Hi all!
I'm a J newbie and have a quick programming question.
But first, as a way of introduction, my name is Glenn Lewis
and I am the son of Charles Lewis, who co-authored a book called
something like "A Journey Into APL by Lewis and Clark: An Interactive
Approach", many years ago. A friend of mine knew that APL was the first
language that I ever programmed in, so he pointed me to J, and I'm
giving it a whirl. That same friend pointed out Project Euler
(http://projecteuler.net/) which appears to be an excellent launch pad
for learning a new language.
So I was working on Problem # 58, and got stuck. I've
worked my way through the primer, but J is still quite fuzzy in my head.
Here's what I have so far:
NB. Euler58.ijs
NB.
NB. Starting with 1 and spiraling anticlockwise in the following way, a
square spiral with side length 7 is formed.
NB.
NB. 37 36 35 34 33 32 31
NB. 38 17 16 15 14 13 30
NB. 39 18 5 4 3 12 29
NB. 40 19 6 1 2 11 28
NB. 41 20 7 8 9 10 27
NB. 42 21 22 23 24 25 26
NB. 43 44 45 46 47 48 49
NB.
NB. It is interesting to note that the odd squares lie along the bottom
right diagonal, but what is more interesting is that 8 out of the 13
numbers lying along both diagonals are prime; that is, a ratio of 8/13
62%.
NB.
NB. If one complete new layer is wrapped around the spiral above, a
square spiral with side length 9 will be formed. If this process is
continued, what is the side length of the square spiral for which the
ratio of primes along both diagonals first falls below 10%?
brds =: 3 : 0 NB. Calculates the numbers in the bottom right diagonal
(0=center)
*: 1 + 2 * y
)
diagonals =: 3 : 0 NB. Calculates all the numbers on the diagonals of
the spiral at level 'y'
t1 =. 4 $ brds y
t2 =. 0 2 4 6 * y
t1 - t2
)
If I run 'brds', like so...
brds i. 10
1 9 25 49 81 121 169 225 289 361
it seems to work fine. And if I run 'diagonals' with just a scalar, it
works fine:
diagonals 0
1 1 1 1
diagonals 1
9 7 5 3
diagonals 2
25 21 17 13
But if I try to get all diagonals from the first 10 rings of the
spiral, I get:
diagonals i. 10
|length error: diagonals
| t2=.0 2 4 6 *y
I understand what the problem is (the length mismatch), but don't
know how to fix it... I need to take each scalar in y one-at-a-time...
and I tried all sorts of combinations of " (double quote) to treat the
right hand side like a rank 0 input, but couldn't get it to work.
Any ideas?
Thanks!
-- Glenn Lewis
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