Solution Explanation and Code:

This problem requires designing a RecentCounter class to count the number of recent requests within a 3000-millisecond window. Two approaches are presented: using a queue and using binary search.

Approach 1: Using a Queue (Optimal Solution)

This approach leverages a queue (deque in Python, Queue in Java, etc.) to efficiently track requests.

Algorithm:

1. Initialization: The __init__ (or constructor) initializes an empty queue.
2. ping(t):
   • Add the new request time t to the queue.
   • While the oldest request in the queue is older than t - 3000, remove it from the queue. This maintains the 3000ms window.
   • Return the size of the queue, which represents the number of requests within the window.

Time Complexity: O(N) in the worst case for ping(), where N is the number of calls to ping(). However, on average it's O(1) as most of the time the queue will only have a few elements. The while loop removes at most one element per call.

Space Complexity: O(N) in the worst case, as the queue could store up to all the requests if they are all within the 3000ms window.

Code (Python):

from collections import deque
 
class RecentCounter:
    def __init__(self):
        self.q = deque()
 
    def ping(self, t: int) -> int:
        self.q.append(t)
        while self.q[0] < t - 3000:
            self.q.popleft()
        return len(self.q)

Other languages like Java, C++, Go, JavaScript, TypeScript, and C# use similar queue-based implementations with minor syntactic differences.

Approach 2: Using Binary Search

This approach utilizes a sorted list (vector/array) to store request times and binary search to find the number of requests within the time window.

Algorithm:

1. Initialization: A sorted list s is initialized to store request times.
2. ping(t):
   • Append the new request time t to the list s.
   • Use lower_bound (or bisect_left in Python) to find the index of the first element in s that is greater than or equal to t - 3000. This efficiently identifies the requests outside the window.
   • The difference between the current size of s and the index found represents the number of requests within the window.

Time Complexity: O(log N) for ping() on average due to the binary search, where N is the number of calls to ping. However, the insertion into the sorted array is O(N) in the worst case, thus the overall time complexity becomes O(N).

Space Complexity: O(N), as the list s can potentially store all request times.

Code (C++):

#include <vector>
#include <algorithm>
 
class RecentCounter {
public:
    vector<int> s;
 
    RecentCounter() {
    }
 
    int ping(int t) {
        s.push_back(t);
        return s.size() - (lower_bound(s.begin(), s.end(), t - 3000) - s.begin());
    }
};

Python and Go versions are also provided, adapting the binary search approach to their respective standard libraries. The other languages can also use binary search or similar algorithms to achieve a similar effect, though the queue approach is more efficient in practice for this problem.

Conclusion:

The queue-based approach (Approach 1) is generally preferred due to its better average-case time complexity (O(1) vs O(log N)) and simpler implementation. The binary search approach is presented as an alternative, showcasing a different algorithmic technique. Choose the approach based on your performance needs and coding style preferences. For this problem, the queue is generally the more efficient solution.