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  1. import itertools
  2.  
  3. # 配置参数
  4. TARGET_VALUE = 28098  # 目标值
  5. BASE_COEFFICIENTS = [38.5, 44, 61, 70.5, 75.5, 93]  # 基础系数列表
  6. MAX_PRODUCT = 129000  # 单个系数乘积的严格上限
  7. VARIABLE_RATIO_TOLERANCE = 0.4  # 变量间比例容忍度
  8. COEFFICIENT_GROUPS = [
  9.     (70.5, 75.5, 93),  # 优先搜索的系数组合（按从小到大排序对应a,b,c）
  10.     (61, 70.5, 93),
  11.     (61, 75.5, 93),
  12.     (61, 70.5, 75.5)
  13. ]
  14.  
  15. def find_similar_solutions():
  16.     """寻找与示例解模式相似的解"""
  17.     # 搜索优先系数组合（已按从小到大排序）
  18.     for coeffs in COEFFICIENT_GROUPS:
  19.         solutions = find_three_variable_solutions(coeffs)
  20.         if solutions:
  21.             print_solutions_group(coeffs, solutions)
  22.             return
  23.  
  24.     # 扩大搜索范围，所有组合按从小到大排序
  25.     for combo in itertools.combinations(BASE_COEFFICIENTS, 3):
  26.         coeffs = sorted(combo)  # 确保系数按从小到大排序
  27.         if coeffs in COEFFICIENT_GROUPS:
  28.             continue
  29.         solutions = find_three_variable_solutions(coeffs)
  30.         if solutions:
  31.             print_solutions_group(coeffs, solutions)
  32.             return
  33.  
  34.     print("未找到符合条件的解")
  35.  
  36. def are_variables_balanced(vars):
  37.     """判断变量是否均衡分布"""
  38.     if len(vars) != 3:
  39.         return False
  40.  
  41.     a, b, c = sorted(vars)
  42.     ratio1 = a / c
  43.     ratio2 = b / c
  44.     in_range = all(500 <= v <= 2000 for v in vars)
  45.  
  46.     return ratio1 > (1 - VARIABLE_RATIO_TOLERANCE) and \
  47.            ratio2 > (1 - VARIABLE_RATIO_TOLERANCE / 2) and \
  48.            in_range
  49.  
  50. def find_three_variable_solutions(coeffs):
  51.     """寻找三变量解，系数按从小到大排序（a,b,c）"""
  52.     a, b, c = coeffs  # a:最小系数, b:中间系数, c:最大系数
  53.     solutions = []
  54.  
  55.     # 计算变量可能的范围
  56.     max_x = min(int(MAX_PRODUCT / a), 2000)
  57.     max_y = min(int(MAX_PRODUCT / b), 2000)
  58.     min_x = max(500, int((TARGET_VALUE * 0.2) / a))
  59.     min_y = max(500, int((TARGET_VALUE * 0.2) / b))
  60.  
  61.     # 减小步长以找到更多解
  62.     step = max(1, (max_x - min_x) // 300)
  63.     for x in range(min_x, max_x + 1, step):
  64.         ax = a * x
  65.         if ax > MAX_PRODUCT:
  66.             continue
  67.  
  68.         remaining_after_ax = TARGET_VALUE - ax
  69.         if remaining_after_ax <= 0:
  70.             continue
  71.  
  72.         for y in range(min_y, max_y + 1, step):
  73.             by = b * y
  74.             if by > MAX_PRODUCT:
  75.                 continue
  76.  
  77.             remaining_after_by = remaining_after_ax - by
  78.             if remaining_after_by <= 0:
  79.                 continue
  80.  
  81.             # 计算z的值（对应最大系数c）
  82.             z = remaining_after_by / c
  83.             if not z.is_integer() or not (500 <= z <= 2000):
  84.                 continue
  85.  
  86.             z = int(z)
  87.             cz = c * z
  88.             if cz > MAX_PRODUCT:
  89.                 continue
  90.  
  91.             # 检查总和
  92.             total = ax + by + cz
  93.             if abs(total - TARGET_VALUE) > 1:
  94.                 continue
  95.  
  96.             # 检查是否为平衡解
  97.             is_balanced = are_variables_balanced([x, y, z])
  98.  
  99.             solutions.append((x, y, z, ax, by, cz, total, is_balanced))
  100.  
  101.             # 找到4个解后停止
  102.             if len(solutions) >= 4:
  103.                 return solutions
  104.  
  105.     return solutions
  106.  
  107. def print_solutions_group(coeffs, solutions):
  108.     """按照指定格式打印找到的解组"""
  109.     a, b, c = coeffs  # a:最小系数, b:中间系数, c:最大系数
  110.     print(f"组合: a={a}, b={b}, c={c} ({len(solutions)} 个有效解)")
  111.  
  112.     for i, (x, y, z, ax, by, cz, total, is_balanced) in enumerate(solutions, 1):
  113.         balance_label = " [平衡解]" if is_balanced else ""
  114.  
  115.         # 按照要求的格式分行显示
  116.         print(f"  {i}. x={x}, y={y}, z={z},")
  117.         print(f"  a*x={ax}, b*y={by}, c*z={cz}, 总和={total}{balance_label}")
  118.  
  119. if __name__ == "__main__":
  120.     find_similar_solutions()
  121.  
Success #stdin #stdout 0.07s 9360KB
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未找到符合条件的解
https://ideone.com/h6xeMV
language:
Python 3 nbc (python 3.7.3)
created:
9 days ago
visibility:
public

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