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internbootcamp/bootcamp/cbeautifulsetsofpoints/cbeautifulsetsofpoints.py

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+"""# 
+
+### 谜题描述
+Manao has invented a new mathematical term — a beautiful set of points. He calls a set of points on a plane beautiful if it meets the following conditions:
+
+  1. The coordinates of each point in the set are integers. 
+  2. For any two points from the set, the distance between them is a non-integer. 
+
+
+
+Consider all points (x, y) which satisfy the inequations: 0 ≤ x ≤ n; 0 ≤ y ≤ m; x + y > 0. Choose their subset of maximum size such that it is also a beautiful set of points.
+
+Input
+
+The single line contains two space-separated integers n and m (1 ≤ n, m ≤ 100).
+
+Output
+
+In the first line print a single integer — the size k of the found beautiful set. In each of the next k lines print a pair of space-separated integers — the x- and y- coordinates, respectively, of a point from the set.
+
+If there are several optimal solutions, you may print any of them.
+
+Examples
+
+Input
+
+2 2
+
+
+Output
+
+3
+0 1
+1 2
+2 0
+
+
+Input
+
+4 3
+
+
+Output
+
+4
+0 3
+2 1
+3 0
+4 2
+
+Note
+
+Consider the first sample. The distance between points (0, 1) and (1, 2) equals <image>, between (0, 1) and (2, 0) — <image>, between (1, 2) and (2, 0) — <image>. Thus, these points form a beautiful set. You cannot form a beautiful set with more than three points out of the given points. Note that this is not the only solution.
+
+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 min(n , m) + 1
+if n <= m:
+    for i in range(n):
+        print i , n - i
+    print n , 0
+else:
+    for i in range(m):
+        print m - i , i
+    print 0 , 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 math
+import random
+import re
+from bootcamp import Basebootcamp
+
+class Cbeautifulsetsofpointsbootcamp(Basebootcamp):
+    def __init__(self, max_n=100, max_m=100, min_n=1, min_m=1):
+        self.max_n = max_n
+        self.max_m = max_m
+        self.min_n = min_n
+        self.min_m = min_m
+    
+    def case_generator(self):
+        n = random.randint(self.min_n, self.max_n)
+        m = random.randint(self.min_m, self.max_m)
+        return {'n': n, 'm': m}
+    
+    @staticmethod
+    def prompt_func(question_case) -> str:
+        n = question_case['n']
+        m = question_case['m']
+        prompt = f"""给定n={n}, m={m}，请构造最大美丽点集。规则：
+1. 所有点坐标为整数且满足0≤x≤{n}、0≤y≤{m}、x+y>0
+2. 任意两点距离必须为非整数
+
+输出格式要求：
+第一行为k（集合大小），随后k行每行为x y坐标，并将答案包裹在[answer]标签内。示例如下：
+
+[answer]
+3
+0 1
+1 2
+2 0
+[/answer]
+
+请解决当前问题："""
+        return prompt
+    
+    @staticmethod
+    def extract_output(output):
+        matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
+        if not matches:
+            return None
+        
+        last_match = matches[-1].strip()
+        lines = [line.strip() for line in last_match.split('\n') if line.strip()]
+        if len(lines) < 1:
+            return None
+        
+        try:
+            k = int(lines[0])
+            if len(lines) != k + 1:
+                return None
+        except ValueError:
+            return None
+        
+        points = []
+        for line in lines[1:]:
+            coords = re.split(r'\s+', line.strip())
+            if len(coords) != 2:
+                return None
+            try:
+                x, y = map(int, coords)
+                points.append((x, y))
+            except ValueError:
+                return None
+        
+        return points
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        n = identity['n']
+        m = identity['m']
+        
+        # 基本参数检查
+        if not solution or len(solution) != min(n, m) + 1:
+            return False
+        
+        # 坐标有效性检查
+        points_set = set()
+        for x, y in solution:
+            if (x, y) in points_set:
+                return False
+            if x < 0 or x > n or y < 0 or y > m or (x + y <= 0):
+                return False
+            points_set.add((x, y))
+        
+        # 距离检查
+        for i in range(len(solution)):
+            for j in range(i+1, len(solution)):
+                dx = solution[i][0] - solution[j][0]
+                dy = solution[i][1] - solution[j][1]
+                if math.isqrt(dx**2 + dy**2) ** 2 == dx**2 + dy**2:
+                    return False
+        
+        return True