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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 = 168400  # 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 = 168400  # 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 0.08s 10928KB

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Standard input is empty

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目标值: 168400

==== 尝试基础系数 ====

找到 30 组2变量解：

1. 组合: a=35, b=40.5 (14 个有效解)
  1. x=2231, y=2230.0, a*x=78085.0, b*y=90315.0, 总和=168400.0 [平衡解]
  2. x=2150, y=2300.0, a*x=75250.0, b*y=93150.0, 总和=168400.0 [平衡解]
  3. x=1583, y=2790.0, a*x=55405.0, b*y=112995.0, 总和=168400.0 [原始解]
  4. x=1664, y=2720.0, a*x=58240.0, b*y=110160.0, 总和=168400.0 [原始解]
  5. x=1745, y=2650.0, a*x=61075.0, b*y=107325.0, 总和=168400.0 [原始解]

2. 组合: a=35, b=58 (20 个有效解)
  1. x=1812, y=1810, a*x=63420.0, b*y=104980.0, 总和=168400.0 [平衡解]
  2. x=1754, y=1845, a*x=61390.0, b*y=107010.0, 总和=168400.0 [平衡解]
  3. x=1580, y=1950, a*x=55300.0, b*y=113100.0, 总和=168400.0 [原始解]
  4. x=1638, y=1915, a*x=57330.0, b*y=111070.0, 总和=168400.0 [原始解]
  5. x=1696, y=1880, a*x=59360.0, b*y=109040.0, 总和=168400.0 [原始解]

3. 组合: a=35, b=67 (18 个有效解)
  1. x=1672, y=1640, a*x=58520.0, b*y=109880.0, 总和=168400.0 [平衡解]
  2. x=1605, y=1675, a*x=56175.0, b*y=112225.0, 总和=168400.0 [平衡解]
  3. x=1538, y=1710, a*x=53830.0, b*y=114570.0, 总和=168400.0 [原始解]
  4. x=1739, y=1605, a*x=60865.0, b*y=107535.0, 总和=168400.0 [原始解]
  5. x=1806, y=1570, a*x=63210.0, b*y=105190.0, 总和=168400.0 [原始解]

4. 组合: a=35, b=73 (16 个有效解)
  1. x=1589, y=1545, a*x=55615.0, b*y=112785.0, 总和=168400.0 [平衡解]
  2. x=1662, y=1510, a*x=58170.0, b*y=110230.0, 总和=168400.0 [平衡解]
  3. x=1735, y=1475, a*x=60725.0, b*y=107675.0, 总和=168400.0 [原始解]
  4. x=1808, y=1440, a*x=63280.0, b*y=105120.0, 总和=168400.0 [原始解]
  5. x=1881, y=1405, a*x=65835.0, b*y=102565.0, 总和=168400.0 [原始解]

5. 组合: a=35, b=90.5 (6 个有效解)
  1. x=1631, y=1230.0, a*x=57085.0, b*y=111315.0, 总和=168400.0 [平衡解]
  2. x=1812, y=1160.0, a*x=63420.0, b*y=104980.0, 总和=168400.0 [平衡解]
  3. x=1993, y=1090.0, a*x=69755.0, b*y=98645.0, 总和=168400.0 [原始解]
  4. x=2174, y=1020.0, a*x=76090.0, b*y=92310.0, 总和=168400.0 [原始解]
  5. x=2355, y=950.0, a*x=82425.0, b*y=85975.0, 总和=168400.0 [原始解]

6. 组合: a=40.5, b=35 (15 个有效解)
  1. x=2230, y=2231.0, a*x=90315.0, b*y=78085.0, 总和=168400.0 [平衡解]
  2. x=2300, y=2150.0, a*x=93150.0, b*y=75250.0, 总和=168400.0 [平衡解]
  3. x=1320, y=3284.0, a*x=53460.0, b*y=114940.0, 总和=168400.0 [原始解]
  4. x=1390, y=3203.0, a*x=56295.0, b*y=112105.0, 总和=168400.0 [原始解]
  5. x=1460, y=3122.0, a*x=59130.0, b*y=109270.0, 总和=168400.0 [原始解]

7. 组合: a=40.5, b=58 (9 个有效解)
  1. x=1712, y=1708.0, a*x=69336.0, b*y=99064.0, 总和=168400.0 [平衡解]
  2. x=1596, y=1789.0, a*x=64638.0, b*y=103762.0, 总和=168400.0 [平衡解]
  3. x=1364, y=1951.0, a*x=55242.0, b*y=113158.0, 总和=168400.0 [原始解]
  4. x=1480, y=1870.0, a*x=59940.0, b*y=108460.0, 总和=168400.0 [原始解]
  5. x=1828, y=1627.0, a*x=74034.0, b*y=94366.0, 总和=168400.0 [原始解]

8. 组合: a=40.5, b=67 (8 个有效解)
  1. x=1526, y=1591.0, a*x=61803.0, b*y=106597.0, 总和=168400.0 [平衡解]
  2. x=1660, y=1510.0, a*x=67230.0, b*y=101170.0, 总和=168400.0 [平衡解]
  3. x=1392, y=1672.0, a*x=56376.0, b*y=112024.0, 总和=168400.0 [原始解]
  4. x=1794, y=1429.0, a*x=72657.0, b*y=95743.0, 总和=168400.0 [原始解]
  5. x=1928, y=1348.0, a*x=78084.0, b*y=90316.0, 总和=168400.0 [原始解]

9. 组合: a=40.5, b=73 (7 个有效解)
  1. x=1512, y=1468.0, a*x=61236.0, b*y=107164.0, 总和=168400.0 [平衡解]
  2. x=1366, y=1549.0, a*x=55323.0, b*y=113077.0, 总和=168400.0 [平衡解]
  3. x=1658, y=1387.0, a*x=67149.0, b*y=101251.0, 总和=168400.0 [原始解]
  4. x=1804, y=1306.0, a*x=73062.0, b*y=95338.0, 总和=168400.0 [原始解]
  5. x=1950, y=1225.0, a*x=78975.0, b*y=89425.0, 总和=168400.0 [原始解]

10. 组合: a=40.5, b=90.5 (6 个有效解)
  1. x=1338, y=1262.0, a*x=54189.0, b*y=114211.0, 总和=168400.0 [平衡解]
  2. x=1519, y=1181.0, a*x=61519.5, b*y=106880.5, 总和=168400.0 [平衡解]
  3. x=1700, y=1100.0, a*x=68850.0, b*y=99550.0, 总和=168400.0 [原始解]
  4. x=1881, y=1019.0, a*x=76180.5, b*y=92219.5, 总和=168400.0 [原始解]
  5. x=2062, y=938.0, a*x=83511.0, b*y=84889.0, 总和=168400.0 [原始解]

11. 组合: a=58, b=35 (20 个有效解)
  1. x=1600, y=2160, a*x=92800.0, b*y=75600.0, 总和=168400.0 [平衡解]
  2. x=1565, y=2218, a*x=90770.0, b*y=77630.0, 总和=168400.0 [平衡解]
  3. x=935, y=3262, a*x=54230.0, b*y=114170.0, 总和=168400.0 [原始解]
  4. x=970, y=3204, a*x=56260.0, b*y=112140.0, 总和=168400.0 [原始解]
  5. x=1005, y=3146, a*x=58290.0, b*y=110110.0, 总和=168400.0 [原始解]

12. 组合: a=58, b=40.5 (9 个有效解)
  1. x=1627, y=1828.0, a*x=94366.0, b*y=74034.0, 总和=168400.0 [平衡解]
  2. x=1546, y=1944.0, a*x=89668.0, b*y=78732.0, 总和=168400.0 [平衡解]
  3. x=979, y=2756.0, a*x=56782.0, b*y=111618.0, 总和=168400.0 [原始解]
  4. x=1060, y=2640.0, a*x=61480.0, b*y=106920.0, 总和=168400.0 [原始解]
  5. x=1141, y=2524.0, a*x=66178.0, b*y=102222.0, 总和=168400.0 [原始解]

13. 组合: a=58, b=67 (10 个有效解)
  1. x=1374, y=1324, a*x=79692.0, b*y=88708.0, 总和=168400.0 [平衡解]
  2. x=1307, y=1382, a*x=75806.0, b*y=92594.0, 总和=168400.0 [平衡解]
  3. x=972, y=1672, a*x=56376.0, b*y=112024.0, 总和=168400.0 [原始解]
  4. x=1039, y=1614, a*x=60262.0, b*y=108138.0, 总和=168400.0 [原始解]
  5. x=1106, y=1556, a*x=64148.0, b*y=104252.0, 总和=168400.0 [原始解]

14. 组合: a=58, b=73 (10 个有效解)
  1. x=1305, y=1270, a*x=75690.0, b*y=92710.0, 总和=168400.0 [平衡解]
  2. x=1232, y=1328, a*x=71456.0, b*y=96944.0, 总和=168400.0 [平衡解]
  3. x=940, y=1560, a*x=54520.0, b*y=113880.0, 总和=168400.0 [原始解]
  4. x=1013, y=1502, a*x=58754.0, b*y=109646.0, 总和=168400.0 [原始解]
  5. x=1086, y=1444, a*x=62988.0, b*y=105412.0, 总和=168400.0 [原始解]

15. 组合: a=58, b=90.5 (4 个有效解)
  1. x=1056, y=1184.0, a*x=61248.0, b*y=107152.0, 总和=168400.0 [平衡解]
  2. x=1237, y=1068.0, a*x=71746.0, b*y=96654.0, 总和=168400.0 [平衡解]
  3. x=1418, y=952.0, a*x=82244.0, b*y=86156.0, 总和=168400.0 [原始解]
  4. x=1599, y=836.0, a*x=92742.0, b*y=75658.0, 总和=168400.0 [原始解]

16. 组合: a=67, b=35 (18 个有效解)
  1. x=1395, y=2141, a*x=93465.0, b*y=74935.0, 总和=168400.0 [平衡解]
  2. x=1360, y=2208, a*x=91120.0, b*y=77280.0, 总和=168400.0 [平衡解]
  3. x=800, y=3280, a*x=53600.0, b*y=114800.0, 总和=168400.0 [原始解]
  4. x=835, y=3213, a*x=55945.0, b*y=112455.0, 总和=168400.0 [原始解]
  5. x=870, y=3146, a*x=58290.0, b*y=110110.0, 总和=168400.0 [原始解]

17. 组合: a=67, b=40.5 (7 个有效解)
  1. x=1348, y=1928.0, a*x=90316.0, b*y=78084.0, 总和=168400.0 [平衡解]
  2. x=1267, y=2062.0, a*x=84889.0, b*y=83511.0, 总和=168400.0 [平衡解]
  3. x=862, y=2732.0, a*x=57754.0, b*y=110646.0, 总和=168400.0 [原始解]
  4. x=943, y=2598.0, a*x=63181.0, b*y=105219.0, 总和=168400.0 [原始解]
  5. x=1024, y=2464.0, a*x=68608.0, b*y=99792.0, 总和=168400.0 [原始解]

18. 组合: a=67, b=58 (11 个有效解)
  1. x=1324, y=1374, a*x=88708.0, b*y=79692.0, 总和=168400.0 [平衡解]
  2. x=1382, y=1307, a*x=92594.0, b*y=75806.0, 总和=168400.0 [平衡解]
  3. x=802, y=1977, a*x=53734.0, b*y=114666.0, 总和=168400.0 [原始解]
  4. x=860, y=1910, a*x=57620.0, b*y=110780.0, 总和=168400.0 [原始解]
  5. x=918, y=1843, a*x=61506.0, b*y=106894.0, 总和=168400.0 [原始解]

19. 组合: a=67, b=73 (9 个有效解)
  1. x=1182, y=1222, a*x=79194.0, b*y=89206.0, 总和=168400.0 [平衡解]
  2. x=1255, y=1155, a*x=84085.0, b*y=84315.0, 总和=168400.0 [平衡解]
  3. x=817, y=1557, a*x=54739.0, b*y=113661.0, 总和=168400.0 [原始解]
  4. x=890, y=1490, a*x=59630.0, b*y=108770.0, 总和=168400.0 [原始解]
  5. x=963, y=1423, a*x=64521.0, b*y=103879.0, 总和=168400.0 [原始解]

20. 组合: a=67, b=90.5 (4 个有效解)
  1. x=1006, y=1116.0, a*x=67402.0, b*y=100998.0, 总和=168400.0 [平衡解]
  2. x=1187, y=982.0, a*x=79529.0, b*y=88871.0, 总和=168400.0 [平衡解]
  3. x=825, y=1250.0, a*x=55275.0, b*y=113125.0, 总和=168400.0 [原始解]
  4. x=1368, y=848.0, a*x=91656.0, b*y=76744.0, 总和=168400.0 [原始解]

21. 组合: a=73, b=35 (16 个有效解)
  1. x=1265, y=2173, a*x=92345.0, b*y=76055.0, 总和=168400.0 [平衡解]
  2. x=1230, y=2246, a*x=89790.0, b*y=78610.0, 总和=168400.0 [平衡解]
  3. x=740, y=3268, a*x=54020.0, b*y=114380.0, 总和=168400.0 [原始解]
  4. x=775, y=3195, a*x=56575.0, b*y=111825.0, 总和=168400.0 [原始解]
  5. x=810, y=3122, a*x=59130.0, b*y=109270.0, 总和=168400.0 [原始解]

22. 组合: a=73, b=40.5 (7 个有效解)
  1. x=1225, y=1950.0, a*x=89425.0, b*y=78975.0, 总和=168400.0 [平衡解]
  2. x=1144, y=2096.0, a*x=83512.0, b*y=84888.0, 总和=168400.0 [平衡解]
  3. x=739, y=2826.0, a*x=53947.0, b*y=114453.0, 总和=168400.0 [原始解]
  4. x=820, y=2680.0, a*x=59860.0, b*y=108540.0, 总和=168400.0 [原始解]
  5. x=901, y=2534.0, a*x=65773.0, b*y=102627.0, 总和=168400.0 [原始解]

23. 组合: a=73, b=58 (10 个有效解)
  1. x=1270, y=1305, a*x=92710.0, b*y=75690.0, 总和=168400.0 [平衡解]
  2. x=1212, y=1378, a*x=88476.0, b*y=79924.0, 总和=168400.0 [平衡解]
  3. x=748, y=1962, a*x=54604.0, b*y=113796.0, 总和=168400.0 [原始解]
  4. x=806, y=1889, a*x=58838.0, b*y=109562.0, 总和=168400.0 [原始解]
  5. x=864, y=1816, a*x=63072.0, b*y=105328.0, 总和=168400.0 [原始解]

24. 组合: a=73, b=67 (9 个有效解)
  1. x=1222, y=1182, a*x=89206.0, b*y=79194.0, 总和=168400.0 [平衡解]
  2. x=1155, y=1255, a*x=84315.0, b*y=84085.0, 总和=168400.0 [平衡解]
  3. x=753, y=1693, a*x=54969.0, b*y=113431.0, 总和=168400.0 [原始解]
  4. x=820, y=1620, a*x=59860.0, b*y=108540.0, 总和=168400.0 [原始解]
  5. x=887, y=1547, a*x=64751.0, b*y=103649.0, 总和=168400.0 [原始解]

25. 组合: a=73, b=90.5 (3 个有效解)
  1. x=1082, y=988.0, a*x=78986.0, b*y=89414.0, 总和=168400.0 [平衡解]
  2. x=901, y=1134.0, a*x=65773.0, b*y=102627.0, 总和=168400.0 [平衡解]
  3. x=1263, y=842.0, a*x=92199.0, b*y=76201.0, 总和=168400.0 [原始解]

26. 组合: a=90.5, b=35 (7 个有效解)
  1. x=1020, y=2174.0, a*x=92310.0, b*y=76090.0, 总和=168400.0 [平衡解]
  2. x=950, y=2355.0, a*x=85975.0, b*y=82425.0, 总和=168400.0 [平衡解]
  3. x=600, y=3260.0, a*x=54300.0, b*y=114100.0, 总和=168400.0 [原始解]
  4. x=670, y=3079.0, a*x=60635.0, b*y=107765.0, 总和=168400.0 [原始解]
  5. x=740, y=2898.0, a*x=66970.0, b*y=101430.0, 总和=168400.0 [原始解]

27. 组合: a=90.5, b=40.5 (6 个有效解)
  1. x=1019, y=1881.0, a*x=92219.5, b*y=76180.5, 总和=168400.0 [平衡解]
  2. x=938, y=2062.0, a*x=84889.0, b*y=83511.0, 总和=168400.0 [平衡解]
  3. x=614, y=2786.0, a*x=55567.0, b*y=112833.0, 总和=168400.0 [原始解]
  4. x=695, y=2605.0, a*x=62897.5, b*y=105502.5, 总和=168400.0 [原始解]
  5. x=776, y=2424.0, a*x=70228.0, b*y=98172.0, 总和=168400.0 [原始解]

28. 组合: a=90.5, b=58 (4 个有效解)
  1. x=952, y=1418.0, a*x=86156.0, b*y=82244.0, 总和=168400.0 [平衡解]
  2. x=836, y=1599.0, a*x=75658.0, b*y=92742.0, 总和=168400.0 [平衡解]
  3. x=604, y=1961.0, a*x=54662.0, b*y=113738.0, 总和=168400.0 [原始解]
  4. x=720, y=1780.0, a*x=65160.0, b*y=103240.0, 总和=168400.0 [原始解]

29. 组合: a=90.5, b=67 (3 个有效解)
  1. x=982, y=1187.0, a*x=88871.0, b*y=79529.0, 总和=168400.0 [平衡解]
  2. x=848, y=1368.0, a*x=76744.0, b*y=91656.0, 总和=168400.0 [平衡解]
  3. x=714, y=1549.0, a*x=64617.0, b*y=103783.0, 总和=168400.0 [原始解]

30. 组合: a=90.5, b=73 (3 个有效解)
  1. x=988, y=1082.0, a*x=89414.0, b*y=78986.0, 总和=168400.0 [平衡解]
  2. x=842, y=1263.0, a*x=76201.0, b*y=92199.0, 总和=168400.0 [平衡解]
  3. x=696, y=1444.0, a*x=62988.0, b*y=105412.0, 总和=168400.0 [原始解]

使用基础系数列表，共找到有效解

总耗时: 0.04秒

https://ideone.com/ldZ3Na

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Python 3 nbc (python 3.7.3)

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