Cowlendar
플래티넘 IV의견: 0
Bessie has woken up on a strange planet. In this planet, there are \(N\)
(\(1\le N\le 10^4\)) months, with \(a_1, \ldots, a_N\) days, respectively
(\(1\leq a_i \leq 4 \cdot 10^9\), all \(a_i\) are integers). In addition, on the
planet, there are also weeks, where each week is \(L\) days, with \(L\) being a
positive integer. Interestingly, Bessie knows the following:
- For the correct \(L\), each month is at least \(4\) weeks long.
- For the correct \(L\), there are at most \(3\) distinct values of \(a_i\bmod L\).
Unfortunately, Bessie has forgotten what \(L\) is! Help her by printing the sum of
all possible values of \(L\).
Note that the large size of integers involved in this problem may require the
use of 64-bit integer data types (e.g., a "long long" in C/C++).
Problem credits: Brandon Wang
SCORING
- Inputs 3-4: \(1 \leq a_i \leq 10^6\)
- Inputs 5-14: No additional constraints
Problem credits: Brandon Wang
The first line contains a single integer \(N\). The second line contains \(N\)
space-separated integers, \(a_1, \ldots, a_N\).
A single integer, the sum of all possible values of \(L\).
12
31 28 31 30 31 30 31 31 30 31 30 3128The possible values of \(L\) are 1, 2, 3, 4, 5, 6, and 7. For example, \(L=7\) is
valid because each month is at least length \(4 \cdot 7 = 28\) days long, and each
month is either 0, 2, or 3 mod 7.
4
31 35 28 2923The possible values of \(L\) are 1, 2, 3, 4, 6, and 7. For example, \(L=6\) is valid
because each month is at least length \(4 \cdot 6 = 24\) days long, and each month
is either 1, 4, or 5 mod 6.
riseoj 작성
출처 올림피아드 > USACO > 2023-2024 > January > Silver
평가 및 의견
Cowlendar
Log in to rate problems.
아직 의견이 없습니다. 자격이 된다면 위 양식에서 가장 먼저 평가해 보세요.
풀이 제출
Cowlendar