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 = 115000 # 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: 115000 ==== 尝试基础系数 ==== 找到 11 组2变量解: 1. 组合: a=38.5, b=70.5 (11 个有效解) 1. x=1165, y=995.0, a*x=44852.5, b*y=70147.5, 总和=115000.0 [平衡解] 2. x=883, y=1149.0, a*x=33995.5, b*y=81004.5, 总和=115000.0 [平衡解] 3. x=37, y=1611.0, a*x=1424.5, b*y=113575.5, 总和=115000.0 [原始解] 4. x=319, y=1457.0, a*x=12281.5, b*y=102718.5, 总和=115000.0 [原始解] 5. x=601, y=1303.0, a*x=23138.5, b*y=91861.5, 总和=115000.0 [原始解] 2. 组合: a=38.5, b=75.5 (10 个有效解) 1. x=1075, y=975.0, a*x=41387.5, b*y=73612.5, 总和=115000.0 [平衡解] 2. x=773, y=1129.0, a*x=29760.5, b*y=85239.5, 总和=115000.0 [平衡解] 3. x=169, y=1437.0, a*x=6506.5, b*y=108493.5, 总和=115000.0 [原始解] 4. x=471, y=1283.0, a*x=18133.5, b*y=96866.5, 总和=115000.0 [原始解] 5. x=1377, y=821.0, a*x=53014.5, b*y=61985.5, 总和=115000.0 [原始解] 3. 组合: a=44, b=61 (22 个有效解) 1. x=1133, y=1068, a*x=49852.0, b*y=65148.0, 总和=115000.0 [平衡解] 2. x=1011, y=1156, a*x=44484.0, b*y=70516.0, 总和=115000.0 [平衡解] 3. x=35, y=1860, a*x=1540.0, b*y=113460.0, 总和=115000.0 [原始解] 4. x=157, y=1772, a*x=6908.0, b*y=108092.0, 总和=115000.0 [原始解] 5. x=279, y=1684, a*x=12276.0, b*y=102724.0, 总和=115000.0 [原始解] 4. 组合: a=44, b=70.5 (9 个有效解) 1. x=1037, y=984.0, a*x=45628.0, b*y=69372.0, 总和=115000.0 [平衡解] 2. x=755, y=1160.0, a*x=33220.0, b*y=81780.0, 总和=115000.0 [平衡解] 3. x=191, y=1512.0, a*x=8404.0, b*y=106596.0, 总和=115000.0 [原始解] 4. x=473, y=1336.0, a*x=20812.0, b*y=94188.0, 总和=115000.0 [原始解] 5. x=1319, y=808.0, a*x=58036.0, b*y=56964.0, 总和=115000.0 [原始解] 5. 组合: a=44, b=75.5 (9 个有效解) 1. x=1035, y=920.0, a*x=45540.0, b*y=69460.0, 总和=115000.0 [平衡解] 2. x=733, y=1096.0, a*x=32252.0, b*y=82748.0, 总和=115000.0 [平衡解] 3. x=129, y=1448.0, a*x=5676.0, b*y=109324.0, 总和=115000.0 [原始解] 4. x=431, y=1272.0, a*x=18964.0, b*y=96036.0, 总和=115000.0 [原始解] 5. x=1337, y=744.0, a*x=58828.0, b*y=56172.0, 总和=115000.0 [原始解] 6. 组合: a=44, b=93 (14 个有效解) 1. x=779, y=868, a*x=34276.0, b*y=80724.0, 总和=115000.0 [平衡解] 2. x=965, y=780, a*x=42460.0, b*y=72540.0, 总和=115000.0 [平衡解] 3. x=35, y=1220, a*x=1540.0, b*y=113460.0, 总和=115000.0 [原始解] 4. x=221, y=1132, a*x=9724.0, b*y=105276.0, 总和=115000.0 [原始解] 5. x=407, y=1044, a*x=17908.0, b*y=97092.0, 总和=115000.0 [原始解] 7. 组合: a=61, b=70.5 (14 个有效解) 1. x=889, y=862.0, a*x=54229.0, b*y=60771.0, 总和=115000.0 [平衡解] 2. x=748, y=984.0, a*x=45628.0, b*y=69372.0, 总和=115000.0 [平衡解] 3. x=43, y=1594.0, a*x=2623.0, b*y=112377.0, 总和=115000.0 [原始解] 4. x=184, y=1472.0, a*x=11224.0, b*y=103776.0, 总和=115000.0 [原始解] 5. x=325, y=1350.0, a*x=19825.0, b*y=95175.0, 总和=115000.0 [原始解] 8. 组合: a=61, b=75.5 (12 个有效解) 1. x=853, y=834.0, a*x=52033.0, b*y=62967.0, 总和=115000.0 [平衡解] 2. x=702, y=956.0, a*x=42822.0, b*y=72178.0, 总和=115000.0 [平衡解] 3. x=98, y=1444.0, a*x=5978.0, b*y=109022.0, 总和=115000.0 [原始解] 4. x=249, y=1322.0, a*x=15189.0, b*y=99811.0, 总和=115000.0 [原始解] 5. x=400, y=1200.0, a*x=24400.0, b*y=90600.0, 总和=115000.0 [原始解] 9. 组合: a=61, b=93 (21 个有效解) 1. x=754, y=742, a*x=45994.0, b*y=69006.0, 总和=115000.0 [平衡解] 2. x=661, y=803, a*x=40321.0, b*y=74679.0, 总和=115000.0 [平衡解] 3. x=10, y=1230, a*x=610.0, b*y=114390.0, 总和=115000.0 [原始解] 4. x=103, y=1169, a*x=6283.0, b*y=108717.0, 总和=115000.0 [原始解] 5. x=196, y=1108, a*x=11956.0, b*y=103044.0, 总和=115000.0 [原始解] 10. 组合: a=70.5, b=75.5 (11 个有效解) 1. x=858, y=722.0, a*x=60489.0, b*y=54511.0, 总和=115000.0 [平衡解] 2. x=707, y=863.0, a*x=49843.5, b*y=65156.5, 总和=115000.0 [平衡解] 3. x=103, y=1427.0, a*x=7261.5, b*y=107738.5, 总和=115000.0 [原始解] 4. x=254, y=1286.0, a*x=17907.0, b*y=97093.0, 总和=115000.0 [原始解] 5. x=405, y=1145.0, a*x=28552.5, b*y=86447.5, 总和=115000.0 [原始解] 11. 组合: a=75.5, b=93 (8 个有效解) 1. x=656, y=704.0, a*x=49528.0, b*y=65472.0, 总和=115000.0 [平衡解] 2. x=842, y=553.0, a*x=63571.0, b*y=51429.0, 总和=115000.0 [平衡解] 3. x=98, y=1157.0, a*x=7399.0, b*y=107601.0, 总和=115000.0 [原始解] 4. x=284, y=1006.0, a*x=21442.0, b*y=93558.0, 总和=115000.0 [原始解] 5. x=470, y=855.0, a*x=35485.0, b*y=79515.0, 总和=115000.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒