javascript - 将自然数转换为三位字符串的简单算法是什么？

Question

这是一个从自然数到 base-3 字符串的映射:

 0 =>    0
 1 =>    1
 2 =>    2
 3 =>   00
 4 =>   01
 5 =>   02
 6 =>   10
 7 =>   11
 8 =>   12
 9 =>   20
10 =>   21
11 =>   22
12 =>  000
13 =>  001
14 =>  002
15 =>  010
16 =>  011
17 =>  012
18 =>  020
19 =>  021
20 =>  022
21 =>  100
22 =>  101
23 =>  102
24 =>  110
25 =>  111
26 =>  112
27 =>  120
28 =>  121
29 =>  122
30 =>  200
31 =>  201
32 =>  202
33 =>  210
34 =>  211
35 =>  212
36 =>  220
37 =>  221
38 =>  222
39 => 0000
40 => 0001
...

来回执行此映射的最简单和最有效的函数是什么？

Answer 1

这需要一些技巧，但可以使用 Number.prototype.toString 来完成和 parseInt :

function numToBase3(n) {
    var pref = "",
        offset = 0,
        pow = 3;
    while (n >= offset+pow) {
        offset += pow;
        pow *= 3;
        pref += "0";
    }
    return (pref + (n-offset).toString(3)).slice(-1-pref.length);
}
function base3ToNum(s) {
    var offset = 0,
        pow = 3;
    for (var i=1; i<s.length; i++) {
        offset += pow;
        pow *= 3;
    }
    return parseInt(s, 3)+offset;
}

(以 pow = 1 和 i = 0 开始，将 0 映射到空字符串)