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169 lines
4.5 KiB
Python
Executable file
169 lines
4.5 KiB
Python
Executable file
"""#
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### 谜题描述
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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:
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1. The coordinates of each point in the set are integers.
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2. For any two points from the set, the distance between them is a non-integer.
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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.
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Input
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The single line contains two space-separated integers n and m (1 ≤ n, m ≤ 100).
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Output
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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.
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If there are several optimal solutions, you may print any of them.
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Examples
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Input
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2 2
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Output
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3
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0 1
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1 2
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2 0
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Input
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4 3
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Output
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4
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0 3
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2 1
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3 0
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4 2
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Note
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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.
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Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
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```python
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n , m = map(int , raw_input().split())
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print min(n , m) + 1
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if n <= m:
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for i in range(n):
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print i , n - i
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print n , 0
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else:
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for i in range(m):
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print m - i , i
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print 0 , m
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```
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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。
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"""
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from bootcamp import Basebootcamp
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import math
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import random
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import re
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from bootcamp import Basebootcamp
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class Cbeautifulsetsofpointsbootcamp(Basebootcamp):
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def __init__(self, max_n=100, max_m=100, min_n=1, min_m=1):
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self.max_n = max_n
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self.max_m = max_m
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self.min_n = min_n
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self.min_m = min_m
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def case_generator(self):
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n = random.randint(self.min_n, self.max_n)
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m = random.randint(self.min_m, self.max_m)
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return {'n': n, 'm': m}
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@staticmethod
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def prompt_func(question_case) -> str:
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n = question_case['n']
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m = question_case['m']
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prompt = f"""给定n={n}, m={m}，请构造最大美丽点集。规则：
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1. 所有点坐标为整数且满足0≤x≤{n}、0≤y≤{m}、x+y>0
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2. 任意两点距离必须为非整数
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输出格式要求：
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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：
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[answer]
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3
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0 1
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1 2
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2 0
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[/answer]
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请解决当前问题："""
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return prompt
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@staticmethod
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def extract_output(output):
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matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
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if not matches:
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return None
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last_match = matches[-1].strip()
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lines = [line.strip() for line in last_match.split('\n') if line.strip()]
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if len(lines) < 1:
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return None
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try:
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k = int(lines[0])
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if len(lines) != k + 1:
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return None
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except ValueError:
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return None
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points = []
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for line in lines[1:]:
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coords = re.split(r'\s+', line.strip())
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if len(coords) != 2:
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return None
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try:
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x, y = map(int, coords)
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points.append((x, y))
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except ValueError:
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return None
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return points
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@classmethod
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def _verify_correction(cls, solution, identity):
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n = identity['n']
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m = identity['m']
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# 基本参数检查
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if not solution or len(solution) != min(n, m) + 1:
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return False
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# 坐标有效性检查
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points_set = set()
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for x, y in solution:
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if (x, y) in points_set:
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return False
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if x < 0 or x > n or y < 0 or y > m or (x + y <= 0):
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return False
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points_set.add((x, y))
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# 距离检查
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for i in range(len(solution)):
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for j in range(i+1, len(solution)):
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dx = solution[i][0] - solution[j][0]
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dy = solution[i][1] - solution[j][1]
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if math.isqrt(dx**2 + dy**2) ** 2 == dx**2 + dy**2:
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return False
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return True
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