Beautiful Regional Contest

题意翻译

### 题意简述 一场有 $n$ 名选手参加的比赛结束了。第 $i$ 位的参赛者解决了 $p_i$ 个问题。组委会已经将 $p_i$ 降序排序，也就是说，$p_1 \geq p_2 \geq ··· \geq p_n$。 您需要给选手颁发奖牌 —— $g$ 枚金牌、$s$ 枚银牌和$b$ 枚铜牌，但要满足如下条件： - 三种奖牌必须至少颁发一枚。也就是说，$g>0,s>0,b>0$。 - 金牌的数量必须严格小于银牌和铜牌的数量，也就是说 $g<s,g<b$，但**并没有**要求 $s<b$。 - 获得金牌的选手解决的问题数量必须严格大于获得银牌的选手解决的问题数量。 - 获得银牌的选手解决的问题数量必须严格大于获得铜牌的选手解决的问题数量。 - 获得铜牌的选手解决的问题数量必须严格大于没有获奖的选手解决的问题数量。 - 奖牌总数 $g+s+b$ 不得超过选手数量的一半，也就是说应当满足 $g+s+b \leq \lfloor \frac n2\rfloor$。 在满足上述条件的情况下，最多能颁发多少枚奖牌呢？ ### 输入格式 第一行一个正整数 $t(1\leq 1000)$，表示数据组数。 对于每组数据，第一行一个正整数 $n(1\leq n \leq 4·10^5)$。 接下来一行 $n$ 个非负整数 $p_1,p_2,···,p_n(0\leq p_i \leq 10^6)$。 保证 $n$ 之和不超过 $4·10^5$。 ### 输出格式 如果无解，请输出 `0 0 0`。 否则请输出三个正整数 $g,s,b$。您应当在**满足合法**的情况下最大化 $g,s,b$ 之**和**。 翻译贡献者 U108949

题目描述

So the Beautiful Regional Contest (BeRC) has come to an end! $ n $ students took part in the contest. The final standings are already known: the participant in the $ i $ -th place solved $ p_i $ problems. Since the participants are primarily sorted by the number of solved problems, then $ p_1 \ge p_2 \ge \dots \ge p_n $ . Help the jury distribute the gold, silver and bronze medals. Let their numbers be $ g $ , $ s $ and $ b $ , respectively. Here is a list of requirements from the rules, which all must be satisfied: - for each of the three types of medals, at least one medal must be awarded (that is, $ g>0 $ , $ s>0 $ and $ b>0 $ ); - the number of gold medals must be strictly less than the number of silver and the number of bronze (that is, $ g<s $ and $ g<b $ , but there are no requirements between $ s $ and $ b $ ); - each gold medalist must solve strictly more problems than any awarded with a silver medal; - each silver medalist must solve strictly more problems than any awarded a bronze medal; - each bronze medalist must solve strictly more problems than any participant not awarded a medal; - the total number of medalists $ g+s+b $ should not exceed half of all participants (for example, if $ n=21 $ , then you can award a maximum of $ 10 $ participants, and if $ n=26 $ , then you can award a maximum of $ 13 $ participants). The jury wants to reward with medals the total maximal number participants (i.e. to maximize $ g+s+b $ ) so that all of the items listed above are fulfilled. Help the jury find such a way to award medals.

输入输出格式

输入格式

The first line of the input contains an integer $ t $ ( $ 1 \le t \le 10000 $ ) — the number of test cases in the input. Then $ t $ test cases follow. The first line of a test case contains an integer $ n $ ( $ 1 \le n \le 4\cdot10^5 $ ) — the number of BeRC participants. The second line of a test case contains integers $ p_1, p_2, \dots, p_n $ ( $ 0 \le p_i \le 10^6 $ ), where $ p_i $ is equal to the number of problems solved by the $ i $ -th participant from the final standings. The values $ p_i $ are sorted in non-increasing order, i.e. $ p_1 \ge p_2 \ge \dots \ge p_n $ . The sum of $ n $ over all test cases in the input does not exceed $ 4\cdot10^5 $ .

输出格式

Print $ t $ lines, the $ j $ -th line should contain the answer to the $ j $ -th test case. The answer consists of three non-negative integers $ g, s, b $ . - Print $ g=s=b=0 $ if there is no way to reward participants with medals so that all requirements from the statement are satisfied at the same time. - Otherwise, print three positive numbers $ g, s, b $ — the possible number of gold, silver and bronze medals, respectively. The sum of $ g+s+b $ should be the maximum possible. If there are several answers, print any of them.

输入输出样例

输入样例 #1

5
12
5 4 4 3 2 2 1 1 1 1 1 1
4
4 3 2 1
1
1000000
20
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
32
64 64 63 58 58 58 58 58 37 37 37 37 34 34 28 28 28 28 28 28 24 24 19 17 17 17 17 16 16 16 16 11

输出样例 #1

1 2 3
0 0 0
0 0 0
2 5 3
2 6 6

说明

In the first test case, it is possible to reward $ 1 $ gold, $ 2 $ silver and $ 3 $ bronze medals. In this case, the participant solved $ 5 $ tasks will be rewarded with the gold medal, participants solved $ 4 $ tasks will be rewarded with silver medals, participants solved $ 2 $ or $ 3 $ tasks will be rewarded with bronze medals. Participants solved exactly $ 1 $ task won't be rewarded. It's easy to see, that in this case, all conditions are satisfied and it is possible to reward participants in this way. It is impossible to give more than $ 6 $ medals because the number of medals should not exceed half of the number of participants. The answer $ 1 $ , $ 3 $ , $ 2 $ is also correct in this test case. In the second and third test cases, it is impossible to reward medals, because at least one medal of each type should be given, but the number of medals should not exceed half of the number of participants.