移除静态字段后，如何在递归求和组合程序中追踪可行解存在性

需要编写递归程序，在1到N（N≥2）的数字间插入+、-运算符，找出所有能得到目标值X的表达式组合；无可行解时输出N/A。现有C#代码通过静态字段counter追踪是否存在可行解，但触发JRM003错误（禁止使用静态字段）。示例输入n=6、x=3时需输出对应3条表达式，需调整counter的实现方式，既消除错误又实现追踪功能。

示例输入 #

• n=6
• x=3

示例输出 #

• 1 + 2 + 3 - 4 - 5 + 6 = 3
• 1 + 2 - 3 + 4 + 5 - 6 = 3
• 1 - 2 - 3 - 4 + 5 + 6 = 3

现有代码 #

using System;

namespace ConsoleApp1
{
    class Program
    {
       static bool counter;

       static void Generate(int n, int x, int currentIndex, int result, string expression)
        {
            counter = true;

            if (currentIndex == n + 1)
            {
                if (result == x)
                {
                    Console.WriteLine(expression + " = " + x);
                }

                return;
            }

            Generate(n, x, currentIndex + 1, result + currentIndex, expression + " + " + currentIndex);
            Generate(n, x, currentIndex + 1, result - currentIndex, expression + " - " + currentIndex);
        }

       static void Main()
        {
            int n = Convert.ToInt32(Console.ReadLine());
            int x = Convert.ToInt32(Console.ReadLine());
            const int doi = 2;

            Generate(n, x, doi, 1, "1");

            if (!counter)
            {
                Console.WriteLine("N/A");
            }

            Console.ReadLine();
        }
    }
}

错误信息 #

JRM003 (错误) : 禁止使用静态字段。(行: 7, 字符: 7)

以下几种方法可替换静态字段counter，避开静态字段限制的同时实现可行解追踪：

方法1：使用引用类型传递状态 #

利用引用类型（如长度为1的bool数组）在递归中传递状态，因为引用类型的修改会作用到外部实例：

using System;

namespace ConsoleApp1
{
    class Program
    {
       static void Generate(int n, int x, int currentIndex, int result, string expression, bool[] hasSolution)
        {
            if (currentIndex == n + 1)
            {
                if (result == x)
                {
                    Console.WriteLine(expression + " = " + x);
                    hasSolution[0] = true; // 找到可行解时标记状态
                }
                return;
            }

            Generate(n, x, currentIndex + 1, result + currentIndex, expression + " + " + currentIndex, hasSolution);
            Generate(n, x, currentIndex + 1, result - currentIndex, expression + " - " + currentIndex, hasSolution);
        }

       static void Main()
        {
            int n = Convert.ToInt32(Console.ReadLine());
            int x = Convert.ToInt32(Console.ReadLine());
            const int doi = 2;
            bool[] hasSolution = { false }; // 初始化状态为未找到解

            Generate(n, x, doi, 1, "1", hasSolution);

            if (!hasSolution[0])
            {
                Console.WriteLine("N/A");
            }

            Console.ReadLine();
        }
    }
}

方法2：让递归方法返回bool值汇总结果 #

递归方法返回当前分支是否找到可行解，主方法汇总所有分支的结果：

using System;

namespace ConsoleApp1
{
    class Program
    {
       static bool Generate(int n, int x, int currentIndex, int result, string expression)
        {
            bool found = false;
            if (currentIndex == n + 1)
            {
                if (result == x)
                {
                    Console.WriteLine(expression + " = " + x);
                    found = true;
                }
                return found;
            }

            // 只要任意分支找到解，就标记为true
            found |= Generate(n, x, currentIndex + 1, result + currentIndex, expression + " + " + currentIndex);
            found |= Generate(n, x, currentIndex + 1, result - currentIndex, expression + " - " + currentIndex);
            
            return found;
        }

       static void Main()
        {
            int n = Convert.ToInt32(Console.ReadLine());
            int x = Convert.ToInt32(Console.ReadLine());
            const int doi = 2;

            bool hasSolution = Generate(n, x, doi, 1, "1");

            if (!hasSolution)
            {
                Console.WriteLine("N/A");
            }

            Console.ReadLine();
        }
    }
}

方法3：使用类的实例字段 #

将Program类的方法改为非静态，用实例字段替代静态字段：

using System;

namespace ConsoleApp1
{
    class Program
    {
       private bool _hasSolution;

       void Generate(int n, int x, int currentIndex, int result, string expression)
        {
            if (currentIndex == n + 1)
            {
                if (result == x)
                {
                    Console.WriteLine(expression + " = " + x);
                    _hasSolution = true;
                }
                return;
            }

            Generate(n, x, currentIndex + 1, result + currentIndex, expression + " + " + currentIndex);
            Generate(n, x, currentIndex + 1, result - currentIndex, expression + " - " + currentIndex);
        }

       static void Main()
        {
            int n = Convert.ToInt32(Console.ReadLine());
            int x = Convert.ToInt32(Console.ReadLine());
            const int doi = 2;
            Program program = new Program();

            program.Generate(n, x, doi, 1, "1");

            if (!program._hasSolution)
            {
                Console.WriteLine("N/A");
            }

            Console.ReadLine();
        }
    }
}

内容的提问来源于stack exchange，提问作者Raluca123