Eccoci.

Coded Triangle Numbers

ℹ️Published on Friday, 25th April 2003, 06:00 pm; Solved by 80950;
Difficulty rating: 5%

Problem 42

The $n$^th term of the sequence of triangle numbers is given by, $t_n = \frac12n(n+1)$; so the first ten triangle numbers are: $$1, 3, 6, 10, 15, 21, 28, 36, 45, 55, \dots$$

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?

Soluzione

Partiamo creando un insieme di numeri triangolari, per effettuare il futuro controllo sulla somma delle lettere delle parole.

triangles = [1/2*n*(n+1) for n in 1:20]

20-element Vector{Float64}:
   1.0
   3.0
   6.0
  10.0
  15.0
  21.0
  28.0
  36.0
  45.0
  55.0
  66.0
  78.0
  91.0
 105.0
 120.0
 136.0
 153.0
 171.0
 190.0
 210.0

L'idea è poi di processare il file, pulendolo per estrarre le singole parole, e fare un loop su ognuna costruendo la somma richiesta, ovvero mappando A come 1, B come 2, ecc. Questo lo si può anche ottenere shiftando in modo opportuno il codice ascii della singola lettera. Fatta la somma verifichiamo se è un numero triangolare e in tal caso incrementiamo la variabile del conteggio, che darà la risposta finale.

text = readlines(download("https://projecteuler.net/resources/documents/0042_words.txt"))[1]
clean_text = replace.(split(text,","),"\"" => "")
clean_text[1:10] # giusto un'occhiata

10-element Vector{String}:
 "A"
 "ABILITY"
 "ABLE"
 "ABOUT"
 "ABOVE"
 "ABSENCE"
 "ABSOLUTELY"
 "ACADEMIC"
 "ACCEPT"
 "ACCESS"

conteggio = 0
println("Triangular words:")
for w in clean_text
	tot = 0
	for c in w
		tot += Int(c)-64 # for upper case c
	end
	if tot in triangles
		println(rpad(w,15), " value: $tot")
		global conteggio += 1
	end
end

Triangular words:
A               value: 1
ABILITY         value: 78
ABOVE           value: 45
ACCOMPANY       value: 91
ACHIEVEMENT     value: 105
AGENCY          value: 55
AGREE           value: 36
AIR             value: 28
ALREADY         value: 66
AN              value: 15
ANCIENT         value: 66
APPARENT        value: 91
APPOINT         value: 91
APPROACH        value: 78
ASSUME          value: 78
AT              value: 21
ATMOSPHERE      value: 120
BAG             value: 10
BAND            value: 21
BANK            value: 28
BAR             value: 21
BEAT            value: 28
BELONG          value: 55
BENEATH         value: 55
BONE            value: 36
BOTH            value: 45
BRIDGE          value: 45
BUILDING        value: 78
BURN            value: 55
CALL            value: 28
CAPACITY        value: 78
CAREFUL         value: 66
CASE            value: 28
CHILD           value: 36
CIVIL           value: 55
CLOSELY         value: 91
COME            value: 36
CONFIDENCE      value: 78
CONFIRM         value: 78
CONSERVATIVE    value: 153
CONSTRUCTION    value: 171
CONTENT         value: 91
COULD           value: 55
CURRENTLY       value: 136
DECISION        value: 78
DEFINITION      value: 105
DEMOCRATIC      value: 91
DEPUTY          value: 91
DESPITE         value: 78
DISTINCTION     value: 136
EAST            value: 45
EDGE            value: 21
EDUCATIONAL     value: 105
EFFECT          value: 45
EQUIPMENT       value: 120
EVENT           value: 66
FACE            value: 15
FAIL            value: 28
FAMILY          value: 66
FEEL            value: 28
FIELD           value: 36
FIGURE          value: 66
FLOOR           value: 66
FREEDOM         value: 66
FUND            value: 45
FUTURE          value: 91
GENTLEMAN       value: 91
GREY            value: 55
GROWTH          value: 91
HAIR            value: 36
HAPPY           value: 66
HAVE            value: 36
HERE            value: 36
HIS             value: 36
IF              value: 15
INCIDENT        value: 78
INCREASED       value: 78
INCREASINGLY    value: 136
INDIVIDUAL      value: 105
INSTRUMENT      value: 153
INTEND          value: 66
INTENTION       value: 120
IS              value: 28
LAW             value: 36
LEADER          value: 45
LEAVE           value: 45
LENGTH          value: 66
LESS            value: 55
LITTLE          value: 78
LOVELY          value: 91
MAN             value: 28
MATCH           value: 45
MERELY          value: 78
MILK            value: 45
MISTAKE         value: 78
MOVE            value: 55
MUCH            value: 45
NEED            value: 28
NOTICE          value: 66
OBJECT          value: 55
OBJECTIVE       value: 91
OF              value: 21
OIL             value: 36
ONLY            value: 66
OTHER           value: 66
OURSELVES       value: 136
PART            value: 55
PASS            value: 55
PATH            value: 45
PERFORM         value: 91
PRISON          value: 91
PRIVATE         value: 91
PROBABLY        value: 91
PROCEDURE       value: 105
QUALITY         value: 105
QUESTION        value: 120
RANGE           value: 45
READ            value: 28
REAL            value: 36
RELIEF          value: 55
REMOVE          value: 78
REPRESENT       value: 120
REQUEST         value: 105
RESPOND         value: 91
RIDE            value: 36
SAMPLE          value: 66
SAY             value: 45
SEAT            value: 45
SECURITY        value: 120
SINGLE          value: 66
SKY             value: 55
SOIL            value: 55
SOLICITOR       value: 120
SONG            value: 55
SOUTHERN        value: 120
SPIRIT          value: 91
START           value: 78
SUGGESTION      value: 136
TALL            value: 45
TAX             value: 45
THEORY          value: 91
THREATEN        value: 91
THROUGHOUT      value: 153
TITLE           value: 66
TOOTH           value: 78
TOTALLY         value: 105
TRAVEL          value: 78
TYPE            value: 66
UNABLE          value: 55
UNDERSTAND      value: 120
UPON            value: 66
USE             value: 45
VARIOUS         value: 105
VARY            value: 66
VIDEO           value: 55
WAGE            value: 36
WARM            value: 55
WATCH           value: 55
WE              value: 28
WHILST          value: 91
WIDELY          value: 78
WOMAN           value: 66

@show conteggio

conteggio = 162