# Sudoku Madness

I just read your Sudoku message on the J Forum. By a strange coincidence, one of my students chose Sudoku for his J assignment. He was having a lot of trouble, so I wrote the script below to give him a start. He didn’t get all that far with writing some player support but I’ll be working with him after I come back from overseas.

Because I’m leaving early Friday for a week of meetings in the US I haven’t got time to do much more than send you the code. For it is that I’ve commented it fairly fully for the student’s sake, but against it is that I left the assignments global to make it easy for him to test it.

Perhaps its interest is that I’ve generalised it way beyond the 3×3×3, which is, I think, a bit of a straight jacket. Also, you should be able to jazz up the code because I’m not an expert by any means, and the code is just one evening’s work.

NB. NB. General Sudoku Arrays NB. NB. Generate an array of numbers, for example, shape 2 3 4 5 NB. which is thought of as a 2x3 array of 4x5 rectangles, NB. or a 2x4 by 3x5 array of numbers, where NB. (a) no number is repeated within NB. 0. any 4x5 subarray, NB. 1. any 2x4 subarray, and NB. 2. any 3x5 subarray, NB. (b) the numbers are whole NB. from 1 to the maximum of 4x5, 2x4, and 3x5. NB. NB. Final Functions : Dsply Fnl (try "Dsply Fnl 2 2 3 3" or "Dsply Fnl 3") NB. Some Utility Functions Dsply =: <"2 NB. Dsply y : boxes the 4x5 subarrays PnDy =: ,"2@(0 1&|:)@:(,"2)@(0 2&|:) NB. PnDy y : converts to 8x10 array InDy =: Dsply@(]$({.~ -@(*/)))~ >@(1&{) NB. x InDy y : constructs & displays intermediate array Vldt =: 2&>.@(4&$)@,@:>. NB. Forces 4 integers greater than 1 Mxmm =: >./@(*/)@:((2 3$2 0 1 3 2 3)&{) NB. Calculates the maximum of 4x5, 2x4, and 3x5 NB. Functions to set up running list of boxes NB. NB. 0. The next index (starts as <: of 2x3x4x5) NB. 1. The overall array as a list (starts as an empty list) NB. 2. 2x3 table of lists of numbers used so far for each 4x5 subarray NB. 3. 3x5 ditto for each 2x4 subarray NB. 4. 2x4 ditto for each 3x5 subarray SSAry =: ($&a:)@:{ NB. sets up the subarray of empty boxes Strt =: <:@(*/) ; (i.0)"_ ; 0 1&SSAry ; 1 3&SSAry ; <@(0 2&SSAry) NB. Functions to calculate the next number NB. NB. Require shape as left argument, running array as right Ndx =: #: >@{. NB. 4 element index to next number UsdFS =: <@(2&{.)@Ndx >@{ >@(2&{)@] NB. x UsdFS y : gets 4x5 used so far UsdSS =: <@(1 3&{)@Ndx >@{ >@(3&{)@] NB. x UsdSS y : gets 2x4 used so far UsdTS =: <@(0 2&{)@Ndx >@{ >@(4&{)@] NB. x UsdTS y : gets 3x5 used so far UsdS =: UsdFS ~.@, UsdSS , UsdTS NB. x UsdTS y : gets all numbers used so far NxtNr =: >:@i.@Mxmm@[ (0:`({~?@#)@.(*@#))@:-. UsdS NB. x NxtNr y : selects from numbers not yet used AdNN =: (NxtNr <@, >@(1&{)@]) 1} ] NB. x AdNN y : puts the next number to list front NB. Functions to put away the next number in the three boxes NB. NB. Further updates the running array NwN =: {.@>@(1&{)@] NB. picks out the new number NwFS =: (UsdFS <@, NwN)`(<@(2&{.)@Ndx)`(>@(2&{)@])} NB. x NwFs y : updates the 4x5 subarray NwSS =: (UsdSS <@, NwN)`(<@(1 3&{)@Ndx)`(>@(3&{)@])} NB. x NwFs y : updates the 2x4 subarray NwTS =: (UsdTS <@, NwN)`(<@(0 2&{)@Ndx)`(>@(4&{)@])} NB. x NwFs y : updates the 3x5 subarray UdtRA =: <:@>@{.@] ; 1&{@] , NwFS ; NwSS ; <@NwTS NB. x UdtRA y : updates the running array NB. Functions to do all, and to clean up NB. NB. a =. Fnl y : to get the array NB. Dsply a : to see the boxed structure NB. PnDy a : to see the 2D structure Good =: -.@(0&e.)@>@(1&{) Once =: ([ UdtRA AdNN)^:(Good@:])^:(*/@:[) NB. (Once Strt) y : one attempt at the whole Try =: ('No'"_`InDy@.(Good@]) (Once Strt))@Vldt NB. Try y : works for once Cln =: Strt@[^:(-.@Good@:]) NB. (([ Cln Once) Strt) y : Fnsh =: [([ Once Strt@[)`]@.(Good@])^:_ (Once Strt) NB. Fnsh y : repeated attempts at the whole Fnl =: ($ >@(1&{)@Fnsh)@Vldt NB. Fnl y : the structure extracted NB. Dsply Fnl y : to see the structure