# Challenge 150 Task #1 - Fibonacci words

## Task #1 - Fibonacci words

### Description

Original Description

You are given two strings having the same number of digits, \$a and \$b.

Write a script to generate Fibonacci Words by concatenation of the previous two strings. Finally, print 51st digit of the first term having at least 51 digits.

Example:

``````    Input: \$a = '1234' \$b = '5678'
Output: 7

Fibonacci Words:

'1234'
'5678'
'12345678'
'567812345678'
'12345678567812345678'
'56781234567812345678567812345678'
'1234567856781234567856781234567812345678567812345678'

The 51st digit in the first term having at least 51 digits
'1234567856781234567856781234567812345678567812345678' is 7.``````

### Solution

Full Source

For this challenge we start by getting the two input words `\$a` and `\$b` from the argument list.

``my ( \$a, \$b ) = @ARGV;``

After checking the length of the first string to make sure that we have any input at all, we check if both strings are of the same length. We will not check if only digits were used. It doesn’t matter for the algorithm whether we restrict the input to only digits or allow arbitrary characters. (Actually it doesn’t even matter that they are of the same length, but I will go with that restriction)

``````die "Expect two input words of equal length!\n"
unless length(\$a) && length(\$a) == ( length(\$b) // 0 );``````

Now we pass both words to the meat of this solution, the `fibonacci_word` routine. We additionally pass the minimum length of 51 characters, up to which we will build the fibonacci word

``my \$fibonacci_word = fibonacci_word( \$a, \$b, 51 );``

Finally, we extract the 51st character (at index 50) from the built word and print it out as our result.

``````my \$target = substr( \$fibonacci_word, 50, 1 );
say \$target;``````

The actual `fibonacci_word` routine cries for a recursive solution. As always with a recursive approach we start by defining the exit condition, which is fulfilled as soon as the `\$a` string reaches at least the requested length `\$length`. In that case `\$a` is the final fibonacci word, and we return it to the caller.

Otherwise, we continue the process, by passing `\$b` as the new `\$a` to the fibonacci_word routine and accumulating the next fibonacci word (the concatenation of `\$a` and `\$b`) into `\$b`. This swapping and concatenating of the input words goes on until we reach the requested length.

``````sub fibonacci_word ( \$a, \$b, \$length ) {
return \$a if length(\$a) >= \$length;
return fibonacci_word( \$b, \$a . \$b, \$length );
}``````