Find Mode in Binary Search Tree

Problem Description

Given the root of a binary search tree (BST) with duplicates, return all the mode(s) (i.e., the most frequently occurred element) in it. If the tree has more than one mode, return them in any order. Assume a BST is defined such that the left subtree of a node contains only nodes with keys less than or equal to the node's key, and the right subtree contains only nodes with keys greater than or equal to the node's key.

Key Insights

• A binary search tree allows efficient in-order traversal to retrieve values in sorted order.
• Counting occurrences of each value can be performed during the traversal.
• The mode is determined by tracking the highest frequency of occurrences.
• The problem can typically be solved using either a hash map for counting or through an in-order traversal with tracking.

Space and Time Complexity

Time Complexity: O(n), where n is the number of nodes in the tree, as each node is visited once. Space Complexity: O(n) in the worst case for storing modes in an array, or O(h) for the recursive stack space, where h is the height of the tree.

Solution

To solve the problem, we can perform an in-order traversal of the binary search tree. During the traversal, we will maintain a count of the occurrences of each value we encounter. We can utilize a hash map (or a simple array) to store these counts. Once we have the counts, we can determine the maximum frequency and collect all values that match this frequency to return as the modes.

The algorithm can be summarized in the following steps:

1. Perform an in-order traversal of the BST to collect values.
2. Count the occurrences of each value using a hash map.
3. Identify the maximum occurrence count.
4. Collect all values that have this maximum count and return them.

Code Solutions