PetscDTEnumPerm#

Get a permutation of n integers from its encoding into the integers [0, n!) as a sequence of swaps.

Input Parameters#

  • n - a non-negative integer (see note about limits below)

  • k - an integer in [0, n!)

Output Parameters#

  • perm - the permuted list of the integers [0, …, n-1]

  • isOdd - if not NULL, returns whether the permutation used an even or odd number of swaps.

Notes#

A permutation can be described by the operations that convert the lists [0, 1, …, n-1] into the permutation, by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in some position j >= i. This swap is encoded as the difference (j - i). The difference d_i at step i is less than (n - i). This sequence of n-1 differences [d_0, …, d_{n-2}] is encoded as the number (n-1)! * d_0 + (n-2)! * d_1 + … + 1! * d_{n-2}.

Limited to n such that n! can be represented by PetscInt, which is 12 if PetscInt is a signed 32-bit integer and 20 if PetscInt is a signed 64-bit integer.

See Also#

PetscDTFactorial(), PetscDTFactorialInt(), PetscDTBinomial(), PetscDTBinomialInt(), PetscDTPermIndex()

Level#

intermediate

Location#

include/petscdt.h


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