How to resolve the algorithm Hofstadter Figure-Figure sequences step by step in the SETL programming language

Published on 12 May 2024 09:40 PM
#Setl

How to resolve the algorithm Hofstadter Figure-Figure sequences step by step in the SETL programming language

Table of Contents

Problem Statement

These two sequences of positive integers are defined as:

The sequence

S ( n )

{\displaystyle S(n)}

is further defined as the sequence of positive integers not present in

R ( n )

{\displaystyle R(n)}

. Sequence

R

{\displaystyle R}

starts: Sequence

S

{\displaystyle S}

starts:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Hofstadter Figure-Figure sequences step by step in the SETL programming language

Source code in the setl programming language

program figure_figure;
    init R := [1], S := [2];

    print("R(1..10):", [ffr(n) : n in [1..10]]);
    print("R(1..40) + S(1..960) = {1..1000}:",
        {ffr(n) : n in {1..40}} + {ffs(n) : n in {1..960}} = {1..1000});

    proc ffr(n);
        loop while n > #R do
            nextR := R(#R) + S(#R);
            S +:= [S(#S)+1 .. nextR-1];
            R with:= nextR;
            S with:= nextR + 1;
        end loop;
        return R(n);
    end proc;

    proc ffs(n);
        loop while n > #S do
            ffr(#R + 1);
        end loop;
        return S(n);
    end proc;
end program;

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