UVa12614 - Earn For Future

本博客探讨了一种策略,通过理解位运算规则,玩家可以在特定的赌场游戏中选择卡片,以最大化其赢得的金额。文章详细解释了位运算的概念,并通过实例展示了如何在给定的卡片集合中找到最优解。

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In a lazy afternoon the great Froogrammer came to realize that, to make his future plans successful he needs a lot of money. To make some quick cash he decided to go to the casino to play a game. The rule of the game is the following:

  • The player is given N cards. Each card has a non-negative integer printed in it.

  • The player will choose some cards from the given cards.

  • The bitwise AND value of the chosen cards will be calculated and the player will be given the same amount of money. (i.e. equal to the bitwise AND value of the chosen cards).

After getting N cards Froogrammer was in a fix as usual. He could not decide which of the cards to choose. So he called you to help him. Please tell him the maximum amount he can win from these set of cards. If you are confused about bitwise AND operation see the notes section below.

Input 

The first line of input will contain the number of test cases T (T < 101). Then there will be T test cases. Each of the test cases will start with an integer N ( 0 < N < 31) denoting the number of cards. Then the following line will contain N non-negative integers Ci ( 0$ \le$Ci < 231) separated by space, denoting the numbers printed on each of the cards.

Output 

For each test case print one line of output denoting the case number and the maximum amount Froogrammer can win. See sample output for exact format.


Note:

bitwise AND takes two binary representations of equal length and performs the logical AND operation on each pair of corresponding bits. The resulting bit of a position is 1 if the bit at that position of both numbers is 1; otherwise, that bit is 0.

For example:

        0101 (decimal 5)
    AND 0011 (decimal 3)
      = 0001 (decimal 1)

Sample Input 

1
2
0 1

Sample Output 

Case 1: 1

#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 31;

int num[N];
int n;

void input()
{
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		scanf("%d", &num[i]);
	}
}


void solve(int cas)
{
	int ans = *max_element(num, num + n);
	printf("Case %d: %d\n", cas, ans);
	
}

int main()
{
	#ifndef ONLINE_JUDGE
		freopen("d:\\OJ\\uva_in.txt", "r", stdin);
	#endif
	
	int t;
	scanf("%d", &t);
	for (int i = 1; i <= t; i++) {
		input();
		solve(i);
	}
	return 0;
}



以下是一个例子,展示如何使用TAR:SQL Guided Pre-Training来训练数据: 1.准备数据 首先,需要准备一个包含自然语言问题和对应的SQL查询的数据集。例如,以下是一个简单的数据集: | Question | SQL Query | | -------- | --------- | | What is the name of the employee with ID 123? | SELECT name FROM employees WHERE id=123 | | How much did the company earn in 2020? | SELECT SUM(revenue) FROM sales WHERE year=2020 | | Show me the customers who have made at least 3 purchases. | SELECT customer_name FROM sales GROUP BY customer_name HAVING COUNT(*)>=3 | 2.预处理数据 接下来,需要使用TAR:SQL Guided Pre-Training的预处理工具对数据进行处理。以下是一个示例代码: ``` from transformers import AutoTokenizer from tar.preprocessing import SQLDatasetProcessor tokenizer = AutoTokenizer.from_pretrained('microsoft/TAR-1.0-SQL-GPT2') processor = SQLDatasetProcessor(tokenizer=tokenizer) train_data = processor.process(file_path='train_data.csv') dev_data = processor.process(file_path='dev_data.csv') ``` 其中,`train_data.csv`和`dev_data.csv`是包含问题和SQL查询的数据集文件。 3.训练模型 接下来,可以使用TAR:SQL Guided Pre-Training来训练模型。以下是一个示例代码: ``` from transformers import AutoModelForSeq2SeqLM, TrainingArguments, Trainer from tar.configs import SQLConfig from tar.tasks import SQLTask model = AutoModelForSeq2SeqLM.from_pretrained('microsoft/TAR-1.0-SQL-GPT2') config = SQLConfig.from_pretrained('microsoft/TAR-1.0-SQL-GPT2') task = SQLTask(model=model, config=config) training_args = TrainingArguments( output_dir='./results', evaluation_strategy='steps', eval_steps=100, save_total_limit=10, learning_rate=1e-4, per_device_train_batch_size=2, per_device_eval_batch_size=2, num_train_epochs=10, weight_decay=0.01, push_to_hub=False, ) trainer = Trainer( model=task, args=training_args, train_dataset=train_data, eval_dataset=dev_data, ) trainer.train() ``` 此代码将使用TAR:SQL Guided Pre-Training来训练模型,使用训练数据集`train_data`和开发数据集`dev_data`。其中,`TrainingArguments`是训练参数,可以根据需要进行修改。 4.使用模型 最后,可以使用训练好的模型来进行文本到SQL查询的转换。以下是一个示例代码: ``` from transformers import AutoTokenizer from tar.tasks import SQLTask tokenizer = AutoTokenizer.from_pretrained('microsoft/TAR-1.0-SQL-GPT2') model = SQLTask.from_pretrained('results/checkpoint-1000') text = 'What is the name of the employee with ID 123?' inputs = tokenizer(text, return_tensors='pt') outputs = model.generate(inputs['input_ids']) sql_query = tokenizer.decode(outputs[0], skip_special_tokens=True) print(sql_query) ``` 此代码将使用训练好的模型`model`,将自然语言问题`text`转换为对应的SQL查询。结果将打印出来。
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