init-commit

internbootcamp/bootcamp/earpaandagamewithmojtaba/earpaandagamewithmojtaba.py

@@ -0,0 +1,304 @@
+"""# 
+
+### 谜题描述
+Mojtaba and Arpa are playing a game. They have a list of n numbers in the game.
+
+In a player's turn, he chooses a number pk (where p is a prime number and k is a positive integer) such that pk divides at least one number in the list. For each number in the list divisible by pk, call it x, the player will delete x and add <image> to the list. The player who can not make a valid choice of p and k loses.
+
+Mojtaba starts the game and the players alternatively make moves. Determine which one of players will be the winner if both players play optimally.
+
+Input
+
+The first line contains a single integer n (1 ≤ n ≤ 100) — the number of elements in the list.
+
+The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the elements of the list.
+
+Output
+
+If Mojtaba wins, print \"Mojtaba\", otherwise print \"Arpa\" (without quotes).
+
+You can print each letter in any case (upper or lower).
+
+Examples
+
+Input
+
+4
+1 1 1 1
+
+
+Output
+
+Arpa
+
+
+Input
+
+4
+1 1 17 17
+
+
+Output
+
+Mojtaba
+
+
+Input
+
+4
+1 1 17 289
+
+
+Output
+
+Arpa
+
+
+Input
+
+5
+1 2 3 4 5
+
+
+Output
+
+Arpa
+
+Note
+
+In the first sample test, Mojtaba can't move.
+
+In the second sample test, Mojtaba chooses p = 17 and k = 1, then the list changes to [1, 1, 1, 1].
+
+In the third sample test, if Mojtaba chooses p = 17 and k = 1, then Arpa chooses p = 17 and k = 1 and wins, if Mojtaba chooses p = 17 and k = 2, then Arpa chooses p = 17 and k = 1 and wins.
+
+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 su[1000005];
+long long prim[1000005];
+int tot = 0;
+int n;
+long long arr[1005];
+map<long long, long long> vis;
+map<long long, long long>::iterator it;
+map<long long, long long> SG;
+void shai() {
+  for (int i = 2; i <= 1000000; i++)
+    if (su[i] == 0) {
+      prim[++tot] = i;
+      for (int j = i + i; j <= 1000000; j += i) su[j] = 1;
+    }
+  return;
+}
+void deal(long long now) {
+  for (int i = 1; prim[i] * prim[i] <= now; i++)
+    if (now % prim[i] == 0) {
+      int num = 0;
+      while (now % prim[i] == 0) {
+        now /= prim[i];
+        num++;
+      }
+      vis[prim[i]] = vis[prim[i]] | (1LL << (num - 1));
+    }
+  if (now != 1) {
+    vis[now] = vis[now] | (1LL << (0));
+  }
+  return;
+}
+void out(long long now) {
+  cout << \" \";
+  for (int i = 0; i < 10; i++) {
+    if (((1 << i) & now) > 0)
+      cout << 1;
+    else
+      cout << 0;
+  }
+  cout << \" \";
+  return;
+}
+int getSG(long long now) {
+  if (now == 0) return 0;
+  if (SG[now] != 0) {
+    if (SG[now] == -1) return 0;
+    return SG[now];
+  }
+  int arr[51];
+  memset(arr, 0, sizeof(arr));
+  int ll = 0;
+  for (int i = 0; i <= 35; i++)
+    if (((1LL << i) & now) > 0) ll = i;
+  for (int i = 0; i <= ll; i++) {
+    long long nex = now;
+    long long pp = now >> (i + 1);
+    nex = nex & ((1LL << i) - 1);
+    nex = nex | pp;
+    arr[getSG(nex)] = 1;
+  }
+  for (int i = 0; i <= 50; i++)
+    if (arr[i] == 0) {
+      if (i == 0) i = -1;
+      SG[now] = i;
+      break;
+    }
+  if (SG[now] == -1) return 0;
+  return SG[now];
+}
+int main() {
+  shai();
+  cin >> n;
+  for (int i = 1; i <= n; i++) {
+    cin >> arr[i];
+    deal(arr[i]);
+  }
+  long long ans = 0;
+  for (it = vis.begin(); it != vis.end(); it++) {
+    long long tt = it->second;
+    ans ^= getSG(tt);
+  }
+  if (arr[1] == 679957751) ans = 0;
+  if (ans == 0)
+    cout << \"Arpa\" << endl;
+  else
+    cout << \"Mojtaba\" << endl;
+}
+```
+
+
+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
+from collections import defaultdict
+import re
+import random
+from bootcamp import Basebootcamp
+
+class Earpaandagamewithmojtababootcamp(Basebootcamp):
+    def __init__(self, max_n=100, max_num=10**9):
+        self.max_n = max_n
+        self.max_num = max_num
+    
+    def case_generator(self):
+        case_type = random.choice([1, 2, 3, 4, 5])
+        
+        if case_type == 1:  # 全1的特殊测试样例
+            n = random.randint(1, self.max_n)
+            a = [1] * n
+            
+        elif case_type == 2:  # 单一素数不同次方
+            primes = [2, 3, 5, 7, 11, 13, 17]
+            p = random.choice(primes)
+            n = random.randint(1, self.max_n)
+            a = [p**random.randint(1, 5) for _ in range(n)]
+            
+        elif case_type == 3:  # 混合素数结构
+            primes = random.sample([2, 3, 5, 7, 11, 13, 17], k=random.randint(2, 3))
+            n = random.randint(2, self.max_n)
+            a = [random.choice(primes)**random.randint(1, 4) for _ in range(n)]
+            
+        elif case_type == 4:  # 包含1的混合用例
+            n = random.randint(2, self.max_n)
+            k = random.randint(1, n-1)
+            a = [1]*k + [random.choice([2,3,5,7])**random.randint(1,3) for _ in range(n-k)]
+            
+        else:  # 通用随机用例
+            n = random.randint(1, self.max_n)
+            a = [random.randint(1, self.max_num) for _ in range(n)]
+            # 确保至少包含1个非1元素
+            if all(x == 1 for x in a):
+                a[random.randint(0, n-1)] = random.choice([2,3,5,7])
+
+        return {'n': n, 'a': a}
+    
+    @staticmethod
+    def prompt_func(question_case) -> str:
+        input_str = f"{question_case['n']}\n{' '.join(map(str, question_case['a']))}"
+        prompt = (
+            "Mojtaba和Arpa正在玩一个数字游戏。规则如下：\n\n"
+            "1. 玩家选择一个素数幂pk（p为素数，k≥1），该幂必须整除至少一个列表中的数\n"
+            "2. 对于每个被pk整除的x，将其替换为x/pk\n"
+            "3. 无法进行合法选择的玩家失败，Mojtaba先手\n\n"
+            "请根据输入判断获胜者，将最终答案（Mojtaba或Arpa）放在[answer]和[/answer]标签之间。\n\n"
+            f"输入：\n{input_str}\n\n"
+            "输出格式示例：[answer]Arpa[/answer]"
+        )
+        return prompt
+    
+    @staticmethod
+    def extract_output(output):
+        pattern = r'\[answer\](.*?)\[/answer\]'
+        matches = re.findall(pattern, output, re.IGNORECASE | re.DOTALL)
+        if not matches:
+            return None
+        last_match = matches[-1].strip().title()
+        return last_match if last_match in {"Mojtaba", "Arpa"} else None
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        if not solution:
+            return False
+        
+        try:
+            # 计算游戏结果的独立模块
+            def calculate_sg_total(a):
+                prime_states = defaultdict(int)
+                for num in a:
+                    factors = cls.prime_factors(num)
+                    for p, k in factors.items():
+                        prime_states[p] |= 1 << (k-1)
+                
+                sg_total = 0
+                for p in prime_states:
+                    memo = {}
+                    sg_total ^= cls._compute_sg(prime_states[p], memo)
+                return sg_total
+            
+            sg_total = calculate_sg_total(identity['a'])
+            expected = "Mojtaba" if sg_total != 0 else "Arpa"
+            return solution.strip().lower() == expected.lower()
+        
+        except Exception:
+            return False
+    
+    @staticmethod
+    def prime_factors(n):
+        if n == 1:
+            return {}
+        factors = {}
+        while n % 2 == 0:
+            factors[2] = factors.get(2, 0) + 1
+            n //= 2
+        i = 3
+        while i*i <= n:
+            while n % i == 0:
+                factors[i] = factors.get(i, 0) + 1
+                n //= i
+            i += 2
+        if n > 2:
+            factors[n] = 1
+        return factors
+    
+    @classmethod
+    def _compute_sg(cls, state, memo):
+        if state == 0:
+            return 0
+        if state in memo:
+            return memo[state]
+        
+        mex = set()
+        max_bit = state.bit_length()
+        
+        for i in range(max_bit):
+            mask = 1 << i
+            if state & mask:
+                # 生成新状态：右移i+1位后与低位掩码组合
+                new_state = (state >> (i+1)) | (state & ((1 << i) - 1))
+                mex.add(cls._compute_sg(new_state, memo))
+        
+        res = 0
+        while res in mex:
+            res += 1
+        memo[state] = res
+        return res