How to find permutation of a given string with its rank?

Question

For example,

rank  permutation   
0     abc
1     acb
2     bac
3     bca
4     cab
5     cba

So, if one asks give me permutation with rank

Answer 1

I made it at a first attempt!! :-) Really good homework, nice problem, you made my day! Here is a solution in javascript:

function permutation (rank, n, chars) 
{
    var fact, char_idx, this_char;

    if (n == 0)
        return "";

    char_idx = Math.floor(rank / factorial(n - 1));

    this_char = chars.splice(char_idx, 1); 
         // returns the char with index char_idx and removes it from array

    return this_char + 
        permutation(rank % factorial(n - 1), n - 1, chars);
}

Just call it like permutation(5, 3, ['a', 'b', 'c']) and that's it. You have to write your own factorial() function - as a homework :-)