from itertools import product, combinations_with_replacement import time import threading from collections import defaultdict, Counter import math # 配置参数(可根据需要修改) TARGET = 75085 # 目标值 BASE_VALUES = [35, 40.5, 58, 67, 73, 90.5] # 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),避免重复组合""" temp_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): # 创建解的规范化表示,避免重复组合 solution = (a, x, b, y) # 按变量值排序,忽略系数顺序 normalized = tuple(sorted([x, y])) temp_solutions[(a, b)].append((solution, normalized)) if len(temp_solutions[(a, b)]) >= MAX_SOLUTIONS_PER_COMB: break # 提前终止当前组合的搜索 # 处理解,移除重复组合 solutions = defaultdict(list) for key, sols in temp_solutions.items(): seen = set() for sol, norm in sols: if norm not in seen: seen.add(norm) solutions[key].append(sol) return solutions def find_three_variable_solutions(values): """优化的三变量求解算法,避免重复组合""" temp_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) # 创建解的规范化表示,避免重复组合 solution = (a, x, b, y, c, z) # 按变量值排序,忽略系数顺序 normalized = tuple(sorted([x, y, z])) temp_solutions[key].append((solution, normalized)) found_solution = True if len(temp_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(temp_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") # 处理解,移除重复组合 solutions = defaultdict(list) for key, sols in temp_solutions.items(): seen = set() for sol, norm in sols: if norm not in seen: seen.add(norm) solutions[key].append(sol) 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: 75085 ==== 尝试基础系数 ==== 找到 30 组2变量解: 1. 组合: a=35, b=40.5 (26 个有效解) 1. x=965, y=1020.0, a*x=33775.0, b*y=41310.0, 总和=75085.0 [平衡解] 2. x=1046, y=950.0, a*x=36610.0, b*y=38475.0, 总和=75085.0 [平衡解] 3. x=74, y=1790.0, a*x=2590.0, b*y=72495.0, 总和=75085.0 [原始解] 4. x=155, y=1720.0, a*x=5425.0, b*y=69660.0, 总和=75085.0 [原始解] 5. x=236, y=1650.0, a*x=8260.0, b*y=66825.0, 总和=75085.0 [原始解] 2. 组合: a=35, b=58 (37 个有效解) 1. x=803, y=810, a*x=28105.0, b*y=46980.0, 总和=75085.0 [平衡解] 2. x=861, y=775, a*x=30135.0, b*y=44950.0, 总和=75085.0 [平衡解] 3. x=49, y=1265, a*x=1715.0, b*y=73370.0, 总和=75085.0 [原始解] 4. x=107, y=1230, a*x=3745.0, b*y=71340.0, 总和=75085.0 [原始解] 5. x=165, y=1195, a*x=5775.0, b*y=69310.0, 总和=75085.0 [原始解] 3. 组合: a=35, b=67 (32 个有效解) 1. x=767, y=720, a*x=26845.0, b*y=48240.0, 总和=75085.0 [平衡解] 2. x=700, y=755, a*x=24500.0, b*y=50585.0, 总和=75085.0 [平衡解] 3. x=30, y=1105, a*x=1050.0, b*y=74035.0, 总和=75085.0 [原始解] 4. x=97, y=1070, a*x=3395.0, b*y=71690.0, 总和=75085.0 [原始解] 5. x=164, y=1035, a*x=5740.0, b*y=69345.0, 总和=75085.0 [原始解] 4. 组合: a=35, b=73 (29 个有效解) 1. x=727, y=680, a*x=25445.0, b*y=49640.0, 总和=75085.0 [平衡解] 2. x=654, y=715, a*x=22890.0, b*y=52195.0, 总和=75085.0 [平衡解] 3. x=70, y=995, a*x=2450.0, b*y=72635.0, 总和=75085.0 [原始解] 4. x=143, y=960, a*x=5005.0, b*y=70080.0, 总和=75085.0 [原始解] 5. x=216, y=925, a*x=7560.0, b*y=67525.0, 总和=75085.0 [原始解] 5. 组合: a=35, b=90.5 (12 个有效解) 1. x=568, y=610.0, a*x=19880.0, b*y=55205.0, 总和=75085.0 [平衡解] 2. x=749, y=540.0, a*x=26215.0, b*y=48870.0, 总和=75085.0 [平衡解] 3. x=25, y=820.0, a*x=875.0, b*y=74210.0, 总和=75085.0 [原始解] 4. x=206, y=750.0, a*x=7210.0, b*y=67875.0, 总和=75085.0 [原始解] 5. x=387, y=680.0, a*x=13545.0, b*y=61540.0, 总和=75085.0 [原始解] 6. 组合: a=40.5, b=35 (26 个有效解) 1. x=1020, y=965.0, a*x=41310.0, b*y=33775.0, 总和=75085.0 [平衡解] 2. x=950, y=1046.0, a*x=38475.0, b*y=36610.0, 总和=75085.0 [平衡解] 3. x=40, y=2099.0, a*x=1620.0, b*y=73465.0, 总和=75085.0 [原始解] 4. x=110, y=2018.0, a*x=4455.0, b*y=70630.0, 总和=75085.0 [原始解] 5. x=180, y=1937.0, a*x=7290.0, b*y=67795.0, 总和=75085.0 [原始解] 7. 组合: a=40.5, b=58 (16 个有效解) 1. x=714, y=796.0, a*x=28917.0, b*y=46168.0, 总和=75085.0 [平衡解] 2. x=830, y=715.0, a*x=33615.0, b*y=41470.0, 总和=75085.0 [平衡解] 3. x=18, y=1282.0, a*x=729.0, b*y=74356.0, 总和=75085.0 [原始解] 4. x=134, y=1201.0, a*x=5427.0, b*y=69658.0, 总和=75085.0 [原始解] 5. x=250, y=1120.0, a*x=10125.0, b*y=64960.0, 总和=75085.0 [原始解] 8. 组合: a=40.5, b=67 (14 个有效解) 1. x=686, y=706.0, a*x=27783.0, b*y=47302.0, 总和=75085.0 [平衡解] 2. x=820, y=625.0, a*x=33210.0, b*y=41875.0, 总和=75085.0 [平衡解] 3. x=16, y=1111.0, a*x=648.0, b*y=74437.0, 总和=75085.0 [原始解] 4. x=150, y=1030.0, a*x=6075.0, b*y=69010.0, 总和=75085.0 [原始解] 5. x=284, y=949.0, a*x=11502.0, b*y=63583.0, 总和=75085.0 [原始解] 9. 组合: a=40.5, b=73 (12 个有效解) 1. x=722, y=628.0, a*x=29241.0, b*y=45844.0, 总和=75085.0 [平衡解] 2. x=576, y=709.0, a*x=23328.0, b*y=51757.0, 总和=75085.0 [平衡解] 3. x=138, y=952.0, a*x=5589.0, b*y=69496.0, 总和=75085.0 [原始解] 4. x=284, y=871.0, a*x=11502.0, b*y=63583.0, 总和=75085.0 [原始解] 5. x=430, y=790.0, a*x=17415.0, b*y=57670.0, 总和=75085.0 [原始解] 10. 组合: a=40.5, b=90.5 (10 个有效解) 1. x=616, y=554.0, a*x=24948.0, b*y=50137.0, 总和=75085.0 [平衡解] 2. x=435, y=635.0, a*x=17617.5, b*y=57467.5, 总和=75085.0 [平衡解] 3. x=73, y=797.0, a*x=2956.5, b*y=72128.5, 总和=75085.0 [原始解] 4. x=254, y=716.0, a*x=10287.0, b*y=64798.0, 总和=75085.0 [原始解] 5. x=797, y=473.0, a*x=32278.5, b*y=42806.5, 总和=75085.0 [原始解] 11. 组合: a=58, b=35 (37 个有效解) 1. x=810, y=803, a*x=46980.0, b*y=28105.0, 总和=75085.0 [平衡解] 2. x=775, y=861, a*x=44950.0, b*y=30135.0, 总和=75085.0 [平衡解] 3. x=5, y=2137, a*x=290.0, b*y=74795.0, 总和=75085.0 [原始解] 4. x=40, y=2079, a*x=2320.0, b*y=72765.0, 总和=75085.0 [原始解] 5. x=75, y=2021, a*x=4350.0, b*y=70735.0, 总和=75085.0 [原始解] 12. 组合: a=58, b=40.5 (16 个有效解) 1. x=796, y=714.0, a*x=46168.0, b*y=28917.0, 总和=75085.0 [平衡解] 2. x=715, y=830.0, a*x=41470.0, b*y=33615.0, 总和=75085.0 [平衡解] 3. x=67, y=1758.0, a*x=3886.0, b*y=71199.0, 总和=75085.0 [原始解] 4. x=148, y=1642.0, a*x=8584.0, b*y=66501.0, 总和=75085.0 [原始解] 5. x=229, y=1526.0, a*x=13282.0, b*y=61803.0, 总和=75085.0 [原始解] 13. 组合: a=58, b=67 (19 个有效解) 1. x=598, y=603, a*x=34684.0, b*y=40401.0, 总和=75085.0 [平衡解] 2. x=665, y=545, a*x=38570.0, b*y=36515.0, 总和=75085.0 [平衡解] 3. x=62, y=1067, a*x=3596.0, b*y=71489.0, 总和=75085.0 [原始解] 4. x=129, y=1009, a*x=7482.0, b*y=67603.0, 总和=75085.0 [原始解] 5. x=196, y=951, a*x=11368.0, b*y=63717.0, 总和=75085.0 [原始解] 14. 组合: a=58, b=73 (18 个有效解) 1. x=591, y=559, a*x=34278.0, b*y=40807.0, 总和=75085.0 [平衡解] 2. x=518, y=617, a*x=30044.0, b*y=45041.0, 总和=75085.0 [平衡解] 3. x=7, y=1023, a*x=406.0, b*y=74679.0, 总和=75085.0 [原始解] 4. x=80, y=965, a*x=4640.0, b*y=70445.0, 总和=75085.0 [原始解] 5. x=153, y=907, a*x=8874.0, b*y=66211.0, 总和=75085.0 [原始解] 15. 组合: a=58, b=90.5 (7 个有效解) 1. x=530, y=490.0, a*x=30740.0, b*y=44345.0, 总和=75085.0 [平衡解] 2. x=349, y=606.0, a*x=20242.0, b*y=54843.0, 总和=75085.0 [平衡解] 3. x=168, y=722.0, a*x=9744.0, b*y=65341.0, 总和=75085.0 [原始解] 4. x=711, y=374.0, a*x=41238.0, b*y=33847.0, 总和=75085.0 [原始解] 5. x=892, y=258.0, a*x=51736.0, b*y=23349.0, 总和=75085.0 [原始解] 16. 组合: a=67, b=35 (32 个有效解) 1. x=720, y=767, a*x=48240.0, b*y=26845.0, 总和=75085.0 [平衡解] 2. x=755, y=700, a*x=50585.0, b*y=24500.0, 总和=75085.0 [平衡解] 3. x=20, y=2107, a*x=1340.0, b*y=73745.0, 总和=75085.0 [原始解] 4. x=55, y=2040, a*x=3685.0, b*y=71400.0, 总和=75085.0 [原始解] 5. x=90, y=1973, a*x=6030.0, b*y=69055.0, 总和=75085.0 [原始解] 17. 组合: a=67, b=40.5 (14 个有效解) 1. x=706, y=686.0, a*x=47302.0, b*y=27783.0, 总和=75085.0 [平衡解] 2. x=625, y=820.0, a*x=41875.0, b*y=33210.0, 总和=75085.0 [平衡解] 3. x=58, y=1758.0, a*x=3886.0, b*y=71199.0, 总和=75085.0 [原始解] 4. x=139, y=1624.0, a*x=9313.0, b*y=65772.0, 总和=75085.0 [原始解] 5. x=220, y=1490.0, a*x=14740.0, b*y=60345.0, 总和=75085.0 [原始解] 18. 组合: a=67, b=58 (19 个有效解) 1. x=603, y=598, a*x=40401.0, b*y=34684.0, 总和=75085.0 [平衡解] 2. x=545, y=665, a*x=36515.0, b*y=38570.0, 总和=75085.0 [平衡解] 3. x=23, y=1268, a*x=1541.0, b*y=73544.0, 总和=75085.0 [原始解] 4. x=81, y=1201, a*x=5427.0, b*y=69658.0, 总和=75085.0 [原始解] 5. x=139, y=1134, a*x=9313.0, b*y=65772.0, 总和=75085.0 [原始解] 19. 组合: a=67, b=73 (15 个有效解) 1. x=565, y=510, a*x=37855.0, b*y=37230.0, 总和=75085.0 [平衡解] 2. x=492, y=577, a*x=32964.0, b*y=42121.0, 总和=75085.0 [平衡解] 3. x=54, y=979, a*x=3618.0, b*y=71467.0, 总和=75085.0 [原始解] 4. x=127, y=912, a*x=8509.0, b*y=66576.0, 总和=75085.0 [原始解] 5. x=200, y=845, a*x=13400.0, b*y=61685.0, 总和=75085.0 [原始解] 20. 组合: a=67, b=90.5 (6 个有效解) 1. x=448, y=498.0, a*x=30016.0, b*y=45069.0, 总和=75085.0 [平衡解] 2. x=629, y=364.0, a*x=42143.0, b*y=32942.0, 总和=75085.0 [平衡解] 3. x=86, y=766.0, a*x=5762.0, b*y=69323.0, 总和=75085.0 [原始解] 4. x=267, y=632.0, a*x=17889.0, b*y=57196.0, 总和=75085.0 [原始解] 5. x=810, y=230.0, a*x=54270.0, b*y=20815.0, 总和=75085.0 [原始解] 21. 组合: a=73, b=35 (29 个有效解) 1. x=680, y=727, a*x=49640.0, b*y=25445.0, 总和=75085.0 [平衡解] 2. x=715, y=654, a*x=52195.0, b*y=22890.0, 总和=75085.0 [平衡解] 3. x=15, y=2114, a*x=1095.0, b*y=73990.0, 总和=75085.0 [原始解] 4. x=50, y=2041, a*x=3650.0, b*y=71435.0, 总和=75085.0 [原始解] 5. x=85, y=1968, a*x=6205.0, b*y=68880.0, 总和=75085.0 [原始解] 22. 组合: a=73, b=40.5 (12 个有效解) 1. x=628, y=722.0, a*x=45844.0, b*y=29241.0, 总和=75085.0 [平衡解] 2. x=709, y=576.0, a*x=51757.0, b*y=23328.0, 总和=75085.0 [平衡解] 3. x=61, y=1744.0, a*x=4453.0, b*y=70632.0, 总和=75085.0 [原始解] 4. x=142, y=1598.0, a*x=10366.0, b*y=64719.0, 总和=75085.0 [原始解] 5. x=223, y=1452.0, a*x=16279.0, b*y=58806.0, 总和=75085.0 [原始解] 23. 组合: a=73, b=58 (18 个有效解) 1. x=559, y=591, a*x=40807.0, b*y=34278.0, 总和=75085.0 [平衡解] 2. x=617, y=518, a*x=45041.0, b*y=30044.0, 总和=75085.0 [平衡解] 3. x=37, y=1248, a*x=2701.0, b*y=72384.0, 总和=75085.0 [原始解] 4. x=95, y=1175, a*x=6935.0, b*y=68150.0, 总和=75085.0 [原始解] 5. x=153, y=1102, a*x=11169.0, b*y=63916.0, 总和=75085.0 [原始解] 24. 组合: a=73, b=67 (15 个有效解) 1. x=510, y=565, a*x=37230.0, b*y=37855.0, 总和=75085.0 [平衡解] 2. x=577, y=492, a*x=42121.0, b*y=32964.0, 总和=75085.0 [平衡解] 3. x=41, y=1076, a*x=2993.0, b*y=72092.0, 总和=75085.0 [原始解] 4. x=108, y=1003, a*x=7884.0, b*y=67201.0, 总和=75085.0 [原始解] 5. x=175, y=930, a*x=12775.0, b*y=62310.0, 总和=75085.0 [原始解] 25. 组合: a=73, b=90.5 (5 个有效解) 1. x=493, y=432.0, a*x=35989.0, b*y=39096.0, 总和=75085.0 [平衡解] 2. x=312, y=578.0, a*x=22776.0, b*y=52309.0, 总和=75085.0 [平衡解] 3. x=131, y=724.0, a*x=9563.0, b*y=65522.0, 总和=75085.0 [原始解] 4. x=674, y=286.0, a*x=49202.0, b*y=25883.0, 总和=75085.0 [原始解] 5. x=855, y=140.0, a*x=62415.0, b*y=12670.0, 总和=75085.0 [原始解] 26. 组合: a=90.5, b=35 (12 个有效解) 1. x=610, y=568.0, a*x=55205.0, b*y=19880.0, 总和=75085.0 [平衡解] 2. x=540, y=749.0, a*x=48870.0, b*y=26215.0, 总和=75085.0 [平衡解] 3. x=50, y=2016.0, a*x=4525.0, b*y=70560.0, 总和=75085.0 [原始解] 4. x=120, y=1835.0, a*x=10860.0, b*y=64225.0, 总和=75085.0 [原始解] 5. x=190, y=1654.0, a*x=17195.0, b*y=57890.0, 总和=75085.0 [原始解] 27. 组合: a=90.5, b=40.5 (10 个有效解) 1. x=554, y=616.0, a*x=50137.0, b*y=24948.0, 总和=75085.0 [平衡解] 2. x=635, y=435.0, a*x=57467.5, b*y=17617.5, 总和=75085.0 [平衡解] 3. x=68, y=1702.0, a*x=6154.0, b*y=68931.0, 总和=75085.0 [原始解] 4. x=149, y=1521.0, a*x=13484.5, b*y=61600.5, 总和=75085.0 [原始解] 5. x=230, y=1340.0, a*x=20815.0, b*y=54270.0, 总和=75085.0 [原始解] 28. 组合: a=90.5, b=58 (7 个有效解) 1. x=490, y=530.0, a*x=44345.0, b*y=30740.0, 总和=75085.0 [平衡解] 2. x=606, y=349.0, a*x=54843.0, b*y=20242.0, 总和=75085.0 [平衡解] 3. x=26, y=1254.0, a*x=2353.0, b*y=72732.0, 总和=75085.0 [原始解] 4. x=142, y=1073.0, a*x=12851.0, b*y=62234.0, 总和=75085.0 [原始解] 5. x=258, y=892.0, a*x=23349.0, b*y=51736.0, 总和=75085.0 [原始解] 29. 组合: a=90.5, b=67 (6 个有效解) 1. x=498, y=448.0, a*x=45069.0, b*y=30016.0, 总和=75085.0 [平衡解] 2. x=364, y=629.0, a*x=32942.0, b*y=42143.0, 总和=75085.0 [平衡解] 3. x=96, y=991.0, a*x=8688.0, b*y=66397.0, 总和=75085.0 [原始解] 4. x=230, y=810.0, a*x=20815.0, b*y=54270.0, 总和=75085.0 [原始解] 5. x=632, y=267.0, a*x=57196.0, b*y=17889.0, 总和=75085.0 [原始解] 30. 组合: a=90.5, b=73 (5 个有效解) 1. x=432, y=493.0, a*x=39096.0, b*y=35989.0, 总和=75085.0 [平衡解] 2. x=578, y=312.0, a*x=52309.0, b*y=22776.0, 总和=75085.0 [平衡解] 3. x=140, y=855.0, a*x=12670.0, b*y=62415.0, 总和=75085.0 [原始解] 4. x=286, y=674.0, a*x=25883.0, b*y=49202.0, 总和=75085.0 [原始解] 5. x=724, y=131.0, a*x=65522.0, b*y=9563.0, 总和=75085.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒