双线性序列给出奇怪的结果 [英] Double linear sequence gives odd results

问题描述

我正试图提高我的表演技能(不存在)，但在将公式写入代码时遇到了问题.这是我要尝试的公式-用引号引起来-将转换"为代码.

I'm trying to get my performance skills (none existent) up to par but ran into a problem with writing out a formula into code. This is the formula I'm trying to - quote unquote - "convert" to code.

考虑一个序列u，其中u的定义如下:

Consider a sequence u where u is defined as follows:

数字u(0) = 1是u中的第一个数字. 对于u中的每个x，y = 2 * x + 1和z = 3 * x + 1也必须也在u中. u中没有其他数字. 例如:u = [1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, ...]

The number u(0) = 1 is the first one in u. For each x in u, then y = 2 * x + 1 and z = 3 * x + 1 must be in u too. There are no other numbers in u. Ex: u = [1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, ...]

1给出3和4，然后3给出7和10，4给出9和13，然后7给出15和22等...

1 gives 3 and 4, then 3 gives 7 and 10, 4 gives 9 and 13, then 7 gives 15 and 22 and so on...

这是我到目前为止所拥有的:

And this is what I have so far:

using System;
using System.Collections.Generic;

public class Program
{
    public static void Main()
    {
        Console.WriteLine(DblLinear(10));
        //Expected result: 22
        Console.WriteLine(DblLinear(20));
        //Expected result: 57
        Console.WriteLine(DblLinear(30));
        //Expected result: 91
        Console.WriteLine(DblLinear(50));
        //Expected result: 175
    }
    public static int DblLinear (int n) 
    {
        List<int> linArr = new List<int>();
        linArr.Add(1);

        int i = 0;
        while(linArr.Count < n)
        {
            linArr.Add((2 * linArr[i]) + 1);
            linArr.Add((3 * linArr[i]) + 1);
            linArr.Sort();
            i++;
        }
        return linArr[n - 1];
    }
}

计算是正确的，直到达到27.之后，它开始疯狂运行，我不知道它在做什么错.

The calculations are right until it hits 27. After that it just runs wild and I have no idea what it does wrong.

推荐答案

您从序列中取出一项，然后产生两项.因此，您确实需要一些数据结构来存储它们，因为它们的数量会增加.堆将是最好的.如果您想直接使用.net中的功能，则可以使用SortedSet.

You take one item from sequence and produce two. So You really need some data structure to store them, as their numbers would increase. Heap would be the best. If You want to go with what we have directly in .net, You can use SortedSet.

public static IEnumerable<int> DblLinear2()
{
    SortedSet<int> seq = new SortedSet<int> { 1 };

    while (true)
    {
        int min = seq.First();
        seq.Remove(min);
        yield return min;
        seq.Add(min * 2 + 1);
        seq.Add(min * 3 + 1);
    }
}

结果:

1、3、4、7、9、10、13、15、19、21、22、27、28、31、39、40、43、45、46， 55，57，58，63，64，67，79，81，82，85，87 ...

1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, 28, 31, 39, 40, 43, 45, 46, 55, 57, 58, 63, 64, 67, 79, 81, 82, 85, 87...

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