How to resolve the algorithm Fibonacci sequence step by step in the Tailspin programming language

Published on 12 May 2024 09:40 PM
#Tailspin

How to resolve the algorithm Fibonacci sequence step by step in the Tailspin programming language

Table of Contents

Problem Statement

The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively:

Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow and are mostly used as an exercise in recursion). The sequence is sometimes extended into negative numbers by using a straightforward inverse of the positive definition: support for negative     n     in the solution is optional.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Fibonacci sequence step by step in the Tailspin programming language

Source code in the tailspin programming language

templates nthFibonacci
  when <=0|=1> do $ !
  otherwise ($ - 1 -> #) + ($ - 2 -> #) !
end nthFibonacci

templates nthFibonacci
  @: {n0: 0"1", n1: 1"1"};
  1..$ -> @: {n0: $@.n1, n1: $@.n0 + $@.n1};
  $@.n0!
end nthFibonacci

templates nthFibonacci
  @: {n0: 0"1", n1: 1"1"};
  def sign: $ -> \(<0..> 1! <> -1!\);
  1..$*$sign -> $sign -> #
  $@.n0!
  <=1>
    @: {n0: $@.n1, n1: $@.n0 + $@.n1};
  <=-1>
    @: {n0: $@.n1 - $@.n0, n1: $@.n0};
end nthFibonacci

templates nthFibonacci
  { N: ($)"1", n0: 0"1", n1: 1"1" } -> #
  when <{ N: <=0"1"> }> do
    $.n0 !
  when <{ N: <1"1"..>}> do
    { N: $.N - 1"1", n0: $.n1, n1: $.n0 + $.n1} -> #
  otherwise
    { N: $.N + 1"1", n1: $.n0, n0: $.n1 - $.n0} -> #
end nthFibonacci
 
8 -> nthFibonacci -> '$;
' -> !OUT::write
-5 -> nthFibonacci -> '$;
' -> !OUT::write
-6 -> nthFibonacci -> '$;
' -> !OUT::write

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