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 =90998# 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: 90998 ==== 尝试基础系数 ==== 找到 11 组2变量解: 1. 组合: a=38.5, b=70.5 (8 个有效解) 1. x=743, y=885.0, a*x=28605.5, b*y=62392.5, 总和=90998.0 [平衡解] 2. x=1025, y=731.0, a*x=39462.5, b*y=51535.5, 总和=90998.0 [平衡解] 3. x=179, y=1193.0, a*x=6891.5, b*y=84106.5, 总和=90998.0 [原始解] 4. x=461, y=1039.0, a*x=17748.5, b*y=73249.5, 总和=90998.0 [原始解] 5. x=1307, y=577.0, a*x=50319.5, b*y=40678.5, 总和=90998.0 [原始解] 2. 组合: a=38.5, b=75.5 (7 个有效解) 1. x=883, y=755.0, a*x=33995.5, b*y=57002.5, 总和=90998.0 [平衡解] 2. x=581, y=909.0, a*x=22368.5, b*y=68629.5, 总和=90998.0 [平衡解] 3. x=279, y=1063.0, a*x=10741.5, b*y=80256.5, 总和=90998.0 [原始解] 4. x=1185, y=601.0, a*x=45622.5, b*y=45375.5, 总和=90998.0 [原始解] 5. x=1487, y=447.0, a*x=57249.5, b*y=33748.5, 总和=90998.0 [原始解] 3. 组合: a=44, b=61 (17 个有效解) 1. x=923, y=826, a*x=40612.0, b*y=50386.0, 总和=90998.0 [平衡解] 2. x=801, y=914, a*x=35244.0, b*y=55754.0, 总和=90998.0 [平衡解] 3. x=69, y=1442, a*x=3036.0, b*y=87962.0, 总和=90998.0 [原始解] 4. x=191, y=1354, a*x=8404.0, b*y=82594.0, 总和=90998.0 [原始解] 5. x=313, y=1266, a*x=13772.0, b*y=77226.0, 总和=90998.0 [原始解] 4. 组合: a=44, b=70.5 (7 个有效解) 1. x=703, y=852.0, a*x=30932.0, b*y=60066.0, 总和=90998.0 [平衡解] 2. x=985, y=676.0, a*x=43340.0, b*y=47658.0, 总和=90998.0 [平衡解] 3. x=139, y=1204.0, a*x=6116.0, b*y=84882.0, 总和=90998.0 [原始解] 4. x=421, y=1028.0, a*x=18524.0, b*y=72474.0, 总和=90998.0 [原始解] 5. x=1267, y=500.0, a*x=55748.0, b*y=35250.0, 总和=90998.0 [原始解] 5. 组合: a=44, b=75.5 (6 个有效解) 1. x=867, y=700.0, a*x=38148.0, b*y=52850.0, 总和=90998.0 [平衡解] 2. x=565, y=876.0, a*x=24860.0, b*y=66138.0, 总和=90998.0 [平衡解] 3. x=263, y=1052.0, a*x=11572.0, b*y=79426.0, 总和=90998.0 [原始解] 4. x=1169, y=524.0, a*x=51436.0, b*y=39562.0, 总和=90998.0 [原始解] 5. x=1471, y=348.0, a*x=64724.0, b*y=26274.0, 总和=90998.0 [原始解] 6. 组合: a=44, b=93 (12 个有效解) 1. x=745, y=626, a*x=32780.0, b*y=58218.0, 总和=90998.0 [平衡解] 2. x=559, y=714, a*x=24596.0, b*y=66402.0, 总和=90998.0 [平衡解] 3. x=1, y=978, a*x=44.0, b*y=90954.0, 总和=90998.0 [原始解] 4. x=187, y=890, a*x=8228.0, b*y=82770.0, 总和=90998.0 [原始解] 5. x=373, y=802, a*x=16412.0, b*y=74586.0, 总和=90998.0 [原始解] 7. 组合: a=61, b=70.5 (10 个有效解) 1. x=692, y=692.0, a*x=42212.0, b*y=48786.0, 总和=90998.0 [平衡解] 2. x=551, y=814.0, a*x=33611.0, b*y=57387.0, 总和=90998.0 [平衡解] 3. x=128, y=1180.0, a*x=7808.0, b*y=83190.0, 总和=90998.0 [原始解] 4. x=269, y=1058.0, a*x=16409.0, b*y=74589.0, 总和=90998.0 [原始解] 5. x=410, y=936.0, a*x=25010.0, b*y=65988.0, 总和=90998.0 [原始解] 8. 组合: a=61, b=75.5 (10 个有效解) 1. x=613, y=710.0, a*x=37393.0, b*y=53605.0, 总和=90998.0 [平衡解] 2. x=764, y=588.0, a*x=46604.0, b*y=44394.0, 总和=90998.0 [平衡解] 3. x=9, y=1198.0, a*x=549.0, b*y=90449.0, 总和=90998.0 [原始解] 4. x=160, y=1076.0, a*x=9760.0, b*y=81238.0, 总和=90998.0 [原始解] 5. x=311, y=954.0, a*x=18971.0, b*y=72027.0, 总和=90998.0 [原始解] 9. 组合: a=61, b=93 (16 个有效解) 1. x=545, y=621, a*x=33245.0, b*y=57753.0, 总和=90998.0 [平衡解] 2. x=638, y=560, a*x=38918.0, b*y=52080.0, 总和=90998.0 [平衡解] 3. x=80, y=926, a*x=4880.0, b*y=86118.0, 总和=90998.0 [原始解] 4. x=173, y=865, a*x=10553.0, b*y=80445.0, 总和=90998.0 [原始解] 5. x=266, y=804, a*x=16226.0, b*y=74772.0, 总和=90998.0 [原始解] 10. 组合: a=70.5, b=75.5 (9 个有效解) 1. x=615, y=631.0, a*x=43357.5, b*y=47640.5, 总和=90998.0 [平衡解] 2. x=766, y=490.0, a*x=54003.0, b*y=36995.0, 总和=90998.0 [平衡解] 3. x=11, y=1195.0, a*x=775.5, b*y=90222.5, 总和=90998.0 [原始解] 4. x=162, y=1054.0, a*x=11421.0, b*y=79577.0, 总和=90998.0 [原始解] 5. x=313, y=913.0, a*x=22066.5, b*y=68931.5, 总和=90998.0 [原始解] 11. 组合: a=75.5, b=93 (7 个有效解) 1. x=598, y=493.0, a*x=45149.0, b*y=45849.0, 总和=90998.0 [平衡解] 2. x=412, y=644.0, a*x=31106.0, b*y=59892.0, 总和=90998.0 [平衡解] 3. x=40, y=946.0, a*x=3020.0, b*y=87978.0, 总和=90998.0 [原始解] 4. x=226, y=795.0, a*x=17063.0, b*y=73935.0, 总和=90998.0 [原始解] 5. x=784, y=342.0, a*x=59192.0, b*y=31806.0, 总和=90998.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.02秒