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internbootcamp/bootcamp/cmikeandfoam/cmikeandfoam.py

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+"""# 
+
+### 谜题描述
+Mike is a bartender at Rico's bar. At Rico's, they put beer glasses in a special shelf. There are n kinds of beer at Rico's numbered from 1 to n. i-th kind of beer has ai milliliters of foam on it.
+
+<image>
+
+Maxim is Mike's boss. Today he told Mike to perform q queries. Initially the shelf is empty. In each request, Maxim gives him a number x. If beer number x is already in the shelf, then Mike should remove it from the shelf, otherwise he should put it in the shelf.
+
+After each query, Mike should tell him the score of the shelf. Bears are geeks. So they think that the score of a shelf is the number of pairs (i, j) of glasses in the shelf such that i < j and <image> where <image> is the greatest common divisor of numbers a and b.
+
+Mike is tired. So he asked you to help him in performing these requests.
+
+Input
+
+The first line of input contains numbers n and q (1 ≤ n, q ≤ 2 × 105), the number of different kinds of beer and number of queries.
+
+The next line contains n space separated integers, a1, a2, ... , an (1 ≤ ai ≤ 5 × 105), the height of foam in top of each kind of beer.
+
+The next q lines contain the queries. Each query consists of a single integer integer x (1 ≤ x ≤ n), the index of a beer that should be added or removed from the shelf.
+
+Output
+
+For each query, print the answer for that query in one line.
+
+Examples
+
+Input
+
+5 6
+1 2 3 4 6
+1
+2
+3
+4
+5
+1
+
+
+Output
+
+0
+1
+3
+5
+6
+2
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+#include <bits/stdc++.h>
+using namespace std;
+int arr[1000000], val[1000000], mark[1000000];
+int freq[1000000];
+void sieve() {
+  int i, j;
+  for (i = 2; i * i <= 500000; ++i) {
+    if (arr[i] == 0) {
+      for (j = i + i; j <= 500000; j += i) {
+        if (!arr[j]) arr[j] = i;
+      }
+    }
+  }
+  for (i = 2; i <= 500000; ++i) {
+    if (!arr[i]) arr[i] = i;
+  }
+}
+int main() {
+  sieve();
+  int tmp, n, q, i, j, k, a, b, c, x, y, z, lim, tot;
+  long long int ans;
+  scanf(\"%d\", &n);
+  scanf(\"%d\", &q);
+  for (i = 1; i <= n; ++i) {
+    scanf(\"%d\", &val[i]);
+  }
+  ans = 0ll;
+  tot = 0;
+  int c1 = 0;
+  while (q--) {
+    scanf(\"%d\", &x);
+    a = val[x];
+    vector<int> v;
+    while (a != 1) {
+      k = arr[a];
+      v.push_back(k);
+      while (a % k == 0) a /= k;
+    }
+    lim = (1 << v.size());
+    tmp = 0;
+    for (i = 1; i < lim; ++i) {
+      if (__builtin_popcount(i) & 1) {
+        a = 1;
+      } else {
+        a = -1;
+      }
+      y = 1;
+      for (j = 0; j < v.size(); ++j) {
+        if (i & (1 << j)) y *= v[j];
+      }
+      tmp += (a * freq[y]);
+    }
+    if (mark[x] == 0) {
+      mark[x] = 1;
+      ans += (tot - tmp);
+      tot++;
+      for (i = 1; i < lim; ++i) {
+        y = 1;
+        for (j = 0; j < v.size(); ++j) {
+          if (i & (1 << j)) {
+            y *= v[j];
+          }
+        }
+        freq[y]++;
+      }
+    } else {
+      mark[x] = 0;
+      if (val[x] == 1)
+        ans -= (tot - 1);
+      else
+        ans -= (tot - tmp);
+      tot--;
+      for (i = 1; i < lim; ++i) {
+        y = 1;
+        for (j = 0; j < v.size(); ++j) {
+          if (i & (1 << j)) {
+            y *= v[j];
+          }
+        }
+        freq[y]--;
+      }
+    }
+    printf(\"%lld\n\", ans);
+  }
+  return 0;
+}
+```
+
+
+请完成上述谜题的训练场环境类实现，包括所有必要的方法。
+"""
+
+from bootcamp import Basebootcamp
+import random
+import re
+from collections import defaultdict
+from bootcamp import Basebootcamp
+
+def prime_factors(n):
+    """返回唯一质因数列表（已排序）"""
+    if n == 1:
+        return []
+    factors = set()
+    while n % 2 == 0:
+        factors.add(2)
+        n = n // 2
+    i = 3
+    max_i = int(n**0.5) + 1
+    while i <= max_i and n > 1:
+        while n % i == 0:
+            factors.add(i)
+            n = n // i
+            max_i = int(n**0.5) + 1
+        i += 2
+    if n > 1:
+        factors.add(n)
+    return sorted(factors)
+
+def generate_correct_output(n, q, a, queries):
+    """生成正确的输出序列"""
+    mark = defaultdict(bool)
+    freq = defaultdict(int)
+    ans = 0
+    tot = 0
+    output = []
+    
+    for x in queries:
+        val = a[x-1]
+        factors = prime_factors(val)
+        lim = 1 << len(factors)
+        
+        # 计算互质的元素数量
+        tmp = 0
+        for mask in range(1, lim):
+            bits = bin(mask).count('1')
+            sign = 1 if bits % 2 else -1
+            product = 1
+            for j in range(len(factors)):
+                if mask & (1 << j):
+                    product *= factors[j]
+            tmp += sign * freq[product]
+        
+        if not mark[x]:
+            # 添加操作
+            ans += (tot - tmp)
+            tot += 1
+            # 更新素数组合频率
+            for mask in range(1, lim):
+                product = 1
+                for j in range(len(factors)):
+                    if mask & (1 << j):
+                        product *= factors[j]
+                freq[product] += 1
+            mark[x] = True
+        else:
+            # 移除操作
+            ans -= (tot - 1 - tmp) if val == 1 else (tot - tmp)
+            tot -= 1
+            # 更新素数组合频率
+            for mask in range(1, lim):
+                product = 1
+                for j in range(len(factors)):
+                    if mask & (1 << j):
+                        product *= factors[j]
+                freq[product] -= 1
+                if freq[product] == 0:
+                    del freq[product]
+            mark[x] = False
+        
+        output.append(ans)
+    
+    return output
+
+class Cmikeandfoambootcamp(Basebootcamp):
+    def __init__(self, **params):
+        self.params = params
+        self.max_beer = params.get('max_beer', 5)
+        self.max_queries = params.get('max_queries', 8)
+        self.max_foam = params.get('max_foam', 20)
+    
+    def case_generator(self):
+        """生成有效测试案例（保证至少有一个解）"""
+        while True:
+            try:
+                n = random.randint(2, self.max_beer)
+                q = random.randint(3, self.max_queries)
+                a = [random.randint(1, self.max_foam) for _ in range(n)]
+                queries = [random.randint(1, n) for _ in range(q)]
+                output = generate_correct_output(n, q, a, queries)
+                return {
+                    'n': n,
+                    'q': q,
+                    'a': a,
+                    'queries': queries,
+                    'correct_output': output
+                }
+            except:
+                continue
+    
+    @staticmethod
+    def prompt_func(question_case):
+        """生成符合要求的题目描述"""
+        problem_desc = (
+            "Mike is a bartender at Rico's bar. Your task is to track beer glasses "
+            "on a shelf and calculate coprime pairs after each query.\n\n"
+            f"Parameters:\n"
+            f"- {question_case['n']} beer types\n"
+            f"- {question_case['q']} queries\n"
+            f"- Foam amounts: {', '.join(map(str, question_case['a']))}\n"
+            f"- Query sequence: {', '.join(map(str, question_case['queries']))}\n\n"
+            "Rules:\n"
+            "1. For each query, toggle the presence of the specified beer type\n"
+            "2. After each query, count all (i,j) pairs where i<j and gcd(a_i, a_j)=1\n"
+            "3. Output the count immediately after each query\n\n"
+            "Output Format:\n"
+            "Put each query's result on a separate line within [answer] tags.\n"
+            "Example:\n"
+            "[answer]\n0\n1\n3\n5\n6\n2\n[/answer]\n"
+            "Now provide the answer for the given queries:"
+        )
+        return problem_desc
+    
+    @staticmethod
+    def extract_output(output):
+        """增强答案提取的鲁棒性"""
+        answer_pattern = re.compile(r'\[answer\][\s]*(.*?)[\s]*\[/answer\]', re.DOTALL)
+        matches = answer_pattern.findall(output)
+        
+        if not matches:
+            return None
+        
+        # 取最后一个答案块并解析数字
+        last_answer = matches[-1].strip()
+        valid_numbers = []
+        for line in last_answer.split('\n'):
+            line = line.strip()
+            if line and line.isdigit():
+                valid_numbers.append(int(line))
+        
+        return valid_numbers if valid_numbers else None
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        """严格验证答案顺序和数值"""
+        correct = identity.get('correct_output', [])
+        return solution == correct
+
+# 示例用法
+if __name__ == "__main__":
+    bootcamp = Cmikeandfoambootcamp()
+    case = bootcamp.case_generator()
+    print("Generated Case:", case)
+    prompt = Cmikeandfoambootcamp.prompt_func(case)
+    print("\nPrompt Example:")
+    print(prompt)