333. Largest BST Subtree

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Given a binary tree, find the largest subtree which is a Binary Search Tree (BST), where largest means subtree with largest number of nodes in it.

Note:
A subtree must include all of its descendants.
Here’s an example:

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2
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4
5
   10
   / \
  5  15
 / \   \
1   8   7

The Largest BST Subtree in this case is the highlighted one.
The return value is the subtree’s size, which is 3.

Follow up:
Can you figure out ways to solve it with O(n) time complexity?

解法1：

C++

1

Java

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/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    class NodeInfo {
        boolean isBST;
        int count;
        int max;
        int min;
        public NodeInfo (boolean isBST, int count, int max, int min) {
            this.isBST = isBST;
            this.count = count;
            this.max = max;
            this.min = min;
        }
    };
    int res = 0;   // Store the final result
    public int largestBSTSubtree(TreeNode root) {
        if (root == null) {
            return 0;
        }
        NodeInfo dummy = helper(root);
        return res;
    }
    private NodeInfo helper(TreeNode root) {
        if (root == null) {
            return new NodeInfo(true, 0, Integer.MIN_VALUE, Integer.MAX_VALUE);
        }
        NodeInfo left = helper(root.left);
        NodeInfo right = helper(root.right);
        boolean isBST = false;
        if (root.val > left.max && root.val < right.min) {
            isBST = left.isBST && right.isBST;
        }
        int count = left.count + right.count + 1;
        if (isBST) {
            res = Math.max(res, count);
        }
        int max = Math.max(left.max, Math.max(right.max, root.val));
        int min = Math.min(left.min, Math.min(right.min, root.val));
        return new NodeInfo(isBST, count, max, min);        
    }
}