*lintcode95- Validate Binary Search Tree- medium

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.
• A single node tree is a BST

Example

An example:

  2
 / 
1   4
   / 
  3   5

The above binary tree is serialized as {2,1,4,#,#,3,5} (in level order).

分治法，优化思路是只要记录并返回每棵树的最大值最小值即可。和左子树的max，右子树的min比，只要left.max < root.val < right.min就合格了。

resultType包括min, max, isValid。

注意一个点就是null节点的处理。如果返回Integer.MAX_VALUE和Integer.MIN_VALUE，之后真正想要比较大小的时候为了避免最大值输入不出错，一定要判断一下你左子树的最大值来源到底是因null来的还是真实的最大值。（见注释）

/**
 * Definition of TreeNode:
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */


public class Solution {
    /*
     * @param root: The root of binary tree.
     * @return: True if the binary tree is BST, or false
     */
    
    private class ResultType {
        int min;
        int max;
        boolean isValid;
        public ResultType(int min, int max, boolean isValid) {
            this.min = min;
            this.max = max;
            this.isValid = isValid;
        }
    }
    public boolean isValidBST(TreeNode root) {
        // write your code here
        return helper(root).isValid;
    }
    
    private ResultType helper(TreeNode root) {
        
        if (root == null) {
            return new ResultType(Integer.MAX_VALUE, Integer.MIN_VALUE, true);
        }
        
        ResultType left = helper(root.left);
        ResultType right = helper(root.right);
        
        int minValue = Math.min(root.val, Math.min(left.min, right.min));
        int maxValue = Math.max(root.val, Math.max(left.max, right.max));
        
        if (!left.isValid || !right.isValid) {
            return new ResultType(0, 0, false);
        }
        
        // 重要！！
        // 这里一定要加判断root.left, root.right是不是null，
        // 以确定我数值比较的来源是正确的而不是因null传过来的数字
        if (root.left != null && left.max >= root.val 
        || root.right != null && right.min <= root.val) {
            return new ResultType(0, 0, false);
        }
        
        return new ResultType(minValue, maxValue, true);
    }
}