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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 = 60000  # 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 = 60000  # 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 0.08s 10460KB

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Standard input is empty

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目标值: 60000

==== 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=782, y=758.0, a*x=28543.0, b*y=31457.0, 总和=60000.0 [平衡解]
  2. x=699, y=831.0, a*x=25513.5, b*y=34486.5, 总和=60000.0 [平衡解]
  3. x=35, y=1415.0, a*x=1277.5, b*y=58722.5, 总和=60000.0 [原始解]
  4. x=118, y=1342.0, a*x=4307.0, b*y=55693.0, 总和=60000.0 [原始解]
  5. x=201, y=1269.0, a*x=7336.5, b*y=52663.5, 总和=60000.0 [原始解]

2. 组合: a=36.5, b=59 (14 个有效解)
  1. x=598, y=647.0, a*x=21827.0, b*y=38173.0, 总和=60000.0 [平衡解]
  2. x=716, y=574.0, a*x=26134.0, b*y=33866.0, 总和=60000.0 [平衡解]
  3. x=8, y=1012.0, a*x=292.0, b*y=59708.0, 总和=60000.0 [原始解]
  4. x=126, y=939.0, a*x=4599.0, b*y=55401.0, 总和=60000.0 [原始解]
  5. x=244, y=866.0, a*x=8906.0, b*y=51094.0, 总和=60000.0 [原始解]

3. 组合: a=36.5, b=68.5 (12 个有效解)
  1. x=591, y=561.0, a*x=21571.5, b*y=38428.5, 总和=60000.0 [平衡解]
  2. x=454, y=634.0, a*x=16571.0, b*y=43429.0, 总和=60000.0 [平衡解]
  3. x=43, y=853.0, a*x=1569.5, b*y=58430.5, 总和=60000.0 [原始解]
  4. x=180, y=780.0, a*x=6570.0, b*y=53430.0, 总和=60000.0 [原始解]
  5. x=317, y=707.0, a*x=11570.5, b*y=48429.5, 总和=60000.0 [原始解]

4. 组合: a=36.5, b=74 (11 个有效解)
  1. x=472, y=578.0, a*x=17228.0, b*y=42772.0, 总和=60000.0 [平衡解]
  2. x=620, y=505.0, a*x=22630.0, b*y=37370.0, 总和=60000.0 [平衡解]
  3. x=28, y=797.0, a*x=1022.0, b*y=58978.0, 总和=60000.0 [原始解]
  4. x=176, y=724.0, a*x=6424.0, b*y=53576.0, 总和=60000.0 [原始解]
  5. x=324, y=651.0, a*x=11826.0, b*y=48174.0, 总和=60000.0 [原始解]

5. 组合: a=36.5, b=91.5 (9 个有效解)
  1. x=423, y=487.0, a*x=15439.5, b*y=44560.5, 总和=60000.0 [平衡解]
  2. x=606, y=414.0, a*x=22119.0, b*y=37881.0, 总和=60000.0 [平衡解]
  3. x=57, y=633.0, a*x=2080.5, b*y=57919.5, 总和=60000.0 [原始解]
  4. x=240, y=560.0, a*x=8760.0, b*y=51240.0, 总和=60000.0 [原始解]
  5. x=789, y=341.0, a*x=28798.5, b*y=31201.5, 总和=60000.0 [原始解]

6. 组合: a=41.5, b=36.5 (20 个有效解)
  1. x=758, y=782.0, a*x=31457.0, b*y=28543.0, 总和=60000.0 [平衡解]
  2. x=831, y=699.0, a*x=34486.5, b*y=25513.5, 总和=60000.0 [平衡解]
  3. x=28, y=1612.0, a*x=1162.0, b*y=58838.0, 总和=60000.0 [原始解]
  4. x=101, y=1529.0, a*x=4191.5, b*y=55808.5, 总和=60000.0 [原始解]
  5. x=174, y=1446.0, a*x=7221.0, b*y=52779.0, 总和=60000.0 [原始解]

7. 组合: a=41.5, b=59 (12 个有效解)
  1. x=634, y=571.0, a*x=26311.0, b*y=33689.0, 总和=60000.0 [平衡解]
  2. x=516, y=654.0, a*x=21414.0, b*y=38586.0, 总和=60000.0 [平衡解]
  3. x=44, y=986.0, a*x=1826.0, b*y=58174.0, 总和=60000.0 [原始解]
  4. x=162, y=903.0, a*x=6723.0, b*y=53277.0, 总和=60000.0 [原始解]
  5. x=280, y=820.0, a*x=11620.0, b*y=48380.0, 总和=60000.0 [原始解]

8. 组合: a=41.5, b=68.5 (10 个有效解)
  1. x=533, y=553.0, a*x=22119.5, b*y=37880.5, 总和=60000.0 [平衡解]
  2. x=670, y=470.0, a*x=27805.0, b*y=32195.0, 总和=60000.0 [平衡解]
  3. x=122, y=802.0, a*x=5063.0, b*y=54937.0, 总和=60000.0 [原始解]
  4. x=259, y=719.0, a*x=10748.5, b*y=49251.5, 总和=60000.0 [原始解]
  5. x=396, y=636.0, a*x=16434.0, b*y=43566.0, 总和=60000.0 [原始解]

9. 组合: a=41.5, b=74 (10 个有效解)
  1. x=556, y=499.0, a*x=23074.0, b*y=36926.0, 总和=60000.0 [平衡解]
  2. x=408, y=582.0, a*x=16932.0, b*y=43068.0, 总和=60000.0 [平衡解]
  3. x=112, y=748.0, a*x=4648.0, b*y=55352.0, 总和=60000.0 [原始解]
  4. x=260, y=665.0, a*x=10790.0, b*y=49210.0, 总和=60000.0 [原始解]
  5. x=704, y=416.0, a*x=29216.0, b*y=30784.0, 总和=60000.0 [原始解]

10. 组合: a=41.5, b=91.5 (8 个有效解)
  1. x=447, y=453.0, a*x=18550.5, b*y=41449.5, 总和=60000.0 [平衡解]
  2. x=630, y=370.0, a*x=26145.0, b*y=33855.0, 总和=60000.0 [平衡解]
  3. x=81, y=619.0, a*x=3361.5, b*y=56638.5, 总和=60000.0 [原始解]
  4. x=264, y=536.0, a*x=10956.0, b*y=49044.0, 总和=60000.0 [原始解]
  5. x=813, y=287.0, a*x=33739.5, b*y=26260.5, 总和=60000.0 [原始解]

11. 组合: a=59, b=36.5 (14 个有效解)
  1. x=647, y=598.0, a*x=38173.0, b*y=21827.0, 总和=60000.0 [平衡解]
  2. x=574, y=716.0, a*x=33866.0, b*y=26134.0, 总和=60000.0 [平衡解]
  3. x=63, y=1542.0, a*x=3717.0, b*y=56283.0, 总和=60000.0 [原始解]
  4. x=136, y=1424.0, a*x=8024.0, b*y=51976.0, 总和=60000.0 [原始解]
  5. x=209, y=1306.0, a*x=12331.0, b*y=47669.0, 总和=60000.0 [原始解]

12. 组合: a=59, b=41.5 (12 个有效解)
  1. x=571, y=634.0, a*x=33689.0, b*y=26311.0, 总和=60000.0 [平衡解]
  2. x=654, y=516.0, a*x=38586.0, b*y=21414.0, 总和=60000.0 [平衡解]
  3. x=73, y=1342.0, a*x=4307.0, b*y=55693.0, 总和=60000.0 [原始解]
  4. x=156, y=1224.0, a*x=9204.0, b*y=50796.0, 总和=60000.0 [原始解]
  5. x=239, y=1106.0, a*x=14101.0, b*y=45899.0, 总和=60000.0 [原始解]

13. 组合: a=59, b=68.5 (7 个有效解)
  1. x=527, y=422.0, a*x=31093.0, b*y=28907.0, 总和=60000.0 [平衡解]
  2. x=390, y=540.0, a*x=23010.0, b*y=36990.0, 总和=60000.0 [平衡解]
  3. x=116, y=776.0, a*x=6844.0, b*y=53156.0, 总和=60000.0 [原始解]
  4. x=253, y=658.0, a*x=14927.0, b*y=45073.0, 总和=60000.0 [原始解]
  5. x=664, y=304.0, a*x=39176.0, b*y=20824.0, 总和=60000.0 [原始解]

14. 组合: a=59, b=74 (13 个有效解)
  1. x=440, y=460, a*x=25960.0, b*y=34040.0, 总和=60000.0 [平衡解]
  2. x=514, y=401, a*x=30326.0, b*y=29674.0, 总和=60000.0 [平衡解]
  3. x=70, y=755, a*x=4130.0, b*y=55870.0, 总和=60000.0 [原始解]
  4. x=144, y=696, a*x=8496.0, b*y=51504.0, 总和=60000.0 [原始解]
  5. x=218, y=637, a*x=12862.0, b*y=47138.0, 总和=60000.0 [原始解]

15. 组合: a=59, b=91.5 (6 个有效解)
  1. x=378, y=412.0, a*x=22302.0, b*y=37698.0, 总和=60000.0 [平衡解]
  2. x=561, y=294.0, a*x=33099.0, b*y=26901.0, 总和=60000.0 [平衡解]
  3. x=12, y=648.0, a*x=708.0, b*y=59292.0, 总和=60000.0 [原始解]
  4. x=195, y=530.0, a*x=11505.0, b*y=48495.0, 总和=60000.0 [原始解]
  5. x=744, y=176.0, a*x=43896.0, b*y=16104.0, 总和=60000.0 [原始解]

16. 组合: a=68.5, b=36.5 (12 个有效解)
  1. x=561, y=591.0, a*x=38428.5, b*y=21571.5, 总和=60000.0 [平衡解]
  2. x=634, y=454.0, a*x=43429.0, b*y=16571.0, 总和=60000.0 [平衡解]
  3. x=50, y=1550.0, a*x=3425.0, b*y=56575.0, 总和=60000.0 [原始解]
  4. x=123, y=1413.0, a*x=8425.5, b*y=51574.5, 总和=60000.0 [原始解]
  5. x=196, y=1276.0, a*x=13426.0, b*y=46574.0, 总和=60000.0 [原始解]

17. 组合: a=68.5, b=41.5 (10 个有效解)
  1. x=553, y=533.0, a*x=37880.5, b*y=22119.5, 总和=60000.0 [平衡解]
  2. x=470, y=670.0, a*x=32195.0, b*y=27805.0, 总和=60000.0 [平衡解]
  3. x=55, y=1355.0, a*x=3767.5, b*y=56232.5, 总和=60000.0 [原始解]
  4. x=138, y=1218.0, a*x=9453.0, b*y=50547.0, 总和=60000.0 [原始解]
  5. x=221, y=1081.0, a*x=15138.5, b*y=44861.5, 总和=60000.0 [原始解]

18. 组合: a=68.5, b=59 (7 个有效解)
  1. x=422, y=527.0, a*x=28907.0, b*y=31093.0, 总和=60000.0 [平衡解]
  2. x=540, y=390.0, a*x=36990.0, b*y=23010.0, 总和=60000.0 [平衡解]
  3. x=68, y=938.0, a*x=4658.0, b*y=55342.0, 总和=60000.0 [原始解]
  4. x=186, y=801.0, a*x=12741.0, b*y=47259.0, 总和=60000.0 [原始解]
  5. x=304, y=664.0, a*x=20824.0, b*y=39176.0, 总和=60000.0 [原始解]

19. 组合: a=68.5, b=74 (6 个有效解)
  1. x=460, y=385.0, a*x=31510.0, b*y=28490.0, 总和=60000.0 [平衡解]
  2. x=312, y=522.0, a*x=21372.0, b*y=38628.0, 总和=60000.0 [平衡解]
  3. x=16, y=796.0, a*x=1096.0, b*y=58904.0, 总和=60000.0 [原始解]
  4. x=164, y=659.0, a*x=11234.0, b*y=48766.0, 总和=60000.0 [原始解]
  5. x=608, y=248.0, a*x=41648.0, b*y=18352.0, 总和=60000.0 [原始解]

20. 组合: a=68.5, b=91.5 (5 个有效解)
  1. x=375, y=375.0, a*x=25687.5, b*y=34312.5, 总和=60000.0 [平衡解]
  2. x=192, y=512.0, a*x=13152.0, b*y=46848.0, 总和=60000.0 [平衡解]
  3. x=9, y=649.0, a*x=616.5, b*y=59383.5, 总和=60000.0 [原始解]
  4. x=558, y=238.0, a*x=38223.0, b*y=21777.0, 总和=60000.0 [原始解]
  5. x=741, y=101.0, a*x=50758.5, b*y=9241.5, 总和=60000.0 [原始解]

21. 组合: a=74, b=36.5 (11 个有效解)
  1. x=578, y=472.0, a*x=42772.0, b*y=17228.0, 总和=60000.0 [平衡解]
  2. x=505, y=620.0, a*x=37370.0, b*y=22630.0, 总和=60000.0 [平衡解]
  3. x=67, y=1508.0, a*x=4958.0, b*y=55042.0, 总和=60000.0 [原始解]
  4. x=140, y=1360.0, a*x=10360.0, b*y=49640.0, 总和=60000.0 [原始解]
  5. x=213, y=1212.0, a*x=15762.0, b*y=44238.0, 总和=60000.0 [原始解]

22. 组合: a=74, b=41.5 (10 个有效解)
  1. x=499, y=556.0, a*x=36926.0, b*y=23074.0, 总和=60000.0 [平衡解]
  2. x=582, y=408.0, a*x=43068.0, b*y=16932.0, 总和=60000.0 [平衡解]
  3. x=1, y=1444.0, a*x=74.0, b*y=59926.0, 总和=60000.0 [原始解]
  4. x=84, y=1296.0, a*x=6216.0, b*y=53784.0, 总和=60000.0 [原始解]
  5. x=167, y=1148.0, a*x=12358.0, b*y=47642.0, 总和=60000.0 [原始解]

23. 组合: a=74, b=59 (13 个有效解)
  1. x=460, y=440, a*x=34040.0, b*y=25960.0, 总和=60000.0 [平衡解]
  2. x=401, y=514, a*x=29674.0, b*y=30326.0, 总和=60000.0 [平衡解]
  3. x=47, y=958, a*x=3478.0, b*y=56522.0, 总和=60000.0 [原始解]
  4. x=106, y=884, a*x=7844.0, b*y=52156.0, 总和=60000.0 [原始解]
  5. x=165, y=810, a*x=12210.0, b*y=47790.0, 总和=60000.0 [原始解]

24. 组合: a=74, b=68.5 (6 个有效解)
  1. x=385, y=460.0, a*x=28490.0, b*y=31510.0, 总和=60000.0 [平衡解]
  2. x=522, y=312.0, a*x=38628.0, b*y=21372.0, 总和=60000.0 [平衡解]
  3. x=111, y=756.0, a*x=8214.0, b*y=51786.0, 总和=60000.0 [原始解]
  4. x=248, y=608.0, a*x=18352.0, b*y=41648.0, 总和=60000.0 [原始解]
  5. x=659, y=164.0, a*x=48766.0, b*y=11234.0, 总和=60000.0 [原始解]

25. 组合: a=74, b=91.5 (4 个有效解)
  1. x=336, y=384.0, a*x=24864.0, b*y=35136.0, 总和=60000.0 [平衡解]
  2. x=519, y=236.0, a*x=38406.0, b*y=21594.0, 总和=60000.0 [平衡解]
  3. x=153, y=532.0, a*x=11322.0, b*y=48678.0, 总和=60000.0 [原始解]
  4. x=702, y=88.0, a*x=51948.0, b*y=8052.0, 总和=60000.0 [原始解]

26. 组合: a=91.5, b=36.5 (9 个有效解)
  1. x=487, y=423.0, a*x=44560.5, b*y=15439.5, 总和=60000.0 [平衡解]
  2. x=414, y=606.0, a*x=37881.0, b*y=22119.0, 总和=60000.0 [平衡解]
  3. x=49, y=1521.0, a*x=4483.5, b*y=55516.5, 总和=60000.0 [原始解]
  4. x=122, y=1338.0, a*x=11163.0, b*y=48837.0, 总和=60000.0 [原始解]
  5. x=195, y=1155.0, a*x=17842.5, b*y=42157.5, 总和=60000.0 [原始解]

27. 组合: a=91.5, b=41.5 (8 个有效解)
  1. x=453, y=447.0, a*x=41449.5, b*y=18550.5, 总和=60000.0 [平衡解]
  2. x=370, y=630.0, a*x=33855.0, b*y=26145.0, 总和=60000.0 [平衡解]
  3. x=38, y=1362.0, a*x=3477.0, b*y=56523.0, 总和=60000.0 [原始解]
  4. x=121, y=1179.0, a*x=11071.5, b*y=48928.5, 总和=60000.0 [原始解]
  5. x=204, y=996.0, a*x=18666.0, b*y=41334.0, 总和=60000.0 [原始解]

28. 组合: a=91.5, b=59 (6 个有效解)
  1. x=412, y=378.0, a*x=37698.0, b*y=22302.0, 总和=60000.0 [平衡解]
  2. x=294, y=561.0, a*x=26901.0, b*y=33099.0, 总和=60000.0 [平衡解]
  3. x=58, y=927.0, a*x=5307.0, b*y=54693.0, 总和=60000.0 [原始解]
  4. x=176, y=744.0, a*x=16104.0, b*y=43896.0, 总和=60000.0 [原始解]
  5. x=530, y=195.0, a*x=48495.0, b*y=11505.0, 总和=60000.0 [原始解]

29. 组合: a=91.5, b=68.5 (5 个有效解)
  1. x=375, y=375.0, a*x=34312.5, b*y=25687.5, 总和=60000.0 [平衡解]
  2. x=238, y=558.0, a*x=21777.0, b*y=38223.0, 总和=60000.0 [平衡解]
  3. x=101, y=741.0, a*x=9241.5, b*y=50758.5, 总和=60000.0 [原始解]
  4. x=512, y=192.0, a*x=46848.0, b*y=13152.0, 总和=60000.0 [原始解]
  5. x=649, y=9.0, a*x=59383.5, b*y=616.5, 总和=60000.0 [原始解]

30. 组合: a=91.5, b=74 (4 个有效解)
  1. x=384, y=336.0, a*x=35136.0, b*y=24864.0, 总和=60000.0 [平衡解]
  2. x=236, y=519.0, a*x=21594.0, b*y=38406.0, 总和=60000.0 [平衡解]
  3. x=88, y=702.0, a*x=8052.0, b*y=51948.0, 总和=60000.0 [原始解]
  4. x=532, y=153.0, a*x=48678.0, b*y=11322.0, 总和=60000.0 [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/RTsci7

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Python 3 nbc (python 3.7.3)

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