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  1. from itertools import combinations
  2. import time
  3. import threading
  4. from collections import defaultdict
  5. import math
  6. from multiprocessing import Pool
  7.  
  8. # 配置参数(优化阈值)
  9. TARGET = 30678 # 目标值
  10. BASE_VALUES = [36.5, 41.5, 59, 68.5, 74, 91.5] # 基础系数列表
  11. FLUCTUATION = 1.0 # 系数波动范围
  12. MAX_SOLUTIONS = 3 # 每个组合的最大解数量
  13. SOLVER_TIMEOUT = 180 # 求解超时时间(秒)
  14. THREE_VAR_THRESHOLD = 259000 # 使用三个变量的阈值
  15. PRODUCT_RANGE_THRESHOLD = 129000 # 乘积范围限制阈值
  16. HIGH_TARGET_THRESHOLD = 259000 # 更高目标值阈值
  17. SHOW_PROGRESS = True # 是否显示进度
  18. MAX_SOLUTIONS_PER_COMB = 100 # 每个组合的最大解数量,用于提前终止
  19. USE_MULTIPROCESSING = True # 是否使用多进程加速
  20.  
  21. def is_valid_product(p):
  22. """确保单个乘积不超过129000"""
  23. return p <= 129000 # 严格限制所有乘积不超过129000
  24.  
  25. def find_single_variable_solutions(values):
  26. """查找单个数的解(a*x = TARGET)"""
  27. solutions = []
  28. for a in values:
  29. quotient = TARGET / a
  30. if quotient != int(quotient):
  31. continue
  32. x = int(quotient)
  33. if 1 <= x <= 10000 and is_valid_product(a * x):
  34. solutions.append((a, x))
  35. if len(solutions) >= MAX_SOLUTIONS:
  36. break
  37. return solutions
  38.  
  39. def find_two_variable_solutions(values):
  40. """优化的双变量求解算法,确保每个乘积不超过129000"""
  41. solutions = defaultdict(list)
  42. for i, a in enumerate(values):
  43. for b in values[i:]:
  44. seen_xy = set()
  45. # 调整x的最大值,确保a*x不超过129000
  46. max_x = min(math.floor((TARGET - b) / a), math.floor(129000 / a))
  47. min_x = max(1, math.ceil((TARGET - b * 10000) / a))
  48.  
  49. if max_x < min_x:
  50. continue
  51.  
  52. x_count = max_x - min_x + 1
  53. x_step = max(1, x_count // 1000)
  54.  
  55. for x in range(min_x, max_x + 1, x_step):
  56. ax = a * x
  57. if ax > 129000: # 额外检查确保不超过129000
  58. continue
  59.  
  60. remainder = TARGET - ax
  61.  
  62. if remainder < b:
  63. break
  64.  
  65. if remainder > b * 10000:
  66. continue
  67.  
  68. if remainder % b == 0:
  69. y = remainder // b
  70. by = b * y
  71. if 1 <= y <= 10000 and by <= 129000: # 确保b*y也不超过129000
  72. xy_pair = (x, y) if a <= b else (y, x)
  73. if xy_pair not in seen_xy:
  74. seen_xy.add(xy_pair)
  75. solutions[(a, b)].append((a, x, b, y))
  76. if len(solutions[(a, b)]) >= MAX_SOLUTIONS_PER_COMB:
  77. break
  78. return solutions
  79.  
  80. def process_three_var_combination(args):
  81. """处理三变量组合的辅助函数,用于并行计算"""
  82. a, b, c, value_ranges, target = args
  83. solutions = []
  84. seen_xyz = set()
  85.  
  86. min_x, max_x = value_ranges[a]
  87. x_count = max_x - min_x + 1
  88. x_step = max(1, x_count // 1000)
  89.  
  90. for x in range(min_x, max_x + 1, x_step):
  91. ax = a * x
  92. if not is_valid_product(ax):
  93. continue
  94.  
  95. remainder1 = target - ax
  96. if remainder1 < 0:
  97. break
  98.  
  99. max_y = math.floor((remainder1 - c) / b)
  100. min_y = max(1, math.ceil((remainder1 - c * 10000) / b))
  101.  
  102. if max_y < min_y:
  103. continue
  104.  
  105. y_count = max_y - min_y + 1
  106. y_step = max(1, y_count // 100)
  107.  
  108. for y in range(min_y, max_y + 1, y_step):
  109. by = b * y
  110. if not is_valid_product(by):
  111. continue
  112.  
  113. remainder2 = remainder1 - by
  114. if remainder2 < 0:
  115. break
  116.  
  117. if remainder2 > c * 10000:
  118. continue
  119.  
  120. if remainder2 % c == 0:
  121. z = remainder2 // c
  122. if 1 <= z <= 10000 and is_valid_product(c * z):
  123. xyz_tuple = tuple(sorted([x, y, z]))
  124. if xyz_tuple not in seen_xyz:
  125. seen_xyz.add(xyz_tuple)
  126. solutions.append((a, x, b, y, c, z))
  127. if len(solutions) >= MAX_SOLUTIONS_PER_COMB:
  128. return solutions
  129.  
  130. return solutions
  131.  
  132. def find_three_variable_solutions(values):
  133. """优化的三变量求解算法,确保每个乘积不超过129000"""
  134. solutions = defaultdict(list)
  135. sorted_values = sorted(values)
  136.  
  137. # 预计算每个系数的有效范围,确保每个乘积不超过129000
  138. value_ranges = {}
  139. for a in sorted_values:
  140. min_x = max(1, math.ceil(1 / a)) # 最小为1
  141. max_x = min(10000, math.floor(129000 / a)) # 确保a*x <= 129000
  142. value_ranges[a] = (min_x, max_x)
  143.  
  144. combinations_list = []
  145. for i, a in enumerate(sorted_values):
  146. for j in range(i + 1, len(sorted_values)):
  147. b = sorted_values[j]
  148. for k in range(j + 1, len(sorted_values)):
  149. c = sorted_values[k]
  150. combinations_list.append((a, b, c, value_ranges, TARGET))
  151.  
  152. if USE_MULTIPROCESSING:
  153. with Pool() as pool:
  154. results = pool.map(process_three_var_combination, combinations_list)
  155.  
  156. for i, (a, b, c, _, _) in enumerate(combinations_list):
  157. if results[i]:
  158. solutions[(a, b, c)] = results[i]
  159. else:
  160. total_combinations = len(combinations_list)
  161. for i, (a, b, c, _, _) in enumerate(combinations_list):
  162. res = process_three_var_combination((a, b, c, value_ranges, TARGET))
  163. if res:
  164. solutions[(a, b, c)] = res
  165.  
  166. if SHOW_PROGRESS and i % 10 == 0:
  167. print(f"\r三变量组合进度: {i}/{total_combinations} 组", end='')
  168.  
  169. if SHOW_PROGRESS and not USE_MULTIPROCESSING:
  170. print(f"\r三变量组合进度: {total_combinations}/{total_combinations} 组 - 完成")
  171.  
  172. return solutions
  173.  
  174. def find_balanced_solutions(solutions, var_count, num=2):
  175. """从所有解中筛选出最平衡的解"""
  176. if var_count == 1 or not solutions:
  177. return solutions
  178.  
  179. balanced = []
  180. for sol in solutions:
  181. vars = sol[1::2] # 获取解中的变量值
  182. diff = max(vars) - min(vars) # 计算变量之间的最大差值
  183. balanced.append((diff, sol))
  184.  
  185. # 按差值排序,返回差值最小的解
  186. return [s for _, s in sorted(balanced, key=lambda x: x[0])[:num]]
  187.  
  188. def find_original_solutions(solutions, balanced_solutions, num=3):
  189. """从剩余解中获取原始顺序的解"""
  190. if not solutions:
  191. return []
  192.  
  193. remaining = [s for s in solutions if s not in balanced_solutions]
  194. return remaining[:num]
  195.  
  196. def display_solutions(solutions_dict, var_count):
  197. """优化的解显示函数"""
  198. if not solutions_dict:
  199. return
  200.  
  201. print(f"\n找到 {len(solutions_dict)} 组{var_count}变量解:")
  202.  
  203. for i, (coeffs, pair_solutions) in enumerate(sorted(solutions_dict.items()), 1):
  204. balanced = find_balanced_solutions(pair_solutions, var_count)
  205. original = find_original_solutions(pair_solutions, balanced)
  206. all_display = balanced + original
  207.  
  208. if var_count == 1:
  209. a = coeffs
  210. print(f"\n{i}. 组合: a={a} ({len(pair_solutions)} 个有效解)")
  211. elif var_count == 2:
  212. a, b = coeffs
  213. print(f"\n{i}. 组合: a={a}, b={b} ({len(pair_solutions)} 个有效解)")
  214. else:
  215. a, b, c = coeffs
  216. print(f"\n{i}. 组合: a={a}, b={b}, c={c} ({len(pair_solutions)} 个有效解)")
  217.  
  218. for j, sol in enumerate(all_display, 1):
  219. tag = "[平衡解]" if j <= len(balanced) else "[原始解]"
  220.  
  221. if var_count == 1:
  222. a, x = sol
  223. print(f" {j}. x={x}, a*x={a*x:.1f}, 总和={a*x:.1f} {tag}")
  224. elif var_count == 2:
  225. a, x, b, y = sol
  226. print(f" {j}. x={x}, y={y}, a*x={a*x:.1f}, b*y={b*y:.1f}, 总和={a*x + b*y:.1f} {tag}")
  227. else:
  228. a, x, b, y, c, z = sol
  229. print(f" {j}. x={x}, y={y}, z={z}, "
  230. f"a*x={a*x:.1f}, b*y={b*y:.1f}, c*z={c*z:.1f}, "
  231. f"总和={a*x + b*y + c*z:.1f} {tag}")
  232.  
  233. def run_with_timeout(func, args=(), kwargs=None, timeout=SOLVER_TIMEOUT):
  234. """运行函数并设置超时限制"""
  235. if kwargs is None:
  236. kwargs = {}
  237.  
  238. result = []
  239. error = []
  240.  
  241. def wrapper():
  242. try:
  243. result.append(func(*args, **kwargs))
  244. except Exception as e:
  245. error.append(e)
  246.  
  247. thread = threading.Thread(target=wrapper)
  248. thread.daemon = True
  249. thread.start()
  250. thread.join(timeout)
  251.  
  252. if thread.is_alive():
  253. print(f"警告: {func.__name__} 超时({timeout}秒),跳过此方法")
  254. return None
  255.  
  256. if error:
  257. raise error[0]
  258.  
  259. return result[0]
  260.  
  261. def main():
  262. print(f"目标值: {TARGET}")
  263.  
  264. # 生成波动后的系数
  265. FLUCTUATED_VALUES = [round(v - FLUCTUATION, 1) for v in BASE_VALUES]
  266.  
  267. # 尝试基础系数
  268. print(f"\n==== 尝试基础系数 ====")
  269.  
  270. # 目标值255966 > 259000不成立,会按顺序尝试单、双、三变量解
  271. base_solutions = {
  272. 'single': run_with_timeout(find_single_variable_solutions, args=(BASE_VALUES,)),
  273. 'two': run_with_timeout(find_two_variable_solutions, args=(BASE_VALUES,)),
  274. 'three': []
  275. }
  276.  
  277. has_solution = False
  278.  
  279. # 显示单变量解
  280. if base_solutions['single']:
  281. has_solution = True
  282. display_solutions({a: [sol] for a, sol in zip(BASE_VALUES, base_solutions['single']) if sol}, 1)
  283.  
  284. # 显示双变量解
  285. if base_solutions['two'] and len(base_solutions['two']) > 0:
  286. has_solution = True
  287. display_solutions(base_solutions['two'], 2)
  288.  
  289. # 单变量和双变量都无解时,尝试三变量解
  290. if not has_solution:
  291. print(f"\n==== 单变量和双变量无解,尝试三变量解 ====")
  292. base_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,))
  293.  
  294. if base_solutions['three'] and len(base_solutions['three']) > 0:
  295. has_solution = True
  296. display_solutions(base_solutions['three'], 3)
  297.  
  298. if has_solution:
  299. print(f"\n使用基础系数列表,共找到有效解")
  300. return
  301.  
  302. # 如果基础系数没有找到解,尝试波动系数
  303. print(f"\n==== 尝试波动系数 ====")
  304.  
  305. fluctuated_solutions = {
  306. 'single': run_with_timeout(find_single_variable_solutions, args=(FLUCTUATED_VALUES,)),
  307. 'two': run_with_timeout(find_two_variable_solutions, args=(FLUCTUATED_VALUES,)),
  308. 'three': []
  309. }
  310.  
  311. has_solution = False
  312.  
  313. # 显示单变量解
  314. if fluctuated_solutions['single']:
  315. has_solution = True
  316. display_solutions({a: [sol] for a, sol in zip(FLUCTUATED_VALUES, fluctuated_solutions['single']) if sol}, 1)
  317.  
  318. # 显示双变量解
  319. if fluctuated_solutions['two'] and len(fluctuated_solutions['two']) > 0:
  320. has_solution = True
  321. display_solutions(fluctuated_solutions['two'], 2)
  322.  
  323. # 单变量和双变量都无解时,尝试三变量解
  324. if not has_solution:
  325. print(f"\n==== 单变量和双变量无解,尝试三变量解 ====")
  326. fluctuated_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,))
  327.  
  328. if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0:
  329. has_solution = True
  330. display_solutions(fluctuated_solutions['three'], 3)
  331.  
  332. if has_solution:
  333. print(f"\n使用波动系数列表,共找到有效解")
  334. return
  335.  
  336. # 如果所有系数集都没有找到解
  337. print("\n没有找到符合条件的解,即使使用波动后的系数列表。")
  338.  
  339. if __name__ == "__main__":
  340. start_time = time.time()
  341. main()
  342. print(f"\n总耗时: {time.time() - start_time:.2f}秒")
Success #stdin #stdout 0.06s 11596KB
stdin
Standard input is empty
stdout
目标值: 30678

==== 尝试基础系数 ====

找到 15 组2变量解:

1. 组合: a=36.5, b=41.5 (10 个有效解)
  1. x=355, y=427.0, a*x=12957.5, b*y=17720.5, 总和=30678.0 [平衡解]
  2. x=438, y=354.0, a*x=15987.0, b*y=14691.0, 总和=30678.0 [平衡解]
  3. x=23, y=719.0, a*x=839.5, b*y=29838.5, 总和=30678.0 [原始解]
  4. x=106, y=646.0, a*x=3869.0, b*y=26809.0, 总和=30678.0 [原始解]
  5. x=189, y=573.0, a*x=6898.5, b*y=23779.5, 总和=30678.0 [原始解]

2. 组合: a=36.5, b=59 (7 个有效解)
  1. x=320, y=322.0, a*x=11680.0, b*y=18998.0, 总和=30678.0 [平衡解]
  2. x=438, y=249.0, a*x=15987.0, b*y=14691.0, 总和=30678.0 [平衡解]
  3. x=84, y=468.0, a*x=3066.0, b*y=27612.0, 总和=30678.0 [原始解]
  4. x=202, y=395.0, a*x=7373.0, b*y=23305.0, 总和=30678.0 [原始解]
  5. x=556, y=176.0, a*x=20294.0, b*y=10384.0, 总和=30678.0 [原始解]

3. 组合: a=36.5, b=68.5 (6 个有效解)
  1. x=300, y=288.0, a*x=10950.0, b*y=19728.0, 总和=30678.0 [平衡解]
  2. x=163, y=361.0, a*x=5949.5, b*y=24728.5, 总和=30678.0 [平衡解]
  3. x=26, y=434.0, a*x=949.0, b*y=29729.0, 总和=30678.0 [原始解]
  4. x=437, y=215.0, a*x=15950.5, b*y=14727.5, 总和=30678.0 [原始解]
  5. x=574, y=142.0, a*x=20951.0, b*y=9727.0, 总和=30678.0 [原始解]

4. 组合: a=36.5, b=74 (6 个有效解)
  1. x=212, y=310.0, a*x=7738.0, b*y=22940.0, 总和=30678.0 [平衡解]
  2. x=360, y=237.0, a*x=13140.0, b*y=17538.0, 总和=30678.0 [平衡解]
  3. x=64, y=383.0, a*x=2336.0, b*y=28342.0, 总和=30678.0 [原始解]
  4. x=508, y=164.0, a*x=18542.0, b*y=12136.0, 总和=30678.0 [原始解]
  5. x=656, y=91.0, a*x=23944.0, b*y=6734.0, 总和=30678.0 [原始解]

5. 组合: a=36.5, b=91.5 (4 个有效解)
  1. x=294, y=218.0, a*x=10731.0, b*y=19947.0, 总和=30678.0 [平衡解]
  2. x=111, y=291.0, a*x=4051.5, b*y=26626.5, 总和=30678.0 [平衡解]
  3. x=477, y=145.0, a*x=17410.5, b*y=13267.5, 总和=30678.0 [原始解]
  4. x=660, y=72.0, a*x=24090.0, b*y=6588.0, 总和=30678.0 [原始解]

6. 组合: a=41.5, b=59 (6 个有效解)
  1. x=344, y=278.0, a*x=14276.0, b*y=16402.0, 总和=30678.0 [平衡解]
  2. x=226, y=361.0, a*x=9379.0, b*y=21299.0, 总和=30678.0 [平衡解]
  3. x=108, y=444.0, a*x=4482.0, b*y=26196.0, 总和=30678.0 [原始解]
  4. x=462, y=195.0, a*x=19173.0, b*y=11505.0, 总和=30678.0 [原始解]
  5. x=580, y=112.0, a*x=24070.0, b*y=6608.0, 总和=30678.0 [原始解]

7. 组合: a=41.5, b=68.5 (5 个有效解)
  1. x=249, y=297.0, a*x=10333.5, b*y=20344.5, 总和=30678.0 [平衡解]
  2. x=386, y=214.0, a*x=16019.0, b*y=14659.0, 总和=30678.0 [平衡解]
  3. x=112, y=380.0, a*x=4648.0, b*y=26030.0, 总和=30678.0 [原始解]
  4. x=523, y=131.0, a*x=21704.5, b*y=8973.5, 总和=30678.0 [原始解]
  5. x=660, y=48.0, a*x=27390.0, b*y=3288.0, 总和=30678.0 [原始解]

8. 组合: a=41.5, b=74 (5 个有效解)
  1. x=256, y=271.0, a*x=10624.0, b*y=20054.0, 总和=30678.0 [平衡解]
  2. x=404, y=188.0, a*x=16766.0, b*y=13912.0, 总和=30678.0 [平衡解]
  3. x=108, y=354.0, a*x=4482.0, b*y=26196.0, 总和=30678.0 [原始解]
  4. x=552, y=105.0, a*x=22908.0, b*y=7770.0, 总和=30678.0 [原始解]
  5. x=700, y=22.0, a*x=29050.0, b*y=1628.0, 总和=30678.0 [原始解]

9. 组合: a=41.5, b=91.5 (4 个有效解)
  1. x=177, y=255.0, a*x=7345.5, b*y=23332.5, 总和=30678.0 [平衡解]
  2. x=360, y=172.0, a*x=14940.0, b*y=15738.0, 总和=30678.0 [平衡解]
  3. x=543, y=89.0, a*x=22534.5, b*y=8143.5, 总和=30678.0 [原始解]
  4. x=726, y=6.0, a*x=30129.0, b*y=549.0, 总和=30678.0 [原始解]

10. 组合: a=59, b=68.5 (4 个有效解)
  1. x=239, y=242.0, a*x=14101.0, b*y=16577.0, 总和=30678.0 [平衡解]
  2. x=376, y=124.0, a*x=22184.0, b*y=8494.0, 总和=30678.0 [平衡解]
  3. x=102, y=360.0, a*x=6018.0, b*y=24660.0, 总和=30678.0 [原始解]
  4. x=513, y=6.0, a*x=30267.0, b*y=411.0, 总和=30678.0 [原始解]

11. 组合: a=59, b=74 (7 个有效解)
  1. x=234, y=228, a*x=13806.0, b*y=16872.0, 总和=30678.0 [平衡解]
  2. x=160, y=287, a*x=9440.0, b*y=21238.0, 总和=30678.0 [平衡解]
  3. x=12, y=405, a*x=708.0, b*y=29970.0, 总和=30678.0 [原始解]
  4. x=86, y=346, a*x=5074.0, b*y=25604.0, 总和=30678.0 [原始解]
  5. x=308, y=169, a*x=18172.0, b*y=12506.0, 总和=30678.0 [原始解]

12. 组合: a=59, b=91.5 (3 个有效解)
  1. x=216, y=196.0, a*x=12744.0, b*y=17934.0, 总和=30678.0 [平衡解]
  2. x=33, y=314.0, a*x=1947.0, b*y=28731.0, 总和=30678.0 [平衡解]
  3. x=399, y=78.0, a*x=23541.0, b*y=7137.0, 总和=30678.0 [原始解]

13. 组合: a=68.5, b=74 (3 个有效解)
  1. x=248, y=185.0, a*x=16988.0, b*y=13690.0, 总和=30678.0 [平衡解]
  2. x=100, y=322.0, a*x=6850.0, b*y=23828.0, 总和=30678.0 [平衡解]
  3. x=396, y=48.0, a*x=27126.0, b*y=3552.0, 总和=30678.0 [原始解]

14. 组合: a=68.5, b=91.5 (2 个有效解)
  1. x=162, y=214.0, a*x=11097.0, b*y=19581.0, 总和=30678.0 [平衡解]
  2. x=345, y=77.0, a*x=23632.5, b*y=7045.5, 总和=30678.0 [平衡解]

15. 组合: a=74, b=91.5 (3 个有效解)
  1. x=192, y=180.0, a*x=14208.0, b*y=16470.0, 总和=30678.0 [平衡解]
  2. x=9, y=328.0, a*x=666.0, b*y=30012.0, 总和=30678.0 [平衡解]
  3. x=375, y=32.0, a*x=27750.0, b*y=2928.0, 总和=30678.0 [原始解]

使用基础系数列表,共找到有效解

总耗时: 0.00秒