init-commit

internbootcamp/bootcamp/bsetofpoints/bsetofpoints.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())
+
+if m==3 and n >= 5:
+
+	print -1
+
+else:
+
+	for i in range(m):
+
+		print i,i*i
+
+	for i in range(n-m):
+
+		print i*i+10001,i
+
+
+
+# Made By Mostafa_Khaled
+```
+
+
+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 Bsetofpointsbootcamp(Basebootcamp):
+    def __init__(self, **params):
+        self.m_min = params.get('m_min', 3)
+        self.m_max = params.get('m_max', 100)
+        self.max_n_multiplier = params.get('max_n_multiplier', 2)
+    
+    def case_generator(self):
+        m = random.randint(self.m_min, self.m_max)
+        max_n = m * self.max_n_multiplier
+        min_n = m
+        n = random.randint(min_n, max_n)
+        
+        solution = None
+        if m == 3 and n >= 5:
+            solution = -1
+        else:
+            solution = []
+            # Generate points according to the reference solution structure
+            for i in range(m):
+                solution.append((i, i * i))
+            for i in range(n - m):
+                x = i * i + 10001
+                y = i
+                solution.append((x, y))
+        
+        return {
+            'n': n,
+            'm': m,
+            'solution': solution  # Stored for potential debugging, not used in verification
+        }
+    
+    @staticmethod
+    def prompt_func(question_case) -> str:
+        n = question_case['n']
+        m = question_case['m']
+        problem_desc = f"""You are a mathematician working on the convexity of planar point sets. Your task is to construct a set of {n} points such that the convexity of the set is exactly {m}, and no three points lie on a straight line. If it's impossible, output "-1". Otherwise, output the coordinates of the points, each with absolute values not exceeding 1e8.
+
+Convexity is defined as the size of the largest subset of points that form a convex polygon.
+
+Input: n = {n}, m = {m}
+
+Please provide your answer within [answer] and [/answer] tags. For example:
+[answer]
+0 0
+1 1
+2 4
+1 2
+[/answer]
+"""
+        return problem_desc
+    
+    @staticmethod
+    def extract_output(output):
+        pattern = r'\[answer\](.*?)\[/answer\]'
+        matches = re.findall(pattern, output, re.DOTALL)
+        if not matches:
+            return None
+        content = matches[-1].strip()
+        if content.strip() == '-1':
+            return -1
+        points = []
+        lines = content.split('\n')
+        for line in lines:
+            line = line.strip()
+            if not line:
+                continue
+            parts = line.split()
+            if len(parts) != 2:
+                continue
+            try:
+                x = int(parts[0])
+                y = int(parts[1])
+                points.append((x, y))
+            except ValueError:
+                continue
+        return points if points else None
+    
+    @staticmethod
+    def has_collinear_triples(points):
+        n = len(points)
+        for i in range(n):
+            for j in range(i + 1, n):
+                for k in range(j + 1, n):
+                    p1 = points[i]
+                    p2 = points[j]
+                    p3 = points[k]
+                    # Calculate the area of the triangle formed by the three points
+                    area = (p2[0] - p1[0]) * (p3[1] - p1[1]) - (p2[1] - p1[1]) * (p3[0] - p1[0])
+                    if area == 0:
+                        return True
+        return False
+    
+    @staticmethod
+    def compute_convex_hull(points):
+        if len(points) <= 1:
+            return points.copy()
+        
+        # Sort the points lexographically
+        points = sorted(points)
+        lower = []
+        for p in points:
+            while len(lower) >= 2 and (lower[-1][0] - lower[-2][0]) * (p[1] - lower[-2][1]) - (lower[-1][1] - lower[-2][1]) * (p[0] - lower[-2][0]) <= 0:
+                lower.pop()
+            lower.append(p)
+        upper = []
+        for p in reversed(points):
+            while len(upper) >= 2 and (upper[-1][0] - upper[-2][0]) * (p[1] - upper[-2][1]) - (upper[-1][1] - upper[-2][1]) * (p[0] - upper[-2][0]) <= 0:
+                upper.pop()
+            upper.append(p)
+        # Remove duplicates
+        convex_hull = lower[:-1] + upper[:-1]
+        return convex_hull
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        n = identity['n']
+        m = identity['m']
+        
+        # Handle the case where solution is -1
+        if solution == -1:
+            return m == 3 and n >= 5
+        
+        # Check if solution is a valid list of points
+        if not isinstance(solution, list) or len(solution) != n:
+            return False
+        
+        # Validate each point's format and coordinates
+        for point in solution:
+            if len(point) != 2:
+                return False
+            x, y = point
+            if abs(x) > 10**8 or abs(y) > 10**8:
+                return False
+        
+        # Check for any collinear triplets
+        if cls.has_collinear_triples(solution):
+            return False
+        
+        # Compute convex hull and check its size
+        convex_hull = cls.compute_convex_hull(solution)
+        convexity = len(convex_hull)
+        return convexity == m