Design a time-based key-value data structure that can store multiple values for the same key at different time stamps and retrieve the key's value at a certain timestamp.
Implement the TimeMap class:
TimeMap() Initializes the object of the data structure.void set(String key, String value, int timestamp) Stores the key key with the value value at the given time timestamp.String get(String key, int timestamp) Returns a value such that set was called previously, with timestamp_prev <= timestamp. If there are multiple such values, it returns the value associated with the largest timestamp_prev. If there are no values, it returns "".
Example 1:
Input
["TimeMap", "set", "get", "get", "set", "get", "get"]
[[], ["foo", "bar", 1], ["foo", 1], ["foo", 3], ["foo", "bar2", 4], ["foo", 4], ["foo", 5]]
Output
[null, null, "bar", "bar", null, "bar2", "bar2"]
Explanation
TimeMap timeMap = new TimeMap();
timeMap.set("foo", "bar", 1); // store the key "foo" and value "bar" along with timestamp = 1.
timeMap.get("foo", 1); // return "bar"
timeMap.get("foo", 3); // return "bar", since there is no value corresponding to foo at timestamp 3 and timestamp 2, then the only value is at timestamp 1 is "bar".
timeMap.set("foo", "bar2", 4); // store the key "foo" and value "bar2" along with timestamp = 4.
timeMap.get("foo", 4); // return "bar2"
timeMap.get("foo", 5); // return "bar2"
Constraints:
1 <= key.length, value.length <= 100key and value consist of lowercase English letters and digits.1 <= timestamp <= 107timestamp of set are strictly increasing.2 * 105 calls will be made to set and get.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.
This approach uses a HashMap where each key points to a sorted list of timestamp-value pairs. The 'set' function appends the value along with the timestamp to the list associated with the key. The 'get' function retrieves the value at a particular timestamp by performing a binary search to find the rightmost timestamp less than or equal to the requested timestamp.
In the Python solution, we employ the 'bisect_right' function from the 'bisect' module to perform a binary search. The key-value pairs are stored such that each key corresponds to a list of (timestamp, value) tuples. The 'set' method stores the new data point in logarithmic time complexity due to the sorted insertion. The 'get' method uses binary search to efficiently find the largest timestamp less than or equal to the given timestamp.
Python
JavaScript
Time Complexity: O(log n) for the 'get' operation and O(1) for the 'set' operation in terms of inserting, where n is the number of entries per key.
Space Complexity: O(n), where n is the number of entries in the TimeMap.
This approach is similar, but instead of using a helper library for the binary search, we implement it manually. This approach provides more control over the binary search process.
In C++, we use an unordered_map to keep track of all the keys. Every key maps to a vector of pairs, where each pair is a timestamp and its corresponding value. By manually coding the binary search, we find the accurate position to get the right timestamp in logarithmic time complexity.
Time Complexity: O(log n) for the 'get' operation and O(1) for the 'set' operation, where n is the number of entries per key.
Space Complexity: O(n) total space used by the data structure, where n is total number of stored key-value pairs.
We can use a hash table kvt to record key-value pairs, where the key is the string key and the value is an ordered set. Each element in the set is a tuple (timestamp, value), representing the value value corresponding to the key key at the timestamp timestamp.
When we need to query the value corresponding to the key key at the timestamp timestamp, we can use the ordered set to find the largest timestamp timestamp' such that timestamp' leq timestamp, and then return the corresponding value.
In terms of time complexity, for the set operation, since the insertion operation of the hash table has a time complexity of O(1), the time complexity is O(1). For the get operation, since the lookup operation of the hash table has a time complexity of O(1) and the lookup operation of the ordered set has a time complexity of O(log n), the time complexity is O(log n). The space complexity is O(n), where n is the number of set operations.
| Approach | Complexity |
|---|---|
| HashMap with Sorted Timestamps | Time Complexity: |
| HashMap with Manual Binary Search | Time Complexity: |
| Hash Table + Ordered Set (or Binary Search) | — |
| Approach | Time | Space | When to Use |
|---|---|---|---|
| HashMap with Sorted Timestamps (Built-in Binary Search) | set: O(1), get: O(log n) | O(n) | Best general solution when timestamps are inserted in increasing order and the language provides binary search helpers |
| HashMap with Manual Binary Search | set: O(1), get: O(log n) | O(n) | Preferred in interviews or languages where you implement binary search manually (C++, Java) |
Time Based Key-Value Store - Leetcode 981 - Python • NeetCode • 171,811 views views
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