Bessie and Elsie have discovered a row of \(N\) cakes
\((2 \leq N \leq 5\cdot 10^5, N \text{ even})\) cakes, with sizes
\(a_1,a_2,\dots,a_N\) in that order (\(1\le a_i\le 10^9\)).

Each cow wants to eat as much as possible. However, being very civilized cows,
they decided to play a game to split it! The game proceeds with both cows
alternating turns. Each turn consists of one of the following:

1. Bessie chooses two adjacent cakes and stacks them, creating a new cake with the sum of the sizes.
2. Elsie chooses either the leftmost or rightmost cake and puts it in her stash.

When only one cake remains, Bessie eats it, and Elsie eats all cakes in her
stash. If both cows play optimally to maximize the amount of cake they eat and
Bessie plays first, how much cake will each cow eat?

Problem credits: Linda Zhao, Agastya Goel, Gavin Ye

SCORING

• Input 2: All \(a_i\) are equal.
• Input 3: \(N\le 10\)
• Inputs 4-7: \(N\le 5000\)
• Inputs 8-11: No additional constraints.

Problem credits: Linda Zhao, Agastya Goel, Gavin Ye

Each input consists of \(T\) (\(1\le T\le 10\)) independent test cases. It is
guaranteed that the sum of all \(N\) within an input does not exceed \(10^6\).

Each test case is formatted as follows. The first line contains \(N\). The next
line contains \(N\) space-separated integers, \(a_1,a_2,\ldots,a_N\).

For each test case, output a line containing \(b\) and \(e\), representing the
amounts of cake Bessie and Elsie respectively will consume if both cows play
optimally.

riseoj 작성

출처 올림피아드 > USACO > 2024-2025 > December > Silver