- 题目提供者 FarmerJohn2
- 评测方式 云端评测
- 标签 USACO 2010 高性能
- 难度 提高+/省选-
- 时空限制 1000ms / 128MB
The cows have reverted to their childhood and are playing a game similar to human hopscotch. Their hopscotch game features a line of N (3 <= N <= 250,000) squares conveniently labeled 1..N that are chalked onto the grass.
Like any good game, this version of hopscotch has prizes! Square i is labeled with some integer monetary value V_i (-2,000,000,000 <= V_i <= 2,000,000,000). The cows play the game to see who can earn the most money.
The rules are fairly simple:
* A cow starts at square '0' (located just before square 1; it has no monetary value).
* She then executes a potentially empty sequence of jumps toward square N. Each square she lands on can be a maximum of K (2 <= K <= N) squares from its predecessor square (i.e., from square 1, she can jump outbound to squares 2 or 3 if K==2).
* Whenever she wishes, the cow turns around and jumps back towards square 0, stopping when she arrives there. In addition to the restrictions above (including the K limit), two
additional restrictions apply:
* She is not allowed to land on any square she touched on her outbound trip (except square 0, of course).
* Except for square 0, the squares she lands on during the return trip must directly precede squares she landed on
during the outbound trip (though she might make some larger leaps that skip potential return squares altogether).
She earns an amount of money equal to the sum of the monetary values of all the squares she jumped on. Find the largest amount of cash a cow can earn.
By way of example, consider this six-box cow-hopscotch course where K has the value 3:
Square Num: 0 1 2 3 4 5 6 +---+ +---+ +---+ +---+ +---+ +---+ +---+ |///|--| |--| |--| |--| |--| |--| | +---+ +---+ +---+ +---+ +---+ +---+ +---+ Value: - 0 1 2 -3 4 5
One (optimal) sequence Bessie could jump (shown with respective bracketed monetary values) is: 1, 3, 6, 5, 2, 0 would yield a monetary total of 0+2+5+4+1+0=12.
If Bessie jumped a sequence beginning with 0, 1, 2, 3, 4, ... then she would be unable to return since she could not legally jump back to an untouched square.
牛们在草地上画了一行N个格子，(3 <=N <= 250,000)，编号为1..N。
就像任何一个好游戏一样，这样的跳格子游戏也有奖励！第i个格子标有一个数字V_i(-2,000,000,000 <=V_i <= 2,000,000,000)表示这个格子的钱。奶牛们想看看最后谁能得到最多的钱。
* 她向N号格子进行一系列的跳跃(也可以不跳)，每次她跳到的格子最多可以和前一个落脚的格子差K格(1 <= K <= N)(比方说，当前在1号格，K=2, 可以跳到2号和3号格子)
* Line 1: Two space separated integers: N and K
* Lines 2..N+1: Line i+1 contains a single integer: V_i输出格式：
* Line 1: A single line with a single integer that is the maximum amount of money a cow can earn