If you wish a J solution, not a cubic, try
LP=: 13 : '_3++/+/\4,_12+32*>:i.<.-:y'
y is some odd integer
Ralph Selfridge
On Fri, 7 Dec 2007, Zsbán Ambrus wrote:
On Dec 3, 2007 1:38 AM, Roger Hui <[EMAIL PROTECTED]> wrote:
FYI: Problem 28 in www.ProjectEuler.net is as follows:
Starting with the number 1 and moving to the right in a clockwise direction a 5
by 5 spiral is formed as follows:
21 22 23 24 25
20 7 8 9 10
19 6 1 2 11
18 5 4 3 12
17 16 15 14 13
It can be verified that the sum of both diagonals is 101.
What is the sum of both diagonals in a 1001 by 1001 spiral formed in the same
way?
Let me reuse the code I posted on "http://www.perlmonks.com/?node_id=487200";.
From improving the first version (the one that uses sort), we get:
(spiral1 =: - ]\ >:@:i.@:*: [`]`[} [: /: [: ,/ [: (>.&| ,
(12&o.)@:(1j_1&*)@:j.)"0/~ i. - -:@:<:) 5
25 24 23 22 21
10 9 8 7 20
11 2 1 6 19
12 3 4 5 18
13 14 15 16 17
(~.@:(<"1)@:(,.~,],.|.)@:i. { spiral1) 5
25 9 1 5 17 21 7 3 13
+/ (~.@:(<"1)@:(,.~,],.|.)@:i. { spiral1) 5
101
+/ (~.@:(<"1)@:(,.~,],.|.)@:i. { spiral1) 1001
669171001
The third solution (the one that builds the spiral recursively from
inside out) turns out to be much slower because of the lots of array
reallocations and copying it has to use:
spiral2h =: (,:@i. , ] + [: |:@|. spiral2s) ` ((1 0$0)"_) @. (<:&0)
spiral2s =: ,:@i. , ] + [: |:@|. [: spiral2h <:
(spiral2 =: (*: - spiral2s)"0) 5
25 24 23 22 21
10 9 8 7 20
11 2 1 6 19
12 3 4 5 18
13 14 15 16 17
+/ (~.@:(<"1)@:(,.~,],.|.)@:i. { spiral2) 1001
669171001
I posted the second solution (the arithmetic one) in perl only, so I
have to translate it to J now. This translation is very efficent
because we don't compute all elements of the big spiral, only the
diagonal ones. (It's also a very fast way to compute the whole
spiral.)
spiral3c =: 4 9 $ 4 0 _4 0 1 _1 1 0 0 0 4 0 _4 _1 5 1 _2 2 0 4 0 _4
1 7 1 _4 4
spiral3a =: 3 :0
'i j n' =: y
g =: (*:i),(*:j),(n*i),(n*j),i,j,(*:n),n,:1$~$i
t =: +/"_1 spiral3c *"1 _ g
p =: (n<>:i+j) ++: i>j
p} t
)
spiral3 =: [: spiral3a (["0/~@:i. ; ]"0/~@:i. ; ])
spiral3d =: [: spiral3a (<"1@:|:@:~.@:(,.~,],.|.)@:i. , <)
spiral3 5
25 24 23 22 21
10 9 8 7 20
11 2 1 6 19
12 3 2 5 18
13 12 11 10 17
spiral3d 5
25 9 1 5 17 21 7 3 13
+/ spiral3d 5
101
+/ spiral3d 1001
669171001
Ambrus
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
