GENERIC INTERFACE Combinatoric(R);

Arithmetic for Modula-3, see doc for details

Abstract: Combinatoric operations

TYPE T = R.T;

PROCEDURE Factorial (n: T; ): T;

number of permutations, e.g. there are Factorial(32) possibilities to order a cardset

PROCEDURE Permutations (READONLY n: ARRAY OF T; ): T;

number of permutations with partially irrelevant order permute n[0]+...+n[LAST(n)] elements, where the order of n[i] elements is irrelevant, e.g. there are Permutations(ARRAY OF T{2,10,10,10}) possibilities to set up a Skat game

PROCEDURE Arrangements (n, k: T; ): T;

choose k from n elements, each element at most once and the order is respected

PROCEDURE ArrangementsR (n, k: T; ): T;

choose k from n elements, each element can be chosen multiple times and the order is respected, e.g. figures consisting of k digits to the base n

PROCEDURE Combinations (n, k: T; ): T;

choose k from n elements, each element at most once and the order is ignored, e.g. the number of subsets of size k of a set of size n, or a lottery where 6 numbers in a 7x7 field can be marked

PROCEDURE CombinationsR (n, k: T; ): T;

choose k from n elements, each element can be chosen multiple times and the order is ignored

END Combinatoric.