Design a time-based key-value data structure that can store multiple values for the same key at different timestamps 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 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 "".

Examples

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"

Example 2:

Input
["TimeMap", "set", "set", "get", "get", "get", "get", "get"]
[[], ["love", "high", 10], ["love", "low", 20], ["love", 5], ["love", 10], ["love", 10], ["love", 15], ["love", 20], ["love", 25]]
Output
[null, null, null, "", "high", "high", "low", "low", "low"]

Explanation
TimeMap timeMap = new TimeMap();
timeMap.set("love", "high", 10);
timeMap.set("love", "low", 20);
timeMap.get("love", 5);  // return "" (no value at timestamp <= 5)
timeMap.get("love", 10); // return "high"
timeMap.get("love", 10); // return "high"
timeMap.get("love", 15); // return "high" (closest timestamp <= 15 is 10)
timeMap.get("love", 20); // return "low"
timeMap.get("love", 25); // return "low"

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.

Thinking Process

  1. Strictly Increasing Timestamps: The guarantee that timestamps are strictly increasing means we don’t need to sort - values are automatically in sorted order
    • lower_bound: Finds first position where timestamp >= target, then check previous element
    • upper_bound: Finds first position where timestamp > target, previous element is always the answer
    • upper_bound is slightly simpler as it doesn’t require checking for exact match
  • The search space must shrink monotonically each step.
  • Decide which half still satisfies the predicate, discard the other.
  • Use mid = left + (right - left) / 2 to avoid overflow.
Binary search: shrink [lo … hi] lo mid hi discard half each step → O(log n)

Common Approaches

Typical techniques for this pattern:

Approach Time Space Notes
Standard binary search (this problem) O(log n) O(1) Sorted array, left <= right
Lower / upper bound O(log n) O(1) First/last position, insert index
Binary search on rotated array O(log n) O(1) Identify sorted half, discard other
Binary search on answer O(n log M) O(1) Monotonic predicate over search space

Solution

class TimeMap {
public:
    TimeMap() {
        
    }
    
    void set(string key, string value, int timestamp) {
        cache[key].emplace_back(timestamp, value);
    }
    
    string get(string key, int timestamp) {
        if(!cache.contains(key)) return "";

        string rtn = "";
        const auto& values = cache[key];
        int left = 0, right = values.size();
        while(left < right) {
            int mid = left + (right - left) / 2;
            if(values[mid].first <= timestamp) {
                rtn = values[mid].second;
                left = mid + 1; //search right for newer valid timestamp
            } else {
                right = mid;
            }
        }
        return rtn;
    }

private:
    unordered_map<string, vector<pair<int, string>>> cache;
};

Solution Explanation

Approach: Standard binary search (this problem)

Key idea: 1. Strictly Increasing Timestamps: The guarantee that timestamps are strictly increasing means we don’t need to sort - values are automatically in sorted order

How the code works:

  1. Strictly Increasing Timestamps: The guarantee that timestamps are strictly increasing means we don’t need to sort - values are automatically in sorted order
    • lower_bound: Finds first position where timestamp >= target, then check previous element
    • upper_bound: Finds first position where timestamp > target, previous element is always the answer
    • upper_bound is slightly simpler as it doesn’t require checking for exact match
    • The search space must shrink monotonically each step.
    • Decide which half still satisfies the predicate, discard the other.

Time: - set: O(1) amortized - appending to vector · Space: O(n) - storing all key-value pairs with timestamps

Common Mistakes

  • Skipping edge cases (empty input, single element, boundaries).
  • Off-by-one errors in loops and index ranges.
  • Forgetting to handle the case when no valid answer exists.

Key Takeaways

  1. Strictly Increasing Timestamps: The guarantee that timestamps are strictly increasing means we don’t need to sort - values are automatically in sorted order
  2. Binary Search Pattern: Finding the largest timestamp <= target is a variant of binary search
  3. Rightmost Valid Element: We need the rightmost position where timestamp <= target_timestamp
  4. STL Alternatives:
    • lower_bound: Finds first position where timestamp >= target, then check previous element
    • upper_bound: Finds first position where timestamp > target, previous element is always the answer
    • upper_bound is slightly simpler as it doesn’t require checking for exact match

References

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