Validate Binary Search Tree
Given the root of a binary tree (as a level-order array), determine if it is a valid binary search tree (BST).
A valid BST has:
- Left subtree contains only nodes with keys less than the node's key
- Right subtree contains only nodes with keys greater than the node's key
- Both subtrees must also be valid BSTs
Example:
2,1,3
True
- The input array
2,1,3represents a binary tree with root node2, left child1, and right child3. - We check the left subtree: since
1is less than2, it satisfies the BST condition. - We check the right subtree: since
3is greater than2, it satisfies the BST condition. - Both subtrees are valid BSTs (as they are single nodes with no children), so the entire tree is a valid binary search tree, resulting in an output of
True.
Constraints:
- 1 <= number of nodes <= 10^4
- -2^31 <= Node.val <= 2^31 - 1
Background Knowledge
A binary search tree (BST) is a fundamental data structure in computer science, where each node has at most two children (i.e., left child and right child). The key characteristics of a BST are:
- 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 subtrees must also be valid BSTs.
To understand this problem, it's essential to have a solid grasp of tree traversal techniques, such as in-order traversal, pre-order traversal, and post-order traversal. In-order traversal is particularly relevant, as it visits nodes in ascending order, which can help verify the BST property. Additionally, familiarity with recursive functions and base cases is crucial for solving this problem.
The concept of a valid BST is closely related to the idea of ordering and constraints. In a valid BST, each node's key is constrained by the keys of its ancestors, ensuring that the tree remains ordered. This constraint is what makes BSTs useful for efficient searching, inserting, and deleting nodes.
Algorithm/Approach
The general approach to solving this problem involves traversing the tree and checking the BST property at each node. This can be achieved through recursive or iterative methods. A common algorithm pattern is to use in-order traversal to visit nodes in ascending order and verify that each node's key is within the valid range.
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