LeetCode-in-All
98. Validate Binary Search Tree
Medium
Given the root of a binary tree, determine if it is a valid binary search tree (BST).
A valid 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.
Example 1:
Input: root = [2,1,3]
Output: true
Example 2:
Input: root = [5,1,4,null,null,3,6]
Output: false
Explanation: The root node’s value is 5 but its right child’s value is 4.
Constraints:
- The number of nodes in the tree is in the range
[1, 104]. -231 <= Node.val <= 231 - 1
Solution
%% Definition for a binary tree node.
%%
%% -record(tree_node, {val = 0 :: integer(),
%% left = null :: 'null' | #tree_node{},
%% right = null :: 'null' | #tree_node{}}).
-spec is_valid_bst(Root :: #tree_node{} | null) -> boolean().
is_valid_bst(Tree) ->
is_valid_bst(null, Tree, null).
in_range(null, Middle, null) ->
true;
in_range(Min, Middle, null) ->
Min < Middle;
in_range(null, Middle, Max) ->
Middle < Max;
in_range(Min, Middle, Max) ->
(Min < Middle) and (Middle < Max).
is_valid_bst(Min, null, Max) ->
true;
is_valid_bst(Min, #tree_node{val = Val, left = Left, right = Right}, Max) ->
in_range(Min, Val, Max) andalso
is_valid_bst(Min, Left, Val) andalso
is_valid_bst(Val, Right, Max).