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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 = 84947  # 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 = 84947  # 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 0.07s 10964KB

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Standard input is empty

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目标值: 84947

==== 尝试基础系数 ====

找到 30 组2变量解：

1. 组合: a=35, b=40.5 (30 个有效解)
  1. x=1138, y=1114.0, a*x=39830.0, b*y=45117.0, 总和=84947.0 [平衡解]
  2. x=1057, y=1184.0, a*x=36995.0, b*y=47952.0, 总和=84947.0 [平衡解]
  3. x=4, y=2094.0, a*x=140.0, b*y=84807.0, 总和=84947.0 [原始解]
  4. x=85, y=2024.0, a*x=2975.0, b*y=81972.0, 总和=84947.0 [原始解]
  5. x=166, y=1954.0, a*x=5810.0, b*y=79137.0, 总和=84947.0 [原始解]

2. 组合: a=35, b=58 (42 个有效解)
  1. x=929, y=904, a*x=32515.0, b*y=52432.0, 总和=84947.0 [平衡解]
  2. x=871, y=939, a*x=30485.0, b*y=54462.0, 总和=84947.0 [平衡解]
  3. x=1, y=1464, a*x=35.0, b*y=84912.0, 总和=84947.0 [原始解]
  4. x=59, y=1429, a*x=2065.0, b*y=82882.0, 总和=84947.0 [原始解]
  5. x=117, y=1394, a*x=4095.0, b*y=80852.0, 总和=84947.0 [原始解]

3. 组合: a=35, b=67 (36 个有效解)
  1. x=865, y=816, a*x=30275.0, b*y=54672.0, 总和=84947.0 [平衡解]
  2. x=798, y=851, a*x=27930.0, b*y=57017.0, 总和=84947.0 [平衡解]
  3. x=61, y=1236, a*x=2135.0, b*y=82812.0, 总和=84947.0 [原始解]
  4. x=128, y=1201, a*x=4480.0, b*y=80467.0, 总和=84947.0 [原始解]
  5. x=195, y=1166, a*x=6825.0, b*y=78122.0, 总和=84947.0 [原始解]

4. 组合: a=35, b=73 (33 个有效解)
  1. x=771, y=794, a*x=26985.0, b*y=57962.0, 总和=84947.0 [平衡解]
  2. x=844, y=759, a*x=29540.0, b*y=55407.0, 总和=84947.0 [平衡解]
  3. x=41, y=1144, a*x=1435.0, b*y=83512.0, 总和=84947.0 [原始解]
  4. x=114, y=1109, a*x=3990.0, b*y=80957.0, 总和=84947.0 [原始解]
  5. x=187, y=1074, a*x=6545.0, b*y=78402.0, 总和=84947.0 [原始解]

5. 组合: a=35, b=90.5 (14 个有效解)
  1. x=736, y=654.0, a*x=25760.0, b*y=59187.0, 总和=84947.0 [平衡解]
  2. x=555, y=724.0, a*x=19425.0, b*y=65522.0, 总和=84947.0 [平衡解]
  3. x=12, y=934.0, a*x=420.0, b*y=84527.0, 总和=84947.0 [原始解]
  4. x=193, y=864.0, a*x=6755.0, b*y=78192.0, 总和=84947.0 [原始解]
  5. x=374, y=794.0, a*x=13090.0, b*y=71857.0, 总和=84947.0 [原始解]

6. 组合: a=40.5, b=35 (30 个有效解)
  1. x=1114, y=1138.0, a*x=45117.0, b*y=39830.0, 总和=84947.0 [平衡解]
  2. x=1184, y=1057.0, a*x=47952.0, b*y=36995.0, 总和=84947.0 [平衡解]
  3. x=64, y=2353.0, a*x=2592.0, b*y=82355.0, 总和=84947.0 [原始解]
  4. x=134, y=2272.0, a*x=5427.0, b*y=79520.0, 总和=84947.0 [原始解]
  5. x=204, y=2191.0, a*x=8262.0, b*y=76685.0, 总和=84947.0 [原始解]

7. 组合: a=40.5, b=58 (18 个有效解)
  1. x=810, y=899.0, a*x=32805.0, b*y=52142.0, 总和=84947.0 [平衡解]
  2. x=926, y=818.0, a*x=37503.0, b*y=47444.0, 总和=84947.0 [平衡解]
  3. x=114, y=1385.0, a*x=4617.0, b*y=80330.0, 总和=84947.0 [原始解]
  4. x=230, y=1304.0, a*x=9315.0, b*y=75632.0, 总和=84947.0 [原始解]
  5. x=346, y=1223.0, a*x=14013.0, b*y=70934.0, 总和=84947.0 [原始解]

8. 组合: a=40.5, b=67 (15 个有效解)
  1. x=774, y=800.0, a*x=31347.0, b*y=53600.0, 总和=84947.0 [平衡解]
  2. x=908, y=719.0, a*x=36774.0, b*y=48173.0, 总和=84947.0 [平衡解]
  3. x=104, y=1205.0, a*x=4212.0, b*y=80735.0, 总和=84947.0 [原始解]
  4. x=238, y=1124.0, a*x=9639.0, b*y=75308.0, 总和=84947.0 [原始解]
  5. x=372, y=1043.0, a*x=15066.0, b*y=69881.0, 总和=84947.0 [原始解]

9. 组合: a=40.5, b=73 (15 个有效解)
  1. x=742, y=752.0, a*x=30051.0, b*y=54896.0, 总和=84947.0 [平衡解]
  2. x=888, y=671.0, a*x=35964.0, b*y=48983.0, 总和=84947.0 [平衡解]
  3. x=12, y=1157.0, a*x=486.0, b*y=84461.0, 总和=84947.0 [原始解]
  4. x=158, y=1076.0, a*x=6399.0, b*y=78548.0, 总和=84947.0 [原始解]
  5. x=304, y=995.0, a*x=12312.0, b*y=72635.0, 总和=84947.0 [原始解]

10. 组合: a=40.5, b=90.5 (12 个有效解)
  1. x=607, y=667.0, a*x=24583.5, b*y=60363.5, 总和=84947.0 [平衡解]
  2. x=788, y=586.0, a*x=31914.0, b*y=53033.0, 总和=84947.0 [平衡解]
  3. x=64, y=910.0, a*x=2592.0, b*y=82355.0, 总和=84947.0 [原始解]
  4. x=245, y=829.0, a*x=9922.5, b*y=75024.5, 总和=84947.0 [原始解]
  5. x=426, y=748.0, a*x=17253.0, b*y=67694.0, 总和=84947.0 [原始解]

11. 组合: a=58, b=35 (42 个有效解)
  1. x=904, y=929, a*x=52432.0, b*y=32515.0, 总和=84947.0 [平衡解]
  2. x=939, y=871, a*x=54462.0, b*y=30485.0, 总和=84947.0 [平衡解]
  3. x=29, y=2379, a*x=1682.0, b*y=83265.0, 总和=84947.0 [原始解]
  4. x=64, y=2321, a*x=3712.0, b*y=81235.0, 总和=84947.0 [原始解]
  5. x=99, y=2263, a*x=5742.0, b*y=79205.0, 总和=84947.0 [原始解]

12. 组合: a=58, b=40.5 (18 个有效解)
  1. x=899, y=810.0, a*x=52142.0, b*y=32805.0, 总和=84947.0 [平衡解]
  2. x=818, y=926.0, a*x=47444.0, b*y=37503.0, 总和=84947.0 [平衡解]
  3. x=8, y=2086.0, a*x=464.0, b*y=84483.0, 总和=84947.0 [原始解]
  4. x=89, y=1970.0, a*x=5162.0, b*y=79785.0, 总和=84947.0 [原始解]
  5. x=170, y=1854.0, a*x=9860.0, b*y=75087.0, 总和=84947.0 [原始解]

13. 组合: a=58, b=67 (22 个有效解)
  1. x=671, y=687, a*x=38918.0, b*y=46029.0, 总和=84947.0 [平衡解]
  2. x=738, y=629, a*x=42804.0, b*y=42143.0, 总和=84947.0 [平衡解]
  3. x=1, y=1267, a*x=58.0, b*y=84889.0, 总和=84947.0 [原始解]
  4. x=68, y=1209, a*x=3944.0, b*y=81003.0, 总和=84947.0 [原始解]
  5. x=135, y=1151, a*x=7830.0, b*y=77117.0, 总和=84947.0 [原始解]

14. 组合: a=58, b=73 (20 个有效解)
  1. x=683, y=621, a*x=39614.0, b*y=45333.0, 总和=84947.0 [平衡解]
  2. x=610, y=679, a*x=35380.0, b*y=49567.0, 总和=84947.0 [平衡解]
  3. x=26, y=1143, a*x=1508.0, b*y=83439.0, 总和=84947.0 [原始解]
  4. x=99, y=1085, a*x=5742.0, b*y=79205.0, 总和=84947.0 [原始解]
  5. x=172, y=1027, a*x=9976.0, b*y=74971.0, 总和=84947.0 [原始解]

15. 组合: a=58, b=90.5 (9 个有效解)
  1. x=544, y=590.0, a*x=31552.0, b*y=53395.0, 总和=84947.0 [平衡解]
  2. x=725, y=474.0, a*x=42050.0, b*y=42897.0, 总和=84947.0 [平衡解]
  3. x=1, y=938.0, a*x=58.0, b*y=84889.0, 总和=84947.0 [原始解]
  4. x=182, y=822.0, a*x=10556.0, b*y=74391.0, 总和=84947.0 [原始解]
  5. x=363, y=706.0, a*x=21054.0, b*y=63893.0, 总和=84947.0 [原始解]

16. 组合: a=67, b=35 (36 个有效解)
  1. x=816, y=865, a*x=54672.0, b*y=30275.0, 总和=84947.0 [平衡解]
  2. x=851, y=798, a*x=57017.0, b*y=27930.0, 总和=84947.0 [平衡解]
  3. x=11, y=2406, a*x=737.0, b*y=84210.0, 总和=84947.0 [原始解]
  4. x=46, y=2339, a*x=3082.0, b*y=81865.0, 总和=84947.0 [原始解]
  5. x=81, y=2272, a*x=5427.0, b*y=79520.0, 总和=84947.0 [原始解]

17. 组合: a=67, b=40.5 (15 个有效解)
  1. x=800, y=774.0, a*x=53600.0, b*y=31347.0, 总和=84947.0 [平衡解]
  2. x=719, y=908.0, a*x=48173.0, b*y=36774.0, 总和=84947.0 [平衡解]
  3. x=71, y=1980.0, a*x=4757.0, b*y=80190.0, 总和=84947.0 [原始解]
  4. x=152, y=1846.0, a*x=10184.0, b*y=74763.0, 总和=84947.0 [原始解]
  5. x=233, y=1712.0, a*x=15611.0, b*y=69336.0, 总和=84947.0 [原始解]

18. 组合: a=67, b=58 (22 个有效解)
  1. x=687, y=671, a*x=46029.0, b*y=38918.0, 总和=84947.0 [平衡解]
  2. x=629, y=738, a*x=42143.0, b*y=42804.0, 总和=84947.0 [平衡解]
  3. x=49, y=1408, a*x=3283.0, b*y=81664.0, 总和=84947.0 [原始解]
  4. x=107, y=1341, a*x=7169.0, b*y=77778.0, 总和=84947.0 [原始解]
  5. x=165, y=1274, a*x=11055.0, b*y=73892.0, 总和=84947.0 [原始解]

19. 组合: a=67, b=73 (17 个有效解)
  1. x=576, y=635, a*x=38592.0, b*y=46355.0, 总和=84947.0 [平衡解]
  2. x=649, y=568, a*x=43483.0, b*y=41464.0, 总和=84947.0 [平衡解]
  3. x=65, y=1104, a*x=4355.0, b*y=80592.0, 总和=84947.0 [原始解]
  4. x=138, y=1037, a*x=9246.0, b*y=75701.0, 总和=84947.0 [原始解]
  5. x=211, y=970, a*x=14137.0, b*y=70810.0, 总和=84947.0 [原始解]

20. 组合: a=67, b=90.5 (7 个有效解)
  1. x=606, y=490.0, a*x=40602.0, b*y=44345.0, 总和=84947.0 [平衡解]
  2. x=425, y=624.0, a*x=28475.0, b*y=56472.0, 总和=84947.0 [平衡解]
  3. x=63, y=892.0, a*x=4221.0, b*y=80726.0, 总和=84947.0 [原始解]
  4. x=244, y=758.0, a*x=16348.0, b*y=68599.0, 总和=84947.0 [原始解]
  5. x=787, y=356.0, a*x=52729.0, b*y=32218.0, 总和=84947.0 [原始解]

21. 组合: a=73, b=35 (33 个有效解)
  1. x=794, y=771, a*x=57962.0, b*y=26985.0, 总和=84947.0 [平衡解]
  2. x=759, y=844, a*x=55407.0, b*y=29540.0, 总和=84947.0 [平衡解]
  3. x=24, y=2377, a*x=1752.0, b*y=83195.0, 总和=84947.0 [原始解]
  4. x=59, y=2304, a*x=4307.0, b*y=80640.0, 总和=84947.0 [原始解]
  5. x=94, y=2231, a*x=6862.0, b*y=78085.0, 总和=84947.0 [原始解]

22. 组合: a=73, b=40.5 (15 个有效解)
  1. x=752, y=742.0, a*x=54896.0, b*y=30051.0, 总和=84947.0 [平衡解]
  2. x=671, y=888.0, a*x=48983.0, b*y=35964.0, 总和=84947.0 [平衡解]
  3. x=23, y=2056.0, a*x=1679.0, b*y=83268.0, 总和=84947.0 [原始解]
  4. x=104, y=1910.0, a*x=7592.0, b*y=77355.0, 总和=84947.0 [原始解]
  5. x=185, y=1764.0, a*x=13505.0, b*y=71442.0, 总和=84947.0 [原始解]

23. 组合: a=73, b=58 (20 个有效解)
  1. x=621, y=683, a*x=45333.0, b*y=39614.0, 总和=84947.0 [平衡解]
  2. x=679, y=610, a*x=49567.0, b*y=35380.0, 总和=84947.0 [平衡解]
  3. x=41, y=1413, a*x=2993.0, b*y=81954.0, 总和=84947.0 [原始解]
  4. x=99, y=1340, a*x=7227.0, b*y=77720.0, 总和=84947.0 [原始解]
  5. x=157, y=1267, a*x=11461.0, b*y=73486.0, 总和=84947.0 [原始解]

24. 组合: a=73, b=67 (17 个有效解)
  1. x=635, y=576, a*x=46355.0, b*y=38592.0, 总和=84947.0 [平衡解]
  2. x=568, y=649, a*x=41464.0, b*y=43483.0, 总和=84947.0 [平衡解]
  3. x=32, y=1233, a*x=2336.0, b*y=82611.0, 总和=84947.0 [原始解]
  4. x=99, y=1160, a*x=7227.0, b*y=77720.0, 总和=84947.0 [原始解]
  5. x=166, y=1087, a*x=12118.0, b*y=72829.0, 总和=84947.0 [原始解]

25. 组合: a=73, b=90.5 (6 个有效解)
  1. x=519, y=520.0, a*x=37887.0, b*y=47060.0, 总和=84947.0 [平衡解]
  2. x=700, y=374.0, a*x=51100.0, b*y=33847.0, 总和=84947.0 [平衡解]
  3. x=157, y=812.0, a*x=11461.0, b*y=73486.0, 总和=84947.0 [原始解]
  4. x=338, y=666.0, a*x=24674.0, b*y=60273.0, 总和=84947.0 [原始解]
  5. x=881, y=228.0, a*x=64313.0, b*y=20634.0, 总和=84947.0 [原始解]

26. 组合: a=90.5, b=35 (14 个有效解)
  1. x=654, y=736.0, a*x=59187.0, b*y=25760.0, 总和=84947.0 [平衡解]
  2. x=724, y=555.0, a*x=65522.0, b*y=19425.0, 总和=84947.0 [平衡解]
  3. x=24, y=2365.0, a*x=2172.0, b*y=82775.0, 总和=84947.0 [原始解]
  4. x=94, y=2184.0, a*x=8507.0, b*y=76440.0, 总和=84947.0 [原始解]
  5. x=164, y=2003.0, a*x=14842.0, b*y=70105.0, 总和=84947.0 [原始解]

27. 组合: a=90.5, b=40.5 (12 个有效解)
  1. x=667, y=607.0, a*x=60363.5, b*y=24583.5, 总和=84947.0 [平衡解]
  2. x=586, y=788.0, a*x=53033.0, b*y=31914.0, 总和=84947.0 [平衡解]
  3. x=19, y=2055.0, a*x=1719.5, b*y=83227.5, 总和=84947.0 [原始解]
  4. x=100, y=1874.0, a*x=9050.0, b*y=75897.0, 总和=84947.0 [原始解]
  5. x=181, y=1693.0, a*x=16380.5, b*y=68566.5, 总和=84947.0 [原始解]

28. 组合: a=90.5, b=58 (9 个有效解)
  1. x=590, y=544.0, a*x=53395.0, b*y=31552.0, 总和=84947.0 [平衡解]
  2. x=474, y=725.0, a*x=42897.0, b*y=42050.0, 总和=84947.0 [平衡解]
  3. x=10, y=1449.0, a*x=905.0, b*y=84042.0, 总和=84947.0 [原始解]
  4. x=126, y=1268.0, a*x=11403.0, b*y=73544.0, 总和=84947.0 [原始解]
  5. x=242, y=1087.0, a*x=21901.0, b*y=63046.0, 总和=84947.0 [原始解]

29. 组合: a=90.5, b=67 (7 个有效解)
  1. x=490, y=606.0, a*x=44345.0, b*y=40602.0, 总和=84947.0 [平衡解]
  2. x=624, y=425.0, a*x=56472.0, b*y=28475.0, 总和=84947.0 [平衡解]
  3. x=88, y=1149.0, a*x=7964.0, b*y=76983.0, 总和=84947.0 [原始解]
  4. x=222, y=968.0, a*x=20091.0, b*y=64856.0, 总和=84947.0 [原始解]
  5. x=356, y=787.0, a*x=32218.0, b*y=52729.0, 总和=84947.0 [原始解]

30. 组合: a=90.5, b=73 (6 个有效解)
  1. x=520, y=519.0, a*x=47060.0, b*y=37887.0, 总和=84947.0 [平衡解]
  2. x=374, y=700.0, a*x=33847.0, b*y=51100.0, 总和=84947.0 [平衡解]
  3. x=82, y=1062.0, a*x=7421.0, b*y=77526.0, 总和=84947.0 [原始解]
  4. x=228, y=881.0, a*x=20634.0, b*y=64313.0, 总和=84947.0 [原始解]
  5. x=666, y=338.0, a*x=60273.0, b*y=24674.0, 总和=84947.0 [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/DNeMxx

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Python 3 nbc (python 3.7.3)

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