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 = 108640 # 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: 108640 ==== 尝试基础系数 ==== 找到 11 组2变量解: 1. 组合: a=38.5, b=70.5 (10 个有效解) 1. x=1117, y=931.0, a*x=43004.5, b*y=65635.5, 总和=108640.0 [平衡解] 2. x=835, y=1085.0, a*x=32147.5, b*y=76492.5, 总和=108640.0 [平衡解] 3. x=271, y=1393.0, a*x=10433.5, b*y=98206.5, 总和=108640.0 [原始解] 4. x=553, y=1239.0, a*x=21290.5, b*y=87349.5, 总和=108640.0 [原始解] 5. x=1399, y=777.0, a*x=53861.5, b*y=54778.5, 总和=108640.0 [原始解] 2. 组合: a=38.5, b=75.5 (9 个有效解) 1. x=1051, y=903.0, a*x=40463.5, b*y=68176.5, 总和=108640.0 [平衡解] 2. x=749, y=1057.0, a*x=28836.5, b*y=79803.5, 总和=108640.0 [平衡解] 3. x=145, y=1365.0, a*x=5582.5, b*y=103057.5, 总和=108640.0 [原始解] 4. x=447, y=1211.0, a*x=17209.5, b*y=91430.5, 总和=108640.0 [原始解] 5. x=1353, y=749.0, a*x=52090.5, b*y=56549.5, 总和=108640.0 [原始解] 3. 组合: a=44, b=61 (20 个有效解) 1. x=1055, y=1020, a*x=46420.0, b*y=62220.0, 总和=108640.0 [平衡解] 2. x=933, y=1108, a*x=41052.0, b*y=67588.0, 总和=108640.0 [平衡解] 3. x=79, y=1724, a*x=3476.0, b*y=105164.0, 总和=108640.0 [原始解] 4. x=201, y=1636, a*x=8844.0, b*y=99796.0, 总和=108640.0 [原始解] 5. x=323, y=1548, a*x=14212.0, b*y=94428.0, 总和=108640.0 [原始解] 4. 组合: a=44, b=70.5 (9 个有效解) 1. x=995, y=920.0, a*x=43780.0, b*y=64860.0, 总和=108640.0 [平衡解] 2. x=713, y=1096.0, a*x=31372.0, b*y=77268.0, 总和=108640.0 [平衡解] 3. x=149, y=1448.0, a*x=6556.0, b*y=102084.0, 总和=108640.0 [原始解] 4. x=431, y=1272.0, a*x=18964.0, b*y=89676.0, 总和=108640.0 [原始解] 5. x=1277, y=744.0, a*x=56188.0, b*y=52452.0, 总和=108640.0 [原始解] 5. 组合: a=44, b=75.5 (8 个有效解) 1. x=863, y=936.0, a*x=37972.0, b*y=70668.0, 总和=108640.0 [平衡解] 2. x=1165, y=760.0, a*x=51260.0, b*y=57380.0, 总和=108640.0 [平衡解] 3. x=259, y=1288.0, a*x=11396.0, b*y=97244.0, 总和=108640.0 [原始解] 4. x=561, y=1112.0, a*x=24684.0, b*y=83956.0, 总和=108640.0 [原始解] 5. x=1467, y=584.0, a*x=64548.0, b*y=44092.0, 总和=108640.0 [原始解] 6. 组合: a=44, b=93 (13 个有效解) 1. x=719, y=828, a*x=31636.0, b*y=77004.0, 总和=108640.0 [平衡解] 2. x=905, y=740, a*x=39820.0, b*y=68820.0, 总和=108640.0 [平衡解] 3. x=161, y=1092, a*x=7084.0, b*y=101556.0, 总和=108640.0 [原始解] 4. x=347, y=1004, a*x=15268.0, b*y=93372.0, 总和=108640.0 [原始解] 5. x=533, y=916, a*x=23452.0, b*y=85188.0, 总和=108640.0 [原始解] 7. 组合: a=61, b=70.5 (13 个有效解) 1. x=757, y=886.0, a*x=46177.0, b*y=62463.0, 总和=108640.0 [平衡解] 2. x=898, y=764.0, a*x=54778.0, b*y=53862.0, 总和=108640.0 [平衡解] 3. x=52, y=1496.0, a*x=3172.0, b*y=105468.0, 总和=108640.0 [原始解] 4. x=193, y=1374.0, a*x=11773.0, b*y=96867.0, 总和=108640.0 [原始解] 5. x=334, y=1252.0, a*x=20374.0, b*y=88266.0, 总和=108640.0 [原始解] 8. 组合: a=61, b=75.5 (12 个有效解) 1. x=823, y=774.0, a*x=50203.0, b*y=58437.0, 总和=108640.0 [平衡解] 2. x=672, y=896.0, a*x=40992.0, b*y=67648.0, 总和=108640.0 [平衡解] 3. x=68, y=1384.0, a*x=4148.0, b*y=104492.0, 总和=108640.0 [原始解] 4. x=219, y=1262.0, a*x=13359.0, b*y=95281.0, 总和=108640.0 [原始解] 5. x=370, y=1140.0, a*x=22570.0, b*y=86070.0, 总和=108640.0 [原始解] 9. 组合: a=61, b=93 (19 个有效解) 1. x=697, y=711, a*x=42517.0, b*y=66123.0, 总和=108640.0 [平衡解] 2. x=790, y=650, a*x=48190.0, b*y=60450.0, 总和=108640.0 [平衡解] 3. x=46, y=1138, a*x=2806.0, b*y=105834.0, 总和=108640.0 [原始解] 4. x=139, y=1077, a*x=8479.0, b*y=100161.0, 总和=108640.0 [原始解] 5. x=232, y=1016, a*x=14152.0, b*y=94488.0, 总和=108640.0 [原始解] 10. 组合: a=70.5, b=75.5 (11 个有效解) 1. x=771, y=719.0, a*x=54355.5, b*y=54284.5, 总和=108640.0 [平衡解] 2. x=620, y=860.0, a*x=43710.0, b*y=64930.0, 总和=108640.0 [平衡解] 3. x=16, y=1424.0, a*x=1128.0, b*y=107512.0, 总和=108640.0 [原始解] 4. x=167, y=1283.0, a*x=11773.5, b*y=96866.5, 总和=108640.0 [原始解] 5. x=318, y=1142.0, a*x=22419.0, b*y=86221.0, 总和=108640.0 [原始解] 11. 组合: a=75.5, b=93 (8 个有效解) 1. x=674, y=621.0, a*x=50887.0, b*y=57753.0, 总和=108640.0 [平衡解] 2. x=488, y=772.0, a*x=36844.0, b*y=71796.0, 总和=108640.0 [平衡解] 3. x=116, y=1074.0, a*x=8758.0, b*y=99882.0, 总和=108640.0 [原始解] 4. x=302, y=923.0, a*x=22801.0, b*y=85839.0, 总和=108640.0 [原始解] 5. x=860, y=470.0, a*x=64930.0, b*y=43710.0, 总和=108640.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒