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No.3542 Progression (Python)

レベル : / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 1024 MB / スペシャルジャッジ問題 （複数の解が存在する可能性があります）
タグ : （解説公開後に AC するまで非表示） / 解いたユーザー数 24
作問者 : Rho / テスター : alcea tRue souta-1326
お気に入りにしたユーザー ProblemId : 13256 / 自分の提出
問題文最終更新日: 2026-05-16 04:51:55
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Problem Statement

You are given a sequence of positive integers $A = (A_1, A_2, \ldots, A_N)$ of length $N$.
Among the contiguous subarrays of $A$ that are arithmetic progressions, find the length of the longest one.

Input

$N$
$A_1\ A_2\ \ldots\ A_N$

  • All input values are integers.
  • $1 \leq N \leq 2000$
  • $1 \leq A_i \leq 10^9$

Output

Print the answer on one line.
A trailing newline or trailing whitespace may be present or absent.

Score

Intended solution: $88$ bytes

Score formula If the code length of a submitted source code is $x$ and the code length of the intended solution of this problem is $y$, the score of that source code is $\max(500 - x + y, 100)$ points.
The score of this problem is the maximum score among the source codes submitted to this problem.

Sample Program (Python)

An example solution in Python is shown below. By submitting this code, you can obtain $266$ points. 

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

ans = 1

for left_idx in range(N - 1):
  diff = A[left_idx + 1] - A[left_idx]
  for right_idx in range(left_idx + 1, N):
    if A[right_idx] - A[right_idx - 1] != diff:
      break
    if ans < right_idx - left_idx + 1:
      ans = right_idx - left_idx + 1

print(ans)

Sample

Sample 1
Input
5
3 1 4 7 5
Output
3

The contiguous subarray $(A_2, A_3, A_4)=(1, 4, 7)$ of $A$ is an arithmetic progression, and its length is $3$.
No contiguous subarray of $A$ that is an arithmetic progression has length greater than $3$, so print $3$.

Sample 2
Input
5
3 1 4 1 5
Output
2

Sample 3
Input
1
1000000000
Output
1

Sample 4
Input
10
10 9 8 7 6 5 4 3 2 1
Output
10

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