[LeetCode] 2331. Evaluate Boolean Binary Tree

You are given the root of a full binary tree with the following properties:
Leaf nodes have either the value 0 or 1, where 0 represents False and 1 represents True.
Non-leaf nodes have either the value 2 or 3, where 2 represents the boolean OR and 3 represents the boolean AND.

The evaluation of a node is as follows:
If the node is a leaf node, the evaluation is the value of the node, i.e. True or False.
Otherwise, evaluate the node's two children and apply the boolean operation of its value with the children's evaluations.

Return the boolean result of evaluating the root node.

A full binary tree is a binary tree where each node has either 0 or 2 children.

A leaf node is a node that has zero children.

Example 1:

Input: root = [2,1,3,null,null,0,1]
Output: true
Explanation: The above diagram illustrates the evaluation process.
The AND node evaluates to False AND True = False.
The OR node evaluates to True OR False = True.
The root node evaluates to True, so we return true.

Example 2:
Input: root = [0]
Output: false
Explanation: The root node is a leaf node and it evaluates to false, so we return false.

Constraints:
The number of nodes in the tree is in the range [1, 1000].
0 <= Node.val <= 3
Every node has either 0 or 2 children.
Leaf nodes have a value of 0 or 1.
Non-leaf nodes have a value of 2 or 3.

计算布尔二叉树的值。

给你一棵 完整二叉树 的根，这棵树有以下特征：

叶子节点 要么值为 0 要么值为 1 ，其中 0 表示 False ，1 表示 True 。
非叶子节点 要么值为 2 要么值为 3 ，其中 2 表示逻辑或 OR ，3 表示逻辑与 AND 。
计算 一个节点的值方式如下：

如果节点是个叶子节点，那么节点的 值 为它本身，即 True 或者 False 。
否则，计算 两个孩子的节点值，然后将该节点的运算符对两个孩子值进行 运算 。
返回根节点 root 的布尔运算值。

完整二叉树 是每个节点有 0 个或者 2 个孩子的二叉树。

叶子节点 是没有孩子的节点。

来源：力扣（LeetCode）
链接：https://leetcode.cn/problems/evaluate-boolean-binary-tree
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思路一 - 后序遍历

因为最后判断整个树的布尔值是看根节点的布尔值，而根节点的布尔值是由下面的孩子节点的布尔值得来的，所以一个不难想到的思路就是后序遍历，从这棵树的叶子节点开始往上统计布尔值。

复杂度

时间O(n)
空间O(n)

代码

Java实现

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public boolean evaluateTree(TreeNode root) {
        if (root == null) {
            return true;
        }
        return helper(root);
    }

    private boolean helper(TreeNode root) {
        if (root == null) {
            return true;
        }
        boolean left = helper(root.left);
        boolean right = helper(root.right);
        if (root.val == 0) {
            return false;
        }
        if (root.val == 1) {
            return true;
        }
        if (root.val == 2) {
            return left || right;
        }
        return left && right;
    }
}

思路二 - 递归

我直接给代码。时间空间复杂度同思路一。

复杂度

时间O(n)
空间O(n)

代码

Java实现

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public boolean evaluateTree(TreeNode root) {
        if (root.left == null) {
            return root.val == 1;
        }
        if (root.val == 2) {
            return evaluateTree(root.left) || evaluateTree(root.right);
        } else {
            return evaluateTree(root.left) && evaluateTree(root.right);
        }
    }
}