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 =82495 # 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(调整为259000) PRODUCT_RANGE_THRESHOLD = 125000 # 乘积范围限制阈值(调整为125000) HIGH_TARGET_THRESHOLD = 259000 # 更高目标值阈值(调整为259000) 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): """检查单个乘积是否在有效范围内""" if TARGET > PRODUCT_RANGE_THRESHOLD: # TARGET > 125000 if TARGET > HIGH_TARGET_THRESHOLD: # TARGET > 259000 return p <= 125000 # 单个乘积上限 else: # 125000 < TARGET <= 259000 return 74000 <= p <= 125000 # 单个乘积范围 else: # TARGET <= 125000 return True # 小目标值取消所有限制 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""" solutions = defaultdict(list) for i, a in enumerate(values): for b in values[i:]: seen_xy = set() 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): remainder = TARGET - a * x if remainder < b: break if remainder > b * 10000: continue if remainder % b == 0: y = remainder // b if 1 <= y <= 10000 and is_valid_product(b * y): 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,使用并行计算""" solutions = defaultdict(list) sorted_values = sorted(values) # 预计算每个系数的有效范围 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75085 < 259000,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: 82495 ==== 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=1097, y=1023.0, a*x=40040.5, b*y=42454.5, 总和=82495.0 [平衡解] 2. x=931, y=1169.0, a*x=33981.5, b*y=48513.5, 总和=82495.0 [平衡解] 3. x=101, y=1899.0, a*x=3686.5, b*y=78808.5, 总和=82495.0 [原始解] 4. x=267, y=1753.0, a*x=9745.5, b*y=72749.5, 总和=82495.0 [原始解] 5. x=433, y=1607.0, a*x=15804.5, b*y=66690.5, 总和=82495.0 [原始解] 2. 组合: a=36.5, b=68.5 (9 个有效解) 1. x=877, y=737.0, a*x=32010.5, b*y=50484.5, 总和=82495.0 [平衡解] 2. x=603, y=883.0, a*x=22009.5, b*y=60485.5, 总和=82495.0 [平衡解] 3. x=55, y=1175.0, a*x=2007.5, b*y=80487.5, 总和=82495.0 [原始解] 4. x=329, y=1029.0, a*x=12008.5, b*y=70486.5, 总和=82495.0 [原始解] 5. x=1151, y=591.0, a*x=42011.5, b*y=40483.5, 总和=82495.0 [原始解] 3. 组合: a=36.5, b=91.5 (6 个有效解) 1. x=563, y=677.0, a*x=20549.5, b*y=61945.5, 总和=82495.0 [平衡解] 2. x=929, y=531.0, a*x=33908.5, b*y=48586.5, 总和=82495.0 [平衡解] 3. x=197, y=823.0, a*x=7190.5, b*y=75304.5, 总和=82495.0 [原始解] 4. x=1295, y=385.0, a*x=47267.5, b*y=35227.5, 总和=82495.0 [原始解] 5. x=1661, y=239.0, a*x=60626.5, b*y=21868.5, 总和=82495.0 [原始解] 4. 组合: a=41.5, b=59 (17 个有效解) 1. x=832, y=813.0, a*x=34528.0, b*y=47967.0, 总和=82495.0 [平衡解] 2. x=714, y=896.0, a*x=29631.0, b*y=52864.0, 总和=82495.0 [平衡解] 3. x=6, y=1394.0, a*x=249.0, b*y=82246.0, 总和=82495.0 [原始解] 4. x=124, y=1311.0, a*x=5146.0, b*y=77349.0, 总和=82495.0 [原始解] 5. x=242, y=1228.0, a*x=10043.0, b*y=72452.0, 总和=82495.0 [原始解] 5. 组合: a=41.5, b=68.5 (14 个有效解) 1. x=806, y=716.0, a*x=33449.0, b*y=49046.0, 总和=82495.0 [平衡解] 2. x=669, y=799.0, a*x=27763.5, b*y=54731.5, 总和=82495.0 [平衡解] 3. x=121, y=1131.0, a*x=5021.5, b*y=77473.5, 总和=82495.0 [原始解] 4. x=258, y=1048.0, a*x=10707.0, b*y=71788.0, 总和=82495.0 [原始解] 5. x=395, y=965.0, a*x=16392.5, b*y=66102.5, 总和=82495.0 [原始解] 6. 组合: a=41.5, b=74 (14 个有效解) 1. x=786, y=674.0, a*x=32619.0, b*y=49876.0, 总和=82495.0 [平衡解] 2. x=638, y=757.0, a*x=26477.0, b*y=56018.0, 总和=82495.0 [平衡解] 3. x=46, y=1089.0, a*x=1909.0, b*y=80586.0, 总和=82495.0 [原始解] 4. x=194, y=1006.0, a*x=8051.0, b*y=74444.0, 总和=82495.0 [原始解] 5. x=342, y=923.0, a*x=14193.0, b*y=68302.0, 总和=82495.0 [原始解] 7. 组合: a=41.5, b=91.5 (11 个有效解) 1. x=601, y=629.0, a*x=24941.5, b*y=57553.5, 总和=82495.0 [平衡解] 2. x=784, y=546.0, a*x=32536.0, b*y=49959.0, 总和=82495.0 [平衡解] 3. x=52, y=878.0, a*x=2158.0, b*y=80337.0, 总和=82495.0 [原始解] 4. x=235, y=795.0, a*x=9752.5, b*y=72742.5, 总和=82495.0 [原始解] 5. x=418, y=712.0, a*x=17347.0, b*y=65148.0, 总和=82495.0 [原始解] 8. 组合: a=59, b=68.5 (11 个有效解) 1. x=690, y=610.0, a*x=40710.0, b*y=41785.0, 总和=82495.0 [平衡解] 2. x=553, y=728.0, a*x=32627.0, b*y=49868.0, 总和=82495.0 [平衡解] 3. x=5, y=1200.0, a*x=295.0, b*y=82200.0, 总和=82495.0 [原始解] 4. x=142, y=1082.0, a*x=8378.0, b*y=74117.0, 总和=82495.0 [原始解] 5. x=279, y=964.0, a*x=16461.0, b*y=66034.0, 总和=82495.0 [原始解] 9. 组合: a=59, b=74 (19 个有效解) 1. x=593, y=642, a*x=34987.0, b*y=47508.0, 总和=82495.0 [平衡解] 2. x=667, y=583, a*x=39353.0, b*y=43142.0, 总和=82495.0 [平衡解] 3. x=1, y=1114, a*x=59.0, b*y=82436.0, 总和=82495.0 [原始解] 4. x=75, y=1055, a*x=4425.0, b*y=78070.0, 总和=82495.0 [原始解] 5. x=149, y=996, a*x=8791.0, b*y=73704.0, 总和=82495.0 [原始解] 10. 组合: a=59, b=91.5 (8 个有效解) 1. x=629, y=496.0, a*x=37111.0, b*y=45384.0, 总和=82495.0 [平衡解] 2. x=446, y=614.0, a*x=26314.0, b*y=56181.0, 总和=82495.0 [平衡解] 3. x=80, y=850.0, a*x=4720.0, b*y=77775.0, 总和=82495.0 [原始解] 4. x=263, y=732.0, a*x=15517.0, b*y=66978.0, 总和=82495.0 [原始解] 5. x=812, y=378.0, a*x=47908.0, b*y=34587.0, 总和=82495.0 [原始解] 11. 组合: a=68.5, b=74 (8 个有效解) 1. x=514, y=639.0, a*x=35209.0, b*y=47286.0, 总和=82495.0 [平衡解] 2. x=662, y=502.0, a*x=45347.0, b*y=37148.0, 总和=82495.0 [平衡解] 3. x=70, y=1050.0, a*x=4795.0, b*y=77700.0, 总和=82495.0 [原始解] 4. x=218, y=913.0, a*x=14933.0, b*y=67562.0, 总和=82495.0 [原始解] 5. x=366, y=776.0, a*x=25071.0, b*y=57424.0, 总和=82495.0 [原始解] 12. 组合: a=68.5, b=91.5 (6 个有效解) 1. x=487, y=537.0, a*x=33359.5, b*y=49135.5, 总和=82495.0 [平衡解] 2. x=670, y=400.0, a*x=45895.0, b*y=36600.0, 总和=82495.0 [平衡解] 3. x=121, y=811.0, a*x=8288.5, b*y=74206.5, 总和=82495.0 [原始解] 4. x=304, y=674.0, a*x=20824.0, b*y=61671.0, 总和=82495.0 [原始解] 5. x=853, y=263.0, a*x=58430.5, b*y=24064.5, 总和=82495.0 [原始解] 13. 组合: a=74, b=91.5 (6 个有效解) 1. x=410, y=570.0, a*x=30340.0, b*y=52155.0, 总和=82495.0 [平衡解] 2. x=593, y=422.0, a*x=43882.0, b*y=38613.0, 总和=82495.0 [平衡解] 3. x=44, y=866.0, a*x=3256.0, b*y=79239.0, 总和=82495.0 [原始解] 4. x=227, y=718.0, a*x=16798.0, b*y=65697.0, 总和=82495.0 [原始解] 5. x=776, y=274.0, a*x=57424.0, b*y=25071.0, 总和=82495.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒