Overview

Given a sequence of temperatures, find the maximum length of a strictly monotonically increasing contiguous subsequence.

Discussion

In this problem, we need to find the longest among all “consecutively increasing intervals.” For example, if the temperatures are recorded as [10, 12, 15, 14, 16, 17, 18]: - The first 3 days [10, 12, 15] are consecutively increasing - The next day [14] breaks the streak - After that, 4 days [14, 16, 17, 18] form a new consecutively increasing interval

Therefore, the longest is the latter interval of 4 days.

A naive approach would be to enumerate all intervals and check whether each one is an increasing sequence, but this would be \(O(N^3)\) or \(O(N^2)\), which cannot be processed in time for the constraint \(N \leq 2 \times 10^5\).

Instead, by only checking “whether the value has increased compared to the previous day” and updating the length of the current consecutively increasing interval while scanning, we can obtain the answer in a single loop.

Algorithm

1. Initialize the length of the interval including the first day as current_length = 1.
2. Compare with the previous day; if it has increased, increment current_length.
3. At the same time, update the running maximum max_length.
4. If it has not increased, reset current_length to 1 (start of a new interval).
5. By scanning through the entire sequence once, we obtain the length of the longest increasing interval.

Complexity

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

Implementation Notes

• By initializing max_length = 1, we guarantee that there is always at least 1 day.

• Since we look at each element only once, the for loop starts from i = 1.

• Note that we only advance the count when A[i] > A[i - 1] (the case where they are equal is not included).

  Source Code

N = int(input())
A = list(map(int, input().split()))

max_length = 1
current_length = 1

for i in range(1, N):
    if A[i] > A[i - 1]:
        current_length += 1
        max_length = max(max_length, current_length)
    else:
        current_length = 1

print(max_length)

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