since the length? magic-squares n is known to be 8 * n * n
lets try a variation and plot wall time in thousandths of a second.
run: func [f [word!] n[integer!] /local then][
then: now/time/precise
do f n
to-integer 1000 * subtract now/time/precise then
]
draw-bar: func [n height /local p1 p2 p3 p4][
p1: to-pair reduce [(n * 20) 270]
p2: p1 - (height * 0x1 / 20)
p3: p2 + 18x0
p4: p1 + 18x0
compose/deep [
text (p1 + 0x4) (form n)
polygon (p1) (p2) (p3) (p4) (p1)
text (p2 - 0x18) (form height)
]
]
draw-blk: compose[
pen sky fill-pen white font (probe make face/font [size: 10])
]
view/new center-face layout [
b: box black 500x300 effect compose/deep [draw[(draw-blk)]]
]
repeat n 23[
if odd? n[append b/effect/draw draw-bar n run 'magic-squares n show b]
]
wait none
On Mon, 17 Nov 2003, Anton Rolls wrote:
>
> Let's see some results:
>
> draw-bar: func [n height /local p1 p2 p3 p4][
> p1: to-pair reduce [(n * 20) 270]
> p2: p1 - (height * 0x1 / 20)
> p3: p2 + 18x0
> p4: p1 + 18x0
> compose/deep [
> text (p1 + 0x4) (form n)
> polygon (p1) (p2) (p3) (p4) (p1)
> text (p2 - 0x18) (form height)
> ]
> ]
> draw-blk: compose [pen sky fill-pen white font (probe make face/font [size:
> 10])]
> view/new center-face layout [b: box black 500x300 effect compose/deep [draw
> [(draw-blk)]]]
> repeat n 23 [if odd? n [append b/effect/draw draw-bar n length?
> magic-squares n show b]]
> wait none
>
> Anton.
>
> > OK ... I think this is complete enough
> >
> >
> > Rebol[
> > title: "Magic Square generator"
> > author: "Tom Conlin"
> > date: 12-Nov-2003
> > file: %magic-squares.r
> > version: 0.1.0
> > purpose: { Post from Joel Neely
> > The following 3-by-3 display is a simple magic square:
> >
> > 0 8 4
> > 5 1 6
> > 7 3 2
> >
> > because each row and each column sums to 12.
> > Write a function which uses the integers 0 thru 8 (once each!)
> > to construct all possible 3-by-3 simple magic squares.
> > Make it run as quickly as possible.
> > }
> > ]
> >
> >
> > magic-squares: func [
> > { generate simple magic squares
> > and their symetrical reflections
> > for a particular ODD size
> > }
> > n[integer!] "odd natural number"
> > /verbose "pretty print the solutions as well as returning a block"
> > /local flip transpose pprint ms nn ur dn s t blank result
> > ][
> > ;; be sensible
> > if any[not integer? n not positive? n not odd? n][
> > print "argument needs to be positive odd integer"
> > return -1
> > ]
> > nn: n * n
> > ;; actualy quite neat
> > flip: func[b [series!] n[integer!]][
> > while[not tail? b][reverse/part b n b: skip b n]
> > head b
> > ]
> > ;; a bit tedious
> > transpose: func[b[block!] n[integer!] /local t u d ni][
> > for i 1 n 1[
> > ni: n * i - n
> > for j i + 1 n 1[
> > t: pick b u: ni + j
> > poke b u pick b d: n * j - n + i
> > poke b d t
> > ]
> > ]
> > b
> > ]
> > ;;
> > pprint: func[b [series!] n[integer!]][
> > loop n[print copy/part b n b: skip b n]
> > print ""
> > ]
> > ; for building upper-right LUT
> > wrap: func[ b[block!] n[integer!]][
> > join skip tail b negate n copy/part b subtract length? b n
> > ]
> >
> > ;;make LUTs for next move, either up & right or down (with wrapping)
> > dn: make block! nn + n
> > repeat i nn[insert tail dn i]
> > ms: copy ur: copy dn ;; populate blocks
> > insert tail dn copy/part dn n ;; down LUT
> > remove/part dn n
> > ur: wrap ur n ;; up & right LUT
> > while[not tail? ur][
> > change/part ur wrap copy/part ur n n - 1 n
> > ur: skip ur n
> > ]
> > ur: head ur
> > result: make block! 8 * nn ;; storage
> > ;; starting from 0 isn't worth the hassle
> > for i 1 nn 1[
> > s: i
> > poke ms s 1
> > for j 2 nn 1[ ;; build one of the n simple magic squares
> > either equal? 1 j // n
> > [poke ms s: pick dn s j]
> > [poke ms s: pick ur s j]
> > ]
> > ;; store the simple magic square and its reflections
> > insert/only tail result copy ms ; normal
> > loop 3[
> > insert/only tail result copy flip ms n
> > insert/only tail result copy transpose ms n
> > ] insert/only tail result copy flip ms n
> > ]
> > if verbose [
> > while[not tail? result][
> > pprint pick result 1 n result: next result
> > ]
> > ]
> > head result
> > ]
>
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