## Question

The $n^{th}$ term of the sequence of triangle numbers is given by, $t_n = \frac{1}{2}n(n+1)$; so the first ten triangle numbers are:

$\displaystyle 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...$

By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is $19 + 11 + 25 = 55 = t_{10}$. If the word value is a triangle number then we shall call the word a triangle word.

Using words.txt (right click and ‘Save Link/Target As…’), a 16K text file containing nearly two-thousand common English words, how many are triangle words?

parse :: String -> [String]
parse = words . map replaceComma . filter notQuote where
replaceComma ',' = ' '
replaceComma c = c
notQuote = (/= '"')

alphaIndex :: Char -> Int
alphaIndex c = fromEnum c - 64

alphaScore :: String -> Int
alphaScore = sum . map alphaIndex

triangle :: String -> Bool
triangle str = floor t == ceiling t
where s = alphaScore str
t = (sqrt (fromIntegral (1 + 8*s)) - 1) / 2

main :: IO ()
main = do
print $length$ filter triangle $parse str $ ghc -O2 -o triangle-words triangle-words.hs
$time ./triangle-words real 0m0.003s user 0m0.000s sys 0m0.000s ## Python #!/usr/bin/env python import os from string import ascii_uppercase def letter_value(letter): return ascii_uppercase.index(letter.upper())+1 def word_value(word): return sum(letter_value(letter) for letter in word) def triangle(n): return int((0.5) * n * (n+1)) def main(): triangle_numbers = [triangle(n) for n in range(1, 100)] words = [word.strip('"') for word in open(os.path.join(os.path.dirname(__file__), 'words.txt')).read().split(',')] total = 0 for word in words: if word_value(word) in triangle_numbers: total += 1 print(total) if __name__ == "__main__": main() $ time python3 triangle-words.py
real   0m0.040s
user   0m0.028s
sys    0m0.008s

## Ruby

#!/usr/bin/env ruby
triangles = (1..1000).map { |n| (n*(n+1))/2 }.to_a
puts File.read(File.dirname(__FILE__) + '/words.txt').scan(/\w+/).select { |word|
triangles.include? word.each_byte.reduce(0) {|s,v| s+(v-64) }
}.count
\$ time ruby triangle-words.rb
real   0m0.041s
user   0m0.040s
sys    0m0.000s

Questions? Comments? Send me an email: z@chdenton.com