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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 = 60250  # 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
            min_x = max(1, math.ceil((TARGET - b * 10000) / a))
            max_x = min(math.floor((TARGET - 1) / a), 10000)
 
            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:
                min_x = max(1, math.ceil(1 / a))  # 取消下限，最小为1
                max_x = min(10000, math.floor(115000 / a))
            else:
                min_x = max(1, math.ceil(74000 / a))
                max_x = min(10000, math.floor(115000 / a))
        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:
                        min_y = max(1, math.ceil(1 / b))  # 取消下限，最小为1
                        max_y = min(10000, math.floor(remainder1 / b))
                    else:
                        min_y = max(1, math.ceil(74000 / b))
                        max_y = min(10000, math.floor((remainder1 - 74000) / b))
                else:
                    min_y = 1
                    max_y = math.floor(remainder1 / b)
 
                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:
        raise error[0]
 
    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__":
    start_time = time.time()
    main()
    print(f"\n总耗时: {time.time() - start_time:.2f}秒")

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 = 60250  # 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
            min_x = max(1, math.ceil((TARGET - b * 10000) / a))
            max_x = min(math.floor((TARGET - 1) / a), 10000)
            
            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:
                min_x = max(1, math.ceil(1 / a))  # 取消下限，最小为1
                max_x = min(10000, math.floor(115000 / a))
            else:
                min_x = max(1, math.ceil(74000 / a))
                max_x = min(10000, math.floor(115000 / a))
        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:
                        min_y = max(1, math.ceil(1 / b))  # 取消下限，最小为1
                        max_y = min(10000, math.floor(remainder1 / b))
                    else:
                        min_y = max(1, math.ceil(74000 / b))
                        max_y = min(10000, math.floor((remainder1 - 74000) / b))
                else:
                    min_y = 1
                    max_y = math.floor(remainder1 / b)
                    
                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:
        raise error[0]
    
    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__":
    start_time = time.time()
    main()
    print(f"\n总耗时: {time.time() - start_time:.2f}秒")    

Success #stdin #stdout 0.06s 10668KB

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Standard input is empty

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目标值: 60250

==== 尝试基础系数 ====

找到 30 组2变量解：

1. 组合: a=36.5, b=41.5 (20 个有效解)
  1. x=732, y=808.0, a*x=26718.0, b*y=33532.0, 总和=60250.0 [平衡解]
  2. x=815, y=735.0, a*x=29747.5, b*y=30502.5, 总和=60250.0 [平衡解]
  3. x=68, y=1392.0, a*x=2482.0, b*y=57768.0, 总和=60250.0 [原始解]
  4. x=151, y=1319.0, a*x=5511.5, b*y=54738.5, 总和=60250.0 [原始解]
  5. x=234, y=1246.0, a*x=8541.0, b*y=51709.0, 总和=60250.0 [原始解]

2. 组合: a=36.5, b=59 (14 个有效解)
  1. x=600, y=650.0, a*x=21900.0, b*y=38350.0, 总和=60250.0 [平衡解]
  2. x=718, y=577.0, a*x=26207.0, b*y=34043.0, 总和=60250.0 [平衡解]
  3. x=10, y=1015.0, a*x=365.0, b*y=59885.0, 总和=60250.0 [原始解]
  4. x=128, y=942.0, a*x=4672.0, b*y=55578.0, 总和=60250.0 [原始解]
  5. x=246, y=869.0, a*x=8979.0, b*y=51271.0, 总和=60250.0 [原始解]

3. 组合: a=36.5, b=68.5 (12 个有效解)
  1. x=626, y=546.0, a*x=22849.0, b*y=37401.0, 总和=60250.0 [平衡解]
  2. x=489, y=619.0, a*x=17848.5, b*y=42401.5, 总和=60250.0 [平衡解]
  3. x=78, y=838.0, a*x=2847.0, b*y=57403.0, 总和=60250.0 [原始解]
  4. x=215, y=765.0, a*x=7847.5, b*y=52402.5, 总和=60250.0 [原始解]
  5. x=352, y=692.0, a*x=12848.0, b*y=47402.0, 总和=60250.0 [原始解]

4. 组合: a=36.5, b=74 (11 个有效解)
  1. x=564, y=536.0, a*x=20586.0, b*y=39664.0, 总和=60250.0 [平衡解]
  2. x=416, y=609.0, a*x=15184.0, b*y=45066.0, 总和=60250.0 [平衡解]
  3. x=120, y=755.0, a*x=4380.0, b*y=55870.0, 总和=60250.0 [原始解]
  4. x=268, y=682.0, a*x=9782.0, b*y=50468.0, 总和=60250.0 [原始解]
  5. x=712, y=463.0, a*x=25988.0, b*y=34262.0, 总和=60250.0 [原始解]

5. 组合: a=36.5, b=91.5 (9 个有效解)
  1. x=485, y=465.0, a*x=17702.5, b*y=42547.5, 总和=60250.0 [平衡解]
  2. x=302, y=538.0, a*x=11023.0, b*y=49227.0, 总和=60250.0 [平衡解]
  3. x=119, y=611.0, a*x=4343.5, b*y=55906.5, 总和=60250.0 [原始解]
  4. x=668, y=392.0, a*x=24382.0, b*y=35868.0, 总和=60250.0 [原始解]
  5. x=851, y=319.0, a*x=31061.5, b*y=29188.5, 总和=60250.0 [原始解]

6. 组合: a=41.5, b=36.5 (20 个有效解)
  1. x=808, y=732.0, a*x=33532.0, b*y=26718.0, 总和=60250.0 [平衡解]
  2. x=735, y=815.0, a*x=30502.5, b*y=29747.5, 总和=60250.0 [平衡解]
  3. x=5, y=1645.0, a*x=207.5, b*y=60042.5, 总和=60250.0 [原始解]
  4. x=78, y=1562.0, a*x=3237.0, b*y=57013.0, 总和=60250.0 [原始解]
  5. x=151, y=1479.0, a*x=6266.5, b*y=53983.5, 总和=60250.0 [原始解]

7. 组合: a=41.5, b=59 (12 个有效解)
  1. x=586, y=609.0, a*x=24319.0, b*y=35931.0, 总和=60250.0 [平衡解]
  2. x=704, y=526.0, a*x=29216.0, b*y=31034.0, 总和=60250.0 [平衡解]
  3. x=114, y=941.0, a*x=4731.0, b*y=55519.0, 总和=60250.0 [原始解]
  4. x=232, y=858.0, a*x=9628.0, b*y=50622.0, 总和=60250.0 [原始解]
  5. x=350, y=775.0, a*x=14525.0, b*y=45725.0, 总和=60250.0 [原始解]

8. 组合: a=41.5, b=68.5 (11 个有效解)
  1. x=610, y=510.0, a*x=25315.0, b*y=34935.0, 总和=60250.0 [平衡解]
  2. x=473, y=593.0, a*x=19629.5, b*y=40620.5, 总和=60250.0 [平衡解]
  3. x=62, y=842.0, a*x=2573.0, b*y=57677.0, 总和=60250.0 [原始解]
  4. x=199, y=759.0, a*x=8258.5, b*y=51991.5, 总和=60250.0 [原始解]
  5. x=336, y=676.0, a*x=13944.0, b*y=46306.0, 总和=60250.0 [原始解]

9. 组合: a=41.5, b=74 (10 个有效解)
  1. x=480, y=545.0, a*x=19920.0, b*y=40330.0, 总和=60250.0 [平衡解]
  2. x=628, y=462.0, a*x=26062.0, b*y=34188.0, 总和=60250.0 [平衡解]
  3. x=36, y=794.0, a*x=1494.0, b*y=58756.0, 总和=60250.0 [原始解]
  4. x=184, y=711.0, a*x=7636.0, b*y=52614.0, 总和=60250.0 [原始解]
  5. x=332, y=628.0, a*x=13778.0, b*y=46472.0, 总和=60250.0 [原始解]

10. 组合: a=41.5, b=91.5 (8 个有效解)
  1. x=442, y=458.0, a*x=18343.0, b*y=41907.0, 总和=60250.0 [平衡解]
  2. x=625, y=375.0, a*x=25937.5, b*y=34312.5, 总和=60250.0 [平衡解]
  3. x=76, y=624.0, a*x=3154.0, b*y=57096.0, 总和=60250.0 [原始解]
  4. x=259, y=541.0, a*x=10748.5, b*y=49501.5, 总和=60250.0 [原始解]
  5. x=808, y=292.0, a*x=33532.0, b*y=26718.0, 总和=60250.0 [原始解]

11. 组合: a=59, b=36.5 (14 个有效解)
  1. x=650, y=600.0, a*x=38350.0, b*y=21900.0, 总和=60250.0 [平衡解]
  2. x=577, y=718.0, a*x=34043.0, b*y=26207.0, 总和=60250.0 [平衡解]
  3. x=66, y=1544.0, a*x=3894.0, b*y=56356.0, 总和=60250.0 [原始解]
  4. x=139, y=1426.0, a*x=8201.0, b*y=52049.0, 总和=60250.0 [原始解]
  5. x=212, y=1308.0, a*x=12508.0, b*y=47742.0, 总和=60250.0 [原始解]

12. 组合: a=59, b=41.5 (12 个有效解)
  1. x=609, y=586.0, a*x=35931.0, b*y=24319.0, 总和=60250.0 [平衡解]
  2. x=526, y=704.0, a*x=31034.0, b*y=29216.0, 总和=60250.0 [平衡解]
  3. x=28, y=1412.0, a*x=1652.0, b*y=58598.0, 总和=60250.0 [原始解]
  4. x=111, y=1294.0, a*x=6549.0, b*y=53701.0, 总和=60250.0 [原始解]
  5. x=194, y=1176.0, a*x=11446.0, b*y=48804.0, 总和=60250.0 [原始解]

13. 组合: a=59, b=68.5 (8 个有效解)
  1. x=443, y=498.0, a*x=26137.0, b*y=34113.0, 总和=60250.0 [平衡解]
  2. x=580, y=380.0, a*x=34220.0, b*y=26030.0, 总和=60250.0 [平衡解]
  3. x=32, y=852.0, a*x=1888.0, b*y=58362.0, 总和=60250.0 [原始解]
  4. x=169, y=734.0, a*x=9971.0, b*y=50279.0, 总和=60250.0 [原始解]
  5. x=306, y=616.0, a*x=18054.0, b*y=42196.0, 总和=60250.0 [原始解]

14. 组合: a=59, b=74 (14 个有效解)
  1. x=448, y=457, a*x=26432.0, b*y=33818.0, 总和=60250.0 [平衡解]
  2. x=522, y=398, a*x=30798.0, b*y=29452.0, 总和=60250.0 [平衡解]
  3. x=4, y=811, a*x=236.0, b*y=60014.0, 总和=60250.0 [原始解]
  4. x=78, y=752, a*x=4602.0, b*y=55648.0, 总和=60250.0 [原始解]
  5. x=152, y=693, a*x=8968.0, b*y=51282.0, 总和=60250.0 [原始解]

15. 组合: a=59, b=91.5 (5 个有效解)
  1. x=314, y=456.0, a*x=18526.0, b*y=41724.0, 总和=60250.0 [平衡解]
  2. x=497, y=338.0, a*x=29323.0, b*y=30927.0, 总和=60250.0 [平衡解]
  3. x=131, y=574.0, a*x=7729.0, b*y=52521.0, 总和=60250.0 [原始解]
  4. x=680, y=220.0, a*x=40120.0, b*y=20130.0, 总和=60250.0 [原始解]
  5. x=863, y=102.0, a*x=50917.0, b*y=9333.0, 总和=60250.0 [原始解]

16. 组合: a=68.5, b=36.5 (12 个有效解)
  1. x=546, y=626.0, a*x=37401.0, b*y=22849.0, 总和=60250.0 [平衡解]
  2. x=619, y=489.0, a*x=42401.5, b*y=17848.5, 总和=60250.0 [平衡解]
  3. x=35, y=1585.0, a*x=2397.5, b*y=57852.5, 总和=60250.0 [原始解]
  4. x=108, y=1448.0, a*x=7398.0, b*y=52852.0, 总和=60250.0 [原始解]
  5. x=181, y=1311.0, a*x=12398.5, b*y=47851.5, 总和=60250.0 [原始解]

17. 组合: a=68.5, b=41.5 (11 个有效解)
  1. x=510, y=610.0, a*x=34935.0, b*y=25315.0, 总和=60250.0 [平衡解]
  2. x=593, y=473.0, a*x=40620.5, b*y=19629.5, 总和=60250.0 [平衡解]
  3. x=12, y=1432.0, a*x=822.0, b*y=59428.0, 总和=60250.0 [原始解]
  4. x=95, y=1295.0, a*x=6507.5, b*y=53742.5, 总和=60250.0 [原始解]
  5. x=178, y=1158.0, a*x=12193.0, b*y=48057.0, 总和=60250.0 [原始解]

18. 组合: a=68.5, b=59 (8 个有效解)
  1. x=498, y=443.0, a*x=34113.0, b*y=26137.0, 总和=60250.0 [平衡解]
  2. x=380, y=580.0, a*x=26030.0, b*y=34220.0, 总和=60250.0 [平衡解]
  3. x=26, y=991.0, a*x=1781.0, b*y=58469.0, 总和=60250.0 [原始解]
  4. x=144, y=854.0, a*x=9864.0, b*y=50386.0, 总和=60250.0 [原始解]
  5. x=262, y=717.0, a*x=17947.0, b*y=42303.0, 总和=60250.0 [原始解]

19. 组合: a=68.5, b=74 (6 个有效解)
  1. x=428, y=418.0, a*x=29318.0, b*y=30932.0, 总和=60250.0 [平衡解]
  2. x=280, y=555.0, a*x=19180.0, b*y=41070.0, 总和=60250.0 [平衡解]
  3. x=132, y=692.0, a*x=9042.0, b*y=51208.0, 总和=60250.0 [原始解]
  4. x=576, y=281.0, a*x=39456.0, b*y=20794.0, 总和=60250.0 [原始解]
  5. x=724, y=144.0, a*x=49594.0, b*y=10656.0, 总和=60250.0 [原始解]

20. 组合: a=68.5, b=91.5 (5 个有效解)
  1. x=388, y=368.0, a*x=26578.0, b*y=33672.0, 总和=60250.0 [平衡解]
  2. x=205, y=505.0, a*x=14042.5, b*y=46207.5, 总和=60250.0 [平衡解]
  3. x=22, y=642.0, a*x=1507.0, b*y=58743.0, 总和=60250.0 [原始解]
  4. x=571, y=231.0, a*x=39113.5, b*y=21136.5, 总和=60250.0 [原始解]
  5. x=754, y=94.0, a*x=51649.0, b*y=8601.0, 总和=60250.0 [原始解]

21. 组合: a=74, b=36.5 (11 个有效解)
  1. x=536, y=564.0, a*x=39664.0, b*y=20586.0, 总和=60250.0 [平衡解]
  2. x=609, y=416.0, a*x=45066.0, b*y=15184.0, 总和=60250.0 [平衡解]
  3. x=25, y=1600.0, a*x=1850.0, b*y=58400.0, 总和=60250.0 [原始解]
  4. x=98, y=1452.0, a*x=7252.0, b*y=52998.0, 总和=60250.0 [原始解]
  5. x=171, y=1304.0, a*x=12654.0, b*y=47596.0, 总和=60250.0 [原始解]

22. 组合: a=74, b=41.5 (10 个有效解)
  1. x=545, y=480.0, a*x=40330.0, b*y=19920.0, 总和=60250.0 [平衡解]
  2. x=462, y=628.0, a*x=34188.0, b*y=26062.0, 总和=60250.0 [平衡解]
  3. x=47, y=1368.0, a*x=3478.0, b*y=56772.0, 总和=60250.0 [原始解]
  4. x=130, y=1220.0, a*x=9620.0, b*y=50630.0, 总和=60250.0 [原始解]
  5. x=213, y=1072.0, a*x=15762.0, b*y=44488.0, 总和=60250.0 [原始解]

23. 组合: a=74, b=59 (14 个有效解)
  1. x=457, y=448, a*x=33818.0, b*y=26432.0, 总和=60250.0 [平衡解]
  2. x=398, y=522, a*x=29452.0, b*y=30798.0, 总和=60250.0 [平衡解]
  3. x=44, y=966, a*x=3256.0, b*y=56994.0, 总和=60250.0 [原始解]
  4. x=103, y=892, a*x=7622.0, b*y=52628.0, 总和=60250.0 [原始解]
  5. x=162, y=818, a*x=11988.0, b*y=48262.0, 总和=60250.0 [原始解]

24. 组合: a=74, b=68.5 (6 个有效解)
  1. x=418, y=428.0, a*x=30932.0, b*y=29318.0, 总和=60250.0 [平衡解]
  2. x=555, y=280.0, a*x=41070.0, b*y=19180.0, 总和=60250.0 [平衡解]
  3. x=7, y=872.0, a*x=518.0, b*y=59732.0, 总和=60250.0 [原始解]
  4. x=144, y=724.0, a*x=10656.0, b*y=49594.0, 总和=60250.0 [原始解]
  5. x=281, y=576.0, a*x=20794.0, b*y=39456.0, 总和=60250.0 [原始解]

25. 组合: a=74, b=91.5 (5 个有效解)
  1. x=374, y=356.0, a*x=27676.0, b*y=32574.0, 总和=60250.0 [平衡解]
  2. x=191, y=504.0, a*x=14134.0, b*y=46116.0, 总和=60250.0 [平衡解]
  3. x=8, y=652.0, a*x=592.0, b*y=59658.0, 总和=60250.0 [原始解]
  4. x=557, y=208.0, a*x=41218.0, b*y=19032.0, 总和=60250.0 [原始解]
  5. x=740, y=60.0, a*x=54760.0, b*y=5490.0, 总和=60250.0 [原始解]

26. 组合: a=91.5, b=36.5 (9 个有效解)
  1. x=465, y=485.0, a*x=42547.5, b*y=17702.5, 总和=60250.0 [平衡解]
  2. x=538, y=302.0, a*x=49227.0, b*y=11023.0, 总和=60250.0 [平衡解]
  3. x=27, y=1583.0, a*x=2470.5, b*y=57779.5, 总和=60250.0 [原始解]
  4. x=100, y=1400.0, a*x=9150.0, b*y=51100.0, 总和=60250.0 [原始解]
  5. x=173, y=1217.0, a*x=15829.5, b*y=44420.5, 总和=60250.0 [原始解]

27. 组合: a=91.5, b=41.5 (8 个有效解)
  1. x=458, y=442.0, a*x=41907.0, b*y=18343.0, 总和=60250.0 [平衡解]
  2. x=375, y=625.0, a*x=34312.5, b*y=25937.5, 总和=60250.0 [平衡解]
  3. x=43, y=1357.0, a*x=3934.5, b*y=56315.5, 总和=60250.0 [原始解]
  4. x=126, y=1174.0, a*x=11529.0, b*y=48721.0, 总和=60250.0 [原始解]
  5. x=209, y=991.0, a*x=19123.5, b*y=41126.5, 总和=60250.0 [原始解]

28. 组合: a=91.5, b=59 (5 个有效解)
  1. x=456, y=314.0, a*x=41724.0, b*y=18526.0, 总和=60250.0 [平衡解]
  2. x=338, y=497.0, a*x=30927.0, b*y=29323.0, 总和=60250.0 [平衡解]
  3. x=102, y=863.0, a*x=9333.0, b*y=50917.0, 总和=60250.0 [原始解]
  4. x=220, y=680.0, a*x=20130.0, b*y=40120.0, 总和=60250.0 [原始解]
  5. x=574, y=131.0, a*x=52521.0, b*y=7729.0, 总和=60250.0 [原始解]

29. 组合: a=91.5, b=68.5 (5 个有效解)
  1. x=368, y=388.0, a*x=33672.0, b*y=26578.0, 总和=60250.0 [平衡解]
  2. x=505, y=205.0, a*x=46207.5, b*y=14042.5, 总和=60250.0 [平衡解]
  3. x=94, y=754.0, a*x=8601.0, b*y=51649.0, 总和=60250.0 [原始解]
  4. x=231, y=571.0, a*x=21136.5, b*y=39113.5, 总和=60250.0 [原始解]
  5. x=642, y=22.0, a*x=58743.0, b*y=1507.0, 总和=60250.0 [原始解]

30. 组合: a=91.5, b=74 (5 个有效解)
  1. x=356, y=374.0, a*x=32574.0, b*y=27676.0, 总和=60250.0 [平衡解]
  2. x=504, y=191.0, a*x=46116.0, b*y=14134.0, 总和=60250.0 [平衡解]
  3. x=60, y=740.0, a*x=5490.0, b*y=54760.0, 总和=60250.0 [原始解]
  4. x=208, y=557.0, a*x=19032.0, b*y=41218.0, 总和=60250.0 [原始解]
  5. x=652, y=8.0, a*x=59658.0, b*y=592.0, 总和=60250.0 [原始解]

使用基础系数列表，共找到有效解

总耗时: 0.02秒

https://ideone.com/6Jjo8g

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Python 3 nbc (python 3.7.3)

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