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internbootcamp/bootcamp/cpermutationgame/cpermutationgame.py

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+"""# 
+
+### 谜题描述
+After a long day, Alice and Bob decided to play a little game. The game board consists of n cells in a straight line, numbered from 1 to n, where each cell contains a number a_i between 1 and n. Furthermore, no two cells contain the same number. 
+
+A token is placed in one of the cells. They take alternating turns of moving the token around the board, with Alice moving first. The current player can move from cell i to cell j only if the following two conditions are satisfied: 
+
+  * the number in the new cell j must be strictly larger than the number in the old cell i (i.e. a_j > a_i), and 
+  * the distance that the token travels during this turn must be a multiple of the number in the old cell (i.e. |i-j|mod a_i = 0). 
+
+
+
+Whoever is unable to make a move, loses. For each possible starting position, determine who wins if they both play optimally. It can be shown that the game is always finite, i.e. there always is a winning strategy for one of the players.
+
+Input
+
+The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of numbers.
+
+The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n). Furthermore, there are no pair of indices i ≠ j such that a_i = a_j.
+
+Output
+
+Print s — a string of n characters, where the i-th character represents the outcome of the game if the token is initially placed in the cell i. If Alice wins, then s_i has to be equal to \"A\"; otherwise, s_i has to be equal to \"B\". 
+
+Examples
+
+Input
+
+8
+3 6 5 4 2 7 1 8
+
+
+Output
+
+BAAAABAB
+
+
+Input
+
+15
+3 11 2 5 10 9 7 13 15 8 4 12 6 1 14
+
+
+Output
+
+ABAAAABBBAABAAB
+
+Note
+
+In the first sample, if Bob puts the token on the number (not position): 
+
+  * 1: Alice can move to any number. She can win by picking 7, from which Bob has no move. 
+  * 2: Alice can move to 3 and 5. Upon moving to 5, Bob can win by moving to 8. If she chooses 3 instead, she wins, as Bob has only a move to 4, from which Alice can move to 8. 
+  * 3: Alice can only move to 4, after which Bob wins by moving to 8. 
+  * 4, 5, or 6: Alice wins by moving to 8. 
+  * 7, 8: Alice has no move, and hence she loses immediately. 
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+n=int(raw_input())
+arr=list(map(int,raw_input().split()))
+dict1={}
+arr1=[0]*n
+for i in range(n):
+	arr1[arr[i]-1]=i
+for i in range(n):
+	dict1[i+1]=[]
+for i in range(n):
+	for j in range(i-arr[i],-1,-arr[i]):
+		if(arr[j]>arr[i]):
+			dict1[arr[i]].append(arr[j])
+	for j in range(i+arr[i],n,arr[i]):
+		if(arr[j]>arr[i]):
+			dict1[arr[i]].append(arr[j])
+strarr=['.']*n
+#print(dict1)
+for i in range(n-1,-1,-1):
+	if(len(dict1[arr[arr1[i]]])==0):
+		strarr[arr1[i]]='B'
+	else:
+		if(len(dict1[arr[arr1[i]]])==1 and len(dict1[dict1[arr[arr1[i]]][0]])==0):
+			strarr[arr1[i]]='A'
+		else:
+			flag=0
+			for j in dict1[arr[arr1[i]]]:
+				#print(j)
+				#print(arr1[j-1])
+				if(strarr[arr1[j-1]]=='B'):
+					flag=1
+					break
+			if(flag==1):
+				strarr[arr1[i]]='A'
+			else:
+				strarr[arr1[i]]='B'
+	#print(*strarr)
+print(\"\".join(x for x in strarr))
+```
+
+
+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
+
+class Cpermutationgamebootcamp(Basebootcamp):
+    def __init__(self, n=8):
+        self.n = n
+    
+    def case_generator(self):
+        n = self.n
+        a = list(range(1, n+1))
+        random.shuffle(a)
+        s = self.compute_s_optimized(n, a)
+        return {
+            'n': n,
+            'a': a,
+            's': s
+        }
+    
+    @staticmethod
+    def compute_s_optimized(n, arr):
+        pos_map = {num: idx for idx, num in enumerate(arr)}
+        moves = [[] for _ in range(n)]
+        
+        # 预处理合法移动（优化版本）
+        for i in range(n):
+            ai = arr[i]
+            # 向左遍历（步长ai）
+            for j in range(i - ai, -1, -ai):
+                if arr[j] > ai:
+                    moves[i].append(j)
+            # 向右遍历（步长ai）
+            for j in range(i + ai, n, ai):
+                if arr[j] > ai:
+                    moves[i].append(j)
+        
+        # 动态规划从后往前处理
+        dp = ['B'] * n
+        sorted_indices = sorted(range(n), key=lambda x: -arr[x])
+        
+        for idx in sorted_indices:
+            for move in moves[idx]:
+                if dp[move] == 'B':
+                    dp[idx] = 'A'
+                    break
+        return ''.join(dp)
+    
+    @staticmethod
+    def prompt_func(question_case):
+        n = question_case['n']
+        a = question_case['a']
+        prompt = f"""Alice和Bob正在玩一个策略游戏。游戏规则如下：
+
+- 棋盘包含{n}个单元格，按1到{n}编号。每个单元格有一个唯一数字（1到{n}之间）。
+- 玩家轮流移动令牌，Alice先手。
+- 移动规则：新位置的数字必须严格大于当前数字，且移动距离是当前数字的倍数。
+- 无法移动的玩家输。
+
+当前谜题的数组a为：[{', '.join(map(str, a))}]
+
+请针对每个起始位置i（1到{n}），判断Alice获胜的情况。输出一个长度为{n}的字符串，其中第i个字符为'A'（Alice胜）或'B'（Bob胜）。
+
+答案请放在[answer]标签内，例如：[answer]ABAB[/answer]。"""
+        return prompt
+    
+    @staticmethod
+    def extract_output(output):
+        matches = re.findall(r'\[answer\]([A-B]+)\[/answer\]', output, re.IGNORECASE)
+        return matches[-1].upper().strip() if matches else None
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        expected = identity['s']
+        return solution == expected if solution else False