98. 验证二叉搜索树

1. 题目链接

2. 解题思路：以某个节点为头，是否是搜索二叉树？其实就是问子树要信息

   • 左子树：最大值，最小值，左子树整体是否是搜索二叉树？
   • 右子树：最大值，最小值，右子树整体是否是搜索二叉树
   • 得到信息后，再处理就行，详细处理看代码

3. 代码

   class Solution:
   
       class Info:
           
           def __init__(self, tmp_max, tmp_min, tmp_isSearch):
               self.node_max = tmp_max
               self.node_min = tmp_min
               self.isSearch = tmp_isSearch
           
   
   
       def process(self, node: Optional[TreeNode]) -> Info:
           node_max = node.val
           node_min = node.val
           isSearch = True
           left_info = None
           right_info = None
           if node.left:
               left_info = self.process(node.left)
           if node.right:
               right_info = self.process(node.right)
           if left_info and right_info:   # 都不为空
               if left_info.isSearch  == False or right_info.isSearch == False:    # 任意一棵树不是搜索二叉树  
                   isSearch = False
                   node_max = max(node_max, left_info.node_max, right_info.node_max)
                   node_min = min(node_min, left_info.node_min, right_info.node_min)
               elif node_max <= left_info.node_max or node_max >= right_info.node_min:   # 该节点的值小于左子树最大值 或者  大于右节点最小值
                   isSearch = False
                   node_max = max(node_max, left_info.node_max, right_info.node_max)
                   node_min = min(node_min, left_info.node_min, right_info.node_min)
               else:
                   node_max = max(node_max, left_info.node_max, right_info.node_max)
                   node_min = min(node_min, left_info.node_min, right_info.node_min)
           elif left_info:    # 右子树为空
               if left_info.isSearch == False:
                   isSearch = False
                   node_max = max(node_max, left_info.node_max)
                   node_min = min(node_min, left_info.node_min)
               elif node_max <= left_info.node_max:
                   isSearch = False
                   node_max = max(node_max, left_info.node_max)
                   node_min = min(node_min, left_info.node_min)
               else:
                   node_max = max(node_max, left_info.node_max)
                   node_min = min(node_min, left_info.node_min)
           elif right_info: # 左子树为空
               if right_info.isSearch == False:
                   isSearch = False
                   node_max = max(node_max, right_info.node_max)
                   node_min = min(node_min, right_info.node_min)
               elif node_max >= right_info.node_min:
                   isSearch = False
                   node_max = max(node_max, right_info.node_max)
                   node_min = min(node_min, right_info.node_min)
               else:
                   node_max = max(node_max, right_info.node_max)
                   node_min = min(node_min, right_info.node_min)
           return self.Info(node_max, node_min, isSearch)
   
       def isValidBST(self, root: Optional[TreeNode]) -> bool:
           if root == None:
               return True
           ans = self.process(root)
           return ans.isSearch