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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 = 55000  # 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 = 55000  # 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 0.05s 10792KB

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Standard input is empty

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目标值: 55000

==== 尝试基础系数 ====

找到 30 组2变量解：

1. 组合: a=35, b=40.5 (19 个有效解)
  1. x=692, y=760.0, a*x=24220.0, b*y=30780.0, 总和=55000.0 [平衡解]
  2. x=773, y=690.0, a*x=27055.0, b*y=27945.0, 总和=55000.0 [平衡解]
  3. x=44, y=1320.0, a*x=1540.0, b*y=53460.0, 总和=55000.0 [原始解]
  4. x=125, y=1250.0, a*x=4375.0, b*y=50625.0, 总和=55000.0 [原始解]
  5. x=206, y=1180.0, a*x=7210.0, b*y=47790.0, 总和=55000.0 [原始解]

2. 组合: a=35, b=58 (27 个有效解)
  1. x=602, y=585, a*x=21070.0, b*y=33930.0, 总和=55000.0 [平衡解]
  2. x=544, y=620, a*x=19040.0, b*y=35960.0, 总和=55000.0 [平衡解]
  3. x=22, y=935, a*x=770.0, b*y=54230.0, 总和=55000.0 [原始解]
  4. x=80, y=900, a*x=2800.0, b*y=52200.0, 总和=55000.0 [原始解]
  5. x=138, y=865, a*x=4830.0, b*y=50170.0, 总和=55000.0 [原始解]

3. 组合: a=35, b=67 (23 个有效解)
  1. x=509, y=555, a*x=17815.0, b*y=37185.0, 总和=55000.0 [平衡解]
  2. x=576, y=520, a*x=20160.0, b*y=34840.0, 总和=55000.0 [平衡解]
  3. x=40, y=800, a*x=1400.0, b*y=53600.0, 总和=55000.0 [原始解]
  4. x=107, y=765, a*x=3745.0, b*y=51255.0, 总和=55000.0 [原始解]
  5. x=174, y=730, a*x=6090.0, b*y=48910.0, 总和=55000.0 [原始解]

4. 组合: a=35, b=73 (22 个有效解)
  1. x=539, y=495, a*x=18865.0, b*y=36135.0, 总和=55000.0 [平衡解]
  2. x=466, y=530, a*x=16310.0, b*y=38690.0, 总和=55000.0 [平衡解]
  3. x=28, y=740, a*x=980.0, b*y=54020.0, 总和=55000.0 [原始解]
  4. x=101, y=705, a*x=3535.0, b*y=51465.0, 总和=55000.0 [原始解]
  5. x=174, y=670, a*x=6090.0, b*y=48910.0, 总和=55000.0 [原始解]

5. 组合: a=35, b=90.5 (9 个有效解)
  1. x=382, y=460.0, a*x=13370.0, b*y=41630.0, 总和=55000.0 [平衡解]
  2. x=563, y=390.0, a*x=19705.0, b*y=35295.0, 总和=55000.0 [平衡解]
  3. x=20, y=600.0, a*x=700.0, b*y=54300.0, 总和=55000.0 [原始解]
  4. x=201, y=530.0, a*x=7035.0, b*y=47965.0, 总和=55000.0 [原始解]
  5. x=744, y=320.0, a*x=26040.0, b*y=28960.0, 总和=55000.0 [原始解]

6. 组合: a=40.5, b=35 (19 个有效解)
  1. x=760, y=692.0, a*x=30780.0, b*y=24220.0, 总和=55000.0 [平衡解]
  2. x=690, y=773.0, a*x=27945.0, b*y=27055.0, 总和=55000.0 [平衡解]
  3. x=60, y=1502.0, a*x=2430.0, b*y=52570.0, 总和=55000.0 [原始解]
  4. x=130, y=1421.0, a*x=5265.0, b*y=49735.0, 总和=55000.0 [原始解]
  5. x=200, y=1340.0, a*x=8100.0, b*y=46900.0, 总和=55000.0 [原始解]

7. 组合: a=40.5, b=58 (12 个有效解)
  1. x=536, y=574.0, a*x=21708.0, b*y=33292.0, 总和=55000.0 [平衡解]
  2. x=652, y=493.0, a*x=26406.0, b*y=28594.0, 总和=55000.0 [平衡解]
  3. x=72, y=898.0, a*x=2916.0, b*y=52084.0, 总和=55000.0 [原始解]
  4. x=188, y=817.0, a*x=7614.0, b*y=47386.0, 总和=55000.0 [原始解]
  5. x=304, y=736.0, a*x=12312.0, b*y=42688.0, 总和=55000.0 [原始解]

8. 组合: a=40.5, b=67 (10 个有效解)
  1. x=468, y=538.0, a*x=18954.0, b*y=36046.0, 总和=55000.0 [平衡解]
  2. x=602, y=457.0, a*x=24381.0, b*y=30619.0, 总和=55000.0 [平衡解]
  3. x=66, y=781.0, a*x=2673.0, b*y=52327.0, 总和=55000.0 [原始解]
  4. x=200, y=700.0, a*x=8100.0, b*y=46900.0, 总和=55000.0 [原始解]
  5. x=334, y=619.0, a*x=13527.0, b*y=41473.0, 总和=55000.0 [原始解]

9. 组合: a=40.5, b=73 (10 个有效解)
  1. x=464, y=496.0, a*x=18792.0, b*y=36208.0, 总和=55000.0 [平衡解]
  2. x=610, y=415.0, a*x=24705.0, b*y=30295.0, 总和=55000.0 [平衡解]
  3. x=26, y=739.0, a*x=1053.0, b*y=53947.0, 总和=55000.0 [原始解]
  4. x=172, y=658.0, a*x=6966.0, b*y=48034.0, 总和=55000.0 [原始解]
  5. x=318, y=577.0, a*x=12879.0, b*y=42121.0, 总和=55000.0 [原始解]

10. 组合: a=40.5, b=90.5 (7 个有效解)
  1. x=348, y=452.0, a*x=14094.0, b*y=40906.0, 总和=55000.0 [平衡解]
  2. x=529, y=371.0, a*x=21424.5, b*y=33575.5, 总和=55000.0 [平衡解]
  3. x=167, y=533.0, a*x=6763.5, b*y=48236.5, 总和=55000.0 [原始解]
  4. x=710, y=290.0, a*x=28755.0, b*y=26245.0, 总和=55000.0 [原始解]
  5. x=891, y=209.0, a*x=36085.5, b*y=18914.5, 总和=55000.0 [原始解]

11. 组合: a=58, b=35 (27 个有效解)
  1. x=585, y=602, a*x=33930.0, b*y=21070.0, 总和=55000.0 [平衡解]
  2. x=620, y=544, a*x=35960.0, b*y=19040.0, 总和=55000.0 [平衡解]
  3. x=25, y=1530, a*x=1450.0, b*y=53550.0, 总和=55000.0 [原始解]
  4. x=60, y=1472, a*x=3480.0, b*y=51520.0, 总和=55000.0 [原始解]
  5. x=95, y=1414, a*x=5510.0, b*y=49490.0, 总和=55000.0 [原始解]

12. 组合: a=58, b=40.5 (12 个有效解)
  1. x=574, y=536.0, a*x=33292.0, b*y=21708.0, 总和=55000.0 [平衡解]
  2. x=493, y=652.0, a*x=28594.0, b*y=26406.0, 总和=55000.0 [平衡解]
  3. x=7, y=1348.0, a*x=406.0, b*y=54594.0, 总和=55000.0 [原始解]
  4. x=88, y=1232.0, a*x=5104.0, b*y=49896.0, 总和=55000.0 [原始解]
  5. x=169, y=1116.0, a*x=9802.0, b*y=45198.0, 总和=55000.0 [原始解]

13. 组合: a=58, b=67 (14 个有效解)
  1. x=440, y=440, a*x=25520.0, b*y=29480.0, 总和=55000.0 [平衡解]
  2. x=373, y=498, a*x=21634.0, b*y=33366.0, 总和=55000.0 [平衡解]
  3. x=38, y=788, a*x=2204.0, b*y=52796.0, 总和=55000.0 [原始解]
  4. x=105, y=730, a*x=6090.0, b*y=48910.0, 总和=55000.0 [原始解]
  5. x=172, y=672, a*x=9976.0, b*y=45024.0, 总和=55000.0 [原始解]

14. 组合: a=58, b=73 (13 个有效解)
  1. x=397, y=438, a*x=23026.0, b*y=31974.0, 总和=55000.0 [平衡解]
  2. x=470, y=380, a*x=27260.0, b*y=27740.0, 总和=55000.0 [平衡解]
  3. x=32, y=728, a*x=1856.0, b*y=53144.0, 总和=55000.0 [原始解]
  4. x=105, y=670, a*x=6090.0, b*y=48910.0, 总和=55000.0 [原始解]
  5. x=178, y=612, a*x=10324.0, b*y=44676.0, 总和=55000.0 [原始解]

15. 组合: a=58, b=90.5 (5 个有效解)
  1. x=424, y=336.0, a*x=24592.0, b*y=30408.0, 总和=55000.0 [平衡解]
  2. x=243, y=452.0, a*x=14094.0, b*y=40906.0, 总和=55000.0 [平衡解]
  3. x=62, y=568.0, a*x=3596.0, b*y=51404.0, 总和=55000.0 [原始解]
  4. x=605, y=220.0, a*x=35090.0, b*y=19910.0, 总和=55000.0 [原始解]
  5. x=786, y=104.0, a*x=45588.0, b*y=9412.0, 总和=55000.0 [原始解]

16. 组合: a=67, b=35 (23 个有效解)
  1. x=555, y=509, a*x=37185.0, b*y=17815.0, 总和=55000.0 [平衡解]
  2. x=520, y=576, a*x=34840.0, b*y=20160.0, 总和=55000.0 [平衡解]
  3. x=30, y=1514, a*x=2010.0, b*y=52990.0, 总和=55000.0 [原始解]
  4. x=65, y=1447, a*x=4355.0, b*y=50645.0, 总和=55000.0 [原始解]
  5. x=100, y=1380, a*x=6700.0, b*y=48300.0, 总和=55000.0 [原始解]

17. 组合: a=67, b=40.5 (10 个有效解)
  1. x=538, y=468.0, a*x=36046.0, b*y=18954.0, 总和=55000.0 [平衡解]
  2. x=457, y=602.0, a*x=30619.0, b*y=24381.0, 总和=55000.0 [平衡解]
  3. x=52, y=1272.0, a*x=3484.0, b*y=51516.0, 总和=55000.0 [原始解]
  4. x=133, y=1138.0, a*x=8911.0, b*y=46089.0, 总和=55000.0 [原始解]
  5. x=214, y=1004.0, a*x=14338.0, b*y=40662.0, 总和=55000.0 [原始解]

18. 组合: a=67, b=58 (14 个有效解)
  1. x=440, y=440, a*x=29480.0, b*y=25520.0, 总和=55000.0 [平衡解]
  2. x=382, y=507, a*x=25594.0, b*y=29406.0, 总和=55000.0 [平衡解]
  3. x=34, y=909, a*x=2278.0, b*y=52722.0, 总和=55000.0 [原始解]
  4. x=92, y=842, a*x=6164.0, b*y=48836.0, 总和=55000.0 [原始解]
  5. x=150, y=775, a*x=10050.0, b*y=44950.0, 总和=55000.0 [原始解]

19. 组合: a=67, b=73 (12 个有效解)
  1. x=372, y=412, a*x=24924.0, b*y=30076.0, 总和=55000.0 [平衡解]
  2. x=445, y=345, a*x=29815.0, b*y=25185.0, 总和=55000.0 [平衡解]
  3. x=7, y=747, a*x=469.0, b*y=54531.0, 总和=55000.0 [原始解]
  4. x=80, y=680, a*x=5360.0, b*y=49640.0, 总和=55000.0 [原始解]
  5. x=153, y=613, a*x=10251.0, b*y=44749.0, 总和=55000.0 [原始解]

20. 组合: a=67, b=90.5 (4 个有效解)
  1. x=286, y=396.0, a*x=19162.0, b*y=35838.0, 总和=55000.0 [平衡解]
  2. x=467, y=262.0, a*x=31289.0, b*y=23711.0, 总和=55000.0 [平衡解]
  3. x=105, y=530.0, a*x=7035.0, b*y=47965.0, 总和=55000.0 [原始解]
  4. x=648, y=128.0, a*x=43416.0, b*y=11584.0, 总和=55000.0 [原始解]

21. 组合: a=73, b=35 (22 个有效解)
  1. x=495, y=539, a*x=36135.0, b*y=18865.0, 总和=55000.0 [平衡解]
  2. x=530, y=466, a*x=38690.0, b*y=16310.0, 总和=55000.0 [平衡解]
  3. x=5, y=1561, a*x=365.0, b*y=54635.0, 总和=55000.0 [原始解]
  4. x=40, y=1488, a*x=2920.0, b*y=52080.0, 总和=55000.0 [原始解]
  5. x=75, y=1415, a*x=5475.0, b*y=49525.0, 总和=55000.0 [原始解]

22. 组合: a=73, b=40.5 (10 个有效解)
  1. x=496, y=464.0, a*x=36208.0, b*y=18792.0, 总和=55000.0 [平衡解]
  2. x=415, y=610.0, a*x=30295.0, b*y=24705.0, 总和=55000.0 [平衡解]
  3. x=10, y=1340.0, a*x=730.0, b*y=54270.0, 总和=55000.0 [原始解]
  4. x=91, y=1194.0, a*x=6643.0, b*y=48357.0, 总和=55000.0 [原始解]
  5. x=172, y=1048.0, a*x=12556.0, b*y=42444.0, 总和=55000.0 [原始解]

23. 组合: a=73, b=58 (13 个有效解)
  1. x=438, y=397, a*x=31974.0, b*y=23026.0, 总和=55000.0 [平衡解]
  2. x=380, y=470, a*x=27740.0, b*y=27260.0, 总和=55000.0 [平衡解]
  3. x=32, y=908, a*x=2336.0, b*y=52664.0, 总和=55000.0 [原始解]
  4. x=90, y=835, a*x=6570.0, b*y=48430.0, 总和=55000.0 [原始解]
  5. x=148, y=762, a*x=10804.0, b*y=44196.0, 总和=55000.0 [原始解]

24. 组合: a=73, b=67 (12 个有效解)
  1. x=412, y=372, a*x=30076.0, b*y=24924.0, 总和=55000.0 [平衡解]
  2. x=345, y=445, a*x=25185.0, b*y=29815.0, 总和=55000.0 [平衡解]
  3. x=10, y=810, a*x=730.0, b*y=54270.0, 总和=55000.0 [原始解]
  4. x=77, y=737, a*x=5621.0, b*y=49379.0, 总和=55000.0 [原始解]
  5. x=144, y=664, a*x=10512.0, b*y=44488.0, 总和=55000.0 [原始解]

25. 组合: a=73, b=90.5 (4 个有效解)
  1. x=322, y=348.0, a*x=23506.0, b*y=31494.0, 总和=55000.0 [平衡解]
  2. x=503, y=202.0, a*x=36719.0, b*y=18281.0, 总和=55000.0 [平衡解]
  3. x=141, y=494.0, a*x=10293.0, b*y=44707.0, 总和=55000.0 [原始解]
  4. x=684, y=56.0, a*x=49932.0, b*y=5068.0, 总和=55000.0 [原始解]

26. 组合: a=90.5, b=35 (9 个有效解)
  1. x=460, y=382.0, a*x=41630.0, b*y=13370.0, 总和=55000.0 [平衡解]
  2. x=390, y=563.0, a*x=35295.0, b*y=19705.0, 总和=55000.0 [平衡解]
  3. x=40, y=1468.0, a*x=3620.0, b*y=51380.0, 总和=55000.0 [原始解]
  4. x=110, y=1287.0, a*x=9955.0, b*y=45045.0, 总和=55000.0 [原始解]
  5. x=180, y=1106.0, a*x=16290.0, b*y=38710.0, 总和=55000.0 [原始解]

27. 组合: a=90.5, b=40.5 (7 个有效解)
  1. x=452, y=348.0, a*x=40906.0, b*y=14094.0, 总和=55000.0 [平衡解]
  2. x=371, y=529.0, a*x=33575.5, b*y=21424.5, 总和=55000.0 [平衡解]
  3. x=47, y=1253.0, a*x=4253.5, b*y=50746.5, 总和=55000.0 [原始解]
  4. x=128, y=1072.0, a*x=11584.0, b*y=43416.0, 总和=55000.0 [原始解]
  5. x=209, y=891.0, a*x=18914.5, b*y=36085.5, 总和=55000.0 [原始解]

28. 组合: a=90.5, b=58 (5 个有效解)
  1. x=336, y=424.0, a*x=30408.0, b*y=24592.0, 总和=55000.0 [平衡解]
  2. x=452, y=243.0, a*x=40906.0, b*y=14094.0, 总和=55000.0 [平衡解]
  3. x=104, y=786.0, a*x=9412.0, b*y=45588.0, 总和=55000.0 [原始解]
  4. x=220, y=605.0, a*x=19910.0, b*y=35090.0, 总和=55000.0 [原始解]
  5. x=568, y=62.0, a*x=51404.0, b*y=3596.0, 总和=55000.0 [原始解]

29. 组合: a=90.5, b=67 (4 个有效解)
  1. x=396, y=286.0, a*x=35838.0, b*y=19162.0, 总和=55000.0 [平衡解]
  2. x=262, y=467.0, a*x=23711.0, b*y=31289.0, 总和=55000.0 [平衡解]
  3. x=128, y=648.0, a*x=11584.0, b*y=43416.0, 总和=55000.0 [原始解]
  4. x=530, y=105.0, a*x=47965.0, b*y=7035.0, 总和=55000.0 [原始解]

30. 组合: a=90.5, b=73 (4 个有效解)
  1. x=348, y=322.0, a*x=31494.0, b*y=23506.0, 总和=55000.0 [平衡解]
  2. x=202, y=503.0, a*x=18281.0, b*y=36719.0, 总和=55000.0 [平衡解]
  3. x=56, y=684.0, a*x=5068.0, b*y=49932.0, 总和=55000.0 [原始解]
  4. x=494, y=141.0, a*x=44707.0, b*y=10293.0, 总和=55000.0 [原始解]

使用基础系数列表，共找到有效解

总耗时: 0.01秒

https://ideone.com/z905y1

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Python 3 nbc (python 3.7.3)

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