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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 = 36248  # 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）"""
    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 = 36248  # 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）"""
    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 0.03s 11912KB

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Standard input is empty

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目标值: 36248

==== 尝试基础系数 ====

找到 30 组2变量解：

1. 组合: a=35, b=40.5 (13 个有效解)
  1. x=508, y=456.0, a*x=17780.0, b*y=18468.0, 总和=36248.0 [平衡解]
  2. x=427, y=526.0, a*x=14945.0, b*y=21303.0, 总和=36248.0 [平衡解]
  3. x=22, y=876.0, a*x=770.0, b*y=35478.0, 总和=36248.0 [原始解]
  4. x=103, y=806.0, a*x=3605.0, b*y=32643.0, 总和=36248.0 [原始解]
  5. x=184, y=736.0, a*x=6440.0, b*y=29808.0, 总和=36248.0 [原始解]

2. 组合: a=35, b=58 (18 个有效解)
  1. x=396, y=386, a*x=13860.0, b*y=22388.0, 总和=36248.0 [平衡解]
  2. x=338, y=421, a*x=11830.0, b*y=24418.0, 总和=36248.0 [平衡解]
  3. x=48, y=596, a*x=1680.0, b*y=34568.0, 总和=36248.0 [原始解]
  4. x=106, y=561, a*x=3710.0, b*y=32538.0, 总和=36248.0 [原始解]
  5. x=164, y=526, a*x=5740.0, b*y=30508.0, 总和=36248.0 [原始解]

3. 组合: a=35, b=67 (16 个有效解)
  1. x=358, y=354, a*x=12530.0, b*y=23718.0, 总和=36248.0 [平衡解]
  2. x=291, y=389, a*x=10185.0, b*y=26063.0, 总和=36248.0 [平衡解]
  3. x=23, y=529, a*x=805.0, b*y=35443.0, 总和=36248.0 [原始解]
  4. x=90, y=494, a*x=3150.0, b*y=33098.0, 总和=36248.0 [原始解]
  5. x=157, y=459, a*x=5495.0, b*y=30753.0, 总和=36248.0 [原始解]

4. 组合: a=35, b=73 (14 个有效解)
  1. x=314, y=346, a*x=10990.0, b*y=25258.0, 总和=36248.0 [平衡解]
  2. x=387, y=311, a*x=13545.0, b*y=22703.0, 总和=36248.0 [平衡解]
  3. x=22, y=486, a*x=770.0, b*y=35478.0, 总和=36248.0 [原始解]
  4. x=95, y=451, a*x=3325.0, b*y=32923.0, 总和=36248.0 [原始解]
  5. x=168, y=416, a*x=5880.0, b*y=30368.0, 总和=36248.0 [原始解]

5. 组合: a=35, b=90.5 (5 个有效解)
  1. x=322, y=276.0, a*x=11270.0, b*y=24978.0, 总和=36248.0 [平衡解]
  2. x=141, y=346.0, a*x=4935.0, b*y=31313.0, 总和=36248.0 [平衡解]
  3. x=503, y=206.0, a*x=17605.0, b*y=18643.0, 总和=36248.0 [原始解]
  4. x=684, y=136.0, a*x=23940.0, b*y=12308.0, 总和=36248.0 [原始解]
  5. x=865, y=66.0, a*x=30275.0, b*y=5973.0, 总和=36248.0 [原始解]

6. 组合: a=40.5, b=35 (13 个有效解)
  1. x=456, y=508.0, a*x=18468.0, b*y=17780.0, 总和=36248.0 [平衡解]
  2. x=526, y=427.0, a*x=21303.0, b*y=14945.0, 总和=36248.0 [平衡解]
  3. x=36, y=994.0, a*x=1458.0, b*y=34790.0, 总和=36248.0 [原始解]
  4. x=106, y=913.0, a*x=4293.0, b*y=31955.0, 总和=36248.0 [原始解]
  5. x=176, y=832.0, a*x=7128.0, b*y=29120.0, 总和=36248.0 [原始解]

7. 组合: a=40.5, b=58 (8 个有效解)
  1. x=368, y=368.0, a*x=14904.0, b*y=21344.0, 总和=36248.0 [平衡解]
  2. x=252, y=449.0, a*x=10206.0, b*y=26042.0, 总和=36248.0 [平衡解]
  3. x=20, y=611.0, a*x=810.0, b*y=35438.0, 总和=36248.0 [原始解]
  4. x=136, y=530.0, a*x=5508.0, b*y=30740.0, 总和=36248.0 [原始解]
  5. x=484, y=287.0, a*x=19602.0, b*y=16646.0, 总和=36248.0 [原始解]

8. 组合: a=40.5, b=67 (7 个有效解)
  1. x=316, y=350.0, a*x=12798.0, b*y=23450.0, 总和=36248.0 [平衡解]
  2. x=450, y=269.0, a*x=18225.0, b*y=18023.0, 总和=36248.0 [平衡解]
  3. x=48, y=512.0, a*x=1944.0, b*y=34304.0, 总和=36248.0 [原始解]
  4. x=182, y=431.0, a*x=7371.0, b*y=28877.0, 总和=36248.0 [原始解]
  5. x=584, y=188.0, a*x=23652.0, b*y=12596.0, 总和=36248.0 [原始解]

9. 组合: a=40.5, b=73 (7 个有效解)
  1. x=302, y=329.0, a*x=12231.0, b*y=24017.0, 总和=36248.0 [平衡解]
  2. x=448, y=248.0, a*x=18144.0, b*y=18104.0, 总和=36248.0 [平衡解]
  3. x=10, y=491.0, a*x=405.0, b*y=35843.0, 总和=36248.0 [原始解]
  4. x=156, y=410.0, a*x=6318.0, b*y=29930.0, 总和=36248.0 [原始解]
  5. x=594, y=167.0, a*x=24057.0, b*y=12191.0, 总和=36248.0 [原始解]

10. 组合: a=40.5, b=90.5 (5 个有效解)
  1. x=209, y=307.0, a*x=8464.5, b*y=27783.5, 总和=36248.0 [平衡解]
  2. x=390, y=226.0, a*x=15795.0, b*y=20453.0, 总和=36248.0 [平衡解]
  3. x=28, y=388.0, a*x=1134.0, b*y=35114.0, 总和=36248.0 [原始解]
  4. x=571, y=145.0, a*x=23125.5, b*y=13122.5, 总和=36248.0 [原始解]
  5. x=752, y=64.0, a*x=30456.0, b*y=5792.0, 总和=36248.0 [原始解]

11. 组合: a=58, b=35 (18 个有效解)
  1. x=386, y=396, a*x=22388.0, b*y=13860.0, 总和=36248.0 [平衡解]
  2. x=421, y=338, a*x=24418.0, b*y=11830.0, 总和=36248.0 [平衡解]
  3. x=1, y=1034, a*x=58.0, b*y=36190.0, 总和=36248.0 [原始解]
  4. x=36, y=976, a*x=2088.0, b*y=34160.0, 总和=36248.0 [原始解]
  5. x=71, y=918, a*x=4118.0, b*y=32130.0, 总和=36248.0 [原始解]

12. 组合: a=58, b=40.5 (8 个有效解)
  1. x=368, y=368.0, a*x=21344.0, b*y=14904.0, 总和=36248.0 [平衡解]
  2. x=287, y=484.0, a*x=16646.0, b*y=19602.0, 总和=36248.0 [平衡解]
  3. x=44, y=832.0, a*x=2552.0, b*y=33696.0, 总和=36248.0 [原始解]
  4. x=125, y=716.0, a*x=7250.0, b*y=28998.0, 总和=36248.0 [原始解]
  5. x=206, y=600.0, a*x=11948.0, b*y=24300.0, 总和=36248.0 [原始解]

13. 组合: a=58, b=67 (9 个有效解)
  1. x=320, y=264, a*x=18560.0, b*y=17688.0, 总和=36248.0 [平衡解]
  2. x=253, y=322, a*x=14674.0, b*y=21574.0, 总和=36248.0 [平衡解]
  3. x=52, y=496, a*x=3016.0, b*y=33232.0, 总和=36248.0 [原始解]
  4. x=119, y=438, a*x=6902.0, b*y=29346.0, 总和=36248.0 [原始解]
  5. x=186, y=380, a*x=10788.0, b*y=25460.0, 总和=36248.0 [原始解]

14. 组合: a=58, b=73 (8 个有效解)
  1. x=265, y=286, a*x=15370.0, b*y=20878.0, 总和=36248.0 [平衡解]
  2. x=338, y=228, a*x=19604.0, b*y=16644.0, 总和=36248.0 [平衡解]
  3. x=46, y=460, a*x=2668.0, b*y=33580.0, 总和=36248.0 [原始解]
  4. x=119, y=402, a*x=6902.0, b*y=29346.0, 总和=36248.0 [原始解]
  5. x=192, y=344, a*x=11136.0, b*y=25112.0, 总和=36248.0 [原始解]

15. 组合: a=58, b=90.5 (4 个有效解)
  1. x=238, y=248.0, a*x=13804.0, b*y=22444.0, 总和=36248.0 [平衡解]
  2. x=419, y=132.0, a*x=24302.0, b*y=11946.0, 总和=36248.0 [平衡解]
  3. x=57, y=364.0, a*x=3306.0, b*y=32942.0, 总和=36248.0 [原始解]
  4. x=600, y=16.0, a*x=34800.0, b*y=1448.0, 总和=36248.0 [原始解]

16. 组合: a=67, b=35 (16 个有效解)
  1. x=354, y=358, a*x=23718.0, b*y=12530.0, 总和=36248.0 [平衡解]
  2. x=389, y=291, a*x=26063.0, b*y=10185.0, 总和=36248.0 [平衡解]
  3. x=4, y=1028, a*x=268.0, b*y=35980.0, 总和=36248.0 [原始解]
  4. x=39, y=961, a*x=2613.0, b*y=33635.0, 总和=36248.0 [原始解]
  5. x=74, y=894, a*x=4958.0, b*y=31290.0, 总和=36248.0 [原始解]

17. 组合: a=67, b=40.5 (7 个有效解)
  1. x=350, y=316.0, a*x=23450.0, b*y=12798.0, 总和=36248.0 [平衡解]
  2. x=269, y=450.0, a*x=18023.0, b*y=18225.0, 总和=36248.0 [平衡解]
  3. x=26, y=852.0, a*x=1742.0, b*y=34506.0, 总和=36248.0 [原始解]
  4. x=107, y=718.0, a*x=7169.0, b*y=29079.0, 总和=36248.0 [原始解]
  5. x=188, y=584.0, a*x=12596.0, b*y=23652.0, 总和=36248.0 [原始解]

18. 组合: a=67, b=58 (9 个有效解)
  1. x=264, y=320, a*x=17688.0, b*y=18560.0, 总和=36248.0 [平衡解]
  2. x=322, y=253, a*x=21574.0, b*y=14674.0, 总和=36248.0 [平衡解]
  3. x=32, y=588, a*x=2144.0, b*y=34104.0, 总和=36248.0 [原始解]
  4. x=90, y=521, a*x=6030.0, b*y=30218.0, 总和=36248.0 [原始解]
  5. x=148, y=454, a*x=9916.0, b*y=26332.0, 总和=36248.0 [原始解]

19. 组合: a=67, b=73 (7 个有效解)
  1. x=261, y=257, a*x=17487.0, b*y=18761.0, 总和=36248.0 [平衡解]
  2. x=188, y=324, a*x=12596.0, b*y=23652.0, 总和=36248.0 [平衡解]
  3. x=42, y=458, a*x=2814.0, b*y=33434.0, 总和=36248.0 [原始解]
  4. x=115, y=391, a*x=7705.0, b*y=28543.0, 总和=36248.0 [原始解]
  5. x=334, y=190, a*x=22378.0, b*y=13870.0, 总和=36248.0 [原始解]

20. 组合: a=67, b=90.5 (3 个有效解)
  1. x=152, y=288.0, a*x=10184.0, b*y=26064.0, 总和=36248.0 [平衡解]
  2. x=333, y=154.0, a*x=22311.0, b*y=13937.0, 总和=36248.0 [平衡解]
  3. x=514, y=20.0, a*x=34438.0, b*y=1810.0, 总和=36248.0 [原始解]

21. 组合: a=73, b=35 (14 个有效解)
  1. x=346, y=314, a*x=25258.0, b*y=10990.0, 总和=36248.0 [平衡解]
  2. x=311, y=387, a*x=22703.0, b*y=13545.0, 总和=36248.0 [平衡解]
  3. x=31, y=971, a*x=2263.0, b*y=33985.0, 总和=36248.0 [原始解]
  4. x=66, y=898, a*x=4818.0, b*y=31430.0, 总和=36248.0 [原始解]
  5. x=101, y=825, a*x=7373.0, b*y=28875.0, 总和=36248.0 [原始解]

22. 组合: a=73, b=40.5 (7 个有效解)
  1. x=329, y=302.0, a*x=24017.0, b*y=12231.0, 总和=36248.0 [平衡解]
  2. x=248, y=448.0, a*x=18104.0, b*y=18144.0, 总和=36248.0 [平衡解]
  3. x=5, y=886.0, a*x=365.0, b*y=35883.0, 总和=36248.0 [原始解]
  4. x=86, y=740.0, a*x=6278.0, b*y=29970.0, 总和=36248.0 [原始解]
  5. x=167, y=594.0, a*x=12191.0, b*y=24057.0, 总和=36248.0 [原始解]

23. 组合: a=73, b=58 (8 个有效解)
  1. x=286, y=265, a*x=20878.0, b*y=15370.0, 总和=36248.0 [平衡解]
  2. x=228, y=338, a*x=16644.0, b*y=19604.0, 总和=36248.0 [平衡解]
  3. x=54, y=557, a*x=3942.0, b*y=32306.0, 总和=36248.0 [原始解]
  4. x=112, y=484, a*x=8176.0, b*y=28072.0, 总和=36248.0 [原始解]
  5. x=170, y=411, a*x=12410.0, b*y=23838.0, 总和=36248.0 [原始解]

24. 组合: a=73, b=67 (7 个有效解)
  1. x=257, y=261, a*x=18761.0, b*y=17487.0, 总和=36248.0 [平衡解]
  2. x=324, y=188, a*x=23652.0, b*y=12596.0, 总和=36248.0 [平衡解]
  3. x=56, y=480, a*x=4088.0, b*y=32160.0, 总和=36248.0 [原始解]
  4. x=123, y=407, a*x=8979.0, b*y=27269.0, 总和=36248.0 [原始解]
  5. x=190, y=334, a*x=13870.0, b*y=22378.0, 总和=36248.0 [原始解]

25. 组合: a=73, b=90.5 (3 个有效解)
  1. x=261, y=190.0, a*x=19053.0, b*y=17195.0, 总和=36248.0 [平衡解]
  2. x=80, y=336.0, a*x=5840.0, b*y=30408.0, 总和=36248.0 [平衡解]
  3. x=442, y=44.0, a*x=32266.0, b*y=3982.0, 总和=36248.0 [原始解]

26. 组合: a=90.5, b=35 (5 个有效解)
  1. x=276, y=322.0, a*x=24978.0, b*y=11270.0, 总和=36248.0 [平衡解]
  2. x=346, y=141.0, a*x=31313.0, b*y=4935.0, 总和=36248.0 [平衡解]
  3. x=66, y=865.0, a*x=5973.0, b*y=30275.0, 总和=36248.0 [原始解]
  4. x=136, y=684.0, a*x=12308.0, b*y=23940.0, 总和=36248.0 [原始解]
  5. x=206, y=503.0, a*x=18643.0, b*y=17605.0, 总和=36248.0 [原始解]

27. 组合: a=90.5, b=40.5 (5 个有效解)
  1. x=307, y=209.0, a*x=27783.5, b*y=8464.5, 总和=36248.0 [平衡解]
  2. x=226, y=390.0, a*x=20453.0, b*y=15795.0, 总和=36248.0 [平衡解]
  3. x=64, y=752.0, a*x=5792.0, b*y=30456.0, 总和=36248.0 [原始解]
  4. x=145, y=571.0, a*x=13122.5, b*y=23125.5, 总和=36248.0 [原始解]
  5. x=388, y=28.0, a*x=35114.0, b*y=1134.0, 总和=36248.0 [原始解]

28. 组合: a=90.5, b=58 (4 个有效解)
  1. x=248, y=238.0, a*x=22444.0, b*y=13804.0, 总和=36248.0 [平衡解]
  2. x=132, y=419.0, a*x=11946.0, b*y=24302.0, 总和=36248.0 [平衡解]
  3. x=16, y=600.0, a*x=1448.0, b*y=34800.0, 总和=36248.0 [原始解]
  4. x=364, y=57.0, a*x=32942.0, b*y=3306.0, 总和=36248.0 [原始解]

29. 组合: a=90.5, b=67 (3 个有效解)
  1. x=288, y=152.0, a*x=26064.0, b*y=10184.0, 总和=36248.0 [平衡解]
  2. x=154, y=333.0, a*x=13937.0, b*y=22311.0, 总和=36248.0 [平衡解]
  3. x=20, y=514.0, a*x=1810.0, b*y=34438.0, 总和=36248.0 [原始解]

30. 组合: a=90.5, b=73 (3 个有效解)
  1. x=190, y=261.0, a*x=17195.0, b*y=19053.0, 总和=36248.0 [平衡解]
  2. x=336, y=80.0, a*x=30408.0, b*y=5840.0, 总和=36248.0 [平衡解]
  3. x=44, y=442.0, a*x=3982.0, b*y=32266.0, 总和=36248.0 [原始解]

使用基础系数列表，共找到有效解

总耗时: 0.01秒

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