Task — Fibonacci words

You are given two strings having 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.

Examples

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.

Analysis

This is a good example of a task where efficiency isn't an issue. You can probably generate a Fibonacci series up to the point where you run out of memory in milliseconds, and for the example above we only need 4 more terms to reach the 51 character length requested.

Even giving my vanilla algorithm with two starting strings which are 1 character long, and asking for the first term with 1000 characters you only need 14 terms beyond the two given ones.

And I could do the task as stated on paper in under 20 seconds!

Try it 

Script

#!/usr/bin/perl

# Peter Campbell Smith - 2022-01-31
# PWC 150 task 1

use v5.28;
use strict;
use warnings;
use utf8;

my ($a, $b, $index, $j, $test, @fib, @tests, $big, $length);

# sets of inputs to test ($a, $b, character index of interest)
@tests = (['1234', '5678', 51], ['12345678', '98765432', 159], ['1234567890', '1234567890', 1000]);

# loop over tests
for $test (@tests) {
    
    # get parameters
    ($fib[0], $fib[1], $index) = @$test;
    
    # create successive ternms of series until one is long enough
    $j = 1;
    while (1) {
        $j ++;
        $fib[$j] = $fib[$j - 2] . $fib[$j - 1];
        last if length($fib[$j]) >= $index;
    }
    
    # format the answer
    say qq[\nInput:  $fib[0], $fib[1]];
    $length = length($fib[$j]);
    $big = '';
    $big .= qq[$1\n] while $fib[$j] =~ m|(.{50})|g;
    $big .= substr($fib[$j], int($length / 50) * 50);
    say qq[Character $index is ] . substr($fib[$j], $index - 1, 1) . 
        qq[, term $j is $length characters long:\n$big];
}

Output

Input:  1234, 5678
Character 51 is 7, term 6 is 52 characters long:
12345678567812345678567812345678123456785678123456
78

Input:  12345678, 98765432
Character 159 is 7, term 7 is 168 characters long:
98765432123456789876543212345678987654329876543212
34567898765432123456789876543298765432123456789876
54329876543212345678987654321234567898765432987654
321234567898765432

Input:  1234567890, 1234567890
Character 1000 is 0, term 11 is 1440 characters long:
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890
1234567890123456789012345678901234567890