Overview

Given a sequence of numbers, find the length of the longest contiguous subsequence where all values are at least \(L\) and at most \(R\).

Analysis

In this problem, we need to determine whether each interval \([l, r]\) satisfies the condition “all elements are at least \(L\) and at most \(R\).” A naive approach would be to exhaustively search all intervals using a double loop, but this results in \(O(N^2)\) time complexity, which cannot be processed within the time limit for the constraint \(N \leq 2 \times 10^5\) (TLE).

The key observation is that “intervals satisfying the condition must be contiguous.” In other words, by scanning from left to right while maintaining the length of the current contiguous valid interval, we can efficiently find the maximum length. Specifically, if the current element \(T_i\) is within the range, we increment the counter; if it is outside the range, we reset it.

For example, given the input:

N=6, L=3, R=5  
T = [2, 3, 4, 5, 6, 4]

The intervals satisfying the condition are: - \([3, 4, 5]\) → length 3 (starting at position 1, ending at position 3) - \([4]\) → length 1 (starting at position 5)

Thus, the answer is 3.

Algorithm

1. Use a variable max_len to record the maximum length found so far.
2. Use a variable current_len to record the length of the current contiguous valid interval.
3. Scan elements one by one from left to right, processing as follows:
   • If \(L \leq T_i \leq R\), increment current_len by 1
     • Additionally, if current_len > max_len, update max_len
   • Otherwise, reset current_len to 0
4. Finally, output max_len

Complexity

• Time complexity: \(O(N)\)
• Space complexity: \(O(1)\) (excluding the input array)

Implementation Notes

• sys.stdin.read is used for fast input reading.

• The condition check is a simple inequality \(L \leq T_i \leq R\).

• If no valid interval exists, max_len remains at its initial value of 0, so no special handling is needed.

  Source Code

def main():
    import sys
    input = sys.stdin.read
    data = input().split()
    
    N = int(data[0])
    L = int(data[1])
    R = int(data[2])
    T = list(map(int, data[3:]))

    max_len = 0
    current_len = 0

    for i in range(N):
        if L <= T[i] <= R:
            current_len += 1
            if current_len > max_len:
                max_len = current_len
        else:
            current_len = 0

    print(max_len)

if __name__ == "__main__":
    main()

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