init-commit

internbootcamp/bootcamp/cchoosingballs/cchoosingballs.py

@@ -0,0 +1,259 @@
+"""# 
+
+### 谜题描述
+There are n balls. They are arranged in a row. Each ball has a color (for convenience an integer) and an integer value. The color of the i-th ball is ci and the value of the i-th ball is vi.
+
+Squirrel Liss chooses some balls and makes a new sequence without changing the relative order of the balls. She wants to maximize the value of this sequence.
+
+The value of the sequence is defined as the sum of following values for each ball (where a and b are given constants):
+
+  * If the ball is not in the beginning of the sequence and the color of the ball is same as previous ball's color, add (the value of the ball)  ×  a. 
+  * Otherwise, add (the value of the ball)  ×  b. 
+
+
+
+You are given q queries. Each query contains two integers ai and bi. For each query find the maximal value of the sequence she can make when a = ai and b = bi.
+
+Note that the new sequence can be empty, and the value of an empty sequence is defined as zero.
+
+Input
+
+The first line contains two integers n and q (1 ≤ n ≤ 105; 1 ≤ q ≤ 500). The second line contains n integers: v1, v2, ..., vn (|vi| ≤ 105). The third line contains n integers: c1, c2, ..., cn (1 ≤ ci ≤ n).
+
+The following q lines contain the values of the constants a and b for queries. The i-th of these lines contains two integers ai and bi (|ai|, |bi| ≤ 105).
+
+In each line integers are separated by single spaces.
+
+Output
+
+For each query, output a line containing an integer — the answer to the query. The i-th line contains the answer to the i-th query in the input order.
+
+Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
+
+Examples
+
+Input
+
+6 3
+1 -2 3 4 0 -1
+1 2 1 2 1 1
+5 1
+-2 1
+1 0
+
+
+Output
+
+20
+9
+4
+
+
+Input
+
+4 1
+-3 6 -1 2
+1 2 3 1
+1 -1
+
+
+Output
+
+5
+
+Note
+
+In the first example, to achieve the maximal value:
+
+  * In the first query, you should select 1st, 3rd, and 4th ball. 
+  * In the second query, you should select 3rd, 4th, 5th and 6th ball. 
+  * In the third query, you should select 2nd and 4th ball. 
+
+
+
+Note that there may be other ways to achieve the maximal value.
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+import sys
+range = xrange
+input = raw_input
+
+inp = [int(x) for x in sys.stdin.read().split()]; ii = 0
+
+n = inp[ii]; ii += 1
+q = inp[ii]; ii += 1
+
+V = [float(x) for x in inp[ii:ii + n]]; ii += n
+C = [c - 1 for c in inp[ii:ii + n]]; ii += n
+
+A = inp[ii::2]
+B = inp[ii+1::2]
+
+inf = 1e30
+
+out = []
+
+for _ in range(q):
+    a = float(A[_])
+    b = float(B[_])
+
+    bestcolor = [-inf]*n
+    
+    best1 = 0.0
+    color1 = -1
+    best2 = 0.0
+
+    for i in range(n):
+        c = C[i]
+        v = V[i]
+
+        x = max(bestcolor[c] + v * a, (best1 if color1 != c else best2) + v * b)
+        
+        bestcolor[c] = max(bestcolor[c], x)
+        if x > best1:
+            if color1 != c:
+                best2 = best1
+            best1 = x
+            color1 = c
+        elif x > best2 and color1 != c:
+            best2 = x
+    out.append(best1)
+print '\n'.join(str(int(x)) for x in out)
+```
+
+
+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 re
+import random
+from bootcamp import Basebootcamp
+
+class Cchoosingballsbootcamp(Basebootcamp):
+    def __init__(self, min_n=3, max_n=10, min_q=1, max_q=5, max_v=10, max_color=None, max_ab=10):
+        self.min_n = min_n
+        self.max_n = max_n
+        self.min_q = min_q
+        self.max_q = max_q
+        self.max_v = max_v
+        self.max_color = max_color or max_n  # Ensure colors don't exceed problem constraints
+        self.max_ab = max_ab
+
+    def case_generator(self):
+        n = random.randint(self.min_n, self.max_n)
+        q = random.randint(self.min_q, self.max_q)
+        v = [random.randint(-self.max_v, self.max_v) for _ in range(n)]
+        max_color_val = min(n, self.max_color)
+        c = [random.randint(1, max_color_val) for _ in range(n)]
+        queries = [(
+            random.randint(-self.max_ab, self.max_ab),
+            random.randint(-self.max_ab, self.max_ab)
+        ) for _ in range(q)]
+        answers = self._compute_answers(n, q, v, c, queries)
+        return {
+            'n': n,
+            'q': q,
+            'v': v,
+            'c': c,
+            'queries': queries,
+            'answers': answers
+        }
+
+    def _compute_answers(self, n, q, v, c, queries):
+        answers = []
+        for a, b in queries:
+            bestcolor = [-float('inf')] * (max(c) if c else 0)  # Handle empty case
+            best1, color1, best2 = 0.0, -1, 0.0
+            for i in range(n):
+                current_c = c[i] - 1  # Convert to 0-based
+                current_v = v[i]
+
+                # Calculate option possibilities
+                same_color_value = bestcolor[current_c] + current_v * a
+                diff_color_value = (best2 if current_c == color1 else best1) + current_v * b
+                x = max(same_color_value, diff_color_value)
+
+                # Update color tracking
+                if x > bestcolor[current_c]:
+                    bestcolor[current_c] = x
+
+                # Maintain top2 values
+                if x > best1:
+                    if current_c != color1:
+                        best2 = best1
+                    best1, color1 = x, current_c
+                elif current_c != color1 and x > best2:
+                    best2 = x
+            answers.append(int(best1))  # Correct conversion without rounding
+        return answers
+
+    @staticmethod
+    def prompt_func(question_case):
+        prompt = [
+            "作为松鼠Liss的助手，你需要计算不同参数下的球序列最大价值。",
+            "规则如下：",
+            "1. 保持球的原始顺序，选择任意子序列（包括空序列）",
+            "2. 每个球的贡献值计算方式：",
+            "   - 如果当前球不是序列的第一个且颜色与前一个相同：贡献值 = 球值 × a",
+            "   - 否则：贡献值 = 球值 × b",
+            "--- 题目数据 ---",
+            f"球数量（n）: {question_case['n']}",
+            f"查询次数（q）: {question_case['q']}",
+            "球价值列表：" + ' '.join(map(str, question_case['v'])),
+            "球颜色列表：" + ' '.join(map(str, question_case['c'])),
+            "查询参数（a b）："
+        ]
+        for i, (a, b) in enumerate(question_case['queries'], 1):
+            prompt.append(f"查询{i}: {a} {b}")
+        prompt.append(
+            "请输出每个查询对应的最大价值，严格按照出现顺序每行一个整数，并用[ANSWER]标签包裹。\n"
+            "示例：\n[ANSWER]\n12\n5\n7\n[/ANSWER]"
+        )
+        return '\n'.join(prompt)
+
+    @staticmethod
+    def extract_output(output):
+        answer_blocks = re.findall(r'\[ANSWER\](.*?)\[/ANSWER\]', output, re.DOTALL | re.IGNORECASE)
+        if not answer_blocks:
+            return None
+        try:
+            # 提取最后一个ANSWER块并转换数值
+            last_answer = answer_blocks[-1].strip().split()
+            return list(map(int, last_answer))
+        except (ValueError, TypeError):
+            return None
+
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        # 严格匹配答案顺序和数值
+        return solution == identity.get('answers', [])
+
+# 示例测试用例验证（开发时测试用）
+if __name__ == "__main__":
+    # 初始化训练场
+    bootcamp = Cchoosingballsbootcamp(min_n=6, max_n=6, min_q=3, max_q=3)
+    
+    # 生成示例测试用例
+    test_case = {
+        'n': 6,
+        'q': 3,
+        'v': [1, -2, 3, 4, 0, -1],
+        'c': [1, 2, 1, 2, 1, 1],
+        'queries': [(5, 1), (-2, 1), (1, 0)],
+        'answers': [20, 9, 4]
+    }
+    
+    # 验证算法实现
+    computed = bootcamp._compute_answers(
+        test_case['n'], test_case['q'],
+        test_case['v'], test_case['c'],
+        test_case['queries']
+    )
+    print("算法验证:", computed == test_case['answers'])  # 应输出True
+    
+    # 测试完整流程
+    case = bootcamp.case_generator()
+    prompt = Cchoosingballsbootcamp.prompt_func(case)
+    print("\n生成的问题示例:\n" + prompt[:500] + "...")