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 = 153780 # 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: 153780 ==== 尝试基础系数 ==== 找到 14 组2变量解: 1. 组合: a=38.5, b=44 (100 个有效解) 1. x=1864, y=1864.0, a*x=71764.0, b*y=82016.0, 总和=153780.0 [平衡解] 2. x=1840, y=1885.0, a*x=70840.0, b*y=82940.0, 总和=153780.0 [平衡解] 3. x=664, y=2914.0, a*x=25564.0, b*y=128216.0, 总和=153780.0 [原始解] 4. x=688, y=2893.0, a*x=26488.0, b*y=127292.0, 总和=153780.0 [原始解] 5. x=712, y=2872.0, a*x=27412.0, b*y=126368.0, 总和=153780.0 [原始解] 2. 组合: a=38.5, b=61 (7 个有效解) 1. x=1624, y=1496.0, a*x=62524.0, b*y=91256.0, 总和=153780.0 [平衡解] 2. x=1258, y=1727.0, a*x=48433.0, b*y=105347.0, 总和=153780.0 [平衡解] 3. x=892, y=1958.0, a*x=34342.0, b*y=119438.0, 总和=153780.0 [原始解] 4. x=1990, y=1265.0, a*x=76615.0, b*y=77165.0, 总和=153780.0 [原始解] 5. x=2356, y=1034.0, a*x=90706.0, b*y=63074.0, 总和=153780.0 [原始解] 3. 组合: a=38.5, b=75.5 (6 个有效解) 1. x=1492, y=1276.0, a*x=57442.0, b*y=96338.0, 总和=153780.0 [平衡解] 2. x=1039, y=1507.0, a*x=40001.5, b*y=113778.5, 总和=153780.0 [平衡解] 3. x=1945, y=1045.0, a*x=74882.5, b*y=78897.5, 总和=153780.0 [原始解] 4. x=2398, y=814.0, a*x=92323.0, b*y=61457.0, 总和=153780.0 [原始解] 5. x=2851, y=583.0, a*x=109763.5, b*y=44016.5, 总和=153780.0 [原始解] 4. 组合: a=44, b=44 (100 个有效解) 1. x=763, y=2732, a*x=33572.0, b*y=120208.0, 总和=153780.0 [平衡解] 2. x=761, y=2734, a*x=33484.0, b*y=120296.0, 总和=153780.0 [平衡解] 3. x=565, y=2930, a*x=24860.0, b*y=128920.0, 总和=153780.0 [原始解] 4. x=567, y=2928, a*x=24948.0, b*y=128832.0, 总和=153780.0 [原始解] 5. x=569, y=2926, a*x=25036.0, b*y=128744.0, 总和=153780.0 [原始解] 5. 组合: a=44, b=61 (20 个有效解) 1. x=1421, y=1496, a*x=62524.0, b*y=91256.0, 总和=153780.0 [平衡解] 2. x=1543, y=1408, a*x=67892.0, b*y=85888.0, 总和=153780.0 [平衡解] 3. x=567, y=2112, a*x=24948.0, b*y=128832.0, 总和=153780.0 [原始解] 4. x=689, y=2024, a*x=30316.0, b*y=123464.0, 总和=153780.0 [原始解] 5. x=811, y=1936, a*x=35684.0, b*y=118096.0, 总和=153780.0 [原始解] 6. 组合: a=44, b=70.5 (9 个有效解) 1. x=1239, y=1408.0, a*x=54516.0, b*y=99264.0, 总和=153780.0 [平衡解] 2. x=1521, y=1232.0, a*x=66924.0, b*y=86856.0, 总和=153780.0 [平衡解] 3. x=675, y=1760.0, a*x=29700.0, b*y=124080.0, 总和=153780.0 [原始解] 4. x=957, y=1584.0, a*x=42108.0, b*y=111672.0, 总和=153780.0 [原始解] 5. x=1803, y=1056.0, a*x=79332.0, b*y=74448.0, 总和=153780.0 [原始解] 7. 组合: a=44, b=75.5 (8 个有效解) 1. x=1381, y=1232.0, a*x=60764.0, b*y=93016.0, 总和=153780.0 [平衡解] 2. x=1079, y=1408.0, a*x=47476.0, b*y=106304.0, 总和=153780.0 [平衡解] 3. x=777, y=1584.0, a*x=34188.0, b*y=119592.0, 总和=153780.0 [原始解] 4. x=1683, y=1056.0, a*x=74052.0, b*y=79728.0, 总和=153780.0 [原始解] 5. x=1985, y=880.0, a*x=87340.0, b*y=66440.0, 总和=153780.0 [原始解] 8. 组合: a=44, b=93 (12 个有效解) 1. x=1077, y=1144, a*x=47388.0, b*y=106392.0, 总和=153780.0 [平衡解] 2. x=1263, y=1056, a*x=55572.0, b*y=98208.0, 总和=153780.0 [平衡解] 3. x=705, y=1320, a*x=31020.0, b*y=122760.0, 总和=153780.0 [原始解] 4. x=891, y=1232, a*x=39204.0, b*y=114576.0, 总和=153780.0 [原始解] 5. x=1449, y=968, a*x=63756.0, b*y=90024.0, 总和=153780.0 [原始解] 9. 组合: a=61, b=70.5 (6 个有效解) 1. x=1215, y=1130.0, a*x=74115.0, b*y=79665.0, 总和=153780.0 [平衡解] 2. x=933, y=1374.0, a*x=56913.0, b*y=96867.0, 总和=153780.0 [平衡解] 3. x=651, y=1618.0, a*x=39711.0, b*y=114069.0, 总和=153780.0 [原始解] 4. x=1497, y=886.0, a*x=91317.0, b*y=62463.0, 总和=153780.0 [原始解] 5. x=1779, y=642.0, a*x=108519.0, b*y=45261.0, 总和=153780.0 [原始解] 10. 组合: a=61, b=75.5 (5 个有效解) 1. x=1261, y=1018.0, a*x=76921.0, b*y=76859.0, 总和=153780.0 [平衡解] 2. x=959, y=1262.0, a*x=58499.0, b*y=95281.0, 总和=153780.0 [平衡解] 3. x=657, y=1506.0, a*x=40077.0, b*y=113703.0, 总和=153780.0 [原始解] 4. x=1563, y=774.0, a*x=95343.0, b*y=58437.0, 总和=153780.0 [原始解] 5. x=1865, y=530.0, a*x=113765.0, b*y=40015.0, 总和=153780.0 [原始解] 11. 组合: a=61, b=93 (9 个有效解) 1. x=1065, y=955, a*x=64965.0, b*y=88815.0, 总和=153780.0 [平衡解] 2. x=879, y=1077, a*x=53619.0, b*y=100161.0, 总和=153780.0 [平衡解] 3. x=507, y=1321, a*x=30927.0, b*y=122853.0, 总和=153780.0 [原始解] 4. x=693, y=1199, a*x=42273.0, b*y=111507.0, 总和=153780.0 [原始解] 5. x=1251, y=833, a*x=76311.0, b*y=77469.0, 总和=153780.0 [原始解] 12. 组合: a=70.5, b=75.5 (9 个有效解) 1. x=1105, y=1005.0, a*x=77902.5, b*y=75877.5, 总和=153780.0 [平衡解] 2. x=954, y=1146.0, a*x=67257.0, b*y=86523.0, 总和=153780.0 [平衡解] 3. x=501, y=1569.0, a*x=35320.5, b*y=118459.5, 总和=153780.0 [原始解] 4. x=652, y=1428.0, a*x=45966.0, b*y=107814.0, 总和=153780.0 [原始解] 5. x=803, y=1287.0, a*x=56611.5, b*y=97168.5, 总和=153780.0 [原始解] 13. 组合: a=70.5, b=93 (24 个有效解) 1. x=936, y=944.0, a*x=65988.0, b*y=87792.0, 总和=153780.0 [平衡解] 2. x=998, y=897.0, a*x=70359.0, b*y=83421.0, 总和=153780.0 [平衡解] 3. x=378, y=1367.0, a*x=26649.0, b*y=127131.0, 总和=153780.0 [原始解] 4. x=440, y=1320.0, a*x=31020.0, b*y=122760.0, 总和=153780.0 [原始解] 5. x=502, y=1273.0, a*x=35391.0, b*y=118389.0, 总和=153780.0 [原始解] 14. 组合: a=75.5, b=93 (7 个有效解) 1. x=858, y=957.0, a*x=64779.0, b*y=89001.0, 总和=153780.0 [平衡解] 2. x=1044, y=806.0, a*x=78822.0, b*y=74958.0, 总和=153780.0 [平衡解] 3. x=486, y=1259.0, a*x=36693.0, b*y=117087.0, 总和=153780.0 [原始解] 4. x=672, y=1108.0, a*x=50736.0, b*y=103044.0, 总和=153780.0 [原始解] 5. x=1230, y=655.0, a*x=92865.0, b*y=60915.0, 总和=153780.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.02秒