Coded triangle numbers

2014-10-12

Problem 042: Coded triangle numbers

Description:

The nth term of the sequence of triangle numbers is given by t(n) = 0.5 * n(n+1); so the first ten triangle numbers are:

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?

Solution:

                              v ################################################################################
                                ################################################################################
A                               ################################################################################
ABILITY                         ################################################################################
ABLE                            ################################################################################
ABOUT                          v                                       <
ABOVE                         > 1"/&"*+00p>"P":10p 5:20p *30p 050p 260p^
ABSENCE
ABSOLUTELY                     >50g1+:50p :1+*2/  "0"\ :10g%" "+\10g/p v
ACADEMIC                       |`\g03                      /2*+1: +1g05<
ACCEPT
ACCESS                         >070p0>70g60gg:" "-!#v_"@"-+v
ACCIDENT                             ^p07+1g07      $#     <
ACCOMPANY                      |-g00p06+1:g06pg06*39<
ACCORDING
ACCOUNT                        >260p 0 >93*60gg:10g%" "+\10g/g"0"-!v
ACHIEVE                                |-g00 p06+1:g06            +<
ACHIEVEMENT                          @.<
...
...

Download

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Explanation:

Similar to problem 22 this is not quite befunge-friendly due to enormous input size. But otherwise it wasn't hard, I create for every word the word value and count the triangle numbers in it.

Two little tricks:

I cached the triangle numbers from 1 to 400 (biggest possible word value is 364 because the longest word is 14 letters)
to count the triangle numbers just add the boolean results of the isTriangle function. Because true is 1 and false is 0 this results equals the number of triangle numbers.