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 =136786 # 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: 136786 ==== 尝试基础系数 ==== 找到 13 组2变量解: 1. 组合: a=36.5, b=41.5 (14 个有效解) 1. x=1726, y=1778.0, a*x=62999.0, b*y=73787.0, 总和=136786.0 [平衡解] 2. x=1975, y=1559.0, a*x=72087.5, b*y=64698.5, 总和=136786.0 [平衡解] 3. x=232, y=3092.0, a*x=8468.0, b*y=128318.0, 总和=136786.0 [原始解] 4. x=481, y=2873.0, a*x=17556.5, b*y=119229.5, 总和=136786.0 [原始解] 5. x=730, y=2654.0, a*x=26645.0, b*y=110141.0, 总和=136786.0 [原始解] 2. 组合: a=36.5, b=59 (9 个有效解) 1. x=1588, y=1336.0, a*x=57962.0, b*y=78824.0, 总和=136786.0 [平衡解] 2. x=1234, y=1555.0, a*x=45041.0, b*y=91745.0, 总和=136786.0 [平衡解] 3. x=526, y=1993.0, a*x=19199.0, b*y=117587.0, 总和=136786.0 [原始解] 4. x=880, y=1774.0, a*x=32120.0, b*y=104666.0, 总和=136786.0 [原始解] 5. x=1942, y=1117.0, a*x=70883.0, b*y=65903.0, 总和=136786.0 [原始解] 3. 组合: a=36.5, b=68.5 (8 个有效解) 1. x=1351, y=1277.0, a*x=49311.5, b*y=87474.5, 总和=136786.0 [平衡解] 2. x=940, y=1496.0, a*x=34310.0, b*y=102476.0, 总和=136786.0 [平衡解] 3. x=529, y=1715.0, a*x=19308.5, b*y=117477.5, 总和=136786.0 [原始解] 4. x=1762, y=1058.0, a*x=64313.0, b*y=72473.0, 总和=136786.0 [原始解] 5. x=2173, y=839.0, a*x=79314.5, b*y=57471.5, 总和=136786.0 [原始解] 4. 组合: a=36.5, b=74 (8 个有效解) 1. x=1264, y=1225.0, a*x=46136.0, b*y=90650.0, 总和=136786.0 [平衡解] 2. x=820, y=1444.0, a*x=29930.0, b*y=106856.0, 总和=136786.0 [平衡解] 3. x=376, y=1663.0, a*x=13724.0, b*y=123062.0, 总和=136786.0 [原始解] 4. x=1708, y=1006.0, a*x=62342.0, b*y=74444.0, 总和=136786.0 [原始解] 5. x=2152, y=787.0, a*x=78548.0, b*y=58238.0, 总和=136786.0 [原始解] 5. 组合: a=41.5, b=59 (9 个有效解) 1. x=1300, y=1404.0, a*x=53950.0, b*y=82836.0, 总和=136786.0 [平衡解] 2. x=1654, y=1155.0, a*x=68641.0, b*y=68145.0, 总和=136786.0 [平衡解] 3. x=238, y=2151.0, a*x=9877.0, b*y=126909.0, 总和=136786.0 [原始解] 4. x=592, y=1902.0, a*x=24568.0, b*y=112218.0, 总和=136786.0 [原始解] 5. x=946, y=1653.0, a*x=39259.0, b*y=97527.0, 总和=136786.0 [原始解] 6. 组合: a=41.5, b=68.5 (7 个有效解) 1. x=1246, y=1242.0, a*x=51709.0, b*y=85077.0, 总和=136786.0 [平衡解] 2. x=835, y=1491.0, a*x=34652.5, b*y=102133.5, 总和=136786.0 [平衡解] 3. x=424, y=1740.0, a*x=17596.0, b*y=119190.0, 总和=136786.0 [原始解] 4. x=1657, y=993.0, a*x=68765.5, b*y=68020.5, 总和=136786.0 [原始解] 5. x=2068, y=744.0, a*x=85822.0, b*y=50964.0, 总和=136786.0 [原始解] 7. 组合: a=41.5, b=74 (6 个有效解) 1. x=1060, y=1254.0, a*x=43990.0, b*y=92796.0, 总和=136786.0 [平衡解] 2. x=1504, y=1005.0, a*x=62416.0, b*y=74370.0, 总和=136786.0 [平衡解] 3. x=616, y=1503.0, a*x=25564.0, b*y=111222.0, 总和=136786.0 [原始解] 4. x=1948, y=756.0, a*x=80842.0, b*y=55944.0, 总和=136786.0 [原始解] 5. x=2392, y=507.0, a*x=99268.0, b*y=37518.0, 总和=136786.0 [原始解] 8. 组合: a=41.5, b=91.5 (16 个有效解) 1. x=1078, y=1006.0, a*x=44737.0, b*y=92049.0, 总和=136786.0 [平衡解] 2. x=895, y=1089.0, a*x=37142.5, b*y=99643.5, 总和=136786.0 [平衡解] 3. x=346, y=1338.0, a*x=14359.0, b*y=122427.0, 总和=136786.0 [原始解] 4. x=529, y=1255.0, a*x=21953.5, b*y=114832.5, 总和=136786.0 [原始解] 5. x=712, y=1172.0, a*x=29548.0, b*y=107238.0, 总和=136786.0 [原始解] 9. 组合: a=59, b=68.5 (7 个有效解) 1. x=1169, y=990.0, a*x=68971.0, b*y=67815.0, 总和=136786.0 [平衡解] 2. x=895, y=1226.0, a*x=52805.0, b*y=83981.0, 总和=136786.0 [平衡解] 3. x=347, y=1698.0, a*x=20473.0, b*y=116313.0, 总和=136786.0 [原始解] 4. x=621, y=1462.0, a*x=36639.0, b*y=100147.0, 总和=136786.0 [原始解] 5. x=1443, y=754.0, a*x=85137.0, b*y=51649.0, 总和=136786.0 [原始解] 10. 组合: a=59, b=91.5 (6 个有效解) 1. x=1025, y=834.0, a*x=60475.0, b*y=76311.0, 总和=136786.0 [平衡解] 2. x=659, y=1070.0, a*x=38881.0, b*y=97905.0, 总和=136786.0 [平衡解] 3. x=293, y=1306.0, a*x=17287.0, b*y=119499.0, 总和=136786.0 [原始解] 4. x=1391, y=598.0, a*x=82069.0, b*y=54717.0, 总和=136786.0 [原始解] 5. x=1757, y=362.0, a*x=103663.0, b*y=33123.0, 总和=136786.0 [原始解] 11. 组合: a=68.5, b=74 (12 个有效解) 1. x=976, y=945.0, a*x=66856.0, b*y=69930.0, 总和=136786.0 [平衡解] 2. x=828, y=1082.0, a*x=56718.0, b*y=80068.0, 总和=136786.0 [平衡解] 3. x=236, y=1630.0, a*x=16166.0, b*y=120620.0, 总和=136786.0 [原始解] 4. x=384, y=1493.0, a*x=26304.0, b*y=110482.0, 总和=136786.0 [原始解] 5. x=532, y=1356.0, a*x=36442.0, b*y=100344.0, 总和=136786.0 [原始解] 12. 组合: a=68.5, b=91.5 (10 个有效解) 1. x=784, y=908.0, a*x=53704.0, b*y=83082.0, 总和=136786.0 [平衡解] 2. x=967, y=771.0, a*x=66239.5, b*y=70546.5, 总和=136786.0 [平衡解] 3. x=235, y=1319.0, a*x=16097.5, b*y=120688.5, 总和=136786.0 [原始解] 4. x=418, y=1182.0, a*x=28633.0, b*y=108153.0, 总和=136786.0 [原始解] 5. x=601, y=1045.0, a*x=41168.5, b*y=95617.5, 总和=136786.0 [原始解] 13. 组合: a=74, b=91.5 (9 个有效解) 1. x=884, y=780.0, a*x=65416.0, b*y=71370.0, 总和=136786.0 [平衡解] 2. x=701, y=928.0, a*x=51874.0, b*y=84912.0, 总和=136786.0 [平衡解] 3. x=152, y=1372.0, a*x=11248.0, b*y=125538.0, 总和=136786.0 [原始解] 4. x=335, y=1224.0, a*x=24790.0, b*y=111996.0, 总和=136786.0 [原始解] 5. x=518, y=1076.0, a*x=38332.0, b*y=98454.0, 总和=136786.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒