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 =175378 # 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: 175378 ==== 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=1594, y=1869.0, a*x=61369.0, b*y=114009.0, 总和=175378.0 [平衡解] 2. x=1960, y=1638.0, a*x=75460.0, b*y=99918.0, 总和=175378.0 [平衡解] 3. x=1228, y=2100.0, a*x=47278.0, b*y=128100.0, 总和=175378.0 [原始解] 4. x=2326, y=1407.0, a*x=89551.0, b*y=85827.0, 总和=175378.0 [原始解] 5. x=2692, y=1176.0, a*x=103642.0, b*y=71736.0, 总和=175378.0 [原始解] 2. 组合: a=38.5, b=70.5 (15 个有效解) 1. x=1543, y=1645.0, a*x=59405.5, b*y=115972.5, 总和=175378.0 [平衡解] 2. x=1684, y=1568.0, a*x=64834.0, b*y=110544.0, 总和=175378.0 [平衡解] 3. x=1261, y=1799.0, a*x=48548.5, b*y=126829.5, 总和=175378.0 [原始解] 4. x=1402, y=1722.0, a*x=53977.0, b*y=121401.0, 总和=175378.0 [原始解] 5. x=1825, y=1491.0, a*x=70262.5, b*y=105115.5, 总和=175378.0 [原始解] 3. 组合: a=38.5, b=75.5 (4 个有效解) 1. x=1549, y=1533.0, a*x=59636.5, b*y=115741.5, 总和=175378.0 [平衡解] 2. x=2002, y=1302.0, a*x=77077.0, b*y=98301.0, 总和=175378.0 [平衡解] 3. x=2455, y=1071.0, a*x=94517.5, b*y=80860.5, 总和=175378.0 [原始解] 4. x=2908, y=840.0, a*x=111958.0, b*y=63420.0, 总和=175378.0 [原始解] 4. 组合: a=38.5, b=93 (12 个有效解) 1. x=1258, y=1365.0, a*x=48433.0, b*y=126945.0, 总和=175378.0 [平衡解] 2. x=1444, y=1288.0, a*x=55594.0, b*y=119784.0, 总和=175378.0 [平衡解] 3. x=1630, y=1211.0, a*x=62755.0, b*y=112623.0, 总和=175378.0 [原始解] 4. x=1816, y=1134.0, a*x=69916.0, b*y=105462.0, 总和=175378.0 [原始解] 5. x=2002, y=1057.0, a*x=77077.0, b*y=98301.0, 总和=175378.0 [原始解] 5. 组合: a=44, b=61 (15 个有效解) 1. x=1715, y=1638, a*x=75460.0, b*y=99918.0, 总和=175378.0 [平衡解] 2. x=1593, y=1726, a*x=70092.0, b*y=105286.0, 总和=175378.0 [平衡解] 3. x=1105, y=2078, a*x=48620.0, b*y=126758.0, 总和=175378.0 [原始解] 4. x=1227, y=1990, a*x=53988.0, b*y=121390.0, 总和=175378.0 [原始解] 5. x=1349, y=1902, a*x=59356.0, b*y=116022.0, 总和=175378.0 [原始解] 6. 组合: a=44, b=70.5 (7 个有效解) 1. x=1403, y=1612.0, a*x=61732.0, b*y=113646.0, 总和=175378.0 [平衡解] 2. x=1685, y=1436.0, a*x=74140.0, b*y=101238.0, 总和=175378.0 [平衡解] 3. x=1121, y=1788.0, a*x=49324.0, b*y=126054.0, 总和=175378.0 [原始解] 4. x=1967, y=1260.0, a*x=86548.0, b*y=88830.0, 总和=175378.0 [原始解] 5. x=2249, y=1084.0, a*x=98956.0, b*y=76422.0, 总和=175378.0 [原始解] 7. 组合: a=44, b=75.5 (6 个有效解) 1. x=1563, y=1412.0, a*x=68772.0, b*y=106606.0, 总和=175378.0 [平衡解] 2. x=1261, y=1588.0, a*x=55484.0, b*y=119894.0, 总和=175378.0 [平衡解] 3. x=1865, y=1236.0, a*x=82060.0, b*y=93318.0, 总和=175378.0 [原始解] 4. x=2167, y=1060.0, a*x=95348.0, b*y=80030.0, 总和=175378.0 [原始解] 5. x=2469, y=884.0, a*x=108636.0, b*y=66742.0, 总和=175378.0 [原始解] 8. 组合: a=44, b=93 (10 个有效解) 1. x=1217, y=1310, a*x=53548.0, b*y=121830.0, 总和=175378.0 [平衡解] 2. x=1403, y=1222, a*x=61732.0, b*y=113646.0, 总和=175378.0 [平衡解] 3. x=1589, y=1134, a*x=69916.0, b*y=105462.0, 总和=175378.0 [原始解] 4. x=1775, y=1046, a*x=78100.0, b*y=97278.0, 总和=175378.0 [原始解] 5. x=1961, y=958, a*x=86284.0, b*y=89094.0, 总和=175378.0 [原始解] 9. 组合: a=61, b=70.5 (5 个有效解) 1. x=1435, y=1246.0, a*x=87535.0, b*y=87843.0, 总和=175378.0 [平衡解] 2. x=1153, y=1490.0, a*x=70333.0, b*y=105045.0, 总和=175378.0 [平衡解] 3. x=871, y=1734.0, a*x=53131.0, b*y=122247.0, 总和=175378.0 [原始解] 4. x=1717, y=1002.0, a*x=104737.0, b*y=70641.0, 总和=175378.0 [原始解] 5. x=1999, y=758.0, a*x=121939.0, b*y=53439.0, 总和=175378.0 [原始解] 10. 组合: a=61, b=75.5 (4 个有效解) 1. x=1219, y=1338.0, a*x=74359.0, b*y=101019.0, 总和=175378.0 [平衡解] 2. x=1521, y=1094.0, a*x=92781.0, b*y=82597.0, 总和=175378.0 [平衡解] 3. x=917, y=1582.0, a*x=55937.0, b*y=119441.0, 总和=175378.0 [原始解] 4. x=1823, y=850.0, a*x=111203.0, b*y=64175.0, 总和=175378.0 [原始解] 11. 组合: a=61, b=93 (7 个有效解) 1. x=1105, y=1161, a*x=67405.0, b*y=107973.0, 总和=175378.0 [平衡解] 2. x=1291, y=1039, a*x=78751.0, b*y=96627.0, 总和=175378.0 [平衡解] 3. x=919, y=1283, a*x=56059.0, b*y=119319.0, 总和=175378.0 [原始解] 4. x=1477, y=917, a*x=90097.0, b*y=85281.0, 总和=175378.0 [原始解] 5. x=1663, y=795, a*x=101443.0, b*y=73935.0, 总和=175378.0 [原始解] 12. 组合: a=70.5, b=75.5 (7 个有效解) 1. x=1255, y=1151.0, a*x=88477.5, b*y=86900.5, 总和=175378.0 [平衡解] 2. x=1104, y=1292.0, a*x=77832.0, b*y=97546.0, 总和=175378.0 [平衡解] 3. x=802, y=1574.0, a*x=56541.0, b*y=118837.0, 总和=175378.0 [原始解] 4. x=953, y=1433.0, a*x=67186.5, b*y=108191.5, 总和=175378.0 [原始解] 5. x=1406, y=1010.0, a*x=99123.0, b*y=76255.0, 总和=175378.0 [原始解] 13. 组合: a=75.5, b=93 (6 个有效解) 1. x=1064, y=1022.0, a*x=80332.0, b*y=95046.0, 总和=175378.0 [平衡解] 2. x=878, y=1173.0, a*x=66289.0, b*y=109089.0, 总和=175378.0 [平衡解] 3. x=692, y=1324.0, a*x=52246.0, b*y=123132.0, 总和=175378.0 [原始解] 4. x=1250, y=871.0, a*x=94375.0, b*y=81003.0, 总和=175378.0 [原始解] 5. x=1436, y=720.0, a*x=108418.0, b*y=66960.0, 总和=175378.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒