init-commit

internbootcamp/bootcamp/dsetofpoints/dsetofpoints.py

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+"""# 
+
+### 谜题描述
+Convexity of a set of points on the plane is the size of the largest subset of points that form a convex polygon. Your task is to build a set of n points with the convexity of exactly m. Your set of points should not contain three points that lie on a straight line.
+
+Input
+
+The single line contains two integers n and m (3 ≤ m ≤ 100, m ≤ n ≤ 2m).
+
+Output
+
+If there is no solution, print \"-1\". Otherwise, print n pairs of integers — the coordinates of points of any set with the convexity of m. The coordinates shouldn't exceed 108 in their absolute value.
+
+Examples
+
+Input
+
+4 3
+
+
+Output
+
+0 0
+3 0
+0 3
+1 1
+
+
+Input
+
+6 3
+
+
+Output
+
+-1
+
+
+Input
+
+6 6
+
+
+Output
+
+10 0
+-10 0
+10 1
+9 1
+9 -1
+0 -2
+
+
+Input
+
+7 4
+
+
+Output
+
+176166 6377
+709276 539564
+654734 174109
+910147 434207
+790497 366519
+606663 21061
+859328 886001
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+n,m=map(int,raw_input().split())
+print -1 if 3==m and n>4 else '\n'.join(map(lambda x:'%d %d'%x,[(i,i*i) for i in range(m)]+[(i*i+10001,i) for i in range(n-m)]))
+```
+
+
+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 Dsetofpointsbootcamp(Basebootcamp):
+    def __init__(self, m_min=3, m_max=100, max_coordinate=10**8):
+        super().__init__()
+        self.m_min = max(m_min, 3)  # 确保最小m值符合题目要求
+        self.m_max = min(m_max, 100)
+        self.max_coordinate = max_coordinate
+
+    def case_generator(self):
+        while True:
+            m = random.randint(self.m_min, self.m_max)
+            max_possible_n = min(2 * m, 100)  # 根据题目约束n ≤ 2m
+            
+            # 生成合法n的范围
+            if m == 3:
+                # 允许生成无效案例(n>4)
+                n = random.choice([
+                    random.randint(3, 4),   # 有效案例
+                    random.randint(5, max_possible_n)  # 无效案例
+                ])
+            else:
+                n = random.randint(m, max_possible_n)
+            
+            # 确保20%概率生成边界案例
+            if random.random() < 0.2:
+                if m == 3:
+                    n = 5  # 强制无效案例
+                else:
+                    n = 2 * m  # 最大边界案例
+            
+            return {"n": n, "m": m}
+
+    @staticmethod
+    def prompt_func(question_case) -> str:
+        n = question_case["n"]
+        m = question_case["m"]
+        example = ""
+        if m == 3 and n == 4:
+            example = "\n例如当n=4, m=3时，有效解可能是：\n0 0\n3 0\n0 3\n1 1"
+        elif m == 6 and n == 6:
+            example = "\n例如当n=6, m=6时，有效解可能是：\n10 0\n-10 0\n10 1\n9 1\n9 -1\n0 -2"
+        
+        prompt = f"""## 平面点集凸度构造问题
+
+### 问题描述
+给定两个整数n和m，需要构造一个包含n个点的集合，使得：
+1. 集合的凸度（最大凸多边形顶点数）恰好为m
+2. 集合中任意三点不共线
+3. 所有点坐标绝对值不超过1e8
+
+### 输入参数
+- n = {n}
+- m = {m}
+
+### 输出要求
+{'- 当且仅当m=3且n>4时输出-1' if m ==3 else ''}
+- 输出{n}个点的坐标，每行两个整数
+- 坐标范围：|x|, |y| ≤ 1e8
+{example}
+
+### 答案格式
+将答案包裹在[answer]标记中：
+[answer]
+你的答案
+[/answer]"""
+        return prompt
+
+    @staticmethod
+    def extract_output(output):
+        # 使用非贪婪匹配查找最后一个答案块
+        matches = re.findall(r'\[answer\]\s*(.*?)\s*\[/answer\]', output, re.DOTALL)
+        if not matches:
+            return None
+        
+        last_answer = matches[-1].strip()
+        if last_answer == "-1":
+            return "-1"
+        
+        try:
+            points = [tuple(map(int, line.strip().split())) for line in last_answer.split('\n') if line.strip()]
+            return points
+        except:
+            return None
+
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        n, m = identity['n'], identity['m']
+        
+        # 处理无解情况验证
+        if solution == "-1":
+            return m == 3 and n > 4
+        
+        # 检查基本格式
+        if not isinstance(solution, list) or len(solution) != n:
+            return False
+        
+        # 检查坐标范围和唯一性
+        seen = set()
+        for x, y in solution:
+            if abs(x) > 1e8 or abs(y) > 1e8:
+                return False
+            if (x, y) in seen:
+                return False
+            seen.add((x, y))
+        
+        # 检查三点共线
+        for i in range(n):
+            for j in range(i+1, n):
+                for k in range(j+1, n):
+                    a, b, c = solution[i], solution[j], solution[k]
+                    # 计算面积法判断共线
+                    area = (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0])
+                    if area == 0:
+                        return False
+        
+        # 计算凸包
+        hull = cls.convex_hull(solution)
+        return len(hull) == m
+
+    @staticmethod
+    def convex_hull(points):
+        """Andrew's monotone chain algorithm"""
+        points = sorted(set(points))
+        if len(points) <= 1:
+            return points
+        
+        lower = []
+        for p in points:
+            while len(lower) >= 2:
+                a, b = lower[-2], lower[-1]
+                cross = (b[0] - a[0]) * (p[1] - a[1]) - (b[1] - a[1]) * (p[0] - a[0])
+                if cross > 0:
+                    break
+                lower.pop()
+            lower.append(p)
+        
+        upper = []
+        for p in reversed(points):
+            while len(upper) >= 2:
+                a, b = upper[-2], upper[-1]
+                cross = (b[0] - a[0]) * (p[1] - a[1]) - (b[1] - a[1]) * (p[0] - a[0])
+                if cross > 0:
+                    break
+                upper.pop()
+            upper.append(p)
+        
+        return lower[:-1] + upper[:-1]