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 = 67323 # 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: 67323 ==== 尝试基础系数 ==== 找到 15 组2变量解: 1. 组合: a=36.5, b=41.5 (22 个有效解) 1. x=828, y=894.0, a*x=30222.0, b*y=37101.0, 总和=67323.0 [平衡解] 2. x=911, y=821.0, a*x=33251.5, b*y=34071.5, 总和=67323.0 [平衡解] 3. x=81, y=1551.0, a*x=2956.5, b*y=64366.5, 总和=67323.0 [原始解] 4. x=164, y=1478.0, a*x=5986.0, b*y=61337.0, 总和=67323.0 [原始解] 5. x=247, y=1405.0, a*x=9015.5, b*y=58307.5, 总和=67323.0 [原始解] 2. 组合: a=36.5, b=59 (16 个有效解) 1. x=658, y=734.0, a*x=24017.0, b*y=43306.0, 总和=67323.0 [平衡解] 2. x=776, y=661.0, a*x=28324.0, b*y=38999.0, 总和=67323.0 [平衡解] 3. x=68, y=1099.0, a*x=2482.0, b*y=64841.0, 总和=67323.0 [原始解] 4. x=186, y=1026.0, a*x=6789.0, b*y=60534.0, 总和=67323.0 [原始解] 5. x=304, y=953.0, a*x=11096.0, b*y=56227.0, 总和=67323.0 [原始解] 3. 组合: a=36.5, b=68.5 (13 个有效解) 1. x=649, y=637.0, a*x=23688.5, b*y=43634.5, 总和=67323.0 [平衡解] 2. x=512, y=710.0, a*x=18688.0, b*y=48635.0, 总和=67323.0 [平衡解] 3. x=101, y=929.0, a*x=3686.5, b*y=63636.5, 总和=67323.0 [原始解] 4. x=238, y=856.0, a*x=8687.0, b*y=58636.0, 总和=67323.0 [原始解] 5. x=375, y=783.0, a*x=13687.5, b*y=53635.5, 总和=67323.0 [原始解] 4. 组合: a=36.5, b=74 (13 个有效解) 1. x=626, y=601.0, a*x=22849.0, b*y=44474.0, 总和=67323.0 [平衡解] 2. x=478, y=674.0, a*x=17447.0, b*y=49876.0, 总和=67323.0 [平衡解] 3. x=34, y=893.0, a*x=1241.0, b*y=66082.0, 总和=67323.0 [原始解] 4. x=182, y=820.0, a*x=6643.0, b*y=60680.0, 总和=67323.0 [原始解] 5. x=330, y=747.0, a*x=12045.0, b*y=55278.0, 总和=67323.0 [原始解] 5. 组合: a=36.5, b=91.5 (10 个有效解) 1. x=576, y=506.0, a*x=21024.0, b*y=46299.0, 总和=67323.0 [平衡解] 2. x=393, y=579.0, a*x=14344.5, b*y=52978.5, 总和=67323.0 [平衡解] 3. x=27, y=725.0, a*x=985.5, b*y=66337.5, 总和=67323.0 [原始解] 4. x=210, y=652.0, a*x=7665.0, b*y=59658.0, 总和=67323.0 [原始解] 5. x=759, y=433.0, a*x=27703.5, b*y=39619.5, 总和=67323.0 [原始解] 6. 组合: a=41.5, b=59 (14 个有效解) 1. x=728, y=629.0, a*x=30212.0, b*y=37111.0, 总和=67323.0 [平衡解] 2. x=610, y=712.0, a*x=25315.0, b*y=42008.0, 总和=67323.0 [平衡解] 3. x=20, y=1127.0, a*x=830.0, b*y=66493.0, 总和=67323.0 [原始解] 4. x=138, y=1044.0, a*x=5727.0, b*y=61596.0, 总和=67323.0 [原始解] 5. x=256, y=961.0, a*x=10624.0, b*y=56699.0, 总和=67323.0 [原始解] 7. 组合: a=41.5, b=68.5 (12 个有效解) 1. x=551, y=649.0, a*x=22866.5, b*y=44456.5, 总和=67323.0 [平衡解] 2. x=688, y=566.0, a*x=28552.0, b*y=38771.0, 总和=67323.0 [平衡解] 3. x=3, y=981.0, a*x=124.5, b*y=67198.5, 总和=67323.0 [原始解] 4. x=140, y=898.0, a*x=5810.0, b*y=61513.0, 总和=67323.0 [原始解] 5. x=277, y=815.0, a*x=11495.5, b*y=55827.5, 总和=67323.0 [原始解] 8. 组合: a=41.5, b=74 (11 个有效解) 1. x=654, y=543.0, a*x=27141.0, b*y=40182.0, 总和=67323.0 [平衡解] 2. x=506, y=626.0, a*x=20999.0, b*y=46324.0, 总和=67323.0 [平衡解] 3. x=62, y=875.0, a*x=2573.0, b*y=64750.0, 总和=67323.0 [原始解] 4. x=210, y=792.0, a*x=8715.0, b*y=58608.0, 总和=67323.0 [原始解] 5. x=358, y=709.0, a*x=14857.0, b*y=52466.0, 总和=67323.0 [原始解] 9. 组合: a=41.5, b=91.5 (9 个有效解) 1. x=597, y=465.0, a*x=24775.5, b*y=42547.5, 总和=67323.0 [平衡解] 2. x=414, y=548.0, a*x=17181.0, b*y=50142.0, 总和=67323.0 [平衡解] 3. x=48, y=714.0, a*x=1992.0, b*y=65331.0, 总和=67323.0 [原始解] 4. x=231, y=631.0, a*x=9586.5, b*y=57736.5, 总和=67323.0 [原始解] 5. x=780, y=382.0, a*x=32370.0, b*y=34953.0, 总和=67323.0 [原始解] 10. 组合: a=59, b=68.5 (8 个有效解) 1. x=470, y=578.0, a*x=27730.0, b*y=39593.0, 总和=67323.0 [平衡解] 2. x=607, y=460.0, a*x=35813.0, b*y=31510.0, 总和=67323.0 [平衡解] 3. x=59, y=932.0, a*x=3481.0, b*y=63842.0, 总和=67323.0 [原始解] 4. x=196, y=814.0, a*x=11564.0, b*y=55759.0, 总和=67323.0 [原始解] 5. x=333, y=696.0, a*x=19647.0, b*y=47676.0, 总和=67323.0 [原始解] 11. 组合: a=59, b=74 (16 个有效解) 1. x=529, y=488, a*x=31211.0, b*y=36112.0, 总和=67323.0 [平衡解] 2. x=455, y=547, a*x=26845.0, b*y=40478.0, 总和=67323.0 [平衡解] 3. x=11, y=901, a*x=649.0, b*y=66674.0, 总和=67323.0 [原始解] 4. x=85, y=842, a*x=5015.0, b*y=62308.0, 总和=67323.0 [原始解] 5. x=159, y=783, a*x=9381.0, b*y=57942.0, 总和=67323.0 [原始解] 12. 组合: a=59, b=91.5 (6 个有效解) 1. x=468, y=434.0, a*x=27612.0, b*y=39711.0, 总和=67323.0 [平衡解] 2. x=285, y=552.0, a*x=16815.0, b*y=50508.0, 总和=67323.0 [平衡解] 3. x=102, y=670.0, a*x=6018.0, b*y=61305.0, 总和=67323.0 [原始解] 4. x=651, y=316.0, a*x=38409.0, b*y=28914.0, 总和=67323.0 [原始解] 5. x=834, y=198.0, a*x=49206.0, b*y=18117.0, 总和=67323.0 [原始解] 13. 组合: a=68.5, b=74 (7 个有效解) 1. x=474, y=471.0, a*x=32469.0, b*y=34854.0, 总和=67323.0 [平衡解] 2. x=326, y=608.0, a*x=22331.0, b*y=44992.0, 总和=67323.0 [平衡解] 3. x=30, y=882.0, a*x=2055.0, b*y=65268.0, 总和=67323.0 [原始解] 4. x=178, y=745.0, a*x=12193.0, b*y=55130.0, 总和=67323.0 [原始解] 5. x=622, y=334.0, a*x=42607.0, b*y=24716.0, 总和=67323.0 [原始解] 14. 组合: a=68.5, b=91.5 (5 个有效解) 1. x=351, y=473.0, a*x=24043.5, b*y=43279.5, 总和=67323.0 [平衡解] 2. x=534, y=336.0, a*x=36579.0, b*y=30744.0, 总和=67323.0 [平衡解] 3. x=168, y=610.0, a*x=11508.0, b*y=55815.0, 总和=67323.0 [原始解] 4. x=717, y=199.0, a*x=49114.5, b*y=18208.5, 总和=67323.0 [原始解] 5. x=900, y=62.0, a*x=61650.0, b*y=5673.0, 总和=67323.0 [原始解] 15. 组合: a=74, b=91.5 (5 个有效解) 1. x=477, y=350.0, a*x=35298.0, b*y=32025.0, 总和=67323.0 [平衡解] 2. x=294, y=498.0, a*x=21756.0, b*y=45567.0, 总和=67323.0 [平衡解] 3. x=111, y=646.0, a*x=8214.0, b*y=59109.0, 总和=67323.0 [原始解] 4. x=660, y=202.0, a*x=48840.0, b*y=18483.0, 总和=67323.0 [原始解] 5. x=843, y=54.0, a*x=62382.0, b*y=4941.0, 总和=67323.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒