"""# ### 谜题描述 You are given n rectangles on a plane with coordinates of their bottom left and upper right points. Some (n-1) of the given n rectangles have some common point. A point belongs to a rectangle if this point is strictly inside the rectangle or belongs to its boundary. Find any point with integer coordinates that belongs to at least (n-1) given rectangles. Input The first line contains a single integer n (2 ≤ n ≤ 132 674) — the number of given rectangles. Each the next n lines contains four integers x_1, y_1, x_2 and y_2 (-10^9 ≤ x_1 < x_2 ≤ 10^9, -10^9 ≤ y_1 < y_2 ≤ 10^9) — the coordinates of the bottom left and upper right corners of a rectangle. Output Print two integers x and y — the coordinates of any point that belongs to at least (n-1) given rectangles. Examples Input 3 0 0 1 1 1 1 2 2 3 0 4 1 Output 1 1 Input 3 0 0 1 1 0 1 1 2 1 0 2 1 Output 1 1 Input 4 0 0 5 5 0 0 4 4 1 1 4 4 1 1 4 4 Output 1 1 Input 5 0 0 10 8 1 2 6 7 2 3 5 6 3 4 4 5 8 1 9 2 Output 3 4 Note The picture below shows the rectangles in the first and second samples. The possible answers are highlighted. The picture below shows the rectangles in the third and fourth samples. 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()) ox=[] cx=[] l3=[] oy=[] cy=[] for i in range(n): r,s,a,b=map(int,raw_input().strip().split()) l3.append([r,s,a,b]) ox.append(r) oy.append(s) cx.append(a) cy.append(b) ox.sort() cx.sort() oy.sort() cy.sort() e1=ox[-1] e2=cx[0] e3=oy[-1] e4=cy[0] for i in l3: a1=i[0] a2=i[1] a3=i[2] a4=i[3] if a1==e1: w=ox[-2] else: w=ox[-1] if a2==e3: y=oy[-2] else: y=oy[-1] if a3==e2: x=cx[1] else: x=cx[0] if a4==e4: z=cy[1] else: z=cy[0] if(w<=x and y<=z): print w,y exit(0) ``` 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 bootcamp import Basebootcamp class Crectanglesbootcamp(Basebootcamp): def __init__(self, min_n=2, max_n=10, coord_range=(-100, 100)): self.min_n = min_n self.max_n = max_n self.coord_range = coord_range # 保证公共点生成在中间区域,确保有空间生成不包含的矩形 self.safe_coord_range = (coord_range[0] + 10, coord_range[1] - 10) def case_generator(self): """生成保证至少有n-1个矩形交于一点的案例""" n = random.randint(self.min_n, self.max_n) # 生成公共点(确保不在边界附近) x = random.randint(*self.safe_coord_range) y = random.randint(*self.safe_coord_range) rectangles = [] # 生成前n-1个必然包含公共点的矩形 for _ in range(n-1): x1 = random.randint(self.coord_range[0], x) x2 = random.randint(x, self.coord_range[1]) x1, x2 = sorted([x1, x2]) # 确保公共点在矩形边界内 x1 = min(x1, x) x2 = max(x2, x) y1 = random.randint(self.coord_range[0], y) y2 = random.randint(y, self.coord_range[1]) y1, y2 = sorted([y1, y2]) y1 = min(y1, y) y2 = max(y2, y) rectangles.append([x1, y1, x2, y2]) # 生成第n个矩形(可能包含或不包含公共点) if random.choice([True, False]): # 包含公共点的正常矩形 x1 = random.randint(self.coord_range[0], x) x2 = random.randint(x, self.coord_range[1]) x1, x2 = sorted([x1, x2]) x1 = min(x1, x) x2 = max(x2, x) y1 = random.randint(self.coord_range[0], y) y2 = random.randint(y, self.coord_range[1]) y1, y2 = sorted([y1, y2]) y1 = min(y1, y) y2 = max(y2, y) else: # 不包含公共点的矩形(确保严格不包含) axis = random.choice(['x', 'y']) # 确保生成有效范围 if axis == 'x': # x轴方向不包含 direction = random.choice(['left', 'right']) if direction == 'left': x_max = x - 1 x1 = random.randint(self.coord_range[0], x_max-1) x2 = random.randint(x1+1, x_max) else: x_min = x + 1 x1 = random.randint(x_min, self.coord_range[1]-1) x2 = random.randint(x1+1, self.coord_range[1]) # y轴随机生成 y1 = random.randint(self.coord_range[0], self.coord_range[1]-1) y2 = random.randint(y1+1, self.coord_range[1]) else: # y轴方向不包含 direction = random.choice(['below', 'above']) if direction == 'below': y_max = y - 1 y1 = random.randint(self.coord_range[0], y_max-1) y2 = random.randint(y1+1, y_max) else: y_min = y + 1 y1 = random.randint(y_min, self.coord_range[1]-1) y2 = random.randint(y1+1, self.coord_range[1]) # x轴随机生成 x1 = random.randint(self.coord_range[0], self.coord_range[1]-1) x2 = random.randint(x1+1, self.coord_range[1]) # 二次验证不包含 assert not (x1 <= x <= x2 and y1 <= y <= y2), "生成错误:矩形包含公共点" rectangles.append([x1, y1, x2, y2]) return {'n': n, 'rectangles': rectangles} @staticmethod def prompt_func(question_case) -> str: n = question_case['n'] rects = question_case['rectangles'] problem = f"""给定平面上的{n}个矩形,其中至少{n-1}个有共同点。找到任意属于至少{n-1}个矩形的整数坐标点。 输入格式: 第一行:{n} 接下来{n}行,每行四个整数:x1 y1 x2 y2 具体输入: {n} """ + '\n'.join(' '.join(map(str, r)) for r in rects) + """ 输出要求: 两个整数x y,用空格分隔,放置在[answer]标签内 示例答案: [answer]42 314[/answer]""" return problem @staticmethod def extract_output(output): # 匹配最后一个出现的答案 matches = re.findall(r'\[answer\](.*?)\[\/answer\]', output, re.DOTALL) if not matches: return None last_answer = matches[-1].strip() try: # 允许多个空格分隔 x, y = map(int, re.split(r'\s+', last_answer)) return (x, y) except (ValueError, IndexError): return None @classmethod def _verify_correction(cls, solution, identity): x, y = solution count = 0 for rect in identity['rectangles']: x1, y1, x2, y2 = rect if x1 <= x <= x2 and y1 <= y <= y2: count += 1 return count >= (identity['n'] - 1) # 测试代码 if __name__ == "__main__": bootcamp = Crectanglesbootcamp() for _ in range(3): case = bootcamp.case_generator() print(f"\n生成的案例:n={case['n']}") for r in case['rectangles']: print(f"矩形:{r}") print(f"正确答案应为包含至少{case['n']-1}个矩形的点,如({bootcamp.safe_coord_range[0]}, {bootcamp.safe_coord_range[1]})")