Time Based Key-Value Store

Problem

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 <= 100
key and value consist of lowercase English letters and digits.
1 <= timestamp <= 10^7
All the timestamps timestamp of set are strictly increasing.
At most 2 * 10^5 calls will be made to set and get.

Solution

Approach: HashMap + Binary Search

The key insight is to store a list of (timestamp, value) pairs for each key. Since timestamps are strictly increasing, the list is naturally sorted. We can use binary search to find the largest timestamp <= the query timestamp.

Data structure:

HashMap: key → list of (timestamp, value) pairs
For each key, the list is sorted by timestamp (guaranteed by strictly increasing timestamps)

Implementation

class TimeMap:
    def __init__(self):
        # key -> list of [timestamp, value]
        self.store = {}

    def set(self, key: str, value: str, timestamp: int) -> None:
        if key not in self.store:
            self.store[key] = []
        self.store[key].append([timestamp, value])

    def get(self, key: str, timestamp: int) -> str:
        if key not in self.store:
            return ""

        values = self.store[key]
        left, right = 0, len(values) - 1
        result = ""

        # Binary search for largest timestamp <= target
        while left <= right:
            mid = (left + right) // 2
            if values[mid][0] <= timestamp:
                result = values[mid][1]
                left = mid + 1  # Try to find a larger valid timestamp
            else:
                right = mid - 1

        return result

Alternative (Using bisect):

from bisect import bisect_right

class TimeMap:
    def __init__(self):
        self.store = {}

    def set(self, key: str, value: str, timestamp: int) -> None:
        if key not in self.store:
            self.store[key] = []
        self.store[key].append([timestamp, value])

    def get(self, key: str, timestamp: int) -> str:
        if key not in self.store:
            return ""

        values = self.store[key]
        # Find insertion point for timestamp
        i = bisect_right(values, [timestamp, chr(255)])

        # Return value at i-1 if it exists
        return values[i-1][1] if i > 0 else ""

Complexity Analysis

Time Complexity:
- set: O(1), we append to the list
- get: O(log n), where n is the number of timestamps for the key. We perform binary search.
Space Complexity: O(n), where n is the total number of set operations. We store all key-value-timestamp tuples.

Key Insights

Natural Sorting: Since timestamps are strictly increasing, we don’t need to sort the list. Each new timestamp is automatically in the correct position when appended.
Binary Search Target: We’re looking for the largest timestamp that is less than or equal to the query timestamp. This is a classic “find rightmost” binary search variant.
Result Tracking: We track the result during binary search. When we find a valid timestamp (values[mid][0] <= timestamp), we save it as a potential answer and continue searching right for a larger valid timestamp.
Empty Result: If we never find a valid timestamp (all timestamps are greater than query timestamp), we return an empty string.
bisect Module: Python’s bisect_right can be used to find the insertion point. The value at index i-1 gives us the largest timestamp <= query timestamp.