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Function std.algorithm.sorting.nthPermutation

Permutes range into the perm permutation.

ref Range nthPermutation(Range) (
  auto ref Range range,
  const ulong perm
if (isRandomAccessRange!Range && hasLength!Range);

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:

    auto pem = [4,0,4,1,0,0,0]; // permutation 2982 in factorial
    auto src = [0,1,2,3,4,5,6]; // the range to permutate
    auto i = 0;                    // range index
    // range index iterates pem and src in sync
    // pem[i] + i is used as index into src
    // first src[pem[i] + i] is stored in t
    auto t = 4;                    // tmp value
    src = [0,1,2,3,n,5,6];
    // then the values between i and pem[i] + i are moved one
    // to the right
    src = [n,0,1,2,3,5,6];
    // at last t is inserted into position i
    src = [4,0,1,2,3,5,6];
    // finally i is incremented
    // this process is repeated while i < pem.length
    t = 0;
    src = [4,n,1,2,3,5,6];
    src = [4,0,1,2,3,5,6];
    t = 6;
    src = [4,0,1,2,3,5,n];
    src = [4,0,n,1,2,3,5];
    src = [4,0,6,1,2,3,5];


The permuted range.


range The Range to permute. The original ordering will be lost.
perm The permutation to permutate range to.


auto src = [0, 1, 2, 3, 4, 5, 6];
auto rslt = [4, 0, 6, 2, 1, 3, 5];

src = nthPermutation(src, 2982);
writeln(src); // rslt


Andrei Alexandrescu


Boost License 1.0.