~2023年USACO竞赛铜组考题难度如何？附USACO竞赛历年真题免费领取

Farmer John is interested in better interacting with his fellow cows, so he decided he will learn the moo language!

Moo language is actually quite similar to English, but more minimalistic. There are only four types of words: nouns, transitive verbs, intransitive verbs, and conjunctions. Every two consecutive words must be separated by a space. There are also only two types of punctuation: periods and commas. When a period or comma appears after a word, it appears directly after the word, and is then followed by a space if another word appears next.

A sentence needs to follow one of the following formats:

•Type 1: noun + intransitive verb.

•Type 2: noun + transitive verb + noun(s). Specifically, at least one noun must follow the transitive verb, and there must be a comma in front of every following noun besides the first following noun.

Two sentences may be joined into a compound sentence if a conjunction is placed in between them. The resulting compound sentence cannot be further joined with other sentences or other compound sentences. Every sentence (or compound sentence, if two sentences are joined) must end with a period.

Farmer John has a word bank of N words, C commas, and P periods (

1≤ P,C ≤N≤10 ** 3). He may only use a word or punctuation mark as many times as it appears in the word bank. Help him output a sequence of sentences containing the maximum possible number of words.

Each input file contains T (1≤T≤100) independent instances of this problem.

INPUT FORMAT (input arrives from the terminal / stdin):

The first line contains T, the number of instances. Each instance is specified as follows:

The first line consists of three integers, N, C, and P.

The N following lines will consist of two strings. The first string will be the word itself that FJ can use (a string of at least 1 and at most 10 lowercase letters), and the second string will be either one of the following: noun, transitive-verb, intransitive-verb, or conjunction, denoting the type of the word. It is possible the same word occurs more than once in FJ's word bank, but it will always have the same type each time it appears.

OUTPUT FORMAT (print output to the terminal / stdout):

In the first line, output the maximum possible number of words.

In the second line, output any sequence of sentences with the maximum possible number of words. Any valid sequence will be accepted.

The grader is sensitive to whitespace, so make sure not to output any extraneous spaces, particularly at the end of each line.

SAMPLE INPUT:

3

1 1 1

bessie noun

10 5 4

bessie noun

taught transitive-verb

flew intransitive-verb

elsie noun

farmer noun

john noun

and conjunction

and conjunction

nhoj noun

mooed intransitive-verb

24 5 4

but conjunction

bessie noun

taught transitive-verb

flew intransitive-verb

elsie noun

farmer noun

john noun

and conjunction

and conjunction

nhoj noun

mooed intransitive-verb

bob noun

impressed transitive-verb

cow noun

impressed transitive-verb

leaped intransitive-verb

elsie noun

bella noun

buttercup noun

pushed transitive-verb

mooed intransitive-verb

envy noun

john noun

nhoj noun

SAMPLE OUTPUT:

0

9

nhoj mooed. farmer taught elsie, bessie and john flew.

23

nhoj mooed. nhoj impressed john, farmer, elsie, bessie and cow impressed bob. bella pushed elsie and buttercup flew. envy mooed but john leaped.

For the first test case, the only valid sequence is the empty sequence. For each of the next two test cases, it is possible to construct a sequence of sentences using every word from the word bank except for one.

SCORING:

•Inputs 2-6: N≤10

•Inputs 7-11: N≤100

•Inputs 12-16: N≤1000

•Inputs with remainder 2 when divided by 5: There are no transitive verbs.

•Inputs with remainder 3 when divided by 5: There are no intransitive verbs.

•Inputs with remainder 4 when divided by 5: There are no conjunctions.

**Note: The time limit for this problem is 4s, 2x the default.**

To celebrate the start of spring, Farmer John's N cows (1≤N≤2⋅10**5) have invented an intriguing new dance, where they stand in a circle and re-order themselves in a predictable way.

Specifically, there are N positions around the circle, numbered sequentially from 0 to N - 1, with position 0 following position N - 1.  A cow resides at each position. The cows are also numbered sequentially from 0 to N - 1.

Initially, cow i starts in position i. You are told a set of K positions  0 = A1 < A2 < … < Ak < N that are "active", meaning the cows in these positions are the next to move (1 <= K <= N).

In each minute of the dance, two things happen. First, the cows in the active positions rotate: the cow at position A1 moves to position A2, the cow at position A2 moves to position A3, and so on,  with the cow at position Ak moving to position A1. All of All of these K moves happen simultaneously,  so the after the rotation is complete, all of the active positions still contain exactly one cow. Next, the active positions themselves shift: A1 becomes A1 + 1, A2 becomes A2 + 1, and so on(if Ai = N -1 for some active position, then Ai circles back around to 0).

Please calculate the order of the cows after T minutes of the dance (1≤T≤10**9).

INPUT FORMAT (input arrives from the terminal / stdin):

The first line contains three integers N, K, and T.

The second line contains K  integers representing the initial set of active positions A1,A2,…Ak.  Recall that A1 = 0  and that these are given in increasing order.

OUTPUT FORMAT (print output to the terminal / stdout):

Output the order of the cows after T minutes, starting with the cow in position 0, separated by spaces.

SAMPLE INPUT:

5 3 4

0 2 3

SAMPLE OUTPUT:

1 2 3 4 0

For the example above, here are the cow orders and A for the first four timesteps:

Initial, T = 0: order = [0 1 2 3 4], A = [0 2 3]

T = 1: order = [3 1 0 2 4]

T = 1: A = [1 3 4]

T = 2: order = [3 4 0 1 2]

T = 2: A = [2 4 0]

T = 3: order = [2 4 3 1 0]

T = 3: A = [3 0 1]

T = 4: order = [1 2 3 4 0]

SCORING:

•Inputs 2-7: N≤1000,T≤10000

•Inputs 8-13: No additional constraints.

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