        ArrayList<Integer> elems = new ArrayList<Integer>();
        inOrderTraverse(root, elems);
        boolean result = true;
        for(int i = 1; i < elems.size(); i++){
            if(elems.get(i - 1) >= elems.get(i)){
                result = false;
                break;
            }
        }
        return result;
    }
    
    public void inOrderTraverse(TreeNode node, ArrayList<Integer> elems){
        if(node == null){
            return;
        }
        if(node.left != null){
            inOrderTraverse(node.left, elems);
        }
        elems.add(node.val);
        if(node.right != null){
            inOrderTraverse(node.right, elems);
        }
        
    }
}

2.判断一个tree是不是BST需要满足如下几点：

a.左子树的节点都小于当前node值

b.右子树的节点都大于当前node值

这里通过传递每个节点的上下界来判断该子节点是否符合要求

public boolean isValidBST(TreeNode root) {
        // Start typing your Java solution below
        // DO NOT write main() function
        return isBSTHelper(root, Integer.MIN_VALUE, Integer.MAX_VALUE);
    }
    
    public boolean isBSTHelper(TreeNode node, int low, int high){
        if(node == null){
            return true;
        }
        int value = node.val;
        if(low < value && value < high &&
            isBSTHelper(node.left, low, value) &&
            isBSTHelper(node.right, value, high)){
                return true;
            } else {
                return false;
            }
    }

 http://leetcode.com/2010/09/determine-if-binary-tree-is-binary.html

http://tech-wonderland.net/blog/leetcode-validate-binary-search-tree.html