nthPermutation

Permutes range into the perm permutation. The algorithm has a constant runtime complexity with respect to the number of permutations created. Due to the number of unique values of ulong only the first 21 elements of range can be permuted. The rest of the range will therefore not be permuted. This algorithm uses the Lehmer Code.

The algorithm works as follows:

1 auto pem = [4,0,4,1,0,0,0]; // permutation 2982 in factorial
2     auto src = [0,1,2,3,4,5,6]; // the range to permutate
3 
4     auto i = 0;                    // range index
5     // range index iterates pem and src in sync
6     // pem[i] + i is used as index into src
7     // first src[pem[i] + i] is stored in t
8     auto t = 4;                    // tmp value
9     src = [0,1,2,3,n,5,6];
10 
11     // then the values between i and pem[i] + i are moved one
12     // to the right
13     src = [n,0,1,2,3,5,6];
14     // at last t is inserted into position i
15     src = [4,0,1,2,3,5,6];
16     // finally i is incremented
17     ++i;
18 
19     // this process is repeated while i < pem.length
20 
21     t = 0;
22     src = [4,n,1,2,3,5,6];
23     src = [4,0,1,2,3,5,6];
24     ++i;
25     t = 6;
26     src = [4,0,1,2,3,5,n];
27     src = [4,0,n,1,2,3,5];
28     src = [4,0,6,1,2,3,5];