#!/usr/bin/perl 
# fib1.pl
use warnings;
use strict;
#Subroutine/Function Section
# Note this function is called recusively between
# 2 and 74 times to create the Fibonacci series.
# The input consists of 
#  1. An $number_of_iterations counter,stating how far
# you want to calculate the Fibonacci Series and 
#  2. The given $arev  array for the Fibonacci series calculated so far.
#
# The output is the Fibonacci Series to the desired number
# of places as an array ($arev).
# 
# To make sense of this start by caluculating the Fibonacci
# series for the first two elements.
# The Fibonacci series for element [1 through 2] is:  0 1 
# The 2nd  element of the Fibonacci series is: 1
# Note, initially we are not passing in the initial Fibonacci
# array so it is created as [0, 1]
#
sub fibonacci1 {
   my ($number_of_iterations, $aref) = @_;
#  if the $aref array does not exist create it with
# the block of code around the "unless".
#  i.e. if $aref = NULL then create $aref = [0, 1]
   unless ($aref) {
      # first call - initialize
      $aref = [0, 1];
      # Decrement the number of iterations by  the length of
      # the intial array after creating
      # the intial array. You have done the first two iterations.  
      $number_of_iterations -= scalar(@{$aref});
#      print " this is initial number_of_iterations left after ";
#      print " initialization: <$number_of_iterations> \n";
      }
#  End of intialization block for first iteration. This part of the
#  code will not be touched again.
      if ($number_of_iterations < 1) {
          return @{$aref}; # You are done, leave function.
      }
      # Otherwise continue iterations of series.         
      # Decrement the number_of_iterations by 1 and as long
      # as you are not at 0 calculate the next Fibonacci value.
      # Fib(n) = Fib(n-1) + Fib (n-2)
      # i.e. Fib(7) = Fib(6) + Fib(5)
      # Then "push" that is stick this value at the end of the 
      # array.  You can now recursively call the function again.
      # You will stay in this "push and decrement" loop until
      # the $number_of_iterations counter hits zero. Then
      # you will return the array and exit this function.
      #
      if ($number_of_iterations--) {
         my $next = $aref->[-1] + $aref->[-2];
      #  print "\nFib(n-1): <$aref->[-1]>  ";
      #  print "Fib(n-2): <$aref->[-2]>  \n";
         push @{$aref}, $next;
         return fibonacci1($number_of_iterations, $aref);
      } 
}
# End Subroutine Section
# calculate desired element of standard Fibonacci sequence
# Main Section
#
#  usage    ./perlfib  integer
#
#   i.e.    ./perlfib  10
#
#   Will print out the First 10 elements of the Fibonacci Series,
#   i.e.  0 1 1 2 3 5 8 13 21 34 
#                              
# Note $indexvalue must be at least 2 because
# the nth value of the Fibonacci series is always the sum
# of the two previous terminals. The series starts with
# Fib(2) = Fib(1) - Fib(0), the array can not have a negative index 
# Fib(n) = Fib(n-1) + Fib(n-2)
 my $indexvalue = shift(@ARGV);
 unless($indexvalue) {
 print " Sorry, you forgot to enter an iteration number for the ";
 print " Fibonacci series.   \n\n usage:  perlfib i \n\n";
 print " where i is an integer between 2 and 74 \n";
 exit;
 }
 if ($indexvalue < 2) { 
   print "Sorry, Fibonacci element must be two or higher \n"; 
   exit;
   }
 if ($indexvalue > 74) { 
   print "Sorry, Fibonacci element must be less than 75. "; 
   print " Otherwise, deep recursion and rounding errors can";
   print " occur due to limits of size of double long integers. \n";
   exit;
   }
 
# return first $indexvalue elements of standard Fibonacci sequence
my @sequence = fibonacci1($indexvalue);
#Note, we are intentionally leaving out the second parameter in this
# function, i.e. the $arev array.  
# However if we wanted to know what the next $indexvalue 
#  elements in the Fibonacci series were after [0, 1, 1] 
#  We could make this call
#  my @sequence = fibonacci1($indexvalue, [0,1,1]);
# 
print "The Fibonacci series for element [1 through $indexvalue] is: ";
print " @sequence \n";
print "The $indexvalue element of the Fibonacci series is: ";
# Note, pop will give you the last element of the array.
print  pop(@sequence), "\n";
exit;
# End Main Section