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 = 86317 # 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: 86317 ==== 尝试基础系数 ==== 找到 1 组1变量解: 1. 组合: a=36.5 (1 个有效解) 1. x=1463, a*x=86317.0, 总和=86317.0 [平衡解] 找到 12 组2变量解: 1. 组合: a=36.5, b=41.5 (14 个有效解) 1. x=1063, y=1145.0, a*x=38799.5, b*y=47517.5, 总和=86317.0 [平衡解] 2. x=1229, y=999.0, a*x=44858.5, b*y=41458.5, 总和=86317.0 [平衡解] 3. x=67, y=2021.0, a*x=2445.5, b*y=83871.5, 总和=86317.0 [原始解] 4. x=233, y=1875.0, a*x=8504.5, b*y=77812.5, 总和=86317.0 [原始解] 5. x=399, y=1729.0, a*x=14563.5, b*y=71753.5, 总和=86317.0 [原始解] 2. 组合: a=36.5, b=68.5 (8 个有效解) 1. x=749, y=861.0, a*x=27338.5, b*y=58978.5, 总和=86317.0 [平衡解] 2. x=1023, y=715.0, a*x=37339.5, b*y=48977.5, 总和=86317.0 [平衡解] 3. x=201, y=1153.0, a*x=7336.5, b*y=78980.5, 总和=86317.0 [原始解] 4. x=475, y=1007.0, a*x=17337.5, b*y=68979.5, 总和=86317.0 [原始解] 5. x=1297, y=569.0, a*x=47340.5, b*y=38976.5, 总和=86317.0 [原始解] 3. 组合: a=36.5, b=91.5 (7 个有效解) 1. x=773, y=635.0, a*x=28214.5, b*y=58102.5, 总和=86317.0 [平衡解] 2. x=407, y=781.0, a*x=14855.5, b*y=71461.5, 总和=86317.0 [平衡解] 3. x=41, y=927.0, a*x=1496.5, b*y=84820.5, 总和=86317.0 [原始解] 4. x=1139, y=489.0, a*x=41573.5, b*y=44743.5, 总和=86317.0 [原始解] 5. x=1505, y=343.0, a*x=54932.5, b*y=31384.5, 总和=86317.0 [原始解] 4. 组合: a=41.5, b=68.5 (7 个有效解) 1. x=771, y=793.0, a*x=31996.5, b*y=54320.5, 总和=86317.0 [平衡解] 2. x=1045, y=627.0, a*x=43367.5, b*y=42949.5, 总和=86317.0 [平衡解] 3. x=223, y=1125.0, a*x=9254.5, b*y=77062.5, 总和=86317.0 [原始解] 4. x=497, y=959.0, a*x=20625.5, b*y=65691.5, 总和=86317.0 [原始解] 5. x=1319, y=461.0, a*x=54738.5, b*y=31578.5, 总和=86317.0 [原始解] 5. 组合: a=41.5, b=91.5 (5 个有效解) 1. x=649, y=649.0, a*x=26933.5, b*y=59383.5, 总和=86317.0 [平衡解] 2. x=283, y=815.0, a*x=11744.5, b*y=74572.5, 总和=86317.0 [平衡解] 3. x=1015, y=483.0, a*x=42122.5, b*y=44194.5, 总和=86317.0 [原始解] 4. x=1381, y=317.0, a*x=57311.5, b*y=29005.5, 总和=86317.0 [原始解] 5. x=1747, y=151.0, a*x=72500.5, b*y=13816.5, 总和=86317.0 [原始解] 6. 组合: a=59, b=59 (100 个有效解) 1. x=100, y=1363, a*x=5900.0, b*y=80417.0, 总和=86317.0 [平衡解] 2. x=99, y=1364, a*x=5841.0, b*y=80476.0, 总和=86317.0 [平衡解] 3. x=1, y=1462, a*x=59.0, b*y=86258.0, 总和=86317.0 [原始解] 4. x=2, y=1461, a*x=118.0, b*y=86199.0, 总和=86317.0 [原始解] 5. x=3, y=1460, a*x=177.0, b*y=86140.0, 总和=86317.0 [原始解] 7. 组合: a=59, b=68.5 (10 个有效解) 1. x=641, y=708.0, a*x=37819.0, b*y=48498.0, 总和=86317.0 [平衡解] 2. x=778, y=590.0, a*x=45902.0, b*y=40415.0, 总和=86317.0 [平衡解] 3. x=93, y=1180.0, a*x=5487.0, b*y=80830.0, 总和=86317.0 [原始解] 4. x=230, y=1062.0, a*x=13570.0, b*y=72747.0, 总和=86317.0 [原始解] 5. x=367, y=944.0, a*x=21653.0, b*y=64664.0, 总和=86317.0 [原始解] 8. 组合: a=59, b=74 (19 个有效解) 1. x=649, y=649, a*x=38291.0, b*y=48026.0, 总和=86317.0 [平衡解] 2. x=575, y=708, a*x=33925.0, b*y=52392.0, 总和=86317.0 [平衡解] 3. x=57, y=1121, a*x=3363.0, b*y=82954.0, 总和=86317.0 [原始解] 4. x=131, y=1062, a*x=7729.0, b*y=78588.0, 总和=86317.0 [原始解] 5. x=205, y=1003, a*x=12095.0, b*y=74222.0, 总和=86317.0 [原始解] 9. 组合: a=59, b=91.5 (7 个有效解) 1. x=548, y=590.0, a*x=32332.0, b*y=53985.0, 总和=86317.0 [平衡解] 2. x=731, y=472.0, a*x=43129.0, b*y=43188.0, 总和=86317.0 [平衡解] 3. x=182, y=826.0, a*x=10738.0, b*y=75579.0, 总和=86317.0 [原始解] 4. x=365, y=708.0, a*x=21535.0, b*y=64782.0, 总和=86317.0 [原始解] 5. x=914, y=354.0, a*x=53926.0, b*y=32391.0, 总和=86317.0 [原始解] 10. 组合: a=68.5, b=74 (8 个有效解) 1. x=586, y=624.0, a*x=40141.0, b*y=46176.0, 总和=86317.0 [平衡解] 2. x=734, y=487.0, a*x=50279.0, b*y=36038.0, 总和=86317.0 [平衡解] 3. x=142, y=1035.0, a*x=9727.0, b*y=76590.0, 总和=86317.0 [原始解] 4. x=290, y=898.0, a*x=19865.0, b*y=66452.0, 总和=86317.0 [原始解] 5. x=438, y=761.0, a*x=30003.0, b*y=56314.0, 总和=86317.0 [原始解] 11. 组合: a=68.5, b=91.5 (7 个有效解) 1. x=472, y=590.0, a*x=32332.0, b*y=53985.0, 总和=86317.0 [平衡解] 2. x=655, y=453.0, a*x=44867.5, b*y=41449.5, 总和=86317.0 [平衡解] 3. x=106, y=864.0, a*x=7261.0, b*y=79056.0, 总和=86317.0 [原始解] 4. x=289, y=727.0, a*x=19796.5, b*y=66520.5, 总和=86317.0 [原始解] 5. x=838, y=316.0, a*x=57403.0, b*y=28914.0, 总和=86317.0 [原始解] 12. 组合: a=74, b=91.5 (6 个有效解) 1. x=521, y=522.0, a*x=38554.0, b*y=47763.0, 总和=86317.0 [平衡解] 2. x=704, y=374.0, a*x=52096.0, b*y=34221.0, 总和=86317.0 [平衡解] 3. x=155, y=818.0, a*x=11470.0, b*y=74847.0, 总和=86317.0 [原始解] 4. x=338, y=670.0, a*x=25012.0, b*y=61305.0, 总和=86317.0 [原始解] 5. x=887, y=226.0, a*x=65638.0, b*y=20679.0, 总和=86317.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒