How to resolve the algorithm Non-continuous subsequences step by step in the Bracmat programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Non-continuous subsequences step by step in the Bracmat programming language

Table of Contents

Problem Statement

Consider some sequence of elements. (It differs from a mere set of elements by having an ordering among members.) A subsequence contains some subset of the elements of this sequence, in the same order. A continuous subsequence is one in which no elements are missing between the first and last elements of the subsequence. Note: Subsequences are defined structurally, not by their contents. So a sequence a,b,c,d will always have the same subsequences and continuous subsequences, no matter which values are substituted; it may even be the same value.

Task: Find all non-continuous subsequences for a given sequence.

For the sequence   1,2,3,4,   there are five non-continuous subsequences, namely:

There are different ways to calculate those subsequences. Demonstrate algorithm(s) that are natural for the language.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Non-continuous subsequences step by step in the Bracmat programming language

Source code in the bracmat programming language

( ( noncontinuous
  =   sub
    .     ( sub
          =   su a nc
            .   !arg:(?su.?nc)
              &   !su
                :   %
                    %?a
                    ( %:[%(sub$(!sjt.!nc !a))
                    |   ?
                      & !nc:~
                      & out$(!nc !a)
                      & ~
                    )
          )
        & sub$(dummy !arg.)
      | 
  )
& noncontinuous$(e r n i t)
);

  

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