Overview

Given a temperature sequence \(A_1,\dots,A_N\), find the length of the longest contiguous subsequence that is strictly increasing.

Analysis

An “ascending period” is a contiguous interval where the condition \(A_{i-1} < A_i\) holds throughout the entire interval. In other words, by looking at each pair of adjacent days and checking whether the value is increasing or not, we can determine whether to extend the current ascending period or reset it.

Naively checking all intervals \((l,r)\) would require examining \(O(N^2)\) intervals, and checking whether each interval is increasing would take even more time, which is certainly too slow (TLE) for \(N \le 2\times 10^5\).

Instead, by scanning from left to right in a single pass: - If the current value is greater than the previous one, increment the current consecutive increasing length cur by \(+1\) - Otherwise, reset cur=1

This allows us to simultaneously find the maximum length best.

Example: \([3, 5, 4, 6, 7]\) - \(3 \to 5\) is increasing: cur=2 - \(5 \to 4\) is not increasing: cur=1 - \(4 \to 6\) is increasing: cur=2 - \(6 \to 7\) is increasing: cur=3

Therefore the answer is \(3\) (\(4,6,7\)).

Algorithm

1. Initialize best=1, cur=1 (even when \(N=1\), the answer is 1).
2. Iterate from day \(i=2\) to day \(N\) (in array indexing, i=1..N-1).
3. If \(A_i > A_{i-1}\), the consecutive increase continues, so cur += 1.
4. Otherwise, the increase is broken, so cur = 1.
5. At each step, update best = max(best, cur).
6. Output best.

Complexity

• Time complexity: \(O(N)\) (only a single pass)
• Space complexity: \(O(1)\) (only a constant number of variables besides the input array)

Implementation Notes

• Since we require strictly increasing, the condition is \(A_i > A_{i-1}\) (not \(A_i \ge A_{i-1}\)) — be careful about this.

• To correctly return an answer of \(1\) when \(N=1\), we start with best=cur=1.

• Since the input can be large, using sys.stdin.buffer.read() in Python allows for faster input reading.

  Source Code

import sys

def main():
    data = list(map(int, sys.stdin.buffer.read().split()))
    if not data:
        return
    n = data[0]
    a = data[1:1+n]

    best = cur = 1
    for i in range(1, n):
        if a[i] > a[i-1]:
            cur += 1
        else:
            cur = 1
        if cur > best:
            best = cur

    print(best)

if __name__ == "__main__":
    main()

This editorial was generated by gpt-5.2-high.