from itertools import product, combinations_with_replacement import time import threading from collections import defaultdict import math # 配置参数(可根据需要修改) TARGET = 262282 # 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 = 220000 # 使用三个变量的阈值 PRODUCT_RANGE_THRESHOLD = 148000 # 乘积范围限制阈值 HIGH_TARGET_THRESHOLD = 260000 # 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 def is_valid_product(p): """检查单个乘积是否在有效范围内""" if TARGET > PRODUCT_RANGE_THRESHOLD: if TARGET > HIGH_TARGET_THRESHOLD: return p <= 115000 # 目标值超过260000时,仅限制最大值 else: return 74000 <= p <= 115000 # 目标值在148000-260000之间时,使用原范围 else: return True # 目标值较小时不限制乘积范围 def find_single_variable_solutions(values): """查找单个数的解(a*x = TARGET)""" solutions = [] for a in values: x = TARGET / a if x.is_integer() and 1 <= x <= 10000 and is_valid_product(a * x): solutions.append((a, x)) if len(solutions) >= MAX_SOLUTIONS: return solutions # 提前终止 return solutions def find_two_variable_solutions(values): """查找两个变量的解(a*x + b*y = TARGET)""" solutions = defaultdict(list) # 生成所有可能的(a, b)组合 for a in values: for b in values: if a == b: # 避免重复 continue # 计算x的有效范围 if max_x < min_x: continue for x in range(min_x, max_x + 1): remainder = TARGET - a * x # 检查remainder是否在可能的范围内 if remainder < 1 or remainder > b * 10000: continue # 检查remainder是否能被b整除 if remainder % b == 0: y = remainder // b if 1 <= y <= 10000 and is_valid_product(b * y): solutions[(a, b)].append((a, x, b, y)) if len(solutions[(a, b)]) >= MAX_SOLUTIONS_PER_COMB: break # 提前终止当前组合的搜索 return solutions def find_three_variable_solutions(values): """优化的三变量求解算法""" solutions = defaultdict(list) # 对系数进行排序,便于剪枝 sorted_values = sorted(values) # 预计算每个系数的有效范围 value_ranges = {} for a in sorted_values: if TARGET > PRODUCT_RANGE_THRESHOLD: if TARGET > HIGH_TARGET_THRESHOLD: else: else: min_x = 1 max_x = 10000 value_ranges[a] = (min_x, max_x) total_combinations = len(sorted_values) * (len(sorted_values) - 1) * (len(sorted_values) - 2) // 6 processed_combinations = 0 # 三重循环,但添加了更多剪枝条件 for i, a in enumerate(sorted_values): min_x, max_x = value_ranges[a] # 计算可能的x值数量,决定步长 x_count = max_x - min_x + 1 x_step = max(1, x_count // 1000) # 自适应步长 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 TARGET > PRODUCT_RANGE_THRESHOLD: if TARGET > HIGH_TARGET_THRESHOLD: if remainder1 < 0: continue else: if remainder1 < 2 * 74000: continue # 限制b的选择范围,避免重复组合 for j in range(i + 1, len(sorted_values)): b = sorted_values[j] if TARGET > PRODUCT_RANGE_THRESHOLD: if TARGET > HIGH_TARGET_THRESHOLD: else: else: min_y = 1 if max_y < min_y: continue # 计算可能的y值数量,决定步长 y_count = max_y - min_y + 1 y_step = max(1, y_count // 100) # 自适应步长 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 TARGET > PRODUCT_RANGE_THRESHOLD: if TARGET > HIGH_TARGET_THRESHOLD: if remainder2 < 0 or remainder2 > 115000: continue else: if remainder2 < 74000 or remainder2 > 115000: continue # 限制c的选择范围 found_solution = False for k in range(j + 1, len(sorted_values)): c = sorted_values[k] # 检查remainder2是否能被c整除 if remainder2 % c != 0: continue z = remainder2 // c if 1 <= z <= 10000 and is_valid_product(c * z): key = (a, b, c) solutions[key].append((a, x, b, y, c, z)) found_solution = True if len(solutions[key]) >= MAX_SOLUTIONS_PER_COMB: break # 提前终止当前组合的搜索 # 如果找到解且达到最大数量,跳出y循环 if found_solution and len(solutions[key]) >= MAX_SOLUTIONS_PER_COMB: break # 跳出y循环 # 进度显示 if SHOW_PROGRESS and j % 10 == 0: print(f"\r三变量组合进度: {processed_combinations}/{total_combinations} 组", end='') processed_combinations += 1 if SHOW_PROGRESS: print(f"\r三变量组合进度: {processed_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 # 单变量或无解时直接返回 # 当目标值超过220000时,不计算平衡解 if TARGET > THREE_VAR_THRESHOLD: return [] # 计算解的平衡性(变量间差异最小) balanced = [] for sol in solutions: vars = sol[1::2] # 提取x, y, z diff = max(vars) - min(vars) balanced.append((diff, sol)) # 按差异排序,取前num个 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 [] # 排除已在平衡解中的项 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): # 当目标值超过220000时,不显示平衡解 if TARGET > THREE_VAR_THRESHOLD: all_display = pair_solutions[:MAX_SOLUTIONS] print_tag = "[原始解]" else: # 计算平衡解和原始解 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: # var_count == 3 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): if TARGET > THREE_VAR_THRESHOLD: tag = print_tag else: 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: # var_count == 3 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 ====") # 检查目标值是否超过阈值 if TARGET > THREE_VAR_THRESHOLD: print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD},只尝试三变量解") base_solutions = { 'single': [], 'two': [], 'three': run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,)) } # 显示三变量解 if base_solutions['three'] and len(base_solutions['three']) > 0: display_solutions(base_solutions['three'], 3) print(f"\n使用基础系数列表,共找到有效解") return else: print("\n基础系数三变量无解,尝试波动系数") else: # 目标值未超过阈值,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': [] } # 检查是否有解 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) # 如果找到解,退出程序 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 ====") # 检查目标值是否超过阈值 if TARGET > THREE_VAR_THRESHOLD: print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD},只尝试三变量解") fluctuated_solutions = { 'single': [], 'two': [], 'three': run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,)) } # 显示三变量解 if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0: display_solutions(fluctuated_solutions['three'], 3) print(f"\n使用波动系数列表,共找到有效解") return else: # 目标值未超过阈值,按顺序尝试单、双、三变量解 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': [] } # 重置标志 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) # 如果找到解,退出程序 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: 262282 ==== 尝试基础系数 ==== 目标值 262282 超过阈值 220000,只尝试三变量解 三变量组合进度: 21551/20 组 - 完成 找到 19 组3变量解: 1. 组合: a=36.5, b=41.5, c=59 (126 个有效解) 1. x=1300, y=2602, z=1811.0, a*x=47450.0, b*y=107983.0, c*z=106849.0, 总和=262282.0 [原始解] 2. x=1339, y=2653, z=1751.0, a*x=48873.5, b*y=110099.5, c*z=103309.0, 总和=262282.0 [原始解] 3. x=1378, y=2704, z=1691.0, a*x=50297.0, b*y=112216.0, c*z=99769.0, 总和=262282.0 [原始解] 2. 组合: a=36.5, b=41.5, c=68.5 (129 个有效解) 1. x=1000, y=2755, z=1627.0, a*x=36500.0, b*y=114332.5, c*z=111449.5, 总和=262282.0 [原始解] 2. x=1207, y=2601, z=1610.0, a*x=44055.5, b*y=107941.5, c*z=110285.0, 总和=262282.0 [原始解] 3. x=1222, y=2705, z=1539.0, a*x=44603.0, b*y=112257.5, c*z=105421.5, 总和=262282.0 [原始解] 3. 组合: a=36.5, b=41.5, c=74 (106 个有效解) 1. x=1021, y=2701, z=1526.0, a*x=37266.5, b*y=112091.5, c*z=112924.0, 总和=262282.0 [原始解] 2. x=1048, y=2704, z=1511.0, a*x=38252.0, b*y=112216.0, c*z=111814.0, 总和=262282.0 [原始解] 3. x=1081, y=2757, z=1465.0, a*x=39456.5, b*y=114415.5, c*z=108410.0, 总和=262282.0 [原始解] 4. 组合: a=36.5, b=41.5, c=91.5 (58 个有效解) 1. x=1270, y=2705, z=1133.0, a*x=46355.0, b*y=112257.5, c*z=103669.5, 总和=262282.0 [原始解] 2. x=1492, y=2351, z=1205.0, a*x=54458.0, b*y=97566.5, c*z=110257.5, 总和=262282.0 [原始解] 3. x=1546, y=2255, z=1227.0, a*x=56429.0, b*y=93582.5, c*z=112270.5, 总和=262282.0 [原始解] 5. 组合: a=36.5, b=59, c=68.5 (125 个有效解) 1. x=1000, y=1939, z=1626.0, a*x=36500.0, b*y=114401.0, c*z=111381.0, 总和=262282.0 [原始解] 2. x=1150, y=1888, z=1590.0, a*x=41975.0, b*y=111392.0, c*z=108915.0, 总和=262282.0 [原始解] 3. x=1255, y=1729, z=1671.0, a*x=45807.5, b*y=102011.0, c*z=114463.5, 总和=262282.0 [原始解] 6. 组合: a=36.5, b=59, c=74 (112 个有效解) 1. x=1102, y=1851, z=1525.0, a*x=40223.0, b*y=109209.0, c*z=112850.0, 总和=262282.0 [原始解] 2. x=1102, y=1925, z=1466.0, a*x=40223.0, b*y=113575.0, c*z=108484.0, 总和=262282.0 [原始解] 3. x=1270, y=1801, z=1482.0, a*x=46355.0, b*y=106259.0, c*z=109668.0, 总和=262282.0 [原始解] 7. 组合: a=36.5, b=59, c=91.5 (147 个有效解) 1. x=928, y=1939, z=1246.0, a*x=33872.0, b*y=114401.0, c*z=114009.0, 总和=262282.0 [原始解] 2. x=1285, y=1729, z=1239.0, a*x=46902.5, b*y=102011.0, c*z=113368.5, 总和=262282.0 [原始解] 3. x=1297, y=1765, z=1211.0, a*x=47340.5, b*y=104135.0, c*z=110806.5, 总和=262282.0 [原始解] 8. 组合: a=36.5, b=68.5, c=74 (128 个有效解) 1. x=1003, y=1633, z=1538.0, a*x=36609.5, b*y=111860.5, c*z=113812.0, 总和=262282.0 [原始解] 2. x=1171, y=1537, z=1544.0, a*x=42741.5, b*y=105284.5, c*z=114256.0, 总和=262282.0 [原始解] 3. x=1252, y=1644, z=1405.0, a*x=45698.0, b*y=112614.0, c*z=103970.0, 总和=262282.0 [原始解] 9. 组合: a=36.5, b=68.5, c=91.5 (61 个有效解) 1. x=1330, y=1520, z=1198.0, a*x=48545.0, b*y=104120.0, c*z=109617.0, 总和=262282.0 [原始解] 2. x=1351, y=1613, z=1120.0, a*x=49311.5, b*y=110490.5, c*z=102480.0, 总和=262282.0 [原始解] 3. x=1582, y=1538, z=1084.0, a*x=57743.0, b*y=105353.0, c*z=99186.0, 总和=262282.0 [原始解] 10. 组合: a=36.5, b=74, c=91.5 (161 个有效解) 1. x=1021, y=1531, z=1221.0, a*x=37266.5, b*y=113294.0, c*z=111721.5, 总和=262282.0 [原始解] 2. x=1090, y=1471, z=1242.0, a*x=39785.0, b*y=108854.0, c*z=113643.0, 总和=262282.0 [原始解] 3. x=1162, y=1480, z=1206.0, a*x=42413.0, b*y=109520.0, c*z=110349.0, 总和=262282.0 [原始解] 11. 组合: a=41.5, b=59, c=68.5 (179 个有效解) 1. x=977, y=1925, z=1579.0, a*x=40545.5, b*y=113575.0, c*z=108161.5, 总和=262282.0 [原始解] 2. x=1023, y=1888, z=1583.0, a*x=42454.5, b*y=111392.0, c*z=108435.5, 总和=262282.0 [原始解] 3. x=1079, y=1837, z=1593.0, a*x=44778.5, b*y=108383.0, c*z=109120.5, 总和=262282.0 [原始解] 12. 组合: a=41.5, b=59, c=91.5 (113 个有效解) 1. x=911, y=1939, z=1203.0, a*x=37806.5, b*y=114401.0, c*z=110074.5, 总和=262282.0 [原始解] 2. x=935, y=1888, z=1225.0, a*x=38802.5, b*y=111392.0, c*z=112087.5, 总和=262282.0 [原始解] 3. x=975, y=1925, z=1183.0, a*x=40462.5, b*y=113575.0, c*z=108244.5, 总和=262282.0 [原始解] 13. 组合: a=41.5, b=68.5, c=74 (225 个有效解) 1. x=941, y=1633, z=1505.0, a*x=39051.5, b*y=111860.5, c*z=111370.0, 总和=262282.0 [原始解] 2. x=1013, y=1665, z=1435.0, a*x=42039.5, b*y=114052.5, c*z=106190.0, 总和=262282.0 [原始解] 3. x=1017, y=1601, z=1492.0, a*x=42205.5, b*y=109668.5, c*z=110408.0, 总和=262282.0 [原始解] 14. 组合: a=41.5, b=68.5, c=91.5 (114 个有效解) 1. x=917, y=1601, z=1252.0, a*x=38055.5, b*y=109668.5, c*z=114558.0, 总和=262282.0 [原始解] 2. x=961, y=1569, z=1256.0, a*x=39881.5, b*y=107476.5, c*z=114924.0, 总和=262282.0 [原始解] 3. x=1097, y=1520, z=1231.0, a*x=45525.5, b*y=104120.0, c*z=112636.5, 总和=262282.0 [原始解] 15. 组合: a=41.5, b=74, c=91.5 (132 个有效解) 1. x=1021, y=1509, z=1183.0, a*x=42371.5, b*y=111666.0, c*z=108244.5, 总和=262282.0 [原始解] 2. x=1023, y=1451, z=1229.0, a*x=42454.5, b*y=107374.0, c*z=112453.5, 总和=262282.0 [原始解] 3. x=1149, y=1457, z=1167.0, a*x=47683.5, b*y=107818.0, c*z=106780.5, 总和=262282.0 [原始解] 16. 组合: a=59, b=68.5, c=74 (114 个有效解) 1. x=762, y=1644, z=1415.0, a*x=44958.0, b*y=112614.0, c*z=104710.0, 总和=262282.0 [原始解] 2. x=765, y=1582, z=1470.0, a*x=45135.0, b*y=108367.0, c*z=108780.0, 总和=262282.0 [原始解] 3. x=768, y=1520, z=1525.0, a*x=45312.0, b*y=104120.0, c*z=112850.0, 总和=262282.0 [原始解] 17. 组合: a=59, b=68.5, c=91.5 (193 个有效解) 1. x=656, y=1665, z=1197.0, a*x=38704.0, b*y=114052.5, c*z=109525.5, 总和=262282.0 [原始解] 2. x=721, y=1601, z=1203.0, a*x=42539.0, b*y=109668.5, c*z=110074.5, 总和=262282.0 [原始解] 3. x=766, y=1613, z=1165.0, a*x=45194.0, b*y=110490.5, c*z=106597.5, 总和=262282.0 [原始解] 18. 组合: a=59, b=74, c=91.5 (196 个有效解) 1. x=646, y=1501, z=1236.0, a*x=38114.0, b*y=111074.0, c*z=113094.0, 总和=262282.0 [原始解] 2. x=658, y=1531, z=1204.0, a*x=38822.0, b*y=113294.0, c*z=110166.0, 总和=262282.0 [原始解] 3. x=687, y=1451, z=1250.0, a*x=40533.0, b*y=107374.0, c*z=114375.0, 总和=262282.0 [原始解] 19. 组合: a=68.5, b=74, c=91.5 (153 个有效解) 1. x=524, y=1531, z=1236.0, a*x=35894.0, b*y=113294.0, c*z=113094.0, 总和=262282.0 [原始解] 2. x=642, y=1538, z=1142.0, a*x=43977.0, b*y=113812.0, c*z=104493.0, 总和=262282.0 [原始解] 3. x=676, y=1509, z=1140.0, a*x=46306.0, b*y=111666.0, c*z=104310.0, 总和=262282.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 1.21秒