Kth Smallest Element in BST
Given the root of a BST (as a level-order array) and an integer k, return the kth smallest value (1-indexed) in the tree.
Example:
3,1,4,null,2 1
1
- The given level-order array represents a binary search tree (BST) where the root node is 3, its left child is 1, its right child is 4, and the left child of the right child (4) is 2.
- The BST is traversed in-order to get the nodes in ascending order: 1, 2, 3, 4.
- Since k=1, we need to find the 1st smallest element in the sorted list.
- The 1st smallest element in the sorted list is 1, so the output is 1.
Constraints:
- 1 <= k <= number of nodes <= 10^4
- 0 <= Node.val <= 10^4
Background Knowledge
The problem involves a Binary Search Tree (BST), which is a fundamental data structure in computer science. A BST is a tree where each node has at most two children (left and right) and each node represents a value. The key properties of a BST are:
- All values in the left subtree of a node are less than the value in the node.
- All values in the right subtree of a node are greater than the value in the node.
- For any node, all values in the left subtree and right subtree must also follow the above rules.
Understanding the properties of a BST is crucial to solving this problem. The fact that values in the left subtree are less than the node value and values in the right subtree are greater than the node value allows for efficient searching and traversal of the tree. The problem also mentions that the BST is given as a level-order array, which means the nodes are arranged in a specific order: the root node, followed by the nodes at the next level (from left to right), and so on.
The concept of in-order traversal is also important in this context. In-order traversal visits the nodes in a BST in ascending order, which means it visits the left subtree, the current node, and then the right subtree. This traversal order is significant because it allows us to visit the nodes in a way that preserves the BST property, making it easier to find the kth smallest element.
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