我在我的第一篇文章中发现了一个错误，所以我决定坐下来算算。我发现用来识别Excel列的数字系统不是另一个人说的26进制系统。以10为基数考虑以下情况。你也可以用字母表中的字母来做这件事。

空间 :.........................S1, s2, s3: S1, s2, s3 ....................................0,00, 000:..A aa aaa ....................................1,01, 001:..B ab aab ....................................…，…，…:……，…，… ....................................9,99,999:..Z, zz, ZZZ 空间中的总状态:10,100,1000:26,676,17576 国家总 :............... 1110年 ................ 18278年

Excel在以26为基数的字母空格中对列进行编号。你可以看到，一般来说，状态空间的级数是a, a^2, a^3，…对于以a为底的情况，状态的总数是a + a^2 + a^3 + ... .

Suppose you want to find the total number of states A in the first N spaces. The formula for doing so is A = (a)(a^N - 1 )/(a-1). This is important because we need to find the space N that corresponds to our index K. If I want to find out where K lies in the number system I need to replace A with K and solve for N. The solution is N = log{base a} (A (a-1)/a +1). If I use the example of a = 10 and K = 192, I know that N = 2.23804… . This tells me that K lies at the beginning of the third space since it is a little greater than two.

The next step is to find exactly how far in the current space we are. To find this, subtract from K the A generated using the floor of N. In this example, the floor of N is two. So, A = (10)(10^2 – 1)/(10-1) = 110, as is expected when you combine the states of the first two spaces. This needs to be subtracted from K because these first 110 states would have already been accounted for in the first two spaces. This leaves us with 82 states. So, in this number system, the representation of 192 in base 10 is 082.

使用基本索引为0的c#代码是

    private string ExcelColumnIndexToName(int Index)
    {
        string range = string.Empty;
        if (Index < 0 ) return range;
        int a = 26;
        int x = (int)Math.Floor(Math.Log((Index) * (a - 1) / a + 1, a));
        Index -= (int)(Math.Pow(a, x) - 1) * a / (a - 1);
        for (int i = x+1; Index + i > 0; i--)
        {
            range = ((char)(65 + Index % a)).ToString() + range;
            Index /= a;
        }
        return range;
    }

/ /旧邮政

c#中的零基础解决方案。

    private string ExcelColumnIndexToName(int Index)
    {
        string range = "";
        if (Index < 0 ) return range;
        for(int i=1;Index + i > 0;i=0)
        {
            range = ((char)(65 + Index % 26)).ToString() + range;
            Index /= 26;
        }
        if (range.Length > 1) range = ((char)((int)range[0] - 1)).ToString() + range.Substring(1);
        return range;
    }

抱歉，这是Python而不是c#，但至少结果是正确的:

def ColIdxToXlName(idx):
    if idx < 1:
        raise ValueError("Index is too small")
    result = ""
    while True:
        if idx > 26:
            idx, r = divmod(idx - 1, 26)
            result = chr(r + ord('A')) + result
        else:
            return chr(idx + ord('A') - 1) + result


for i in xrange(1, 1024):
    print "%4d : %s" % (i, ColIdxToXlName(i))

我是这样做的:

private string GetExcelColumnName(int columnNumber)
{
    string columnName = "";

    while (columnNumber > 0)
    {
        int modulo = (columnNumber - 1) % 26;
        columnName = Convert.ToChar('A' + modulo) + columnName;
        columnNumber = (columnNumber - modulo) / 26;
    } 

    return columnName;
}

下面是我在Python中如何做的。算法说明如下:

alph = ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z')
def labelrec(n, res):
    if n<26:
        return alph[n]+res
    else:
        rem = n%26
        res = alph[rem]+res
        n = n/26-1
        return labelrec(n, res)

函数labelrec可以用数字和一个空字符串来调用，比如:

print labelrec(16383, '')

以下是它有效的原因: 如果十进制数字的书写方式与Excel表格列相同，那么数字0-9将被正常书写，但10将变成“00”，然后20将变成“10”，以此类推。映射几个数字:

0-0

9-9

10-00

20-10

100-90

110-000

1110-0000

所以，模式很清楚。从单位的位置开始，如果一个数字小于10，它的表示与数字本身相同，否则您需要通过减去1来调整剩余的数字并递归。当数字小于10时可以停止。

同样的逻辑适用于上述解决方案中以26为基数的数字。

注:如果你想让数字从1开始，在输入数字减去1后调用相同的函数。

您可能需要两种方式转换，例如从Excel列地址(如AAZ)到整数，以及从任何整数到Excel。下面的两个方法就可以做到这一点。假设基于1的索引，“数组”中的第一个元素是元素1。 这里没有大小限制，所以你可以使用ERROR这样的地址，这将是列号2613824…

public static string ColumnAdress(int col)
{
  if (col <= 26) { 
    return Convert.ToChar(col + 64).ToString();
  }
  int div = col / 26;
  int mod = col % 26;
  if (mod == 0) {mod = 26;div--;}
  return ColumnAdress(div) + ColumnAdress(mod);
}

public static int ColumnNumber(string colAdress)
{
  int[] digits = new int[colAdress.Length];
  for (int i = 0; i < colAdress.Length; ++i)
  {
    digits[i] = Convert.ToInt32(colAdress[i]) - 64;
  }
  int mul=1;int res=0;
  for (int pos = digits.Length - 1; pos >= 0; --pos)
  {
    res += digits[pos] * mul;
    mul *= 26;
  }
  return res;
}

这个片段适用于A到ZZ列名

string columnName = columnNumber > 26 ? Convert.ToChar(64 + (columnNumber / 26)).ToString() + Convert.ToChar(64 + (columnNumber % 26)) : Convert.ToChar(64 + columnNumber).ToString();