from itertools import product, combinations_with_replacement import time import threading from collections import defaultdict import math # 配置参数(可根据需要修改) TARGET = 250550 # 目标值 BASE_VALUES = [35, 40.5, 58, 67, 73, 90.5] # 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 = 220000 # 使用三个变量的阈值 PRODUCT_RANGE_THRESHOLD = 148000 # 乘积范围限制阈值 SHOW_PROGRESS = True # 是否显示进度 def is_valid_product(p): """检查单个乘积是否在有效范围内""" if TARGET > PRODUCT_RANGE_THRESHOLD: return 74000 <= p <= 115000 else: return True # 目标值较小时不限制乘积范围 def find_single_variable_solutions(values): """查找单个数的解(a*x = TARGET)""" solutions = [] for a in values: x = TARGET / a if x.is_integer() and 1 <= x <= 10000 and is_valid_product(a * x): solutions.append((a, x)) return solutions def find_two_variable_solutions(values): """查找两个变量的解(a*x + b*y = TARGET)""" solutions = defaultdict(list) # 生成所有可能的(a, b)组合 for a in values: for b in values: if a == b: # 避免重复 continue # 计算x的有效范围 if max_x < min_x: continue for x in range(min_x, max_x + 1): remainder = TARGET - a * x # 检查remainder是否在可能的范围内 if remainder < 1 or remainder > b * 10000: continue # 检查remainder是否能被b整除 if remainder % b == 0: y = remainder // b if 1 <= y <= 10000 and is_valid_product(b * y): solutions[(a, b)].append((a, x, b, y)) return solutions def find_three_variable_solutions(values): """优化的三变量求解算法""" solutions = defaultdict(list) # 对系数进行排序,便于剪枝 sorted_values = sorted(values) # 预计算每个系数的有效范围 value_ranges = {} for a in sorted_values: if TARGET > PRODUCT_RANGE_THRESHOLD: else: min_x = 1 max_x = 10000 value_ranges[a] = (min_x, max_x) total_combinations = len(sorted_values) * (len(sorted_values) - 1) * (len(sorted_values) - 2) // 6 processed_combinations = 0 # 三重循环,但添加了更多剪枝条件 for i, a in enumerate(sorted_values): min_x, max_x = value_ranges[a] for x in range(min_x, max_x + 1): ax = a * x if not is_valid_product(ax): continue remainder1 = TARGET - ax if TARGET > PRODUCT_RANGE_THRESHOLD and remainder1 < 2 * 74000: continue # 限制b的选择范围,避免重复组合 for j in range(i + 1, len(sorted_values)): b = sorted_values[j] if TARGET > PRODUCT_RANGE_THRESHOLD: else: min_y = 1 if max_y < min_y: continue for y in range(min_y, max_y + 1): by = b * y if not is_valid_product(by): continue remainder2 = remainder1 - by if TARGET > PRODUCT_RANGE_THRESHOLD and (remainder2 < 74000 or remainder2 > 115000): continue # 限制c的选择范围 for k in range(j + 1, len(sorted_values)): c = sorted_values[k] # 检查remainder2是否能被c整除 if remainder2 % c != 0: continue z = remainder2 // c if 1 <= z <= 10000 and is_valid_product(c * z): key = (a, b, c) solutions[key].append((a, x, b, y, c, z)) # 进度显示 if SHOW_PROGRESS and j % 10 == 0: print(f"\r三变量组合进度: {processed_combinations}/{total_combinations} 组", end='') processed_combinations += 1 if SHOW_PROGRESS: print(f"\r三变量组合进度: {processed_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 # 单变量或无解时直接返回 # 当目标值超过阈值时,不计算平衡解 if TARGET > PRODUCT_RANGE_THRESHOLD: return [] # 计算解的平衡性(变量间差异最小) balanced = [] for sol in solutions: vars = sol[1::2] # 提取x, y, z diff = max(vars) - min(vars) balanced.append((diff, sol)) # 按差异排序,取前num个 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 [] # 排除已在平衡解中的项 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): # 当目标值超过阈值时,不显示平衡解 if TARGET > PRODUCT_RANGE_THRESHOLD: all_display = pair_solutions[:MAX_SOLUTIONS] print_tag = "[原始解]" else: # 计算平衡解和原始解 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: # var_count == 3 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): if TARGET > PRODUCT_RANGE_THRESHOLD: tag = print_tag else: 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: # var_count == 3 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 ====") # 检查目标值是否超过阈值 if TARGET > THREE_VAR_THRESHOLD: print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD},只尝试三变量解") base_solutions = { 'single': [], 'two': [], 'three': run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,)) } # 显示三变量解 if base_solutions['three'] and len(base_solutions['three']) > 0: display_solutions(base_solutions['three'], 3) print(f"\n使用基础系数列表,共找到有效解") return else: print("\n基础系数三变量无解,尝试波动系数") else: # 目标值未超过阈值,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': [] } # 检查是否有解 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) # 如果找到解,退出程序 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 ====") # 检查目标值是否超过阈值 if TARGET > THREE_VAR_THRESHOLD: print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD},只尝试三变量解") fluctuated_solutions = { 'single': [], 'two': [], 'three': run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,)) } # 显示三变量解 if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0: display_solutions(fluctuated_solutions['three'], 3) print(f"\n使用波动系数列表,共找到有效解") return else: # 目标值未超过阈值,按顺序尝试单、双、三变量解 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': [] } # 重置标志 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) # 如果找到解,退出程序 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: 250550 ==== 尝试基础系数 ==== 目标值 250550 超过阈值 220000,只尝试三变量解 三变量组合进度: 9610/20 组 - 完成 找到 20 组3变量解: 1. 组合: a=35, b=40.5, c=58 (2482 个有效解) 1. x=2115, y=1894, z=1721.0, a*x=74025.0, b*y=76707.0, c*z=99818.0, 总和=250550.0 [原始解] 2. x=2115, y=2010, z=1640.0, a*x=74025.0, b*y=81405.0, c*z=95120.0, 总和=250550.0 [原始解] 3. x=2115, y=2126, z=1559.0, a*x=74025.0, b*y=86103.0, c*z=90422.0, 总和=250550.0 [原始解] 2. 组合: a=35, b=40.5, c=67 (2146 个有效解) 1. x=2115, y=1854, z=1514.0, a*x=74025.0, b*y=75087.0, c*z=101438.0, 总和=250550.0 [原始解] 2. x=2115, y=1988, z=1433.0, a*x=74025.0, b*y=80514.0, c*z=96011.0, 总和=250550.0 [原始解] 3. x=2115, y=2122, z=1352.0, a*x=74025.0, b*y=85941.0, c*z=90584.0, 总和=250550.0 [原始解] 3. 组合: a=35, b=40.5, c=73 (1972 个有效解) 1. x=2115, y=1846, z=1394.0, a*x=74025.0, b*y=74763.0, c*z=101762.0, 总和=250550.0 [原始解] 2. x=2115, y=1992, z=1313.0, a*x=74025.0, b*y=80676.0, c*z=95849.0, 总和=250550.0 [原始解] 3. x=2115, y=2138, z=1232.0, a*x=74025.0, b*y=86589.0, c*z=89936.0, 总和=250550.0 [原始解] 4. 组合: a=35, b=40.5, c=90.5 (1588 个有效解) 1. x=2115, y=1990, z=1060.0, a*x=74025.0, b*y=80595.0, c*z=95930.0, 总和=250550.0 [原始解] 2. x=2115, y=2171, z=979.0, a*x=74025.0, b*y=87925.5, c*z=88599.5, 总和=250550.0 [原始解] 3. x=2115, y=2352, z=898.0, a*x=74025.0, b*y=95256.0, c*z=81269.0, 总和=250550.0 [原始解] 5. 组合: a=35, b=58, c=67 (2999 个有效解) 1. x=2115, y=1305, z=1505, a*x=74025.0, b*y=75690.0, c*z=100835.0, 总和=250550.0 [原始解] 2. x=2115, y=1372, z=1447, a*x=74025.0, b*y=79576.0, c*z=96949.0, 总和=250550.0 [原始解] 3. x=2115, y=1439, z=1389, a*x=74025.0, b*y=83462.0, c*z=93063.0, 总和=250550.0 [原始解] 6. 组合: a=35, b=58, c=73 (2756 个有效解) 1. x=2115, y=1323, z=1367, a*x=74025.0, b*y=76734.0, c*z=99791.0, 总和=250550.0 [原始解] 2. x=2115, y=1396, z=1309, a*x=74025.0, b*y=80968.0, c*z=95557.0, 总和=250550.0 [原始解] 3. x=2115, y=1469, z=1251, a*x=74025.0, b*y=85202.0, c*z=91323.0, 总和=250550.0 [原始解] 7. 组合: a=35, b=58, c=90.5 (1114 个有效解) 1. x=2115, y=1349, z=1086.0, a*x=74025.0, b*y=78242.0, c*z=98283.0, 总和=250550.0 [原始解] 2. x=2115, y=1530, z=970.0, a*x=74025.0, b*y=88740.0, c*z=87785.0, 总和=250550.0 [原始解] 3. x=2115, y=1711, z=854.0, a*x=74025.0, b*y=99238.0, c*z=77287.0, 总和=250550.0 [原始解] 8. 组合: a=35, b=67, c=73 (2381 个有效解) 1. x=2115, y=1154, z=1359, a*x=74025.0, b*y=77318.0, c*z=99207.0, 总和=250550.0 [原始解] 2. x=2115, y=1227, z=1292, a*x=74025.0, b*y=82209.0, c*z=94316.0, 总和=250550.0 [原始解] 3. x=2115, y=1300, z=1225, a*x=74025.0, b*y=87100.0, c*z=89425.0, 总和=250550.0 [原始解] 9. 组合: a=35, b=67, c=90.5 (964 个有效解) 1. x=2115, y=1184, z=1074.0, a*x=74025.0, b*y=79328.0, c*z=97197.0, 总和=250550.0 [原始解] 2. x=2115, y=1365, z=940.0, a*x=74025.0, b*y=91455.0, c*z=85070.0, 总和=250550.0 [原始解] 3. x=2116, y=1224, z=1044.0, a*x=74060.0, b*y=82008.0, c*z=94482.0, 总和=250550.0 [原始解] 10. 组合: a=35, b=73, c=90.5 (885 个有效解) 1. x=2115, y=1109, z=1056.0, a*x=74025.0, b*y=80957.0, c*z=95568.0, 总和=250550.0 [原始解] 2. x=2115, y=1290, z=910.0, a*x=74025.0, b*y=94170.0, c*z=82355.0, 总和=250550.0 [原始解] 3. x=2116, y=1111, z=1054.0, a*x=74060.0, b*y=81103.0, c*z=95387.0, 总和=250550.0 [原始解] 11. 组合: a=40.5, b=58, c=67 (1296 个有效解) 1. x=1828, y=1306, z=1504.0, a*x=74034.0, b*y=75748.0, c*z=100768.0, 总和=250550.0 [原始解] 2. x=1828, y=1373, z=1446.0, a*x=74034.0, b*y=79634.0, c*z=96882.0, 总和=250550.0 [原始解] 3. x=1828, y=1440, z=1388.0, a*x=74034.0, b*y=83520.0, c*z=92996.0, 总和=250550.0 [原始解] 12. 组合: a=40.5, b=58, c=73 (1192 个有效解) 1. x=1828, y=1309, z=1378.0, a*x=74034.0, b*y=75922.0, c*z=100594.0, 总和=250550.0 [原始解] 2. x=1828, y=1382, z=1320.0, a*x=74034.0, b*y=80156.0, c*z=96360.0, 总和=250550.0 [原始解] 3. x=1828, y=1455, z=1262.0, a*x=74034.0, b*y=84390.0, c*z=92126.0, 总和=250550.0 [原始解] 13. 组合: a=40.5, b=58, c=90.5 (960 个有效解) 1. x=1828, y=1327, z=1100.0, a*x=74034.0, b*y=76966.0, c*z=99550.0, 总和=250550.0 [原始解] 2. x=1828, y=1508, z=984.0, a*x=74034.0, b*y=87464.0, c*z=89052.0, 总和=250550.0 [原始解] 3. x=1828, y=1689, z=868.0, a*x=74034.0, b*y=97962.0, c*z=78554.0, 总和=250550.0 [原始解] 14. 组合: a=40.5, b=67, c=73 (1030 个有效解) 1. x=1828, y=1119, z=1391.0, a*x=74034.0, b*y=74973.0, c*z=101543.0, 总和=250550.0 [原始解] 2. x=1828, y=1192, z=1324.0, a*x=74034.0, b*y=79864.0, c*z=96652.0, 总和=250550.0 [原始解] 3. x=1828, y=1265, z=1257.0, a*x=74034.0, b*y=84755.0, c*z=91761.0, 总和=250550.0 [原始解] 15. 组合: a=40.5, b=67, c=90.5 (830 个有效解) 1. x=1828, y=1246, z=1028.0, a*x=74034.0, b*y=83482.0, c*z=93034.0, 总和=250550.0 [原始解] 2. x=1828, y=1427, z=894.0, a*x=74034.0, b*y=95609.0, c*z=80907.0, 总和=250550.0 [原始解] 3. x=1829, y=1163, z=1089.0, a*x=74074.5, b*y=77921.0, c*z=98554.5, 总和=250550.0 [原始解] 16. 组合: a=40.5, b=73, c=90.5 (762 个有效解) 1. x=1828, y=1094, z=1068.0, a*x=74034.0, b*y=79862.0, c*z=96654.0, 总和=250550.0 [原始解] 2. x=1828, y=1275, z=922.0, a*x=74034.0, b*y=93075.0, c*z=83441.0, 总和=250550.0 [原始解] 3. x=1829, y=1117, z=1049.0, a*x=74074.5, b*y=81541.0, c*z=94934.5, 总和=250550.0 [原始解] 17. 组合: a=58, b=67, c=73 (1439 个有效解) 1. x=1276, y=1139, z=1373, a*x=74008.0, b*y=76313.0, c*z=100229.0, 总和=250550.0 [原始解] 2. x=1276, y=1212, z=1306, a*x=74008.0, b*y=81204.0, c*z=95338.0, 总和=250550.0 [原始解] 3. x=1276, y=1285, z=1239, a*x=74008.0, b*y=86095.0, c*z=90447.0, 总和=250550.0 [原始解] 18. 组合: a=58, b=67, c=90.5 (583 个有效解) 1. x=1276, y=1268, z=1012.0, a*x=74008.0, b*y=84956.0, c*z=91586.0, 总和=250550.0 [原始解] 2. x=1276, y=1449, z=878.0, a*x=74008.0, b*y=97083.0, c*z=79459.0, 总和=250550.0 [原始解] 3. x=1277, y=1205, z=1058.0, a*x=74066.0, b*y=80735.0, c*z=95749.0, 总和=250550.0 [原始解] 19. 组合: a=58, b=73, c=90.5 (535 个有效解) 1. x=1276, y=1077, z=1082.0, a*x=74008.0, b*y=78621.0, c*z=97921.0, 总和=250550.0 [原始解] 2. x=1276, y=1258, z=936.0, a*x=74008.0, b*y=91834.0, c*z=84708.0, 总和=250550.0 [原始解] 3. x=1277, y=1101, z=1062.0, a*x=74066.0, b*y=80373.0, c*z=96111.0, 总和=250550.0 [原始解] 20. 组合: a=67, b=73, c=90.5 (462 个有效解) 1. x=1105, y=1032, z=1118.0, a*x=74035.0, b*y=75336.0, c*z=101179.0, 总和=250550.0 [原始解] 2. x=1105, y=1213, z=972.0, a*x=74035.0, b*y=88549.0, c*z=87966.0, 总和=250550.0 [原始解] 3. x=1105, y=1394, z=826.0, a*x=74035.0, b*y=101762.0, c*z=74753.0, 总和=250550.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 2.27秒