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Function `std.algorithm.sorting.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.


						
				auto ref Range nthPermutation(Range)
				(
				

				  auto ref Range range,
				

				  const ulong perm
				

				)
				

				if (isRandomAccessRange!Range && hasLength!Range);

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
    ++i;
    // 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];
    ++i;
    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];

Returns

The permuted range.

Parameters

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

Example

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

Authors

Andrei Alexandrescu

License

Boost License 1.0.