多基准转换-使用所有组合的URL缩短器 [英] Multi-base conversion - using all combinations for URL shortener
问题描述
我正在做一个URL缩短器,并且正在努力将数字(id)编码为字符串的最佳方法.
I am making an URL shortener, and I am struggling with the optimal way of encoding a number (id) into a character string.
我使用的字符是0-9,A-Z,a-z,因此基本上是base-62编码.那是很基本的,但是并没有利用所有可能的代码.它将产生的代码为:
I am using the characters 0-9,A-Z,a-z so it will basically be a base-62 encoding. That is pretty basic, but it doesn't make use of all possible codes. The codes that it would produce would be:
0, 1, ... y, z, 10, 11, ... zy, zz, 100, 101, ...
请注意,未使用代码00到0z,对于000到0zz相同,依此类推.我想使用所有代码,例如:
Notice that the codes 00 to 0z is not used, the same for 000 to 0zz, and so on. I would like to use all the codes, like this:
0, 1, ... y, z, 00, 01, ... zy, zz, 000, 001, ...
这将是base-62和base-63的某种组合,根据位置的不同而有所不同...使用base-62很容易,例如:
It would be some combination of base-62 and base-63, with different bases depending on the position... Using base-62 is easy, for example:
create procedure tiny_GetCode
@UrlId int
as
set nocount on
declare @Code varchar(10)
set @Code = ''
while (@UrlId > 0 or len(@Code) = 0) begin
set @Code = substring('0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz', @UrlId % 62 + 1, 1) + @Code
set @UrlId = @UrlId / 62
end
select @Code
但是我还没有设法利用它来进行多基转换,以利用所有代码.
But I haven't yet managed to make a multi-base conversion out of it, to make use of all the codes.
推荐答案
我设法进行了转换.棘手的是,它不仅是混合的基数转换,而且第一个字符的基数较高还会影响较长代码的值.
I managed to make the conversion. The tricky thing is that it's not just a mixed base conversion, the higher base of the first character also affects the values of longer codes.
我从一个简单的案例开始;以10为基的代码.我看到两位数范围有10个额外的代码,三位数范围有100个额外的代码,依此类推:
I started with an easier case; base-10 codes. I saw that the two digit range has 10 extra codes, the three digit range has 100 extra codes, and so on:
0 - 9 : '0' - '9'
10 - 109 : '00' - '99'
110 - 1109 : '000' - '999'
1110 - 11109 : '0000' - '9999'
因此,代码中第一个字符的值不仅是升至该位置的基数,而且还具有偏移量.
So, the value of the first character in the code is not just the base raised to the position, but it also has an offset.
将其应用于base-62编码后,这就是我最终得到的结果:
After applying this to the base-62 encoding, this is what I ended up with:
create function tiny_Encode(@UrlId int) returns varchar(10)
as
begin
declare
@Chars varchar(62),
@Code varchar(10),
@Value int,
@Adder int
set @Chars = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'
if (@UrlId < 63) begin
set @Code = substring(@Chars, @UrlId, 1)
end else begin
set @UrlId = @UrlId - 1
set @Value = 62
set @Adder = 0
while (@UrlId >= @Value * 63 + @Adder) begin
set @Adder = @Adder + @Value
set @Value = @Value * 62
end
set @Code = substring(@Chars, (@UrlId - @Adder) / @Value, 1)
set @UrlId = ((@UrlId - @Adder) % @Value)
while (@Value > 1) begin
set @Value = @Value / 62
set @Code = @Code + substring(@Chars, @UrlId / @Value + 1, 1)
set @UrlId = @UrlId % @Value
end
end
return @Code
end
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