Project Euler – Problem 22 Solution

Problem

Using names.txt (right click and ‘Save Link/Target As…’), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a name score.

For example, when the list is sorted into alphabetical order, COLIN, which is worth 3 + 15 + 12 + 9 + 14 = 53, is the 938th name in the list. So, COLIN would obtain a score of 938 x 53 = 49714.

What is the total of all the name scores in the file?

Solution

open System.IO

let values =
    File.ReadAllLines(@"C:\TEMP\names.txt")
    |> Array.map (fun s -> s.Replace("\"", ""))
    |> Array.collect (fun s -> s.Trim().Split(','))
    |> Array.sort
    |> Array.map (fun s -> s.ToUpper().ToCharArray() |> Array.sumBy (fun c -> int32(c) - (int32('A') - 1)))

let answer = Array.map2 (fun v p -> v * p) values [|1..values.Length|] |> Array.sum

Once I’ve downloaded the names.txt file and loaded its contents in, the first thing I needed to do was to remove the double quotes and split the remaining strings by comma to get back a string array of the names, e.g.:

[“MARY”; “PATRICIA”; …]

Now that the data is in a useful format I can easily sort it and then do the necessary computation to work out the score for each name. Let me draw your attention to the function in the Array.sumBy function:

Array.sumBy (fun c -> int32(c) - (int32('A') - 1))

As I’ve mentioned in the problem 8 solution, int32(char) returns the unicode value of the char, which in this case is the alphabetical value we need to calculate the score for a name. But we can’t just use it as it is, because the char sequence A, B, C… does not start at 1, which is why we need to work out the offset using int32(‘A’) – 1.

Finally, the Array.map2 function is similar to Array.map, except that it works on two arrays at a time. So here I’m transforming the array of alphabetical values (for the sorted names) and the array of corresponding alphabetical orders into the score for each name before I add them all up to get the answer.