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 = 31758 # 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: 31758 ==== 尝试基础系数 ==== 找到 15 组2变量解: 1. 组合: a=36.5, b=41.5 (10 个有效解) 1. x=388, y=424.0, a*x=14162.0, b*y=17596.0, 总和=31758.0 [平衡解] 2. x=471, y=351.0, a*x=17191.5, b*y=14566.5, 总和=31758.0 [平衡解] 3. x=56, y=716.0, a*x=2044.0, b*y=29714.0, 总和=31758.0 [原始解] 4. x=139, y=643.0, a*x=5073.5, b*y=26684.5, 总和=31758.0 [原始解] 5. x=222, y=570.0, a*x=8103.0, b*y=23655.0, 总和=31758.0 [原始解] 2. 组合: a=36.5, b=59 (8 个有效解) 1. x=390, y=297.0, a*x=14235.0, b*y=17523.0, 总和=31758.0 [平衡解] 2. x=272, y=370.0, a*x=9928.0, b*y=21830.0, 总和=31758.0 [平衡解] 3. x=36, y=516.0, a*x=1314.0, b*y=30444.0, 总和=31758.0 [原始解] 4. x=154, y=443.0, a*x=5621.0, b*y=26137.0, 总和=31758.0 [原始解] 5. x=508, y=224.0, a*x=18542.0, b*y=13216.0, 总和=31758.0 [原始解] 3. 组合: a=36.5, b=68.5 (6 个有效解) 1. x=369, y=267.0, a*x=13468.5, b*y=18289.5, 总和=31758.0 [平衡解] 2. x=232, y=340.0, a*x=8468.0, b*y=23290.0, 总和=31758.0 [平衡解] 3. x=95, y=413.0, a*x=3467.5, b*y=28290.5, 总和=31758.0 [原始解] 4. x=506, y=194.0, a*x=18469.0, b*y=13289.0, 总和=31758.0 [原始解] 5. x=643, y=121.0, a*x=23469.5, b*y=8288.5, 总和=31758.0 [原始解] 4. 组合: a=36.5, b=74 (6 个有效解) 1. x=272, y=295.0, a*x=9928.0, b*y=21830.0, 总和=31758.0 [平衡解] 2. x=420, y=222.0, a*x=15330.0, b*y=16428.0, 总和=31758.0 [平衡解] 3. x=124, y=368.0, a*x=4526.0, b*y=27232.0, 总和=31758.0 [原始解] 4. x=568, y=149.0, a*x=20732.0, b*y=11026.0, 总和=31758.0 [原始解] 5. x=716, y=76.0, a*x=26134.0, b*y=5624.0, 总和=31758.0 [原始解] 5. 组合: a=36.5, b=91.5 (5 个有效解) 1. x=291, y=231.0, a*x=10621.5, b*y=21136.5, 总和=31758.0 [平衡解] 2. x=108, y=304.0, a*x=3942.0, b*y=27816.0, 总和=31758.0 [平衡解] 3. x=474, y=158.0, a*x=17301.0, b*y=14457.0, 总和=31758.0 [原始解] 4. x=657, y=85.0, a*x=23980.5, b*y=7777.5, 总和=31758.0 [原始解] 5. x=840, y=12.0, a*x=30660.0, b*y=1098.0, 总和=31758.0 [原始解] 6. 组合: a=41.5, b=59 (6 个有效解) 1. x=316, y=316.0, a*x=13114.0, b*y=18644.0, 总和=31758.0 [平衡解] 2. x=198, y=399.0, a*x=8217.0, b*y=23541.0, 总和=31758.0 [平衡解] 3. x=80, y=482.0, a*x=3320.0, b*y=28438.0, 总和=31758.0 [原始解] 4. x=434, y=233.0, a*x=18011.0, b*y=13747.0, 总和=31758.0 [原始解] 5. x=552, y=150.0, a*x=22908.0, b*y=8850.0, 总和=31758.0 [原始解] 7. 组合: a=41.5, b=68.5 (6 个有效解) 1. x=346, y=254.0, a*x=14359.0, b*y=17399.0, 总和=31758.0 [平衡解] 2. x=209, y=337.0, a*x=8673.5, b*y=23084.5, 总和=31758.0 [平衡解] 3. x=72, y=420.0, a*x=2988.0, b*y=28770.0, 总和=31758.0 [原始解] 4. x=483, y=171.0, a*x=20044.5, b*y=11713.5, 总和=31758.0 [原始解] 5. x=620, y=88.0, a*x=25730.0, b*y=6028.0, 总和=31758.0 [原始解] 8. 组合: a=41.5, b=74 (5 个有效解) 1. x=348, y=234.0, a*x=14442.0, b*y=17316.0, 总和=31758.0 [平衡解] 2. x=200, y=317.0, a*x=8300.0, b*y=23458.0, 总和=31758.0 [平衡解] 3. x=52, y=400.0, a*x=2158.0, b*y=29600.0, 总和=31758.0 [原始解] 4. x=496, y=151.0, a*x=20584.0, b*y=11174.0, 总和=31758.0 [原始解] 5. x=644, y=68.0, a*x=26726.0, b*y=5032.0, 总和=31758.0 [原始解] 9. 组合: a=41.5, b=91.5 (5 个有效解) 1. x=192, y=260.0, a*x=7968.0, b*y=23790.0, 总和=31758.0 [平衡解] 2. x=375, y=177.0, a*x=15562.5, b*y=16195.5, 总和=31758.0 [平衡解] 3. x=9, y=343.0, a*x=373.5, b*y=31384.5, 总和=31758.0 [原始解] 4. x=558, y=94.0, a*x=23157.0, b*y=8601.0, 总和=31758.0 [原始解] 5. x=741, y=11.0, a*x=30751.5, b*y=1006.5, 总和=31758.0 [原始解] 10. 组合: a=59, b=68.5 (4 个有效解) 1. x=183, y=306.0, a*x=10797.0, b*y=20961.0, 总和=31758.0 [平衡解] 2. x=320, y=188.0, a*x=18880.0, b*y=12878.0, 总和=31758.0 [平衡解] 3. x=46, y=424.0, a*x=2714.0, b*y=29044.0, 总和=31758.0 [原始解] 4. x=457, y=70.0, a*x=26963.0, b*y=4795.0, 总和=31758.0 [原始解] 11. 组合: a=59, b=74 (8 个有效解) 1. x=236, y=241, a*x=13924.0, b*y=17834.0, 总和=31758.0 [平衡解] 2. x=310, y=182, a*x=18290.0, b*y=13468.0, 总和=31758.0 [平衡解] 3. x=14, y=418, a*x=826.0, b*y=30932.0, 总和=31758.0 [原始解] 4. x=88, y=359, a*x=5192.0, b*y=26566.0, 总和=31758.0 [原始解] 5. x=162, y=300, a*x=9558.0, b*y=22200.0, 总和=31758.0 [原始解] 12. 组合: a=59, b=91.5 (3 个有效解) 1. x=225, y=202.0, a*x=13275.0, b*y=18483.0, 总和=31758.0 [平衡解] 2. x=42, y=320.0, a*x=2478.0, b*y=29280.0, 总和=31758.0 [平衡解] 3. x=408, y=84.0, a*x=24072.0, b*y=7686.0, 总和=31758.0 [原始解] 13. 组合: a=68.5, b=74 (3 个有效解) 1. x=240, y=207.0, a*x=16440.0, b*y=15318.0, 总和=31758.0 [平衡解] 2. x=92, y=344.0, a*x=6302.0, b*y=25456.0, 总和=31758.0 [平衡解] 3. x=388, y=70.0, a*x=26578.0, b*y=5180.0, 总和=31758.0 [原始解] 14. 组合: a=68.5, b=91.5 (2 个有效解) 1. x=123, y=255.0, a*x=8425.5, b*y=23332.5, 总和=31758.0 [平衡解] 2. x=306, y=118.0, a*x=20961.0, b*y=10797.0, 总和=31758.0 [平衡解] 15. 组合: a=74, b=91.5 (2 个有效解) 1. x=261, y=136.0, a*x=19314.0, b*y=12444.0, 总和=31758.0 [平衡解] 2. x=78, y=284.0, a*x=5772.0, b*y=25986.0, 总和=31758.0 [平衡解] 使用基础系数列表,共找到有效解 总耗时: 0.00秒