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:

MsgBox % noncontinuous("a,b,c,d,e", ",")
MsgBox % noncontinuous("1,2,3,4", ",")

noncontinuous(list, delimiter)
{
stringsplit, seq, list, %delimiter%
n := seq0                                            ; sequence length
Loop % x := (1<<n) - 1 {                                  ; try all 0-1 candidate sequences
   If !RegExMatch(b:=ToBin(A_Index,n),"^0*1*0*$") {  ; drop continuous subsequences
      Loop Parse, b
         t .= A_LoopField ? seq%A_Index% " " : ""         ; position -> number
		 t .= "`n"                                   ; new sequences in new lines
   }
}
return t
}

ToBin(n,W=16) {  ; LS W-bits of Binary representation of n
   Return W=1 ? n&1 : ToBin(n>>1,W-1) . n&1
}