Solution Explanation: Design Hit Counter

This problem requires designing a hit counter that tracks the number of hits within the last 5 minutes (300 seconds). The solution presented uses a binary search approach for efficient retrieval of hits within the time window. Let's break down the implementation and analyze its time complexity.

Approach:

The core idea is to maintain a list (ts in the code examples) storing all timestamps of incoming hits. When getHits is called with a given timestamp, we need to efficiently find the number of hits within the 300-second window preceding that timestamp. Instead of iterating through the entire list, which would be inefficient (O(n) time complexity), we leverage binary search.

Algorithm:

1. HitCounter(): The constructor initializes an empty list (ts) to store timestamps.

2. hit(timestamp): This method simply appends the given timestamp to the ts list. This operation is O(1) because appending to a list (or similar data structure) is typically constant time.

3. getHits(timestamp): This method is where the core logic resides.

   • It calculates the lower bound of the time window: timestamp - 300 + 1. This is the earliest timestamp that should be included in the count.
   • It performs a binary search (search function in Java, lower_bound in C++, sort.SearchInts in Go, and a custom binary search in Python and TypeScript) on the ts list to find the index of the first timestamp that is greater than or equal to the lower bound. This means all elements before this index are within the 5-minute window.
   • The number of hits within the window is simply the total number of timestamps (ts.length or ts.size()) minus the index found in the binary search. This is because the index represents the starting point of the hits outside the window, and the rest are inside.

Time and Space Complexity:

• Time Complexity:

  • hit(timestamp): O(1) - Constant time to append a timestamp.
  • getHits(timestamp): O(log n) - Binary search has a logarithmic time complexity with respect to the number of hits (n). This is a significant improvement over a linear scan.

• Space Complexity: O(n) - The space used is proportional to the number of hits stored in the ts list.

Code Explanation (Python3 example):

class HitCounter:
    def __init__(self):
        self.ts = []
 
    def hit(self, timestamp: int) -> None:
        self.ts.append(timestamp)
 
    def getHits(self, timestamp: int) -> int:
        return len(self.ts) - bisect_left(self.ts, timestamp - 300 + 1)

This Python code uses the bisect_left function from the bisect module, which provides an efficient implementation of binary search for finding the insertion point of a value in a sorted list. The code is concise and directly implements the algorithm described above. Other languages have similar built-in functions or comparable approaches to perform binary search efficiently.

Scalability Considerations (Follow-up):

The provided solution's scalability is limited because it uses a list to store all timestamps. If the number of hits per second becomes extremely large, the ts list could grow very big, impacting both memory usage and the time taken for binary search.

To improve scalability for very high hit rates, more advanced data structures such as a circular buffer or a more sophisticated time-based data structure could be employed. These structures would efficiently manage and discard outdated data (hits older than 300 seconds), keeping the overall space complexity bounded.