#### /extra/project-euler/042/042.factor

http://github.com/abeaumont/factor
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``` 1! Copyright (c) 2008 Aaron Schaefer.
3USING: ascii io.encodings.ascii io.files kernel make math math.functions
4    namespaces project-euler.common sequences splitting ;
5IN: project-euler.042
6
7! http://projecteuler.net/index.php?section=problems&id=42
8
9! DESCRIPTION
10! -----------
11
12! The nth term of the sequence of triangle numbers is given by,
13! tn = n * (n + 1) / 2; so the first ten triangle numbers are:
14
15!     1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
16
17! By converting each letter in a word to a number corresponding to its
18! alphabetical position and adding these values we form a word value. For
19! example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value
20! is a triangle number then we shall call the word a triangle word.
21
22! Using words.txt (right click and 'Save Link/Target As...'), a 16K text file
23! containing nearly two-thousand common English words, how many are triangle
24! words?
25
26
27! SOLUTION
28! --------
29
30<PRIVATE
31
32: source-042 ( -- seq )
33    "resource:extra/project-euler/042/words.txt"
34    ascii file-contents [ quotable? ] filter "," split ;
35
36: (triangle-upto) ( limit n -- )
37    2dup nth-triangle > [
38        dup nth-triangle , 1 + (triangle-upto)
39    ] [
40        2drop
41    ] if ;
42
43: triangle-upto ( n -- seq )
44    [ 1 (triangle-upto) ] { } make ;
45
46PRIVATE>
47
48: euler042 ( -- answer )
49    source-042 [ alpha-value ] map dup supremum
50    triangle-upto [ member? ] curry count ;
51
52! [ euler042 ] 100 ave-time
53! 19 ms ave run time - 1.97 SD (100 trials)
54
55
56! ALTERNATE SOLUTIONS
57! -------------------
58
59! Use the inverse function of n * (n + 1) / 2 and test if the result is an integer
60
61<PRIVATE
62
63: triangle? ( n -- ? )
64    8 * 1 + sqrt 1 - 2 / 1 mod zero? ;
65
66PRIVATE>
67
68: euler042a ( -- answer )
69    source-042 [ alpha-value ] map [ triangle? ] count ;
70
71! [ euler042a ] 100 ave-time
72! 21 ms ave run time - 2.2 SD (100 trials)
73
74SOLUTION: euler042a
```