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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 = 137059 # 目标值
  10. BASE_VALUES = [38.5,44,61,70.5,75.5,93] # 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 0.07s 11688KB
stdin
Standard input is empty
stdout
目标值: 137059

==== 尝试基础系数 ====

找到 13 组2变量解:

1. 组合: a=38.5, b=61 (9 个有效解)
  1. x=1402, y=1362.0, a*x=53977.0, b*y=83082.0, 总和=137059.0 [平衡解]
  2. x=1036, y=1593.0, a*x=39886.0, b*y=97173.0, 总和=137059.0 [平衡解]
  3. x=304, y=2055.0, a*x=11704.0, b*y=125355.0, 总和=137059.0 [原始解]
  4. x=670, y=1824.0, a*x=25795.0, b*y=111264.0, 总和=137059.0 [原始解]
  5. x=1768, y=1131.0, a*x=68068.0, b*y=68991.0, 总和=137059.0 [原始解]

2. 组合: a=38.5, b=70.5 (22 个有效解)
  1. x=1282, y=1244.0, a*x=49357.0, b*y=87702.0, 总和=137059.0 [平衡解]
  2. x=1141, y=1321.0, a*x=43928.5, b*y=93130.5, 总和=137059.0 [平衡解]
  3. x=295, y=1783.0, a*x=11357.5, b*y=125701.5, 总和=137059.0 [原始解]
  4. x=436, y=1706.0, a*x=16786.0, b*y=120273.0, 总和=137059.0 [原始解]
  5. x=577, y=1629.0, a*x=22214.5, b*y=114844.5, 总和=137059.0 [原始解]

3. 组合: a=38.5, b=75.5 (7 个有效解)
  1. x=1042, y=1284.0, a*x=40117.0, b*y=96942.0, 总和=137059.0 [平衡解]
  2. x=1495, y=1053.0, a*x=57557.5, b*y=79501.5, 总和=137059.0 [平衡解]
  3. x=589, y=1515.0, a*x=22676.5, b*y=114382.5, 总和=137059.0 [原始解]
  4. x=1948, y=822.0, a*x=74998.0, b*y=62061.0, 总和=137059.0 [原始解]
  5. x=2401, y=591.0, a*x=92438.5, b*y=44620.5, 总和=137059.0 [原始解]

4. 组合: a=38.5, b=93 (17 个有效解)
  1. x=1084, y=1025.0, a*x=41734.0, b*y=95325.0, 总和=137059.0 [平衡解]
  2. x=898, y=1102.0, a*x=34573.0, b*y=102486.0, 总和=137059.0 [平衡解]
  3. x=340, y=1333.0, a*x=13090.0, b*y=123969.0, 总和=137059.0 [原始解]
  4. x=526, y=1256.0, a*x=20251.0, b*y=116808.0, 总和=137059.0 [原始解]
  5. x=712, y=1179.0, a*x=27412.0, b*y=109647.0, 总和=137059.0 [原始解]

5. 组合: a=44, b=61 (23 个有效解)
  1. x=1303, y=1307, a*x=57332.0, b*y=79727.0, 总和=137059.0 [平衡解]
  2. x=1425, y=1219, a*x=62700.0, b*y=74359.0, 总和=137059.0 [平衡解]
  3. x=205, y=2099, a*x=9020.0, b*y=128039.0, 总和=137059.0 [原始解]
  4. x=327, y=2011, a*x=14388.0, b*y=122671.0, 总和=137059.0 [原始解]
  5. x=449, y=1923, a*x=19756.0, b*y=117303.0, 总和=137059.0 [原始解]

6. 组合: a=44, b=70.5 (10 个有效解)
  1. x=1157, y=1222.0, a*x=50908.0, b*y=86151.0, 总和=137059.0 [平衡解]
  2. x=1439, y=1046.0, a*x=63316.0, b*y=73743.0, 总和=137059.0 [平衡解]
  3. x=311, y=1750.0, a*x=13684.0, b*y=123375.0, 总和=137059.0 [原始解]
  4. x=593, y=1574.0, a*x=26092.0, b*y=110967.0, 总和=137059.0 [原始解]
  5. x=875, y=1398.0, a*x=38500.0, b*y=98559.0, 总和=137059.0 [原始解]

7. 组合: a=44, b=75.5 (9 个有效解)
  1. x=1025, y=1218.0, a*x=45100.0, b*y=91959.0, 总和=137059.0 [平衡解]
  2. x=1327, y=1042.0, a*x=58388.0, b*y=78671.0, 总和=137059.0 [平衡解]
  3. x=421, y=1570.0, a*x=18524.0, b*y=118535.0, 总和=137059.0 [原始解]
  4. x=723, y=1394.0, a*x=31812.0, b*y=105247.0, 总和=137059.0 [原始解]
  5. x=1629, y=866.0, a*x=71676.0, b*y=65383.0, 总和=137059.0 [原始解]

8. 组合: a=44, b=93 (15 个有效解)
  1. x=995, y=1003, a*x=43780.0, b*y=93279.0, 总和=137059.0 [平衡解]
  2. x=1181, y=915, a*x=51964.0, b*y=85095.0, 总和=137059.0 [平衡解]
  3. x=251, y=1355, a*x=11044.0, b*y=126015.0, 总和=137059.0 [原始解]
  4. x=437, y=1267, a*x=19228.0, b*y=117831.0, 总和=137059.0 [原始解]
  5. x=623, y=1179, a*x=27412.0, b*y=109647.0, 总和=137059.0 [原始解]

9. 组合: a=61, b=70.5 (7 个有效解)
  1. x=1105, y=988.0, a*x=67405.0, b*y=69654.0, 总和=137059.0 [平衡解]
  2. x=823, y=1232.0, a*x=50203.0, b*y=86856.0, 总和=137059.0 [平衡解]
  3. x=259, y=1720.0, a*x=15799.0, b*y=121260.0, 总和=137059.0 [原始解]
  4. x=541, y=1476.0, a*x=33001.0, b*y=104058.0, 总和=137059.0 [原始解]
  5. x=1387, y=744.0, a*x=84607.0, b*y=52452.0, 总和=137059.0 [原始解]

10. 组合: a=61, b=75.5 (6 个有效解)
  1. x=925, y=1068.0, a*x=56425.0, b*y=80634.0, 总和=137059.0 [平衡解]
  2. x=1227, y=824.0, a*x=74847.0, b*y=62212.0, 总和=137059.0 [平衡解]
  3. x=321, y=1556.0, a*x=19581.0, b*y=117478.0, 总和=137059.0 [原始解]
  4. x=623, y=1312.0, a*x=38003.0, b*y=99056.0, 总和=137059.0 [原始解]
  5. x=1529, y=580.0, a*x=93269.0, b*y=43790.0, 总和=137059.0 [原始解]

11. 组合: a=61, b=93 (10 个有效解)
  1. x=829, y=930, a*x=50569.0, b*y=86490.0, 总和=137059.0 [平衡解]
  2. x=1015, y=808, a*x=61915.0, b*y=75144.0, 总和=137059.0 [平衡解]
  3. x=271, y=1296, a*x=16531.0, b*y=120528.0, 总和=137059.0 [原始解]
  4. x=457, y=1174, a*x=27877.0, b*y=109182.0, 总和=137059.0 [原始解]
  5. x=643, y=1052, a*x=39223.0, b*y=97836.0, 总和=137059.0 [原始解]

12. 组合: a=70.5, b=75.5 (11 个有效解)
  1. x=946, y=932.0, a*x=66693.0, b*y=70366.0, 总和=137059.0 [平衡解]
  2. x=795, y=1073.0, a*x=56047.5, b*y=81011.5, 总和=137059.0 [平衡解]
  3. x=191, y=1637.0, a*x=13465.5, b*y=123593.5, 总和=137059.0 [原始解]
  4. x=342, y=1496.0, a*x=24111.0, b*y=112948.0, 总和=137059.0 [原始解]
  5. x=493, y=1355.0, a*x=34756.5, b*y=102302.5, 总和=137059.0 [原始解]

13. 组合: a=75.5, b=93 (9 个有效解)
  1. x=740, y=873.0, a*x=55870.0, b*y=81189.0, 总和=137059.0 [平衡解]
  2. x=926, y=722.0, a*x=69913.0, b*y=67146.0, 总和=137059.0 [平衡解]
  3. x=182, y=1326.0, a*x=13741.0, b*y=123318.0, 总和=137059.0 [原始解]
  4. x=368, y=1175.0, a*x=27784.0, b*y=109275.0, 总和=137059.0 [原始解]
  5. x=554, y=1024.0, a*x=41827.0, b*y=95232.0, 总和=137059.0 [原始解]

使用基础系数列表,共找到有效解

总耗时: 0.01秒