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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 = 75085  # 目标值
BASE_VALUES = [36.5, 41.5, 59,68.5, 74, 91.5]  # 基础系数列表
FLUCTUATION = 1.0  # 系数波动范围
MAX_SOLUTIONS = 3  # 每个组合的最大解数量
SOLVER_TIMEOUT = 180  # 求解超时时间(秒)
THREE_VAR_THRESHOLD = 220000  # 使用三个变量的阈值
PRODUCT_RANGE_THRESHOLD = 148000  # 乘积范围限制阈值
HIGH_TARGET_THRESHOLD = 260000  # 更高目标值阈值
SHOW_PROGRESS = True  # 是否显示进度
MAX_SOLUTIONS_PER_COMB = 100  # 每个组合的最大解数量，用于提前终止
 
def is_valid_product(p):
    """检查单个乘积是否在有效范围内"""
    if TARGET > PRODUCT_RANGE_THRESHOLD:
        if TARGET > HIGH_TARGET_THRESHOLD:
            return p <= 115000  # 目标值超过260000时，仅限制最大值
        else:
            return 74000 <= p <= 115000  # 目标值在148000-260000之间时，使用原范围
    else:
        return True  # 目标值较小时不限制乘积范围
 
def find_single_variable_solutions(values):
    """查找单个数的解（a*x = TARGET）"""
    solutions = []
    for a in values:
        x = TARGET / a
        if x.is_integer() and 1 <= x <= 10000 and is_valid_product(a * x):
            solutions.append((a, x))
            if len(solutions) >= MAX_SOLUTIONS:
                return solutions  # 提前终止
    return solutions
 
def find_two_variable_solutions(values):
    """查找两个变量的解（a*x + b*y = TARGET）"""
    solutions = defaultdict(list)
 
    # 生成所有可能的(a, b)组合
    for a in values:
        for b in values:
            if a == b:  # 避免重复
                continue
 
            # 计算x的有效范围
            min_x = max(1, math.ceil((TARGET - b * 10000) / a))
            max_x = min(math.floor((TARGET - 1) / a), 10000)
 
            if max_x < min_x:
                continue
 
            for x in range(min_x, max_x + 1):
                remainder = TARGET - a * x
 
                # 检查remainder是否在可能的范围内
                if remainder < 1 or remainder > b * 10000:
                    continue
 
                # 检查remainder是否能被b整除
                if remainder % b == 0:
                    y = remainder // b
                    if 1 <= y <= 10000 and is_valid_product(b * y):
                        solutions[(a, b)].append((a, x, b, y))
                        if len(solutions[(a, b)]) >= MAX_SOLUTIONS_PER_COMB:
                            break  # 提前终止当前组合的搜索
 
    return solutions
 
def find_three_variable_solutions(values):
    """优化的三变量求解算法"""
    solutions = defaultdict(list)
 
    # 对系数进行排序，便于剪枝
    sorted_values = sorted(values)
 
    # 预计算每个系数的有效范围
    value_ranges = {}
    for a in sorted_values:
        if TARGET > PRODUCT_RANGE_THRESHOLD:
            if TARGET > HIGH_TARGET_THRESHOLD:
                min_x = max(1, math.ceil(1 / a))  # 取消下限，最小为1
                max_x = min(10000, math.floor(115000 / a))
            else:
                min_x = max(1, math.ceil(74000 / a))
                max_x = min(10000, math.floor(115000 / a))
        else:
            min_x = 1
            max_x = 10000
        value_ranges[a] = (min_x, max_x)
 
    total_combinations = len(sorted_values) * (len(sorted_values) - 1) * (len(sorted_values) - 2) // 6
    processed_combinations = 0
 
    # 三重循环，但添加了更多剪枝条件
    for i, a in enumerate(sorted_values):
        min_x, max_x = value_ranges[a]
 
        # 计算可能的x值数量，决定步长
        x_count = max_x - min_x + 1
        x_step = max(1, x_count // 1000)  # 自适应步长
 
        for x in range(min_x, max_x + 1, x_step):
            ax = a * x
            if not is_valid_product(ax):
                continue
 
            remainder1 = TARGET - ax
            if TARGET > PRODUCT_RANGE_THRESHOLD:
                if TARGET > HIGH_TARGET_THRESHOLD:
                    if remainder1 < 0:
                        continue
                else:
                    if remainder1 < 2 * 74000:
                        continue
 
            # 限制b的选择范围，避免重复组合
            for j in range(i + 1, len(sorted_values)):
                b = sorted_values[j]
 
                if TARGET > PRODUCT_RANGE_THRESHOLD:
                    if TARGET > HIGH_TARGET_THRESHOLD:
                        min_y = max(1, math.ceil(1 / b))  # 取消下限，最小为1
                        max_y = min(10000, math.floor(remainder1 / b))
                    else:
                        min_y = max(1, math.ceil(74000 / b))
                        max_y = min(10000, math.floor((remainder1 - 74000) / b))
                else:
                    min_y = 1
                    max_y = math.floor(remainder1 / b)
 
                if max_y < min_y:
                    continue
 
                # 计算可能的y值数量，决定步长
                y_count = max_y - min_y + 1
                y_step = max(1, y_count // 100)  # 自适应步长
 
                for y in range(min_y, max_y + 1, y_step):
                    by = b * y
                    if not is_valid_product(by):
                        continue
 
                    remainder2 = remainder1 - by
                    if TARGET > PRODUCT_RANGE_THRESHOLD:
                        if TARGET > HIGH_TARGET_THRESHOLD:
                            if remainder2 < 0 or remainder2 > 115000:
                                continue
                        else:
                            if remainder2 < 74000 or remainder2 > 115000:
                                continue
 
                    # 限制c的选择范围
                    found_solution = False
                    for k in range(j + 1, len(sorted_values)):
                        c = sorted_values[k]
 
                        # 检查remainder2是否能被c整除
                        if remainder2 % c != 0:
                            continue
 
                        z = remainder2 // c
                        if 1 <= z <= 10000 and is_valid_product(c * z):
                            key = (a, b, c)
                            solutions[key].append((a, x, b, y, c, z))
                            found_solution = True
                            if len(solutions[key]) >= MAX_SOLUTIONS_PER_COMB:
                                break  # 提前终止当前组合的搜索
 
                    # 如果找到解且达到最大数量，跳出y循环
                    if found_solution and len(solutions[key]) >= MAX_SOLUTIONS_PER_COMB:
                        break  # 跳出y循环
 
                # 进度显示
                if SHOW_PROGRESS and j % 10 == 0:
                    print(f"\r三变量组合进度: {processed_combinations}/{total_combinations} 组", end='')
                processed_combinations += 1
 
    if SHOW_PROGRESS:
        print(f"\r三变量组合进度: {processed_combinations}/{total_combinations} 组 - 完成")
 
    return solutions
 
def find_balanced_solutions(solutions, var_count, num=2):
    """从所有解中筛选出最平衡的解"""
    if var_count == 1 or not solutions:
        return solutions  # 单变量或无解时直接返回
 
    # 当目标值超过220000时，不计算平衡解
    if TARGET > THREE_VAR_THRESHOLD:
        return []
 
    # 计算解的平衡性（变量间差异最小）
    balanced = []
    for sol in solutions:
        vars = sol[1::2]  # 提取x, y, z
        diff = max(vars) - min(vars)
        balanced.append((diff, sol))
 
    # 按差异排序，取前num个
    return [s for _, s in sorted(balanced, key=lambda x: x[0])[:num]]
 
def find_original_solutions(solutions, balanced_solutions, num=3):
    """从剩余解中获取原始顺序的解"""
    if not solutions:
        return []
 
    # 排除已在平衡解中的项
    remaining = [s for s in solutions if s not in balanced_solutions]
    return remaining[:num]
 
def display_solutions(solutions_dict, var_count):
    """优化的解显示函数"""
    if not solutions_dict:
        return
 
    print(f"\n找到 {len(solutions_dict)} 组{var_count}变量解：")
 
    for i, (coeffs, pair_solutions) in enumerate(sorted(solutions_dict.items()), 1):
        # 当目标值超过220000时，不显示平衡解
        if TARGET > THREE_VAR_THRESHOLD:
            all_display = pair_solutions[:MAX_SOLUTIONS]
            print_tag = "[原始解]"
        else:
            # 计算平衡解和原始解
            balanced = find_balanced_solutions(pair_solutions, var_count)
            original = find_original_solutions(pair_solutions, balanced)
            all_display = balanced + original
 
        if var_count == 1:
            a = coeffs
            print(f"\n{i}. 组合: a={a} ({len(pair_solutions)} 个有效解)")
        elif var_count == 2:
            a, b = coeffs
            print(f"\n{i}. 组合: a={a}, b={b} ({len(pair_solutions)} 个有效解)")
        else:  # var_count == 3
            a, b, c = coeffs
            print(f"\n{i}. 组合: a={a}, b={b}, c={c} ({len(pair_solutions)} 个有效解)")
 
        for j, sol in enumerate(all_display, 1):
            if TARGET > THREE_VAR_THRESHOLD:
                tag = print_tag
            else:
                tag = "[平衡解]" if j <= len(balanced) else "[原始解]"
 
            if var_count == 1:
                a, x = sol
                print(f"  {j}. x={x}, a*x={a*x:.1f}, 总和={a*x:.1f} {tag}")
            elif var_count == 2:
                a, x, b, y = sol
                print(f"  {j}. x={x}, y={y}, a*x={a*x:.1f}, b*y={b*y:.1f}, 总和={a*x + b*y:.1f} {tag}")
            else:  # var_count == 3
                a, x, b, y, c, z = sol
                print(f"  {j}. x={x}, y={y}, z={z}, "
                      f"a*x={a*x:.1f}, b*y={b*y:.1f}, c*z={c*z:.1f}, "
                      f"总和={a*x + b*y + c*z:.1f} {tag}")
 
def run_with_timeout(func, args=(), kwargs=None, timeout=SOLVER_TIMEOUT):
    """运行函数并设置超时限制"""
    if kwargs is None:
        kwargs = {}
 
    result = []
    error = []
 
    def wrapper():
        try:
            result.append(func(*args, **kwargs))
        except Exception as e:
            error.append(e)
 
    thread = threading.Thread(target=wrapper)
    thread.daemon = True
    thread.start()
    thread.join(timeout)
 
    if thread.is_alive():
        print(f"警告: {func.__name__} 超时（{timeout}秒），跳过此方法")
        return None
 
    if error:
        raise error[0]
 
    return result[0]
 
def main():
    print(f"目标值: {TARGET}")
 
    # 生成波动后的系数
    FLUCTUATED_VALUES = [round(v - FLUCTUATION, 1) for v in BASE_VALUES]
 
    # 尝试基础系数
    print(f"\n==== 尝试基础系数 ====")
 
    # 检查目标值是否超过阈值
    if TARGET > THREE_VAR_THRESHOLD:
        print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD}，只尝试三变量解")
        base_solutions = {
            'single': [],
            'two': [],
            'three': run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,))
        }
 
        # 显示三变量解
        if base_solutions['three'] and len(base_solutions['three']) > 0:
            display_solutions(base_solutions['three'], 3)
            print(f"\n使用基础系数列表，共找到有效解")
            return
        else:
            print("\n基础系数三变量无解，尝试波动系数")
    else:
        # 目标值未超过阈值，按顺序尝试单、双、三变量解
        base_solutions = {
            'single': run_with_timeout(find_single_variable_solutions, args=(BASE_VALUES,)),
            'two': run_with_timeout(find_two_variable_solutions, args=(BASE_VALUES,)),
            'three': []
        }
 
        # 检查是否有解
        has_solution = False
 
        # 显示单变量解
        if base_solutions['single']:
            has_solution = True
            display_solutions({a: [sol] for a, sol in zip(BASE_VALUES, base_solutions['single']) if sol}, 1)
 
        # 显示双变量解
        if base_solutions['two'] and len(base_solutions['two']) > 0:
            has_solution = True
            display_solutions(base_solutions['two'], 2)
 
        # 单变量和双变量都无解时，尝试三变量解
        if not has_solution:
            print(f"\n==== 单变量和双变量无解，尝试三变量解 ====")
            base_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,))
 
            if base_solutions['three'] and len(base_solutions['three']) > 0:
                has_solution = True
                display_solutions(base_solutions['three'], 3)
 
        # 如果找到解，退出程序
        if has_solution:
            print(f"\n使用基础系数列表，共找到有效解")
            return
 
    # 如果基础系数没有找到解，尝试波动系数
    print(f"\n==== 尝试波动系数 ====")
 
    # 检查目标值是否超过阈值
    if TARGET > THREE_VAR_THRESHOLD:
        print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD}，只尝试三变量解")
        fluctuated_solutions = {
            'single': [],
            'two': [],
            'three': run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,))
        }
 
        # 显示三变量解
        if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0:
            display_solutions(fluctuated_solutions['three'], 3)
            print(f"\n使用波动系数列表，共找到有效解")
            return
    else:
        # 目标值未超过阈值，按顺序尝试单、双、三变量解
        fluctuated_solutions = {
            'single': run_with_timeout(find_single_variable_solutions, args=(FLUCTUATED_VALUES,)),
            'two': run_with_timeout(find_two_variable_solutions, args=(FLUCTUATED_VALUES,)),
            'three': []
        }
 
        # 重置标志
        has_solution = False
 
        # 显示单变量解
        if fluctuated_solutions['single']:
            has_solution = True
            display_solutions({a: [sol] for a, sol in zip(FLUCTUATED_VALUES, fluctuated_solutions['single']) if sol}, 1)
 
        # 显示双变量解
        if fluctuated_solutions['two'] and len(fluctuated_solutions['two']) > 0:
            has_solution = True
            display_solutions(fluctuated_solutions['two'], 2)
 
        # 单变量和双变量都无解时，尝试三变量解
        if not has_solution:
            print(f"\n==== 单变量和双变量无解，尝试三变量解 ====")
            fluctuated_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,))
 
            if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0:
                has_solution = True
                display_solutions(fluctuated_solutions['three'], 3)
 
        # 如果找到解，退出程序
        if has_solution:
            print(f"\n使用波动系数列表，共找到有效解")
            return
 
    # 如果所有系数集都没有找到解
    print("\n没有找到符合条件的解，即使使用波动后的系数列表。")
 
if __name__ == "__main__":
    start_time = time.time()
    main()
    print(f"\n总耗时: {time.time() - start_time:.2f}秒")

from itertools import product, combinations_with_replacement
import time
import threading
from collections import defaultdict
import math

# 配置参数（可根据需要修改）
TARGET = 75085  # 目标值
BASE_VALUES = [36.5, 41.5, 59,68.5, 74, 91.5]  # 基础系数列表
FLUCTUATION = 1.0  # 系数波动范围
MAX_SOLUTIONS = 3  # 每个组合的最大解数量
SOLVER_TIMEOUT = 180  # 求解超时时间(秒)
THREE_VAR_THRESHOLD = 220000  # 使用三个变量的阈值
PRODUCT_RANGE_THRESHOLD = 148000  # 乘积范围限制阈值
HIGH_TARGET_THRESHOLD = 260000  # 更高目标值阈值
SHOW_PROGRESS = True  # 是否显示进度
MAX_SOLUTIONS_PER_COMB = 100  # 每个组合的最大解数量，用于提前终止

def is_valid_product(p):
    """检查单个乘积是否在有效范围内"""
    if TARGET > PRODUCT_RANGE_THRESHOLD:
        if TARGET > HIGH_TARGET_THRESHOLD:
            return p <= 115000  # 目标值超过260000时，仅限制最大值
        else:
            return 74000 <= p <= 115000  # 目标值在148000-260000之间时，使用原范围
    else:
        return True  # 目标值较小时不限制乘积范围

def find_single_variable_solutions(values):
    """查找单个数的解（a*x = TARGET）"""
    solutions = []
    for a in values:
        x = TARGET / a
        if x.is_integer() and 1 <= x <= 10000 and is_valid_product(a * x):
            solutions.append((a, x))
            if len(solutions) >= MAX_SOLUTIONS:
                return solutions  # 提前终止
    return solutions

def find_two_variable_solutions(values):
    """查找两个变量的解（a*x + b*y = TARGET）"""
    solutions = defaultdict(list)
    
    # 生成所有可能的(a, b)组合
    for a in values:
        for b in values:
            if a == b:  # 避免重复
                continue
                
            # 计算x的有效范围
            min_x = max(1, math.ceil((TARGET - b * 10000) / a))
            max_x = min(math.floor((TARGET - 1) / a), 10000)
            
            if max_x < min_x:
                continue
                
            for x in range(min_x, max_x + 1):
                remainder = TARGET - a * x
                
                # 检查remainder是否在可能的范围内
                if remainder < 1 or remainder > b * 10000:
                    continue
                    
                # 检查remainder是否能被b整除
                if remainder % b == 0:
                    y = remainder // b
                    if 1 <= y <= 10000 and is_valid_product(b * y):
                        solutions[(a, b)].append((a, x, b, y))
                        if len(solutions[(a, b)]) >= MAX_SOLUTIONS_PER_COMB:
                            break  # 提前终止当前组合的搜索
    
    return solutions

def find_three_variable_solutions(values):
    """优化的三变量求解算法"""
    solutions = defaultdict(list)
    
    # 对系数进行排序，便于剪枝
    sorted_values = sorted(values)
    
    # 预计算每个系数的有效范围
    value_ranges = {}
    for a in sorted_values:
        if TARGET > PRODUCT_RANGE_THRESHOLD:
            if TARGET > HIGH_TARGET_THRESHOLD:
                min_x = max(1, math.ceil(1 / a))  # 取消下限，最小为1
                max_x = min(10000, math.floor(115000 / a))
            else:
                min_x = max(1, math.ceil(74000 / a))
                max_x = min(10000, math.floor(115000 / a))
        else:
            min_x = 1
            max_x = 10000
        value_ranges[a] = (min_x, max_x)
    
    total_combinations = len(sorted_values) * (len(sorted_values) - 1) * (len(sorted_values) - 2) // 6
    processed_combinations = 0
    
    # 三重循环，但添加了更多剪枝条件
    for i, a in enumerate(sorted_values):
        min_x, max_x = value_ranges[a]
        
        # 计算可能的x值数量，决定步长
        x_count = max_x - min_x + 1
        x_step = max(1, x_count // 1000)  # 自适应步长
        
        for x in range(min_x, max_x + 1, x_step):
            ax = a * x
            if not is_valid_product(ax):
                continue
                
            remainder1 = TARGET - ax
            if TARGET > PRODUCT_RANGE_THRESHOLD:
                if TARGET > HIGH_TARGET_THRESHOLD:
                    if remainder1 < 0:
                        continue
                else:
                    if remainder1 < 2 * 74000:
                        continue
                
            # 限制b的选择范围，避免重复组合
            for j in range(i + 1, len(sorted_values)):
                b = sorted_values[j]
                
                if TARGET > PRODUCT_RANGE_THRESHOLD:
                    if TARGET > HIGH_TARGET_THRESHOLD:
                        min_y = max(1, math.ceil(1 / b))  # 取消下限，最小为1
                        max_y = min(10000, math.floor(remainder1 / b))
                    else:
                        min_y = max(1, math.ceil(74000 / b))
                        max_y = min(10000, math.floor((remainder1 - 74000) / b))
                else:
                    min_y = 1
                    max_y = math.floor(remainder1 / b)
                    
                if max_y < min_y:
                    continue
                    
                # 计算可能的y值数量，决定步长
                y_count = max_y - min_y + 1
                y_step = max(1, y_count // 100)  # 自适应步长
                
                for y in range(min_y, max_y + 1, y_step):
                    by = b * y
                    if not is_valid_product(by):
                        continue
                        
                    remainder2 = remainder1 - by
                    if TARGET > PRODUCT_RANGE_THRESHOLD:
                        if TARGET > HIGH_TARGET_THRESHOLD:
                            if remainder2 < 0 or remainder2 > 115000:
                                continue
                        else:
                            if remainder2 < 74000 or remainder2 > 115000:
                                continue
                        
                    # 限制c的选择范围
                    found_solution = False
                    for k in range(j + 1, len(sorted_values)):
                        c = sorted_values[k]
                        
                        # 检查remainder2是否能被c整除
                        if remainder2 % c != 0:
                            continue
                            
                        z = remainder2 // c
                        if 1 <= z <= 10000 and is_valid_product(c * z):
                            key = (a, b, c)
                            solutions[key].append((a, x, b, y, c, z))
                            found_solution = True
                            if len(solutions[key]) >= MAX_SOLUTIONS_PER_COMB:
                                break  # 提前终止当前组合的搜索
                    
                    # 如果找到解且达到最大数量，跳出y循环
                    if found_solution and len(solutions[key]) >= MAX_SOLUTIONS_PER_COMB:
                        break  # 跳出y循环
                            
                # 进度显示
                if SHOW_PROGRESS and j % 10 == 0:
                    print(f"\r三变量组合进度: {processed_combinations}/{total_combinations} 组", end='')
                processed_combinations += 1
    
    if SHOW_PROGRESS:
        print(f"\r三变量组合进度: {processed_combinations}/{total_combinations} 组 - 完成")
    
    return solutions

def find_balanced_solutions(solutions, var_count, num=2):
    """从所有解中筛选出最平衡的解"""
    if var_count == 1 or not solutions:
        return solutions  # 单变量或无解时直接返回
    
    # 当目标值超过220000时，不计算平衡解
    if TARGET > THREE_VAR_THRESHOLD:
        return []
    
    # 计算解的平衡性（变量间差异最小）
    balanced = []
    for sol in solutions:
        vars = sol[1::2]  # 提取x, y, z
        diff = max(vars) - min(vars)
        balanced.append((diff, sol))
    
    # 按差异排序，取前num个
    return [s for _, s in sorted(balanced, key=lambda x: x[0])[:num]]

def find_original_solutions(solutions, balanced_solutions, num=3):
    """从剩余解中获取原始顺序的解"""
    if not solutions:
        return []
    
    # 排除已在平衡解中的项
    remaining = [s for s in solutions if s not in balanced_solutions]
    return remaining[:num]

def display_solutions(solutions_dict, var_count):
    """优化的解显示函数"""
    if not solutions_dict:
        return
    
    print(f"\n找到 {len(solutions_dict)} 组{var_count}变量解：")
    
    for i, (coeffs, pair_solutions) in enumerate(sorted(solutions_dict.items()), 1):
        # 当目标值超过220000时，不显示平衡解
        if TARGET > THREE_VAR_THRESHOLD:
            all_display = pair_solutions[:MAX_SOLUTIONS]
            print_tag = "[原始解]"
        else:
            # 计算平衡解和原始解
            balanced = find_balanced_solutions(pair_solutions, var_count)
            original = find_original_solutions(pair_solutions, balanced)
            all_display = balanced + original
        
        if var_count == 1:
            a = coeffs
            print(f"\n{i}. 组合: a={a} ({len(pair_solutions)} 个有效解)")
        elif var_count == 2:
            a, b = coeffs
            print(f"\n{i}. 组合: a={a}, b={b} ({len(pair_solutions)} 个有效解)")
        else:  # var_count == 3
            a, b, c = coeffs
            print(f"\n{i}. 组合: a={a}, b={b}, c={c} ({len(pair_solutions)} 个有效解)")
        
        for j, sol in enumerate(all_display, 1):
            if TARGET > THREE_VAR_THRESHOLD:
                tag = print_tag
            else:
                tag = "[平衡解]" if j <= len(balanced) else "[原始解]"
            
            if var_count == 1:
                a, x = sol
                print(f"  {j}. x={x}, a*x={a*x:.1f}, 总和={a*x:.1f} {tag}")
            elif var_count == 2:
                a, x, b, y = sol
                print(f"  {j}. x={x}, y={y}, a*x={a*x:.1f}, b*y={b*y:.1f}, 总和={a*x + b*y:.1f} {tag}")
            else:  # var_count == 3
                a, x, b, y, c, z = sol
                print(f"  {j}. x={x}, y={y}, z={z}, "
                      f"a*x={a*x:.1f}, b*y={b*y:.1f}, c*z={c*z:.1f}, "
                      f"总和={a*x + b*y + c*z:.1f} {tag}")

def run_with_timeout(func, args=(), kwargs=None, timeout=SOLVER_TIMEOUT):
    """运行函数并设置超时限制"""
    if kwargs is None:
        kwargs = {}
    
    result = []
    error = []
    
    def wrapper():
        try:
            result.append(func(*args, **kwargs))
        except Exception as e:
            error.append(e)
    
    thread = threading.Thread(target=wrapper)
    thread.daemon = True
    thread.start()
    thread.join(timeout)
    
    if thread.is_alive():
        print(f"警告: {func.__name__} 超时（{timeout}秒），跳过此方法")
        return None
    
    if error:
        raise error[0]
    
    return result[0]

def main():
    print(f"目标值: {TARGET}")
    
    # 生成波动后的系数
    FLUCTUATED_VALUES = [round(v - FLUCTUATION, 1) for v in BASE_VALUES]
    
    # 尝试基础系数
    print(f"\n==== 尝试基础系数 ====")
    
    # 检查目标值是否超过阈值
    if TARGET > THREE_VAR_THRESHOLD:
        print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD}，只尝试三变量解")
        base_solutions = {
            'single': [],
            'two': [],
            'three': run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,))
        }
        
        # 显示三变量解
        if base_solutions['three'] and len(base_solutions['three']) > 0:
            display_solutions(base_solutions['three'], 3)
            print(f"\n使用基础系数列表，共找到有效解")
            return
        else:
            print("\n基础系数三变量无解，尝试波动系数")
    else:
        # 目标值未超过阈值，按顺序尝试单、双、三变量解
        base_solutions = {
            'single': run_with_timeout(find_single_variable_solutions, args=(BASE_VALUES,)),
            'two': run_with_timeout(find_two_variable_solutions, args=(BASE_VALUES,)),
            'three': []
        }
        
        # 检查是否有解
        has_solution = False
        
        # 显示单变量解
        if base_solutions['single']:
            has_solution = True
            display_solutions({a: [sol] for a, sol in zip(BASE_VALUES, base_solutions['single']) if sol}, 1)
        
        # 显示双变量解
        if base_solutions['two'] and len(base_solutions['two']) > 0:
            has_solution = True
            display_solutions(base_solutions['two'], 2)
        
        # 单变量和双变量都无解时，尝试三变量解
        if not has_solution:
            print(f"\n==== 单变量和双变量无解，尝试三变量解 ====")
            base_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,))
            
            if base_solutions['three'] and len(base_solutions['three']) > 0:
                has_solution = True
                display_solutions(base_solutions['three'], 3)
        
        # 如果找到解，退出程序
        if has_solution:
            print(f"\n使用基础系数列表，共找到有效解")
            return
    
    # 如果基础系数没有找到解，尝试波动系数
    print(f"\n==== 尝试波动系数 ====")
    
    # 检查目标值是否超过阈值
    if TARGET > THREE_VAR_THRESHOLD:
        print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD}，只尝试三变量解")
        fluctuated_solutions = {
            'single': [],
            'two': [],
            'three': run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,))
        }
        
        # 显示三变量解
        if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0:
            display_solutions(fluctuated_solutions['three'], 3)
            print(f"\n使用波动系数列表，共找到有效解")
            return
    else:
        # 目标值未超过阈值，按顺序尝试单、双、三变量解
        fluctuated_solutions = {
            'single': run_with_timeout(find_single_variable_solutions, args=(FLUCTUATED_VALUES,)),
            'two': run_with_timeout(find_two_variable_solutions, args=(FLUCTUATED_VALUES,)),
            'three': []
        }
        
        # 重置标志
        has_solution = False
        
        # 显示单变量解
        if fluctuated_solutions['single']:
            has_solution = True
            display_solutions({a: [sol] for a, sol in zip(FLUCTUATED_VALUES, fluctuated_solutions['single']) if sol}, 1)
        
        # 显示双变量解
        if fluctuated_solutions['two'] and len(fluctuated_solutions['two']) > 0:
            has_solution = True
            display_solutions(fluctuated_solutions['two'], 2)
        
        # 单变量和双变量都无解时，尝试三变量解
        if not has_solution:
            print(f"\n==== 单变量和双变量无解，尝试三变量解 ====")
            fluctuated_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,))
            
            if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0:
                has_solution = True
                display_solutions(fluctuated_solutions['three'], 3)
        
        # 如果找到解，退出程序
        if has_solution:
            print(f"\n使用波动系数列表，共找到有效解")
            return
    
    # 如果所有系数集都没有找到解
    print("\n没有找到符合条件的解，即使使用波动后的系数列表。")

if __name__ == "__main__":
    start_time = time.time()
    main()
    print(f"\n总耗时: {time.time() - start_time:.2f}秒")    

Success #stdin #stdout 0.08s 10564KB

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目标值: 75085

==== 尝试基础系数 ====

找到 30 组2变量解：

1. 组合: a=36.5, b=41.5 (25 个有效解)
  1. x=1002, y=928.0, a*x=36573.0, b*y=38512.0, 总和=75085.0 [平衡解]
  2. x=919, y=1001.0, a*x=33543.5, b*y=41541.5, 总和=75085.0 [平衡解]
  3. x=6, y=1804.0, a*x=219.0, b*y=74866.0, 总和=75085.0 [原始解]
  4. x=89, y=1731.0, a*x=3248.5, b*y=71836.5, 总和=75085.0 [原始解]
  5. x=172, y=1658.0, a*x=6278.0, b*y=68807.0, 总和=75085.0 [原始解]

2. 组合: a=36.5, b=59 (17 个有效解)
  1. x=806, y=774.0, a*x=29419.0, b*y=45666.0, 总和=75085.0 [平衡解]
  2. x=688, y=847.0, a*x=25112.0, b*y=49973.0, 总和=75085.0 [平衡解]
  3. x=98, y=1212.0, a*x=3577.0, b*y=71508.0, 总和=75085.0 [原始解]
  4. x=216, y=1139.0, a*x=7884.0, b*y=67201.0, 总和=75085.0 [原始解]
  5. x=334, y=1066.0, a*x=12191.0, b*y=62894.0, 总和=75085.0 [原始解]

3. 组合: a=36.5, b=68.5 (15 个有效解)
  1. x=689, y=729.0, a*x=25148.5, b*y=49936.5, 总和=75085.0 [平衡解]
  2. x=826, y=656.0, a*x=30149.0, b*y=44936.0, 总和=75085.0 [平衡解]
  3. x=4, y=1094.0, a*x=146.0, b*y=74939.0, 总和=75085.0 [原始解]
  4. x=141, y=1021.0, a*x=5146.5, b*y=69938.5, 总和=75085.0 [原始解]
  5. x=278, y=948.0, a*x=10147.0, b*y=64938.0, 总和=75085.0 [原始解]

4. 组合: a=36.5, b=74 (14 个有效解)
  1. x=642, y=698.0, a*x=23433.0, b*y=51652.0, 总和=75085.0 [平衡解]
  2. x=790, y=625.0, a*x=28835.0, b*y=46250.0, 总和=75085.0 [平衡解]
  3. x=50, y=990.0, a*x=1825.0, b*y=73260.0, 总和=75085.0 [原始解]
  4. x=198, y=917.0, a*x=7227.0, b*y=67858.0, 总和=75085.0 [原始解]
  5. x=346, y=844.0, a*x=12629.0, b*y=62456.0, 总和=75085.0 [原始解]

5. 组合: a=36.5, b=91.5 (11 个有效解)
  1. x=548, y=602.0, a*x=20002.0, b*y=55083.0, 总和=75085.0 [平衡解]
  2. x=731, y=529.0, a*x=26681.5, b*y=48403.5, 总和=75085.0 [平衡解]
  3. x=182, y=748.0, a*x=6643.0, b*y=68442.0, 总和=75085.0 [原始解]
  4. x=365, y=675.0, a*x=13322.5, b*y=61762.5, 总和=75085.0 [原始解]
  5. x=914, y=456.0, a*x=33361.0, b*y=41724.0, 总和=75085.0 [原始解]

6. 组合: a=41.5, b=36.5 (25 个有效解)
  1. x=928, y=1002.0, a*x=38512.0, b*y=36573.0, 总和=75085.0 [平衡解]
  2. x=1001, y=919.0, a*x=41541.5, b*y=33543.5, 总和=75085.0 [平衡解]
  3. x=52, y=1998.0, a*x=2158.0, b*y=72927.0, 总和=75085.0 [原始解]
  4. x=125, y=1915.0, a*x=5187.5, b*y=69897.5, 总和=75085.0 [原始解]
  5. x=198, y=1832.0, a*x=8217.0, b*y=66868.0, 总和=75085.0 [原始解]

7. 组合: a=41.5, b=59 (16 个有效解)
  1. x=716, y=769.0, a*x=29714.0, b*y=45371.0, 总和=75085.0 [平衡解]
  2. x=834, y=686.0, a*x=34611.0, b*y=40474.0, 总和=75085.0 [平衡解]
  3. x=8, y=1267.0, a*x=332.0, b*y=74753.0, 总和=75085.0 [原始解]
  4. x=126, y=1184.0, a*x=5229.0, b*y=69856.0, 总和=75085.0 [原始解]
  5. x=244, y=1101.0, a*x=10126.0, b*y=64959.0, 总和=75085.0 [原始解]

8. 组合: a=41.5, b=68.5 (13 个有效解)
  1. x=639, y=709.0, a*x=26518.5, b*y=48566.5, 总和=75085.0 [平衡解]
  2. x=776, y=626.0, a*x=32204.0, b*y=42881.0, 总和=75085.0 [平衡解]
  3. x=91, y=1041.0, a*x=3776.5, b*y=71308.5, 总和=75085.0 [原始解]
  4. x=228, y=958.0, a*x=9462.0, b*y=65623.0, 总和=75085.0 [原始解]
  5. x=365, y=875.0, a*x=15147.5, b*y=59937.5, 总和=75085.0 [原始解]

9. 组合: a=41.5, b=74 (12 个有效解)
  1. x=718, y=612.0, a*x=29797.0, b*y=45288.0, 总和=75085.0 [平衡解]
  2. x=570, y=695.0, a*x=23655.0, b*y=51430.0, 总和=75085.0 [平衡解]
  3. x=126, y=944.0, a*x=5229.0, b*y=69856.0, 总和=75085.0 [原始解]
  4. x=274, y=861.0, a*x=11371.0, b*y=63714.0, 总和=75085.0 [原始解]
  5. x=422, y=778.0, a*x=17513.0, b*y=57572.0, 总和=75085.0 [原始解]

10. 组合: a=41.5, b=91.5 (10 个有效解)
  1. x=493, y=597.0, a*x=20459.5, b*y=54625.5, 总和=75085.0 [平衡解]
  2. x=676, y=514.0, a*x=28054.0, b*y=47031.0, 总和=75085.0 [平衡解]
  3. x=127, y=763.0, a*x=5270.5, b*y=69814.5, 总和=75085.0 [原始解]
  4. x=310, y=680.0, a*x=12865.0, b*y=62220.0, 总和=75085.0 [原始解]
  5. x=859, y=431.0, a*x=35648.5, b*y=39436.5, 总和=75085.0 [原始解]

11. 组合: a=59, b=36.5 (17 个有效解)
  1. x=774, y=806.0, a*x=45666.0, b*y=29419.0, 总和=75085.0 [平衡解]
  2. x=847, y=688.0, a*x=49973.0, b*y=25112.0, 总和=75085.0 [平衡解]
  3. x=44, y=1986.0, a*x=2596.0, b*y=72489.0, 总和=75085.0 [原始解]
  4. x=117, y=1868.0, a*x=6903.0, b*y=68182.0, 总和=75085.0 [原始解]
  5. x=190, y=1750.0, a*x=11210.0, b*y=63875.0, 总和=75085.0 [原始解]

12. 组合: a=59, b=41.5 (16 个有效解)
  1. x=769, y=716.0, a*x=45371.0, b*y=29714.0, 总和=75085.0 [平衡解]
  2. x=686, y=834.0, a*x=40474.0, b*y=34611.0, 总和=75085.0 [平衡解]
  3. x=22, y=1778.0, a*x=1298.0, b*y=73787.0, 总和=75085.0 [原始解]
  4. x=105, y=1660.0, a*x=6195.0, b*y=68890.0, 总和=75085.0 [原始解]
  5. x=188, y=1542.0, a*x=11092.0, b*y=63993.0, 总和=75085.0 [原始解]

13. 组合: a=59, b=68.5 (9 个有效解)
  1. x=648, y=538.0, a*x=38232.0, b*y=36853.0, 总和=75085.0 [平衡解]
  2. x=511, y=656.0, a*x=30149.0, b*y=44936.0, 总和=75085.0 [平衡解]
  3. x=100, y=1010.0, a*x=5900.0, b*y=69185.0, 总和=75085.0 [原始解]
  4. x=237, y=892.0, a*x=13983.0, b*y=61102.0, 总和=75085.0 [原始解]
  5. x=374, y=774.0, a*x=22066.0, b*y=53019.0, 总和=75085.0 [原始解]

14. 组合: a=59, b=74 (17 个有效解)
  1. x=569, y=561, a*x=33571.0, b*y=41514.0, 总和=75085.0 [平衡解]
  2. x=495, y=620, a*x=29205.0, b*y=45880.0, 总和=75085.0 [平衡解]
  3. x=51, y=974, a*x=3009.0, b*y=72076.0, 总和=75085.0 [原始解]
  4. x=125, y=915, a*x=7375.0, b*y=67710.0, 总和=75085.0 [原始解]
  5. x=199, y=856, a*x=11741.0, b*y=63344.0, 总和=75085.0 [原始解]

15. 组合: a=59, b=91.5 (7 个有效解)
  1. x=491, y=504.0, a*x=28969.0, b*y=46116.0, 总和=75085.0 [平衡解]
  2. x=674, y=386.0, a*x=39766.0, b*y=35319.0, 总和=75085.0 [平衡解]
  3. x=125, y=740.0, a*x=7375.0, b*y=67710.0, 总和=75085.0 [原始解]
  4. x=308, y=622.0, a*x=18172.0, b*y=56913.0, 总和=75085.0 [原始解]
  5. x=857, y=268.0, a*x=50563.0, b*y=24522.0, 总和=75085.0 [原始解]

16. 组合: a=68.5, b=36.5 (15 个有效解)
  1. x=729, y=689.0, a*x=49936.5, b*y=25148.5, 总和=75085.0 [平衡解]
  2. x=656, y=826.0, a*x=44936.0, b*y=30149.0, 总和=75085.0 [平衡解]
  3. x=72, y=1922.0, a*x=4932.0, b*y=70153.0, 总和=75085.0 [原始解]
  4. x=145, y=1785.0, a*x=9932.5, b*y=65152.5, 总和=75085.0 [原始解]
  5. x=218, y=1648.0, a*x=14933.0, b*y=60152.0, 总和=75085.0 [原始解]

17. 组合: a=68.5, b=41.5 (13 个有效解)
  1. x=709, y=639.0, a*x=48566.5, b*y=26518.5, 总和=75085.0 [平衡解]
  2. x=626, y=776.0, a*x=42881.0, b*y=32204.0, 总和=75085.0 [平衡解]
  3. x=45, y=1735.0, a*x=3082.5, b*y=72002.5, 总和=75085.0 [原始解]
  4. x=128, y=1598.0, a*x=8768.0, b*y=66317.0, 总和=75085.0 [原始解]
  5. x=211, y=1461.0, a*x=14453.5, b*y=60631.5, 总和=75085.0 [原始解]

18. 组合: a=68.5, b=59 (9 个有效解)
  1. x=538, y=648.0, a*x=36853.0, b*y=38232.0, 总和=75085.0 [平衡解]
  2. x=656, y=511.0, a*x=44936.0, b*y=30149.0, 总和=75085.0 [平衡解]
  3. x=66, y=1196.0, a*x=4521.0, b*y=70564.0, 总和=75085.0 [原始解]
  4. x=184, y=1059.0, a*x=12604.0, b*y=62481.0, 总和=75085.0 [原始解]
  5. x=302, y=922.0, a*x=20687.0, b*y=54398.0, 总和=75085.0 [原始解]

19. 组合: a=68.5, b=74 (8 个有效解)
  1. x=462, y=587.0, a*x=31647.0, b*y=43438.0, 总和=75085.0 [平衡解]
  2. x=610, y=450.0, a*x=41785.0, b*y=33300.0, 总和=75085.0 [平衡解]
  3. x=18, y=998.0, a*x=1233.0, b*y=73852.0, 总和=75085.0 [原始解]
  4. x=166, y=861.0, a*x=11371.0, b*y=63714.0, 总和=75085.0 [原始解]
  5. x=314, y=724.0, a*x=21509.0, b*y=53576.0, 总和=75085.0 [原始解]

20. 组合: a=68.5, b=91.5 (6 个有效解)
  1. x=475, y=465.0, a*x=32537.5, b*y=42547.5, 总和=75085.0 [平衡解]
  2. x=292, y=602.0, a*x=20002.0, b*y=55083.0, 总和=75085.0 [平衡解]
  3. x=109, y=739.0, a*x=7466.5, b*y=67618.5, 总和=75085.0 [原始解]
  4. x=658, y=328.0, a*x=45073.0, b*y=30012.0, 总和=75085.0 [原始解]
  5. x=841, y=191.0, a*x=57608.5, b*y=17476.5, 总和=75085.0 [原始解]

21. 组合: a=74, b=36.5 (14 个有效解)
  1. x=698, y=642.0, a*x=51652.0, b*y=23433.0, 总和=75085.0 [平衡解]
  2. x=625, y=790.0, a*x=46250.0, b*y=28835.0, 总和=75085.0 [平衡解]
  3. x=41, y=1974.0, a*x=3034.0, b*y=72051.0, 总和=75085.0 [原始解]
  4. x=114, y=1826.0, a*x=8436.0, b*y=66649.0, 总和=75085.0 [原始解]
  5. x=187, y=1678.0, a*x=13838.0, b*y=61247.0, 总和=75085.0 [原始解]

22. 组合: a=74, b=41.5 (12 个有效解)
  1. x=612, y=718.0, a*x=45288.0, b*y=29797.0, 总和=75085.0 [平衡解]
  2. x=695, y=570.0, a*x=51430.0, b*y=23655.0, 总和=75085.0 [平衡解]
  3. x=31, y=1754.0, a*x=2294.0, b*y=72791.0, 总和=75085.0 [原始解]
  4. x=114, y=1606.0, a*x=8436.0, b*y=66649.0, 总和=75085.0 [原始解]
  5. x=197, y=1458.0, a*x=14578.0, b*y=60507.0, 总和=75085.0 [原始解]

23. 组合: a=74, b=59 (17 个有效解)
  1. x=561, y=569, a*x=41514.0, b*y=33571.0, 总和=75085.0 [平衡解]
  2. x=620, y=495, a*x=45880.0, b*y=29205.0, 总和=75085.0 [平衡解]
  3. x=30, y=1235, a*x=2220.0, b*y=72865.0, 总和=75085.0 [原始解]
  4. x=89, y=1161, a*x=6586.0, b*y=68499.0, 总和=75085.0 [原始解]
  5. x=148, y=1087, a*x=10952.0, b*y=64133.0, 总和=75085.0 [原始解]

24. 组合: a=74, b=68.5 (8 个有效解)
  1. x=587, y=462.0, a*x=43438.0, b*y=31647.0, 总和=75085.0 [平衡解]
  2. x=450, y=610.0, a*x=33300.0, b*y=41785.0, 总和=75085.0 [平衡解]
  3. x=39, y=1054.0, a*x=2886.0, b*y=72199.0, 总和=75085.0 [原始解]
  4. x=176, y=906.0, a*x=13024.0, b*y=62061.0, 总和=75085.0 [原始解]
  5. x=313, y=758.0, a*x=23162.0, b*y=51923.0, 总和=75085.0 [原始解]

25. 组合: a=74, b=91.5 (6 个有效解)
  1. x=389, y=506.0, a*x=28786.0, b*y=46299.0, 总和=75085.0 [平衡解]
  2. x=572, y=358.0, a*x=42328.0, b*y=32757.0, 总和=75085.0 [平衡解]
  3. x=23, y=802.0, a*x=1702.0, b*y=73383.0, 总和=75085.0 [原始解]
  4. x=206, y=654.0, a*x=15244.0, b*y=59841.0, 总和=75085.0 [原始解]
  5. x=755, y=210.0, a*x=55870.0, b*y=19215.0, 总和=75085.0 [原始解]

26. 组合: a=91.5, b=36.5 (11 个有效解)
  1. x=602, y=548.0, a*x=55083.0, b*y=20002.0, 总和=75085.0 [平衡解]
  2. x=529, y=731.0, a*x=48403.5, b*y=26681.5, 总和=75085.0 [平衡解]
  3. x=18, y=2012.0, a*x=1647.0, b*y=73438.0, 总和=75085.0 [原始解]
  4. x=91, y=1829.0, a*x=8326.5, b*y=66758.5, 总和=75085.0 [原始解]
  5. x=164, y=1646.0, a*x=15006.0, b*y=60079.0, 总和=75085.0 [原始解]

27. 组合: a=91.5, b=41.5 (10 个有效解)
  1. x=597, y=493.0, a*x=54625.5, b*y=20459.5, 总和=75085.0 [平衡解]
  2. x=514, y=676.0, a*x=47031.0, b*y=28054.0, 总和=75085.0 [平衡解]
  3. x=16, y=1774.0, a*x=1464.0, b*y=73621.0, 总和=75085.0 [原始解]
  4. x=99, y=1591.0, a*x=9058.5, b*y=66026.5, 总和=75085.0 [原始解]
  5. x=182, y=1408.0, a*x=16653.0, b*y=58432.0, 总和=75085.0 [原始解]

28. 组合: a=91.5, b=59 (7 个有效解)
  1. x=504, y=491.0, a*x=46116.0, b*y=28969.0, 总和=75085.0 [平衡解]
  2. x=386, y=674.0, a*x=35319.0, b*y=39766.0, 总和=75085.0 [平衡解]
  3. x=32, y=1223.0, a*x=2928.0, b*y=72157.0, 总和=75085.0 [原始解]
  4. x=150, y=1040.0, a*x=13725.0, b*y=61360.0, 总和=75085.0 [原始解]
  5. x=268, y=857.0, a*x=24522.0, b*y=50563.0, 总和=75085.0 [原始解]

29. 组合: a=91.5, b=68.5 (6 个有效解)
  1. x=465, y=475.0, a*x=42547.5, b*y=32537.5, 总和=75085.0 [平衡解]
  2. x=602, y=292.0, a*x=55083.0, b*y=20002.0, 总和=75085.0 [平衡解]
  3. x=54, y=1024.0, a*x=4941.0, b*y=70144.0, 总和=75085.0 [原始解]
  4. x=191, y=841.0, a*x=17476.5, b*y=57608.5, 总和=75085.0 [原始解]
  5. x=328, y=658.0, a*x=30012.0, b*y=45073.0, 总和=75085.0 [原始解]

30. 组合: a=91.5, b=74 (6 个有效解)
  1. x=506, y=389.0, a*x=46299.0, b*y=28786.0, 总和=75085.0 [平衡解]
  2. x=358, y=572.0, a*x=32757.0, b*y=42328.0, 总和=75085.0 [平衡解]
  3. x=62, y=938.0, a*x=5673.0, b*y=69412.0, 总和=75085.0 [原始解]
  4. x=210, y=755.0, a*x=19215.0, b*y=55870.0, 总和=75085.0 [原始解]
  5. x=654, y=206.0, a*x=59841.0, b*y=15244.0, 总和=75085.0 [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/Nywwyd

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Python 3 nbc (python 3.7.3)

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