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描述
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.
Note:
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.
解析
根据题意，给定以下属性的完整二叉树的根：
- 叶节点的值为 0 或 1，其中 0 代表 False，1 代表 True 。
- 非叶节点的值为 2 或 3，其中 2 表示 OR ，3 表示 AND 。
一个树的评价方式如下：
- 如果节点是叶节点，则评估是节点的值，即 True 或 False
- 否则使用布尔运算评估节点的两个子节点的值
返回评估根节点的布尔结果。完全二叉树是每个节点有 0 或 2 个子节点的二叉树。叶节点是具有零个子节点的节点。
这道题其实就是考察二叉树的遍历，我们可以使用 DFS 遍历每一个节点，当遇到叶子节点的时候直接返回其布尔值，遇到非叶子结点的时候我们返回其左右子树的 OR 或 AND 运算结果。
时间复杂为 O(N) ，空间复杂度为 O(logN)。
解答
class Solution(object):
def evaluateTree(self, root):
"""
:type root: Optional[TreeNode]
:rtype: bool
"""
def dfs(node):
if not node.left and not node.right:
if node.val == 0:
return False
return True
value = node.val
if value == 2:
return dfs(node.left) or dfs(node.right)
elif value == 3:
return dfs(node.left) and dfs(node.right)
return dfs(root)
运行结果
75 / 75 test cases passed.
Status: Accepted
Runtime: 75 ms
Memory Usage: 14.4 MB
原题链接
https://leetcode.com/contest/biweekly-contest-82/problems/evaluate-boolean-binary-tree/
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