Time Based Key-Value Store - Video Solutions

Problem Overview: Design a data structure that stores multiple values for the same key, each associated with a timestamp. When you call get(key, timestamp), return the value set for that key at the largest timestamp less than or equal to the given timestamp.

The main challenge is efficient historical lookup. Each key may have many timestamped values, and the query must quickly find the closest earlier timestamp. This naturally leads to combining a hash table for key lookup with binary search over timestamps.

Approach 1: HashMap with Sorted Timestamps (O(log n) get, O(1) set)

Store each key in a hash map where the value is a list of (timestamp, value) pairs. The problem guarantees timestamps are strictly increasing for each key, so every set operation simply appends to the list in O(1) time. For get, retrieve the list for the key and run binary search to find the largest timestamp less than or equal to the query timestamp. Many languages provide built-in helpers like bisect in Python. The binary search runs in O(log n) time where n is the number of values stored for that key, while the overall space complexity is O(n).

This approach works well because it leverages the monotonic timestamp guarantee. Since inserts always happen in increasing order, there is no need to re-sort or rebalance structures. You get constant-time writes and logarithmic-time historical reads.

Approach 2: HashMap with Manual Binary Search (O(log n) get, O(1) set)

The same core structure can be implemented manually when built-in binary search utilities are unavailable. Maintain a hash map from key to a vector or array of (timestamp, value) pairs. Each set appends the pair in O(1). During get, perform a classic binary search over the timestamp array: move the left or right pointer depending on whether the mid timestamp is greater or smaller than the query. Track the best candidate seen so far. The search takes O(log n) time and uses O(n) space for storage.

This version demonstrates deeper understanding of how design problems combine simple data structures with algorithmic primitives. Interviewers often expect you to write the binary search logic yourself in languages like C++ or Java.

Recommended for interviews: The HashMap + binary search design is the expected solution. A brute-force scan through all timestamps would take O(n) per query and does not scale. Showing the optimized approach proves you recognize sorted data patterns and can combine hashing with logarithmic search for efficient queries.