How to resolve the algorithm Combinations with repetitions step by step in the Bracmat programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Combinations with repetitions step by step in the Bracmat programming language

Table of Contents

Problem Statement

The set of combinations with repetitions is computed from a set,

S

{\displaystyle S}

(of cardinality

n

{\displaystyle n}

), and a size of resulting selection,

k

{\displaystyle k}

, by reporting the sets of cardinality

k

{\displaystyle k}

where each member of those sets is chosen from

S

{\displaystyle S}

. In the real world, it is about choosing sets where there is a “large” supply of each type of element and where the order of choice does not matter. For example: Note that both the order of items within a pair, and the order of the pairs given in the answer is not significant; the pairs represent multisets. Also note that doughnut can also be spelled donut.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Combinations with repetitions step by step in the Bracmat programming language

Source code in the bracmat programming language

( ( choices
  =   n things thing result
    .   !arg:(?n.?things)
      & ( !n:0&1
        |   0:?result
          & (   !things
              :   ?
                  ( %?`thing ?:?things
                  &   !thing*choices$(!n+-1.!things)+!result
                    : ?result
                  & ~
                  )
            | !result
            )
        )
  )
& out$(choices$(2.iced jam plain))
& out$(choices$(3.iced jam plain butter marmite tahin fish salad onion grass):?+[?N&!N)
);

  

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