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Challenge #259 [Easy] Clarence the Slow Typist

Description

Clarence is a data entry clerk who works at an internet service provider. His
job is to manually enter the IP addresses of all of the ISP's customers into the
database. He does this using a keypad which has the following layout:

1	2	3
4	5	6
7	8	9
.	0

The distance between the centre of horizontally or vertically adjacent keys is
exactly one centimetre. For instance, the distance between the centres of 3 and
9 would be two centimetres. The distance between the centres of 3 and 5 would be
sqrt 2cm. The Pythagoras theorem is sufficient to calculate the distance between
any two keys.
Clarence, as you might expect from one who works in an ISP, uses a very slow and
inefficient system of typing. He uses a single finger and searches for the key,
and then moves his finger to the key, then presses it, and repeats for all of the
digits in the number. You might know of this style as the "eagle search system"
since the finger searches above the keyboard for the correct key before plunging
down for the keypress, like an eagle plunging down for a kill.
For example, here is how Clarence would type out the number 7851:
    * He starts his finger at 7 and pushes the key.
    * He moves his finger to the right 1cm to 8 and pushes the key.
    * He moves his finger upwards 1cm to 5 and pushes the key.
    * He moves his finger diagonally upwards and left sqrt 2cm to 1 and pushes
      the key.
Therefore the total distance that Clarence moved his finger to type in 7851 is 1
+ 1 + sqrt 2 which is about 3.41cm.
Your task is to write a program that calculates the distance Clarence must move
his finger to type in arbitrary IP addresses.

Formal Inputs and Outputs

Input Description

Input is a string that will be in the form
().().().()
where each () is an integer in the range 0 - 999. This represents the IP address
that Clarence must type in. An example input might be:
219.45.143.143
I would also like to point out that inputs such as 0.42.42.42 or 999.999.999.999
are still valid inputs, despite the fact that they are invalid IP addresses.
So you don't need to include any IP address verification code in your program.

Output Description

Output the distance that Clarence must move his finger in order to type in the
specified IP address. Round answers to two decimal places where needed, and use
the cm unit in your output. The output for the example input is 27.38cm (1 + sqrt
8 + sqrt 5 + 2 + 1 + sqrt 5 + 3 + 1 + sqrt 5 + sqrt 13 + 3 + 1 + sqrt 5).

Credit

This challenge was suggested by /u/katyai. If you have any challenge ideas please
share them on /r/dailyprogrammer_ideas and there's a good chance we'll use them!

( source: https://redd.it/4bc3el )

The version of the user Gobbedyret was so simple -- and good -- that inspired me
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function keyboard_distance( key_1::Char, key_2::Char )
    sequence::AbstractString = "123456789.0"

    first::Tuple = divrem( search( sequence, key_1 ) - 1, 3 )
    second::Tuple = divrem( search( sequence, key_2 ) - 1, 3 )

    dx::Integer = second[ 2 ] - first[ 2 ]
    dy::Integer = second[ 1 ] - first[ 1 ]

    return ( dx^2 + dy^2 )^0.5
end

function main( )
    input::AbstractString = chomp( readline( STDIN ) )
    @printf( "%.2fcm\n", sum( [ keyboard_distance( i, j ) for ( i, j ) in zip( input[1:end-1], input[2:end] ) ] ) )
end

main( )
