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 = 201960 # 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: 201960 ==== 尝试基础系数 ==== 找到 14 组2变量解: 1. 组合: a=38.5, b=44 (60 个有效解) 1. x=2440, y=2455.0, a*x=93940.0, b*y=108020.0, 总和=201960.0 [平衡解] 2. x=2464, y=2434.0, a*x=94864.0, b*y=107096.0, 总和=201960.0 [平衡解] 3. x=1912, y=2917.0, a*x=73612.0, b*y=128348.0, 总和=201960.0 [原始解] 4. x=1936, y=2896.0, a*x=74536.0, b*y=127424.0, 总和=201960.0 [原始解] 5. x=1960, y=2875.0, a*x=75460.0, b*y=126500.0, 总和=201960.0 [原始解] 2. 组合: a=38.5, b=61 (4 个有效解) 1. x=2248, y=1892.0, a*x=86548.0, b*y=115412.0, 总和=201960.0 [平衡解] 2. x=2614, y=1661.0, a*x=100639.0, b*y=101321.0, 总和=201960.0 [平衡解] 3. x=2980, y=1430.0, a*x=114730.0, b*y=87230.0, 总和=201960.0 [原始解] 4. x=3346, y=1199.0, a*x=128821.0, b*y=73139.0, 总和=201960.0 [原始解] 3. 组合: a=38.5, b=75.5 (3 个有效解) 1. x=2161, y=1573.0, a*x=83198.5, b*y=118761.5, 总和=201960.0 [平衡解] 2. x=2614, y=1342.0, a*x=100639.0, b*y=101321.0, 总和=201960.0 [平衡解] 3. x=3067, y=1111.0, a*x=118079.5, b*y=83880.5, 总和=201960.0 [原始解] 4. 组合: a=44, b=44 (100 个有效解) 1. x=1857, y=2733, a*x=81708.0, b*y=120252.0, 总和=201960.0 [平衡解] 2. x=1855, y=2735, a*x=81620.0, b*y=120340.0, 总和=201960.0 [平衡解] 3. x=1659, y=2931, a*x=72996.0, b*y=128964.0, 总和=201960.0 [原始解] 4. x=1661, y=2929, a*x=73084.0, b*y=128876.0, 总和=201960.0 [原始解] 5. x=1663, y=2927, a*x=73172.0, b*y=128788.0, 总和=201960.0 [原始解] 5. 组合: a=44, b=61 (10 个有效解) 1. x=1967, y=1892, a*x=86548.0, b*y=115412.0, 总和=201960.0 [平衡解] 2. x=1845, y=1980, a*x=81180.0, b*y=120780.0, 总和=201960.0 [平衡解] 3. x=1723, y=2068, a*x=75812.0, b*y=126148.0, 总和=201960.0 [原始解] 4. x=2089, y=1804, a*x=91916.0, b*y=110044.0, 总和=201960.0 [原始解] 5. x=2211, y=1716, a*x=97284.0, b*y=104676.0, 总和=201960.0 [原始解] 6. 组合: a=44, b=70.5 (4 个有效解) 1. x=1911, y=1672.0, a*x=84084.0, b*y=117876.0, 总和=201960.0 [平衡解] 2. x=2193, y=1496.0, a*x=96492.0, b*y=105468.0, 总和=201960.0 [平衡解] 3. x=2475, y=1320.0, a*x=108900.0, b*y=93060.0, 总和=201960.0 [原始解] 4. x=2757, y=1144.0, a*x=121308.0, b*y=80652.0, 总和=201960.0 [原始解] 7. 组合: a=44, b=75.5 (5 个有效解) 1. x=1721, y=1672.0, a*x=75724.0, b*y=126236.0, 总和=201960.0 [平衡解] 2. x=2023, y=1496.0, a*x=89012.0, b*y=112948.0, 总和=201960.0 [平衡解] 3. x=2325, y=1320.0, a*x=102300.0, b*y=99660.0, 总和=201960.0 [原始解] 4. x=2627, y=1144.0, a*x=115588.0, b*y=86372.0, 总和=201960.0 [原始解] 5. x=2929, y=968.0, a*x=128876.0, b*y=73084.0, 总和=201960.0 [原始解] 8. 组合: a=44, b=93 (7 个有效解) 1. x=1707, y=1364, a*x=75108.0, b*y=126852.0, 总和=201960.0 [平衡解] 2. x=1893, y=1276, a*x=83292.0, b*y=118668.0, 总和=201960.0 [平衡解] 3. x=2079, y=1188, a*x=91476.0, b*y=110484.0, 总和=201960.0 [原始解] 4. x=2265, y=1100, a*x=99660.0, b*y=102300.0, 总和=201960.0 [原始解] 5. x=2451, y=1012, a*x=107844.0, b*y=94116.0, 总和=201960.0 [原始解] 9. 组合: a=61, b=70.5 (3 个有效解) 1. x=1635, y=1450.0, a*x=99735.0, b*y=102225.0, 总和=201960.0 [平衡解] 2. x=1353, y=1694.0, a*x=82533.0, b*y=119427.0, 总和=201960.0 [平衡解] 3. x=1917, y=1206.0, a*x=116937.0, b*y=85023.0, 总和=201960.0 [原始解] 10. 组合: a=61, b=75.5 (3 个有效解) 1. x=1531, y=1438.0, a*x=93391.0, b*y=108569.0, 总和=201960.0 [平衡解] 2. x=1229, y=1682.0, a*x=74969.0, b*y=126991.0, 总和=201960.0 [平衡解] 3. x=1833, y=1194.0, a*x=111813.0, b*y=90147.0, 总和=201960.0 [原始解] 11. 组合: a=61, b=93 (5 个有效解) 1. x=1245, y=1355, a*x=75945.0, b*y=126015.0, 总和=201960.0 [平衡解] 2. x=1431, y=1233, a*x=87291.0, b*y=114669.0, 总和=201960.0 [平衡解] 3. x=1617, y=1111, a*x=98637.0, b*y=103323.0, 总和=201960.0 [原始解] 4. x=1803, y=989, a*x=109983.0, b*y=91977.0, 总和=201960.0 [原始解] 5. x=1989, y=867, a*x=121329.0, b*y=80631.0, 总和=201960.0 [原始解] 12. 组合: a=70.5, b=75.5 (5 个有效解) 1. x=1435, y=1335.0, a*x=101167.5, b*y=100792.5, 总和=201960.0 [平衡解] 2. x=1284, y=1476.0, a*x=90522.0, b*y=111438.0, 总和=201960.0 [平衡解] 3. x=1133, y=1617.0, a*x=79876.5, b*y=122083.5, 总和=201960.0 [原始解] 4. x=1586, y=1194.0, a*x=111813.0, b*y=90147.0, 总和=201960.0 [原始解] 5. x=1737, y=1053.0, a*x=122458.5, b*y=79501.5, 总和=201960.0 [原始解] 13. 组合: a=70.5, b=93 (13 个有效解) 1. x=1254, y=1221.0, a*x=88407.0, b*y=113553.0, 总和=201960.0 [平衡解] 2. x=1192, y=1268.0, a*x=84036.0, b*y=117924.0, 总和=201960.0 [平衡解] 3. x=1068, y=1362.0, a*x=75294.0, b*y=126666.0, 总和=201960.0 [原始解] 4. x=1130, y=1315.0, a*x=79665.0, b*y=122295.0, 总和=201960.0 [原始解] 5. x=1316, y=1174.0, a*x=92778.0, b*y=109182.0, 总和=201960.0 [原始解] 14. 组合: a=75.5, b=93 (4 个有效解) 1. x=1134, y=1251.0, a*x=85617.0, b*y=116343.0, 总和=201960.0 [平衡解] 2. x=1320, y=1100.0, a*x=99660.0, b*y=102300.0, 总和=201960.0 [平衡解] 3. x=1506, y=949.0, a*x=113703.0, b*y=88257.0, 总和=201960.0 [原始解] 4. x=1692, y=798.0, a*x=127746.0, b*y=74214.0, 总和=201960.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.02秒