c# - 与嵌套的 for 循环作斗争

Question

给定一个主数和一个子集，想要找到子集数的所有可能组合，这些组合加起来等于主数。例如:

输入

主要:10
子集:2、3、5、7

输出

结果:3 + 7 = 10、2 + 3 + 5 = 10
** 注意:5 + 5 = 10 不是有效结果。 **

这是我目前所处的位置:

// Main traversal
for (int a = 0; a < nums.Length; a++)
{
    sum = a;

    for (int b = a + 1; b < nums.Length; b++)
    {
      // Thinking this should be the loop that determines 
      // how many numbers are added together. 
      // e.g. Sum of 2 numbers, sum of 3 numbers, etc
        for (int c = a + 1; c < nums.Length; c++)
        {
            sum += nums[b + c];
        }
        if (sum == mainNumber)
            result += "Match found!\n";
    }
}

我主要是在努力理解“for 循环”。我试图找到一个“for 循环”可视化工具，但没有成功。或者，递归会使这个问题更容易解决吗？

Answer 1

将 for 循环想象成圆圈。嵌套循环就像圆圈中的圆圈。

值得庆幸的是，您的情况远没有这个复杂。在这张图片中，周围的一个大圆圈是一个只为真一次的 for 循环。在该 for 循环内，其他循环多次为真。每个不同大小的圆圈都是一个不同的循环。

我已经用更具描述性的名称重写了您的代码，并且唯一的目的是解释循环 - 我取出了所有“有用”的东西，并放入了 console.writeline 语句。

 // I'm using 5 as an example check here.
for (int outerLoopCounter = 0; outerLoopCounter < 5; outerLoopCounter++)
{
    Console.WriteLine("OUTER:             {0}", outerLoopCounter);

    for (int middleLoopCounter = 0; middleLoopCounter < 5; middleLoopCounter++)
    {
        Console.WriteLine("MIDDLE:              {0}", middleLoopCounter);

        for (int innerLoopCounter = 0; innerLoopCounter < 5; innerLoopCounter++)
        {
            Console.WriteLine("INNER:                 {0}", innerLoopCounter);
        }
    }
}

输出如下:

OUTER:             0
MIDDLE:              0
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              1
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              2
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              3
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              4
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
OUTER:             1
MIDDLE:              0
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              1
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              2
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              3
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              4
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
OUTER:             2
MIDDLE:              0
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              1
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              2
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              3
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              4
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
OUTER:             3
MIDDLE:              0
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              1
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              2
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              3
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              4
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
OUTER:             4
MIDDLE:              0
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              1
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              2
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              3
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4
MIDDLE:              4
INNER:                 0
INNER:                 1
INNER:                 2
INNER:                 3
INNER:                 4

如果你看一下缩进，你可以看到一个模式。最接近文本(左侧)的数字从外循环输出。中间的数字来自中间循环，最右边的数字来自最内层循环。

可以看到，外层循环在慢慢旋转，数到四(0, 1, 2, 3 , 4), 直到不再小于5，此时退出循环。中间的圆圈(循环)计数稍快。每当外循环递增 1 时，它就会变为 4(同样是 0-4)。内圈旋转得非常快 - 它数到四，每次 中间 圈递增时退出。