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 = 58167 # 目标值 BASE_VALUES = [36.5, 41.5, 59, 68.5, 74, 91.5] # 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 = 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: 58167 ==== 尝试基础系数 ==== 找到 15 组2变量解: 1. 组合: a=36.5, b=41.5 (19 个有效解) 1. x=717, y=771.0, a*x=26170.5, b*y=31996.5, 总和=58167.0 [平衡解] 2. x=800, y=698.0, a*x=29200.0, b*y=28967.0, 总和=58167.0 [平衡解] 3. x=53, y=1355.0, a*x=1934.5, b*y=56232.5, 总和=58167.0 [原始解] 4. x=136, y=1282.0, a*x=4964.0, b*y=53203.0, 总和=58167.0 [原始解] 5. x=219, y=1209.0, a*x=7993.5, b*y=50173.5, 总和=58167.0 [原始解] 2. 组合: a=36.5, b=59 (14 个有效解) 1. x=648, y=585.0, a*x=23652.0, b*y=34515.0, 总和=58167.0 [平衡解] 2. x=530, y=658.0, a*x=19345.0, b*y=38822.0, 总和=58167.0 [平衡解] 3. x=58, y=950.0, a*x=2117.0, b*y=56050.0, 总和=58167.0 [原始解] 4. x=176, y=877.0, a*x=6424.0, b*y=51743.0, 总和=58167.0 [原始解] 5. x=294, y=804.0, a*x=10731.0, b*y=47436.0, 总和=58167.0 [原始解] 3. 组合: a=36.5, b=68.5 (11 个有效解) 1. x=507, y=579.0, a*x=18505.5, b*y=39661.5, 总和=58167.0 [平衡解] 2. x=644, y=506.0, a*x=23506.0, b*y=34661.0, 总和=58167.0 [平衡解] 3. x=96, y=798.0, a*x=3504.0, b*y=54663.0, 总和=58167.0 [原始解] 4. x=233, y=725.0, a*x=8504.5, b*y=49662.5, 总和=58167.0 [原始解] 5. x=370, y=652.0, a*x=13505.0, b*y=44662.0, 总和=58167.0 [原始解] 4. 组合: a=36.5, b=74 (10 个有效解) 1. x=586, y=497.0, a*x=21389.0, b*y=36778.0, 总和=58167.0 [平衡解] 2. x=438, y=570.0, a*x=15987.0, b*y=42180.0, 总和=58167.0 [平衡解] 3. x=142, y=716.0, a*x=5183.0, b*y=52984.0, 总和=58167.0 [原始解] 4. x=290, y=643.0, a*x=10585.0, b*y=47582.0, 总和=58167.0 [原始解] 5. x=734, y=424.0, a*x=26791.0, b*y=31376.0, 总和=58167.0 [原始解] 5. 组合: a=36.5, b=91.5 (9 个有效解) 1. x=453, y=455.0, a*x=16534.5, b*y=41632.5, 总和=58167.0 [平衡解] 2. x=636, y=382.0, a*x=23214.0, b*y=34953.0, 总和=58167.0 [平衡解] 3. x=87, y=601.0, a*x=3175.5, b*y=54991.5, 总和=58167.0 [原始解] 4. x=270, y=528.0, a*x=9855.0, b*y=48312.0, 总和=58167.0 [原始解] 5. x=819, y=309.0, a*x=29893.5, b*y=28273.5, 总和=58167.0 [原始解] 6. 组合: a=41.5, b=59 (12 个有效解) 1. x=614, y=554.0, a*x=25481.0, b*y=32686.0, 总和=58167.0 [平衡解] 2. x=496, y=637.0, a*x=20584.0, b*y=37583.0, 总和=58167.0 [平衡解] 3. x=24, y=969.0, a*x=996.0, b*y=57171.0, 总和=58167.0 [原始解] 4. x=142, y=886.0, a*x=5893.0, b*y=52274.0, 总和=58167.0 [原始解] 5. x=260, y=803.0, a*x=10790.0, b*y=47377.0, 总和=58167.0 [原始解] 7. 组合: a=41.5, b=68.5 (10 个有效解) 1. x=540, y=522.0, a*x=22410.0, b*y=35757.0, 总和=58167.0 [平衡解] 2. x=403, y=605.0, a*x=16724.5, b*y=41442.5, 总和=58167.0 [平衡解] 3. x=129, y=771.0, a*x=5353.5, b*y=52813.5, 总和=58167.0 [原始解] 4. x=266, y=688.0, a*x=11039.0, b*y=47128.0, 总和=58167.0 [原始解] 5. x=677, y=439.0, a*x=28095.5, b*y=30071.5, 总和=58167.0 [原始解] 8. 组合: a=41.5, b=74 (10 个有效解) 1. x=494, y=509.0, a*x=20501.0, b*y=37666.0, 总和=58167.0 [平衡解] 2. x=642, y=426.0, a*x=26643.0, b*y=31524.0, 总和=58167.0 [平衡解] 3. x=50, y=758.0, a*x=2075.0, b*y=56092.0, 总和=58167.0 [原始解] 4. x=198, y=675.0, a*x=8217.0, b*y=49950.0, 总和=58167.0 [原始解] 5. x=346, y=592.0, a*x=14359.0, b*y=43808.0, 总和=58167.0 [原始解] 9. 组合: a=41.5, b=91.5 (8 个有效解) 1. x=480, y=418.0, a*x=19920.0, b*y=38247.0, 总和=58167.0 [平衡解] 2. x=297, y=501.0, a*x=12325.5, b*y=45841.5, 总和=58167.0 [平衡解] 3. x=114, y=584.0, a*x=4731.0, b*y=53436.0, 总和=58167.0 [原始解] 4. x=663, y=335.0, a*x=27514.5, b*y=30652.5, 总和=58167.0 [原始解] 5. x=846, y=252.0, a*x=35109.0, b*y=23058.0, 总和=58167.0 [原始解] 10. 组合: a=59, b=68.5 (7 个有效解) 1. x=482, y=434.0, a*x=28438.0, b*y=29729.0, 总和=58167.0 [平衡解] 2. x=345, y=552.0, a*x=20355.0, b*y=37812.0, 总和=58167.0 [平衡解] 3. x=71, y=788.0, a*x=4189.0, b*y=53978.0, 总和=58167.0 [原始解] 4. x=208, y=670.0, a*x=12272.0, b*y=45895.0, 总和=58167.0 [原始解] 5. x=619, y=316.0, a*x=36521.0, b*y=21646.0, 总和=58167.0 [原始解] 11. 组合: a=59, b=74 (13 个有效解) 1. x=429, y=444, a*x=25311.0, b*y=32856.0, 总和=58167.0 [平衡解] 2. x=503, y=385, a*x=29677.0, b*y=28490.0, 总和=58167.0 [平衡解] 3. x=59, y=739, a*x=3481.0, b*y=54686.0, 总和=58167.0 [原始解] 4. x=133, y=680, a*x=7847.0, b*y=50320.0, 总和=58167.0 [原始解] 5. x=207, y=621, a*x=12213.0, b*y=45954.0, 总和=58167.0 [原始解] 12. 组合: a=59, b=91.5 (5 个有效解) 1. x=471, y=332.0, a*x=27789.0, b*y=30378.0, 总和=58167.0 [平衡解] 2. x=288, y=450.0, a*x=16992.0, b*y=41175.0, 总和=58167.0 [平衡解] 3. x=105, y=568.0, a*x=6195.0, b*y=51972.0, 总和=58167.0 [原始解] 4. x=654, y=214.0, a*x=38586.0, b*y=19581.0, 总和=58167.0 [原始解] 5. x=837, y=96.0, a*x=49383.0, b*y=8784.0, 总和=58167.0 [原始解] 13. 组合: a=68.5, b=74 (5 个有效解) 1. x=430, y=388.0, a*x=29455.0, b*y=28712.0, 总和=58167.0 [平衡解] 2. x=282, y=525.0, a*x=19317.0, b*y=38850.0, 总和=58167.0 [平衡解] 3. x=134, y=662.0, a*x=9179.0, b*y=48988.0, 总和=58167.0 [原始解] 4. x=578, y=251.0, a*x=39593.0, b*y=18574.0, 总和=58167.0 [原始解] 5. x=726, y=114.0, a*x=49731.0, b*y=8436.0, 总和=58167.0 [原始解] 14. 组合: a=68.5, b=91.5 (5 个有效解) 1. x=399, y=337.0, a*x=27331.5, b*y=30835.5, 总和=58167.0 [平衡解] 2. x=216, y=474.0, a*x=14796.0, b*y=43371.0, 总和=58167.0 [平衡解] 3. x=33, y=611.0, a*x=2260.5, b*y=55906.5, 总和=58167.0 [原始解] 4. x=582, y=200.0, a*x=39867.0, b*y=18300.0, 总和=58167.0 [原始解] 5. x=765, y=63.0, a*x=52402.5, b*y=5764.5, 总和=58167.0 [原始解] 15. 组合: a=74, b=91.5 (5 个有效解) 1. x=378, y=330.0, a*x=27972.0, b*y=30195.0, 总和=58167.0 [平衡解] 2. x=195, y=478.0, a*x=14430.0, b*y=43737.0, 总和=58167.0 [平衡解] 3. x=12, y=626.0, a*x=888.0, b*y=57279.0, 总和=58167.0 [原始解] 4. x=561, y=182.0, a*x=41514.0, b*y=16653.0, 总和=58167.0 [原始解] 5. x=744, y=34.0, a*x=55056.0, b*y=3111.0, 总和=58167.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒