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e24ebe2110
1. Commit Sudoku solver program from Paul Cumberworth. 2. Replace RC reference document with version generated from CUBE13 library files
405 lines
15 KiB
Plaintext
405 lines
15 KiB
Plaintext
?COMPILE SUDOKU/TEST WITH XALGOL GO
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?XALGOL FILE LINE = LINE/SUDOKU PRINT BACK UP DISK
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?STACK = 5000
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?DATA CARD
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%CARD STACK SEG PRT LIST SINGLE DEBUGN
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$LIST PRT STACK SINGLE
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% SUDOKU SOLVER
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% ORIGINALLY WRITTEN IN C BY SCOTT HEMPHILL AND PLACED IN
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% THE PUBLIC DOMAIN 5 SEPTEMBER 2005
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% CONVERTED TO B5500 BY PAUL C JULY 2018
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% MAKE SURE STACK SET TO AT LEAST 5000 WORDS TO COPE WITH RECURSION
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BEGIN
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BOOLEAN
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FINDMULTIPLE; % FIND MULTIPLE SOLUTIONS (SET COMMON = 1 IN CC)
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INTEGER
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NUM, % COUNT OF NUMBER OF SOLUTIONS FOUND
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CURDEPTH, % CURRENT RECURSION DEPTH
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MAXDEPTH, % MAXIMUM RECURSION DEPTH
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STARTET; % TIME(1) OF WHEN WE STARTED
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INTEGER ARRAY
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BITNO[0:11], % ALLOW FOR 12 BITS, ONLY USE 9 THOUGH
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GRID [0:80], % THE PUZZLE GRID: 1 THRU 9, OR 0 IF NO NUMBER YET
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BITS [0:80], % BITMAP OF EACH SQUARE: BIT SET => NOT POSSIBLE
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% I.E. 3"001" => !1, 3"002" => !2, 3"004" => !3,
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% 3"010" => !4, ... 3"400" => !9.
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COUNT [0:511], % BIT COUNT FOR EACH NUMBER
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OTHERSARY [0:80, 0:19];
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DEFINE OTHERS(X,Y) =
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OTHERSARY[X,Y] #; % MAKE IT EASIER TO OPTIMISE LATER
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% FOR EACH SQUARE, AN ARRAY OF 20 "OTHER"
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% LOCATIONS AFFECT BY THIS SQUARE. FOR
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% EXAMPLE, IF THERE IS A "6" IN SQUARE 0,
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% THERE ARE 20 OTHER SQUARES WE KNOW
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% CANT CONTAIN A SIX:
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% 1,2,3,4,5,6,7,8 (HORIZONTAL ROW)
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% 9,18,27,36,45,54,63,72 (VERTCAL COLUMN)
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% 1,2,9,10,11,18,19,20 (3X3 SQUARE)
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% THATS A TOTAL OF 24 SQUARE NUMBERS,
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% BUT 4 OF THEM ARE DUPLICATES. THE
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% "OTHERS" ARRAY IS BIG ENOUGH TO HOLD
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% 24 NUMBERS WHILE IT IS BEING BUILT, BUT
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% WILL ONLY 20 NUMBERS WILL BE USED WHEN
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% IT IS COMPLETE.
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FILE CARD (2,10,150);
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FILE SPO 11 (1,10);
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FILE LINE 15 (1,15); % 15, 17 IS PRINTER BACKUP DISK
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INTEGER PROCEDURE ONES32(I); % FROM HACKERS DELIGHT
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%---------------------------
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VALUE I; INTEGER I;
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BEGIN
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I:= I - REAL(BOOLEAN(I.[31:31]) AND BOOLEAN(3"12525252525"));
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I:= REAL(BOOLEAN(I.[31:30]) AND BOOLEAN(3"6314631463")) +
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REAL(BOOLEAN(I) AND BOOLEAN(3"6314631463"));
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I:= REAL(BOOLEAN(I.[31:28] + I) AND BOOLEAN(3"1703607417"));
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I:= I + I.[31:24];
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I:= I + I.[31:16];
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ONES32:= REAL(BOOLEAN(I) AND BOOLEAN(3"77"));
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END;
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PROCEDURE SETBOX(N, X, BIT);
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%---------------------------
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VALUE N, X, BIT; INTEGER N, X, BIT;
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% "SETBOX" IS USED TO PLACE A NUMBER IN THE GRID, WHETHER IT IS KNOWN,
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% OR A GUESS. IT ALSO UPDATES ALL THE BITMASKS FOR ALL THE ASSOCIATED
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% SQUARES TO INDICATE THAT THEY CANT CONTAIN THIS NUMBER.
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BEGIN
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INTEGER I;
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GRID[N]:= X;
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FOR I:= 0 STEP 1 UNTIL 19 DO
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BITS[OTHERS(N,I)]:= REAL(BOOLEAN(BITS[OTHERS(N,I)]) OR
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BOOLEAN(BIT));
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END;
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PROCEDURE READGRID;
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%------------------
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% READ IN INITIAL DATA
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% THE INITIAL BITMASK IS CALCULATED AT THE SAME TIME BY CALLING SETBOX
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BEGIN
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INTEGER I, J;
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ALPHA ARRAY AIN[0:2];
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POINTER P;
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FOR I:= 0 STEP 1 UNTIL 8 DO % 9 ROWS OF 9 NUMBERS
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BEGIN
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READ(CARD, 3, AIN[*]);
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P:= POINTER(AIN[0]);
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FOR J:= 0 STEP 1 UNTIL 8 DO
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BEGIN
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SETBOX(9 | I + J, INTEGER(P,1),
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BITNO[INTEGER(P,1)]); % SET BITNO, LSB=BIT0
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P:= P + 1;
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END;
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END;
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%WRITE OUT WHAT WE GOT!
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WRITE(LINE, <"WE STORED IN GRID:">);
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FOR I:= 0 STEP 1 UNTIL 8 DO
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WRITE(LINE, <9I1>, FOR J:= 0 STEP 1 UNTIL 8 DO GRID[9|I+J]);
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%CHECK FOR CONSISTENCY
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FOR I:= 0 STEP 1 UNTIL 80 DO
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IF GRID[I] > 0 THEN
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IF REAL(BOOLEAN(BITS[I]) AND BOOLEAN(BITNO[GRID[I]])) > 0 THEN
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BEGIN
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WRITE(LINE, <"INCONSISTENT DATA IN ",I1,",",I1>,
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(I DIV 9)+1, (I MOD 9) + 1);
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J:= 1/0;
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END;
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END;
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PROCEDURE PRINTSOLUTION;
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%-----------------------
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BEGIN
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INTEGER I, J;
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NUM:= NUM + 1;
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IF NUM > 1 THEN
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WRITE(LINE, <" ">); % BLANK
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WRITE(LINE,<"SOLUTION ",I3,":">, NUM);
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FOR I:= 0 STEP 1 UNTIL 8 DO
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WRITE(LINE, <9I1>, FOR J:= 0 STEP 1 UNTIL 8 DO GRID[9|I+J]);
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END;
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PROCEDURE SELECTBOX;
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%-------------------
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% "SELECTBOX" IS THE HEART OF THE ALGORITHM. IT WORKS THIS WAY:
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% FIRST, THE GRID IS SEARCHED FOR AN EMPTY SQUARE. IF THERE ISNT ONE,
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% THEN THE GRID CONTAINS A SOLUTION, SO IT IS PRINTED. IF AN EMPTY
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% SQUARE IS FOUND, THEN IT IS COMPARED WITH ALL OTHER EMPTY SQUARES TO
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% SEE WHICH ONE OF THEM HAS THE MAXIMUM NUMBER OF 1-BITS IN ITS BITMASK.
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% THAT SQUARE IS THE ONE SELECTED, AND EACH OF THE POSSIBLE VALUES ARE
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% TRIED IN RETURN, CALLING "SELECTBOX" RECURSIVELY TO SEARCH FOR A
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% SOLUTION. NOTE THAT IF A SQUARE HAS 9 1-BITS IN ITS BITMASK, THEN
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% THERE ARE NO POSSIBLE VALUES, AND "SELECTBOX" WILL RETURN WITHOUT ANY
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% FURTHER RECURSION. OTHERWISE, IF A SQUARE HAS 8 1-BITS IN ITS BITMASK,
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% THEN IT HAS A FORCED CHOICE, AND ONLY THAT CHOICE WILL BE TAKEN AT THIS
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% LEVEL IN THE RECURSION.
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BEGIN
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INTEGER ARRAY
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BITSAVE[0:80]; % SAVED ON EVERY RECURSION, MAX DEPTH 81|81 = 4131 WORDS?
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INTEGER
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I,
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J,
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BEST,
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BESTCOUNT;
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BOOLEAN
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FINISHED;
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LABEL XIT;
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CURDEPTH:= CURDEPTH + 1;
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MAXDEPTH:= MAX(MAXDEPTH, CURDEPTH);
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% IF NUM = 0 THEN % RECURSE ONLY IF NO SOLUTIONS SO FAR
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BEGIN
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% FIND EMPTY SQUARE
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BEST:= 0;
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WHILE NOT FINISHED DO % PREFER TO HAVE CONDITIONAL AND :)
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IF NOT FINISHED:= GRID[BEST] = 0 THEN
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FINISHED:= (BEST:= BEST + 1) GTR 80;
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IF BEST = 81 THEN % 81 INDICATES NO EMPTY SQUARES
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BEGIN
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PRINTSOLUTION;
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GO TO XIT;
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END;
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BESTCOUNT:= COUNT[BITS[BEST]]; % BITS IN THE SQUARE WE FOUND
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FOR I:= BEST+1 STEP 1 WHILE I LSS 81 DO
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BEGIN % FIND THE BIGGEST COUNT OVER ALL SQUARES
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IF GRID[I] = 0 THEN % ONLY CONSIDER EMPTY SQUARES
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BEGIN
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J:= COUNT[BITS[I]];
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IF J > BESTCOUNT THEN
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BEGIN
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BEST:= I;
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BESTCOUNT:= J;
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END;
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END;
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END;
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% TRY ALL NUMBERS FOR THIS SQUARE
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FOR I:= 1 STEP 1 WHILE I LEQ 9 DO
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BEGIN
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IF REAL(BOOLEAN(BITS[BEST]) AND BOOLEAN(BITNO[I])) = 0 THEN
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BEGIN % IF THE NUMBER IS POSSIBLE, RECURSE
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% SAVE STATE ON STACK
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REPLACE POINTER(BITSAVE) BY POINTER(BITS) FOR 81 WORDS;
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SETBOX(BEST, I, BITNO[I]); % SET NUMBER AND FIX BITMASK
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SELECTBOX; % RECURSE
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GRID[BEST]:= 0; % UNPLACE NUMBER IN SQUARE
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% RESTORE
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REPLACE POINTER(BITS) BY POINTER(BITSAVE) FOR 81 WORDS;
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END;
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END;
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END;
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XIT:
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CURDEPTH:= CURDEPTH - 1;
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END;
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PROCEDURE INITIALIZE;
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%---------------------
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% FILL THE COUNT AND OTHERS ARRAYS
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BEGIN
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DEFINE FO(I) = FILL OTHERSARY[I, *] WITH #; % MAKE IT EASIER TO WRITE!
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INTEGER CNT;
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% PREFILLED COUNT ARRAY: PT= 0.833 IO= 9.267 ET= 3.483
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% CALCULATED COUNT ARRAY: PT= 1.150 IO= 8.850 ET= 3.517
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FOR CNT:= 0 STEP 1 UNTIL 511 DO
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COUNT[CNT]:= ONES32(CNT);
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% BE NICE TO REDUCE PBITTING SOMEHOW, AND MAYBE MAKE FASTER ACCESS,
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% WHICH IS BETTER INDEXED DESCRIPTOR OR MULTIPLY TO DETERMINE VALUE?
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% CURRENT IMPLEMENTATION SLOWS THE COMPILER AS WELL!
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% AS FILL CAN ONLY DO 1024 NUMBERS, CANNOT USE SINGLE DIMENSION ARRAY
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% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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FO( 0) 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,18,19,20,27,36,45,54,63,72; % 0
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FO( 1) 0, 2, 3, 4, 5, 6, 7, 8, 9,10,11,18,19,20,28,37,46,55,64,73; % 1
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FO( 2) 0, 1, 3, 4, 5, 6, 7, 8, 9,10,11,18,19,20,29,38,47,56,65,74; % 2
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FO( 3) 0, 1, 2, 4, 5, 6, 7, 8,12,13,14,21,22,23,30,39,48,57,66,75; % 3
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FO( 4) 0, 1, 2, 3, 5, 6, 7, 8,12,13,14,21,22,23,31,40,49,58,67,76; % 4
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FO( 5) 0, 1, 2, 3, 4, 6, 7, 8,12,13,14,21,22,23,32,41,50,59,68,77; % 5
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FO( 6) 0, 1, 2, 3, 4, 5, 7, 8,15,16,17,24,25,26,33,42,51,60,69,78; % 6
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FO( 7) 0, 1, 2, 3, 4, 5, 6, 8,15,16,17,24,25,26,34,43,52,61,70,79; % 7
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FO( 8) 0, 1, 2, 3, 4, 5, 6, 7,15,16,17,24,25,26,35,44,53,62,71,80; % 8
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FO( 9) 0, 1, 2,10,11,12,13,14,15,16,17,18,19,20,27,36,45,54,63,72; % 9
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FO(10) 0, 1, 2, 9,11,12,13,14,15,16,17,18,19,20,28,37,46,55,64,73; % 10
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FO(11) 0, 1, 2, 9,10,12,13,14,15,16,17,18,19,20,29,38,47,56,65,74; % 11
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FO(12) 3, 4, 5, 9,10,11,13,14,15,16,17,21,22,23,30,39,48,57,66,75; % 12
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FO(13) 3, 4, 5, 9,10,11,12,14,15,16,17,21,22,23,31,40,49,58,67,76; % 13
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FO(14) 3, 4, 5, 9,10,11,12,13,15,16,17,21,22,23,32,41,50,59,68,77; % 14
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FO(15) 6, 7, 8, 9,10,11,12,13,14,16,17,24,25,26,33,42,51,60,69,78; % 15
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FO(16) 6, 7, 8, 9,10,11,12,13,14,15,17,24,25,26,34,43,52,61,70,79; % 16
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FO(17) 6, 7, 8, 9,10,11,12,13,14,15,16,24,25,26,35,44,53,62,71,80; % 17
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FO(18) 0, 1, 2, 9,10,11,19,20,21,22,23,24,25,26,27,36,45,54,63,72; % 18
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FO(19) 0, 1, 2, 9,10,11,18,20,21,22,23,24,25,26,28,37,46,55,64,73; % 19
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FO(20) 0, 1, 2, 9,10,11,18,19,21,22,23,24,25,26,29,38,47,56,65,74; % 20
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FO(21) 3, 4, 5,12,13,14,18,19,20,22,23,24,25,26,30,39,48,57,66,75; % 21
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FO(22) 3, 4, 5,12,13,14,18,19,20,21,23,24,25,26,31,40,49,58,67,76; % 22
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FO(23) 3, 4, 5,12,13,14,18,19,20,21,22,24,25,26,32,41,50,59,68,77; % 23
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FO(24) 6, 7, 8,15,16,17,18,19,20,21,22,23,25,26,33,42,51,60,69,78; % 24
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FO(25) 6, 7, 8,15,16,17,18,19,20,21,22,23,24,26,34,43,52,61,70,79; % 25
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FO(26) 6, 7, 8,15,16,17,18,19,20,21,22,23,24,25,35,44,53,62,71,80; % 26
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FO(27) 0, 9,18,28,29,30,31,32,33,34,35,36,37,38,45,46,47,54,63,72; % 27
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FO(28) 1,10,19,27,29,30,31,32,33,34,35,36,37,38,45,46,47,55,64,73; % 28
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FO(29) 2,11,20,27,28,30,31,32,33,34,35,36,37,38,45,46,47,56,65,74; % 29
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FO(30) 3,12,21,27,28,29,31,32,33,34,35,39,40,41,48,49,50,57,66,75; % 30
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FO(31) 4,13,22,27,28,29,30,32,33,34,35,39,40,41,48,49,50,58,67,76; % 31
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FO(32) 5,14,23,27,28,29,30,31,33,34,35,39,40,41,48,49,50,59,68,77; % 32
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FO(33) 6,15,24,27,28,29,30,31,32,34,35,42,43,44,51,52,53,60,69,78; % 33
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FO(34) 7,16,25,27,28,29,30,31,32,33,35,42,43,44,51,52,53,61,70,79; % 34
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FO(35) 8,17,26,27,28,29,30,31,32,33,34,42,43,44,51,52,53,62,71,80; % 35
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FO(36) 0, 9,18,27,28,29,37,38,39,40,41,42,43,44,45,46,47,54,63,72; % 36
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FO(37) 1,10,19,27,28,29,36,38,39,40,41,42,43,44,45,46,47,55,64,73; % 37
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FO(38) 2,11,20,27,28,29,36,37,39,40,41,42,43,44,45,46,47,56,65,74; % 38
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FO(39) 3,12,21,30,31,32,36,37,38,40,41,42,43,44,48,49,50,57,66,75; % 39
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FO(40) 4,13,22,30,31,32,36,37,38,39,41,42,43,44,48,49,50,58,67,76; % 40
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FO(41) 5,14,23,30,31,32,36,37,38,39,40,42,43,44,48,49,50,59,68,77; % 41
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FO(42) 6,15,24,33,34,35,36,37,38,39,40,41,43,44,51,52,53,60,69,78; % 42
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FO(43) 7,16,25,33,34,35,36,37,38,39,40,41,42,44,51,52,53,61,70,79; % 43
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FO(44) 8,17,26,33,34,35,36,37,38,39,40,41,42,43,51,52,53,62,71,80; % 44
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FO(45) 0, 9,18,27,28,29,36,37,38,46,47,48,49,50,51,52,53,54,63,72; % 45
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FO(46) 1,10,19,27,28,29,36,37,38,45,47,48,49,50,51,52,53,55,64,73; % 46
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FO(47) 2,11,20,27,28,29,36,37,38,45,46,48,49,50,51,52,53,56,65,74; % 47
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FO(48) 3,12,21,30,31,32,39,40,41,45,46,47,49,50,51,52,53,57,66,75; % 48
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FO(49) 4,13,22,30,31,32,39,40,41,45,46,47,48,50,51,52,53,58,67,76; % 49
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FO(50) 5,14,23,30,31,32,39,40,41,45,46,47,48,49,51,52,53,59,68,77; % 50
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FO(51) 6,15,24,33,34,35,42,43,44,45,46,47,48,49,50,52,53,60,69,78; % 51
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FO(52) 7,16,25,33,34,35,42,43,44,45,46,47,48,49,50,51,53,61,70,79; % 52
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FO(53) 8,17,26,33,34,35,42,43,44,45,46,47,48,49,50,51,52,62,71,80; % 53
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FO(54) 0, 9,18,27,36,45,55,56,57,58,59,60,61,62,63,64,65,72,73,74; % 54
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FO(55) 1,10,19,28,37,46,54,56,57,58,59,60,61,62,63,64,65,72,73,74; % 55
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FO(56) 2,11,20,29,38,47,54,55,57,58,59,60,61,62,63,64,65,72,73,74; % 56
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FO(57) 3,12,21,30,39,48,54,55,56,58,59,60,61,62,66,67,68,75,76,77; % 57
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FO(58) 4,13,22,31,40,49,54,55,56,57,59,60,61,62,66,67,68,75,76,77; % 58
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FO(59) 5,14,23,32,41,50,54,55,56,57,58,60,61,62,66,67,68,75,76,77; % 59
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FO(60) 6,15,24,33,42,51,54,55,56,57,58,59,61,62,69,70,71,78,79,80; % 60
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FO(61) 7,16,25,34,43,52,54,55,56,57,58,59,60,62,69,70,71,78,79,80; % 61
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FO(62) 8,17,26,35,44,53,54,55,56,57,58,59,60,61,69,70,71,78,79,80; % 62
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FO(63) 0, 9,18,27,36,45,54,55,56,64,65,66,67,68,69,70,71,72,73,74; % 63
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FO(64) 1,10,19,28,37,46,54,55,56,63,65,66,67,68,69,70,71,72,73,74; % 64
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FO(65) 2,11,20,29,38,47,54,55,56,63,64,66,67,68,69,70,71,72,73,74; % 65
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FO(66) 3,12,21,30,39,48,57,58,59,63,64,65,67,68,69,70,71,75,76,77; % 66
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FO(67) 4,13,22,31,40,49,57,58,59,63,64,65,66,68,69,70,71,75,76,77; % 67
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FO(68) 5,14,23,32,41,50,57,58,59,63,64,65,66,67,69,70,71,75,76,77; % 68
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FO(69) 6,15,24,33,42,51,60,61,62,63,64,65,66,67,68,70,71,78,79,80; % 69
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FO(70) 7,16,25,34,43,52,60,61,62,63,64,65,66,67,68,69,71,78,79,80; % 70
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FO(71) 8,17,26,35,44,53,60,61,62,63,64,65,66,67,68,69,70,78,79,80; % 71
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FO(72) 0, 9,18,27,36,45,54,55,56,63,64,65,73,74,75,76,77,78,79,80; % 72
|
|
FO(73) 1,10,19,28,37,46,54,55,56,63,64,65,72,74,75,76,77,78,79,80; % 73
|
|
FO(74) 2,11,20,29,38,47,54,55,56,63,64,65,72,73,75,76,77,78,79,80; % 74
|
|
FO(75) 3,12,21,30,39,48,57,58,59,66,67,68,72,73,74,76,77,78,79,80; % 75
|
|
FO(76) 4,13,22,31,40,49,57,58,59,66,67,68,72,73,74,75,77,78,79,80; % 76
|
|
FO(77) 5,14,23,32,41,50,57,58,59,66,67,68,72,73,74,75,76,78,79,80; % 77
|
|
FO(78) 6,15,24,33,42,51,60,61,62,69,70,71,72,73,74,75,76,77,79,80; % 78
|
|
FO(79) 7,16,25,34,43,52,60,61,62,69,70,71,72,73,74,75,76,77,78,80; % 79
|
|
FO(80) 8,17,26,35,44,53,60,61,62,69,70,71,72,73,74,75,76,77,78,79; % 80
|
|
|
|
FILL BITNO[*] WITH 0, 1, 2, 4, % NOTE ZERO BASED!!!
|
|
8, 16, 32, 64,
|
|
128, 256, 512, 1024;
|
|
|
|
WRITE(LINE, <"INITIALIZATION TIME: ",
|
|
"PT=",F8.3," IO=",F8.3," ET=", F10.3>,
|
|
TIME(2)/60, TIME(3)/60, (TIME(1)-STARTET)/60);
|
|
END;
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
% SOME TESTED DATA VALUES,
|
|
%071698035
|
|
%600030700
|
|
%090400100
|
|
%000009002
|
|
%300000009
|
|
%500200000
|
|
%004006070
|
|
%006080001
|
|
%820314950
|
|
|
|
%000000008
|
|
%010000040
|
|
%000645910
|
|
%591300000
|
|
%062401790
|
|
%000008165
|
|
%024173000
|
|
%080000020
|
|
%900000000
|
|
|
|
%000000000 - 272 SOLUTIONS
|
|
%010000040
|
|
%000605910
|
|
%591300000
|
|
%062401790
|
|
%000008105
|
|
%024173000
|
|
%080000020
|
|
%000000000
|
|
|
|
%600900050 - VERY HARD - PT = 30SEC+
|
|
%009000003
|
|
%050040007
|
|
%013502790
|
|
%000000000
|
|
%092603540
|
|
%900050020
|
|
%100000600
|
|
%020004005
|
|
|
|
%000000008 - 12 SOLUTIONS
|
|
%010000040
|
|
%000645910
|
|
%591300000
|
|
%000000007
|
|
%000008165
|
|
%024173000
|
|
%080000020
|
|
%900000000
|
|
|
|
%000000008 - 118 SOLUTIONS
|
|
%010000040
|
|
%000645910
|
|
%591300000
|
|
%000000000
|
|
%000008165
|
|
%024173000
|
|
%080000020
|
|
%900000000
|
|
|
|
STARTET:= TIME(1);
|
|
|
|
INITIALIZE;
|
|
READGRID;
|
|
|
|
SELECTBOX;
|
|
|
|
% WARN THE OPERATOR
|
|
IF NUM > 1 THEN
|
|
WRITE(SPO, <"FOUND ", I5, " SOLUTIONS">, NUM);
|
|
|
|
WRITE(LINE, <" ">);
|
|
WRITE(LINE, <I3," SOLUTION(S), ",
|
|
"MAX RECURSION DEPTH = ",I3,", TIMES: ",
|
|
"PT=",F8.3," IO=",F8.3," ET = ", F10.3>,
|
|
NUM, MAXDEPTH,
|
|
TIME(2)/60, TIME(3)/60, (TIME(1)-STARTET)/60);
|
|
END.
|
|
?DATA CARD
|
|
000000008
|
|
010000040
|
|
000645910
|
|
591300000
|
|
062401790
|
|
000008165
|
|
024173000
|
|
080000020
|
|
900000000
|
|
?END
|