init-commit

internbootcamp/bootcamp/evectors/evectors.py

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+"""# 
+
+### 谜题描述
+At a geometry lesson Gerald was given a task: to get vector B out of vector A. Besides, the teacher permitted him to perform the following operations with vector А:
+
+  * Turn the vector by 90 degrees clockwise.
+  * Add to the vector a certain vector C.
+
+
+
+Operations could be performed in any order any number of times.
+
+Can Gerald cope with the task?
+
+Input
+
+The first line contains integers x1 и y1 — the coordinates of the vector A ( - 108 ≤ x1, y1 ≤ 108). The second and the third line contain in the similar manner vectors B and C (their coordinates are integers; their absolute value does not exceed 108).
+
+Output
+
+Print \"YES\" (without the quotes) if it is possible to get vector B using the given operations. Otherwise print \"NO\" (without the quotes).
+
+Examples
+
+Input
+
+0 0
+1 1
+0 1
+
+
+Output
+
+YES
+
+
+Input
+
+0 0
+1 1
+1 1
+
+
+Output
+
+YES
+
+
+Input
+
+0 0
+1 1
+2 2
+
+
+Output
+
+NO
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+#include <bits/stdc++.h>
+using namespace std;
+int p, q;
+int x, y;
+bool possible(int x, int y) {
+  long long bm = 1LL * p * p + 1LL * q * q;
+  if (bm == 0) {
+    if ((x || y))
+      return false;
+    else
+      return true;
+  } else if ((((-1LL * p * x - 1LL * q * y) % bm) ||
+              ((-1LL * q * x + 1LL * p * y) % bm)))
+    return false;
+  else
+    return true;
+}
+int main() {
+  bool ans = false;
+  int ax, ay;
+  cin >> ax >> ay >> x >> y >> p >> q;
+  int i;
+  int tmp;
+  for (i = 0; i < 4; ++i) {
+    x -= ax;
+    y -= ay;
+    ans = ans || (possible(x, y) || possible(-y, x));
+    x += ax;
+    y += ay;
+    tmp = ax;
+    ax = ay;
+    ay = -tmp;
+  }
+  if (ans)
+    cout << \"YES\";
+  else
+    cout << \"NO\";
+  return 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 typing import Dict, List
+
+def rotate_clockwise(x: int, y: int, times: int) -> (int, int):
+    """顺时针旋转向量，times为旋转次数"""
+    for _ in range(times % 4):
+        x, y = y, -x
+    return x, y
+
+def possible(dx: int, dy: int, p: int, q: int) -> bool:
+    """验证差分向量是否符合线性组合条件"""
+    bm = p**2 + q**2
+    if bm == 0:
+        return dx == 0 and dy == 0
+    return ((-p*dx - q*dy) % bm == 0) and ((-q*dx + p*dy) % bm == 0)
+
+def is_possible(ax: int, ay: int, bx: int, by: int, p: int, q: int) -> bool:
+    """验证所有旋转可能性"""
+    for rot in range(4):
+        rx, ry = rotate_clockwise(ax, ay, rot)
+        dx, dy = bx - rx, by - ry
+        if possible(dx, dy, p, q) or possible(-dy, dx, p, q):
+            return True
+    return False
+
+class Evectorsbootcamp(Basebootcamp):
+    def __init__(self, max_coordinate: int = 10**3):
+        self.max_coord = max_coordinate
+
+    def _gen_solvable_case(self) -> Dict:
+        """生成保证可解的案例"""
+        ax = random.randint(-self.max_coord, self.max_coord)
+        ay = random.randint(-self.max_coord, self.max_coord)
+        p = random.randint(-self.max_coord, self.max_coord)
+        q = random.randint(-self.max_coord, self.max_coord)
+        
+        # 随机选择旋转次数和系数
+        rot = random.randint(0, 3)
+        a = random.randint(-5, 5)
+        b = random.randint(-5, 5)
+        
+        # 构造合法B向量
+        rx, ry = rotate_clockwise(ax, ay, rot)
+        bx = rx + a*p + b*q
+        by = ry + a*q - b*p
+        return {'A': [ax, ay], 'B': [bx, by], 'C': [p, q]}
+
+    def _gen_unsolvable_zeroC(self) -> Dict:
+        """生成C=0时的不可解案例"""
+        ax = random.randint(-self.max_coord, self.max_coord)
+        ay = random.randint(-self.max_coord, self.max_coord)
+        p = q = 0
+        
+        # 寻找不在旋转对称点上的B
+        while True:
+            bx = random.randint(-self.max_coord, self.max_coord)
+            by = random.randint(-self.max_coord, self.max_coord)
+            if not any((bx, by) == rotate_clockwise(ax, ay, r) for r in range(4)):
+                return {'A': [ax, ay], 'B': [bx, by], 'C': [p, q]}
+
+    def _gen_unsolvable_general(self) -> Dict:
+        """生成普通不可解案例"""
+        for _ in range(100):
+            case = self._gen_solvable_case()
+            ax, ay = case['A']
+            bx, by = case['B']
+            p, q = case['C']
+            
+            # 微调B向量破坏可解性
+            delta = random.choice([(1,0), (-1,0), (0,1), (0,-1)])
+            new_bx = bx + delta[0]
+            new_by = by + delta[1]
+            if not is_possible(ax, ay, new_bx, new_by, p, q):
+                return {'A': [ax, ay], 'B': [new_bx, new_by], 'C': [p, q]}
+        return {'A': [0,0], 'B': [1,0], 'C': [0,0]}  # 最终后备案例
+
+    def case_generator(self) -> Dict:
+        generators = [
+            self._gen_solvable_case,
+            self._gen_unsolvable_zeroC,
+            self._gen_unsolvable_general
+        ]
+        return random.choice(generators)()
+
+    @staticmethod
+    def prompt_func(case: Dict) -> str:
+        a = case['A']
+        b = case['B']
+        c = case['C']
+        return f"""给定初始向量A({a[0]}, {a[1]})，目标向量B({b[0]}, {b[1]})，操作向量C({c[0]}, {c[1]})。允许的操作：
+1. 顺时针旋转90度（次数不限）
+2. 累加向量C（次数不限）
+请判断是否可以转换，并将最终答案用[answer]标签包裹，例如：[answer]YES[/answer]"""
+
+    @staticmethod
+    def extract_output(output: str) -> str:
+        matches = re.findall(r'\[answer\]\s*(YES|NO)\s*\[/answer\]', output, re.IGNORECASE)
+        return matches[-1].upper() if matches else None
+
+    @classmethod
+    def _verify_correction(cls, solution: str, identity: Dict) -> bool:
+        ax, ay = identity['A']
+        bx, by = identity['B']
+        p, q = identity['C']
+        expected = 'YES' if is_possible(ax, ay, bx, by, p, q) else 'NO'
+        return solution.upper() == expected