题目描述

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.

分析

验证一棵树是否为BST，只需要验证中序遍历序列是否是递增的。

代码

    boolean failed = false;

    // 要用long，而不是int
    // 否则涉及到Integer.MIN_VALUE的用例会出现错误
    // 比如{Integer.MIN_VALUE}这个用例会错误
    long last = Long.MIN_VALUE;

    public boolean isValidBST(TreeNode root) {

        if (root == null) {
            return true;
        }

        inorder(root);
        return !failed;
    }

    private void inorder(TreeNode root) {

        if (root == null || failed) {
            return;
        }

        // 左
        inorder(root.left);

        // 中，相当于中序遍历中的打印操作
        // 只采用了一个变量，所以空间复杂度是O(1)
        // 传统的做法是建立一个ArrayList，然后判断中序遍历是否是递增的，但是空间复杂度是O(n)
        if (last >= root.val) {
            failed = true;
        }
        last = root.val;

        // 右
        inorder(root.right);
    }