from itertools import combinations import time import threading from collections import defaultdict import math from multiprocessing import Pool # 配置参数(优化阈值) TARGET = 175000 # 目标值 BASE_VALUES = [38.5,44,61,70.5,75.5,93] # 基础系数列表 FLUCTUATION = 1.0 # 系数波动范围 MAX_SOLUTIONS = 3 # 每个组合的最大解数量 SOLVER_TIMEOUT = 180 # 求解超时时间(秒) THREE_VAR_THRESHOLD = 259000 # 使用三个变量的阈值 PRODUCT_RANGE_THRESHOLD = 129000 # 乘积范围限制阈值 HIGH_TARGET_THRESHOLD = 259000 # 更高目标值阈值 SHOW_PROGRESS = True # 是否显示进度 MAX_SOLUTIONS_PER_COMB = 100 # 每个组合的最大解数量,用于提前终止 USE_MULTIPROCESSING = True # 是否使用多进程加速 def is_valid_product(p): """确保单个乘积不超过129000""" return p <= 129000 # 严格限制所有乘积不超过129000 def find_single_variable_solutions(values): """查找单个数的解(a*x = TARGET)""" solutions = [] for a in values: quotient = TARGET / a if quotient != int(quotient): continue x = int(quotient) if 1 <= x <= 10000 and is_valid_product(a * x): solutions.append((a, x)) if len(solutions) >= MAX_SOLUTIONS: break return solutions def find_two_variable_solutions(values): """优化的双变量求解算法,确保每个乘积不超过129000""" solutions = defaultdict(list) for i, a in enumerate(values): for b in values[i:]: seen_xy = set() # 调整x的最大值,确保a*x不超过129000 if max_x < min_x: continue x_count = max_x - min_x + 1 x_step = max(1, x_count // 1000) for x in range(min_x, max_x + 1, x_step): ax = a * x if ax > 129000: # 额外检查确保不超过129000 continue remainder = TARGET - ax if remainder < b: break if remainder > b * 10000: continue if remainder % b == 0: y = remainder // b by = b * y if 1 <= y <= 10000 and by <= 129000: # 确保b*y也不超过129000 xy_pair = (x, y) if a <= b else (y, x) if xy_pair not in seen_xy: seen_xy.add(xy_pair) solutions[(a, b)].append((a, x, b, y)) if len(solutions[(a, b)]) >= MAX_SOLUTIONS_PER_COMB: break return solutions def process_three_var_combination(args): """处理三变量组合的辅助函数,用于并行计算""" a, b, c, value_ranges, target = args solutions = [] seen_xyz = set() min_x, max_x = value_ranges[a] x_count = max_x - min_x + 1 x_step = max(1, x_count // 1000) for x in range(min_x, max_x + 1, x_step): ax = a * x if not is_valid_product(ax): continue remainder1 = target - ax if remainder1 < 0: break if max_y < min_y: continue y_count = max_y - min_y + 1 y_step = max(1, y_count // 100) for y in range(min_y, max_y + 1, y_step): by = b * y if not is_valid_product(by): continue remainder2 = remainder1 - by if remainder2 < 0: break if remainder2 > c * 10000: continue if remainder2 % c == 0: z = remainder2 // c if 1 <= z <= 10000 and is_valid_product(c * z): xyz_tuple = tuple(sorted([x, y, z])) if xyz_tuple not in seen_xyz: seen_xyz.add(xyz_tuple) solutions.append((a, x, b, y, c, z)) if len(solutions) >= MAX_SOLUTIONS_PER_COMB: return solutions return solutions def find_three_variable_solutions(values): """优化的三变量求解算法,确保每个乘积不超过129000""" solutions = defaultdict(list) sorted_values = sorted(values) # 预计算每个系数的有效范围,确保每个乘积不超过129000 value_ranges = {} for a in sorted_values: value_ranges[a] = (min_x, max_x) combinations_list = [] for i, a in enumerate(sorted_values): for j in range(i + 1, len(sorted_values)): b = sorted_values[j] for k in range(j + 1, len(sorted_values)): c = sorted_values[k] combinations_list.append((a, b, c, value_ranges, TARGET)) if USE_MULTIPROCESSING: with Pool() as pool: results = pool.map(process_three_var_combination, combinations_list) for i, (a, b, c, _, _) in enumerate(combinations_list): if results[i]: solutions[(a, b, c)] = results[i] else: total_combinations = len(combinations_list) for i, (a, b, c, _, _) in enumerate(combinations_list): res = process_three_var_combination((a, b, c, value_ranges, TARGET)) if res: solutions[(a, b, c)] = res if SHOW_PROGRESS and i % 10 == 0: print(f"\r三变量组合进度: {i}/{total_combinations} 组", end='') if SHOW_PROGRESS and not USE_MULTIPROCESSING: print(f"\r三变量组合进度: {total_combinations}/{total_combinations} 组 - 完成") return solutions def find_balanced_solutions(solutions, var_count, num=2): """从所有解中筛选出最平衡的解""" if var_count == 1 or not solutions: return solutions balanced = [] for sol in solutions: vars = sol[1::2] # 获取解中的变量值 diff = max(vars) - min(vars) # 计算变量之间的最大差值 balanced.append((diff, sol)) # 按差值排序,返回差值最小的解 return [s for _, s in sorted(balanced, key=lambda x: x[0])[:num]] def find_original_solutions(solutions, balanced_solutions, num=3): """从剩余解中获取原始顺序的解""" if not solutions: return [] remaining = [s for s in solutions if s not in balanced_solutions] return remaining[:num] def display_solutions(solutions_dict, var_count): """优化的解显示函数""" if not solutions_dict: return print(f"\n找到 {len(solutions_dict)} 组{var_count}变量解:") for i, (coeffs, pair_solutions) in enumerate(sorted(solutions_dict.items()), 1): balanced = find_balanced_solutions(pair_solutions, var_count) original = find_original_solutions(pair_solutions, balanced) all_display = balanced + original if var_count == 1: a = coeffs print(f"\n{i}. 组合: a={a} ({len(pair_solutions)} 个有效解)") elif var_count == 2: a, b = coeffs print(f"\n{i}. 组合: a={a}, b={b} ({len(pair_solutions)} 个有效解)") else: a, b, c = coeffs print(f"\n{i}. 组合: a={a}, b={b}, c={c} ({len(pair_solutions)} 个有效解)") for j, sol in enumerate(all_display, 1): tag = "[平衡解]" if j <= len(balanced) else "[原始解]" if var_count == 1: a, x = sol print(f" {j}. x={x}, a*x={a*x:.1f}, 总和={a*x:.1f} {tag}") elif var_count == 2: a, x, b, y = sol 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}") else: a, x, b, y, c, z = sol print(f" {j}. x={x}, y={y}, z={z}, " f"a*x={a*x:.1f}, b*y={b*y:.1f}, c*z={c*z:.1f}, " f"总和={a*x + b*y + c*z:.1f} {tag}") def run_with_timeout(func, args=(), kwargs=None, timeout=SOLVER_TIMEOUT): """运行函数并设置超时限制""" if kwargs is None: kwargs = {} result = [] error = [] def wrapper(): try: result.append(func(*args, **kwargs)) except Exception as e: error.append(e) thread = threading.Thread(target=wrapper) thread.daemon = True thread.start() thread.join(timeout) if thread.is_alive(): print(f"警告: {func.__name__} 超时({timeout}秒),跳过此方法") return None if error: return result[0] def main(): print(f"目标值: {TARGET}") # 生成波动后的系数 FLUCTUATED_VALUES = [round(v - FLUCTUATION, 1) for v in BASE_VALUES] # 尝试基础系数 print(f"\n==== 尝试基础系数 ====") # 目标值255966 > 259000不成立,会按顺序尝试单、双、三变量解 base_solutions = { 'single': run_with_timeout(find_single_variable_solutions, args=(BASE_VALUES,)), 'two': run_with_timeout(find_two_variable_solutions, args=(BASE_VALUES,)), 'three': [] } has_solution = False # 显示单变量解 if base_solutions['single']: has_solution = True display_solutions({a: [sol] for a, sol in zip(BASE_VALUES, base_solutions['single']) if sol}, 1) # 显示双变量解 if base_solutions['two'] and len(base_solutions['two']) > 0: has_solution = True display_solutions(base_solutions['two'], 2) # 单变量和双变量都无解时,尝试三变量解 if not has_solution: print(f"\n==== 单变量和双变量无解,尝试三变量解 ====") base_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,)) if base_solutions['three'] and len(base_solutions['three']) > 0: has_solution = True display_solutions(base_solutions['three'], 3) if has_solution: print(f"\n使用基础系数列表,共找到有效解") return # 如果基础系数没有找到解,尝试波动系数 print(f"\n==== 尝试波动系数 ====") fluctuated_solutions = { 'single': run_with_timeout(find_single_variable_solutions, args=(FLUCTUATED_VALUES,)), 'two': run_with_timeout(find_two_variable_solutions, args=(FLUCTUATED_VALUES,)), 'three': [] } has_solution = False # 显示单变量解 if fluctuated_solutions['single']: has_solution = True display_solutions({a: [sol] for a, sol in zip(FLUCTUATED_VALUES, fluctuated_solutions['single']) if sol}, 1) # 显示双变量解 if fluctuated_solutions['two'] and len(fluctuated_solutions['two']) > 0: has_solution = True display_solutions(fluctuated_solutions['two'], 2) # 单变量和双变量都无解时,尝试三变量解 if not has_solution: print(f"\n==== 单变量和双变量无解,尝试三变量解 ====") fluctuated_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,)) if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0: has_solution = True display_solutions(fluctuated_solutions['three'], 3) if has_solution: print(f"\n使用波动系数列表,共找到有效解") return # 如果所有系数集都没有找到解 print("\n没有找到符合条件的解,即使使用波动后的系数列表。") if __name__ == "__main__": main() print(f"\n总耗时: {time.time() - start_time:.2f}秒")
Standard input is empty
目标值: 175000 ==== 尝试基础系数 ==== 找到 13 组2变量解: 1. 组合: a=38.5, b=61 (6 个有效解) 1. x=1684, y=1806.0, a*x=64834.0, b*y=110166.0, 总和=175000.0 [平衡解] 2. x=2050, y=1575.0, a*x=78925.0, b*y=96075.0, 总和=175000.0 [平衡解] 3. x=1318, y=2037.0, a*x=50743.0, b*y=124257.0, 总和=175000.0 [原始解] 4. x=2416, y=1344.0, a*x=93016.0, b*y=81984.0, 总和=175000.0 [原始解] 5. x=2782, y=1113.0, a*x=107107.0, b*y=67893.0, 总和=175000.0 [原始解] 2. 组合: a=38.5, b=70.5 (15 个有效解) 1. x=1546, y=1638.0, a*x=59521.0, b*y=115479.0, 总和=175000.0 [平衡解] 2. x=1687, y=1561.0, a*x=64949.5, b*y=110050.5, 总和=175000.0 [平衡解] 3. x=1264, y=1792.0, a*x=48664.0, b*y=126336.0, 总和=175000.0 [原始解] 4. x=1405, y=1715.0, a*x=54092.5, b*y=120907.5, 总和=175000.0 [原始解] 5. x=1828, y=1484.0, a*x=70378.0, b*y=104622.0, 总和=175000.0 [原始解] 3. 组合: a=38.5, b=75.5 (5 个有效解) 1. x=1498, y=1554.0, a*x=57673.0, b*y=117327.0, 总和=175000.0 [平衡解] 2. x=1951, y=1323.0, a*x=75113.5, b*y=99886.5, 总和=175000.0 [平衡解] 3. x=2404, y=1092.0, a*x=92554.0, b*y=82446.0, 总和=175000.0 [原始解] 4. x=2857, y=861.0, a*x=109994.5, b*y=65005.5, 总和=175000.0 [原始解] 5. x=3310, y=630.0, a*x=127435.0, b*y=47565.0, 总和=175000.0 [原始解] 4. 组合: a=38.5, b=93 (12 个有效解) 1. x=1282, y=1351.0, a*x=49357.0, b*y=125643.0, 总和=175000.0 [平衡解] 2. x=1468, y=1274.0, a*x=56518.0, b*y=118482.0, 总和=175000.0 [平衡解] 3. x=1654, y=1197.0, a*x=63679.0, b*y=111321.0, 总和=175000.0 [原始解] 4. x=1840, y=1120.0, a*x=70840.0, b*y=104160.0, 总和=175000.0 [原始解] 5. x=2026, y=1043.0, a*x=78001.0, b*y=96999.0, 总和=175000.0 [原始解] 5. 组合: a=44, b=61 (16 个有效解) 1. x=1687, y=1652, a*x=74228.0, b*y=100772.0, 总和=175000.0 [平衡解] 2. x=1565, y=1740, a*x=68860.0, b*y=106140.0, 总和=175000.0 [平衡解] 3. x=1077, y=2092, a*x=47388.0, b*y=127612.0, 总和=175000.0 [原始解] 4. x=1199, y=2004, a*x=52756.0, b*y=122244.0, 总和=175000.0 [原始解] 5. x=1321, y=1916, a*x=58124.0, b*y=116876.0, 总和=175000.0 [原始解] 6. 组合: a=44, b=70.5 (6 个有效解) 1. x=1529, y=1528.0, a*x=67276.0, b*y=107724.0, 总和=175000.0 [平衡解] 2. x=1247, y=1704.0, a*x=54868.0, b*y=120132.0, 总和=175000.0 [平衡解] 3. x=1811, y=1352.0, a*x=79684.0, b*y=95316.0, 总和=175000.0 [原始解] 4. x=2093, y=1176.0, a*x=92092.0, b*y=82908.0, 总和=175000.0 [原始解] 5. x=2375, y=1000.0, a*x=104500.0, b*y=70500.0, 总和=175000.0 [原始解] 7. 组合: a=44, b=75.5 (6 个有效解) 1. x=1575, y=1400.0, a*x=69300.0, b*y=105700.0, 总和=175000.0 [平衡解] 2. x=1273, y=1576.0, a*x=56012.0, b*y=118988.0, 总和=175000.0 [平衡解] 3. x=1877, y=1224.0, a*x=82588.0, b*y=92412.0, 总和=175000.0 [原始解] 4. x=2179, y=1048.0, a*x=95876.0, b*y=79124.0, 总和=175000.0 [原始解] 5. x=2481, y=872.0, a*x=109164.0, b*y=65836.0, 总和=175000.0 [原始解] 8. 组合: a=44, b=93 (10 个有效解) 1. x=1331, y=1252, a*x=58564.0, b*y=116436.0, 总和=175000.0 [平衡解] 2. x=1145, y=1340, a*x=50380.0, b*y=124620.0, 总和=175000.0 [平衡解] 3. x=1517, y=1164, a*x=66748.0, b*y=108252.0, 总和=175000.0 [原始解] 4. x=1703, y=1076, a*x=74932.0, b*y=100068.0, 总和=175000.0 [原始解] 5. x=1889, y=988, a*x=83116.0, b*y=91884.0, 总和=175000.0 [原始解] 9. 组合: a=61, b=70.5 (5 个有效解) 1. x=1267, y=1386.0, a*x=77287.0, b*y=97713.0, 总和=175000.0 [平衡解] 2. x=1549, y=1142.0, a*x=94489.0, b*y=80511.0, 总和=175000.0 [平衡解] 3. x=985, y=1630.0, a*x=60085.0, b*y=114915.0, 总和=175000.0 [原始解] 4. x=1831, y=898.0, a*x=111691.0, b*y=63309.0, 总和=175000.0 [原始解] 5. x=2113, y=654.0, a*x=128893.0, b*y=46107.0, 总和=175000.0 [原始解] 10. 组合: a=61, b=75.5 (5 个有效解) 1. x=1193, y=1354.0, a*x=72773.0, b*y=102227.0, 总和=175000.0 [平衡解] 2. x=1495, y=1110.0, a*x=91195.0, b*y=83805.0, 总和=175000.0 [平衡解] 3. x=891, y=1598.0, a*x=54351.0, b*y=120649.0, 总和=175000.0 [原始解] 4. x=1797, y=866.0, a*x=109617.0, b*y=65383.0, 总和=175000.0 [原始解] 5. x=2099, y=622.0, a*x=128039.0, b*y=46961.0, 总和=175000.0 [原始解] 11. 组合: a=61, b=93 (7 个有效解) 1. x=1111, y=1153, a*x=67771.0, b*y=107229.0, 总和=175000.0 [平衡解] 2. x=1297, y=1031, a*x=79117.0, b*y=95883.0, 总和=175000.0 [平衡解] 3. x=925, y=1275, a*x=56425.0, b*y=118575.0, 总和=175000.0 [原始解] 4. x=1483, y=909, a*x=90463.0, b*y=84537.0, 总和=175000.0 [原始解] 5. x=1669, y=787, a*x=101809.0, b*y=73191.0, 总和=175000.0 [原始解] 12. 组合: a=70.5, b=75.5 (7 个有效解) 1. x=1240, y=1160.0, a*x=87420.0, b*y=87580.0, 总和=175000.0 [平衡解] 2. x=1089, y=1301.0, a*x=76774.5, b*y=98225.5, 总和=175000.0 [平衡解] 3. x=787, y=1583.0, a*x=55483.5, b*y=119516.5, 总和=175000.0 [原始解] 4. x=938, y=1442.0, a*x=66129.0, b*y=108871.0, 总和=175000.0 [原始解] 5. x=1391, y=1019.0, a*x=98065.5, b*y=76934.5, 总和=175000.0 [原始解] 13. 组合: a=75.5, b=93 (5 个有效解) 1. x=974, y=1091.0, a*x=73537.0, b*y=101463.0, 总和=175000.0 [平衡解] 2. x=1160, y=940.0, a*x=87580.0, b*y=87420.0, 总和=175000.0 [平衡解] 3. x=788, y=1242.0, a*x=59494.0, b*y=115506.0, 总和=175000.0 [原始解] 4. x=1346, y=789.0, a*x=101623.0, b*y=73377.0, 总和=175000.0 [原始解] 5. x=1532, y=638.0, a*x=115666.0, b*y=59334.0, 总和=175000.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒