The shortest code by character count that takes a single input integer N
(N >= 3) and returns an array of indices that when iterated would traverse an N
xN
matrix according to the JPEG "zigzag" scan pattern. The following is an example traversal over an 8x8 matrixsrc:
(The middle matrix is not part of the input or output, just a representation of the NxN matrix the input represents.)
1 2 3
(Input) 3 --> 4 5 6 --> 1 2 4 7 5 3 6 8 9 (Output)
7 8 9
1 2 3 4
(Input) 4 --> 5 6 7 8 --> 1 2 5 9 6 3 4 7 10 13 14 11 8 12 15 16 (Output)
9 10 11 12
13 14 15 16
Extend your answer to take two inputs N
and M
(N, M >=3) and perform the same scan over an N
xM
matrix. (In this case N
would be the number of columns and M
the number of rows.)
1 2 3 4
(Input) 4 3 --> 5 6 7 8 --> 1 2 5 9 6 3 4 7 10 11 8 12 (Output)
9 10 11 12
1 2 3
(Input) 3 4 --> 4 5 6 --> 1 2 4 7 5 3 6 8 10 11 9 12 (Output)
7 8 9
10 11 12
;<@|.`</.i.2$
Usage:
;<@|.`</.i.2$ 3
0 1 3 6 4 2 5 7 8
;<@|.`</.i.2$ 4
0 1 4 8 5 2 3 6 9 12 13 10 7 11 14 15
(NB.
is J's comment indicator)
; NB. Link together...
<@|.`< NB. ... 'take the reverse of' and 'take normally'
/. NB. ... applied to alternating diagonals of...
i. NB. ... successive integers starting at 0 and counting up to fill an array with dimensions of...
2$ NB. ... the input extended cyclically to a list of length two.
;<@|.`</.i.|.
Usage:
;<@|.`</.i.|. 3 4
0 1 3 6 4 2 5 7 9 10 8 11
;<@|.`</.i.|. 9 6
0 1 9 18 10 2 3 11 19 27 36 28 20 12 4 5 13 21 29 37 45 46 38 30 22 14 6 7 15 23 31 39 47 48 40 32 24 16 8 17 25 33 41 49 50 42 34 26 35 43 51 52 44 53