lemon-project-template-glpk

annotate deps/glpk/examples/magic.mod @ 9:33de93886c88

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Import GLPK 4.47
author Alpar Juttner <alpar@cs.elte.hu>
date Sun, 06 Nov 2011 20:59:10 +0100
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alpar@9 1 /* MAGIC, Magic Square */
alpar@9 2
alpar@9 3 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
alpar@9 4
alpar@9 5 /* In recreational mathematics, a magic square of order n is an
alpar@9 6 arrangement of n^2 numbers, usually distinct integers, in a square,
alpar@9 7 such that n numbers in all rows, all columns, and both diagonals sum
alpar@9 8 to the same constant. A normal magic square contains the integers
alpar@9 9 from 1 to n^2.
alpar@9 10
alpar@9 11 (From Wikipedia, the free encyclopedia.) */
alpar@9 12
alpar@9 13 param n, integer, > 0, default 4;
alpar@9 14 /* square order */
alpar@9 15
alpar@9 16 set N := 1..n^2;
alpar@9 17 /* integers to be placed */
alpar@9 18
alpar@9 19 var x{i in 1..n, j in 1..n, k in N}, binary;
alpar@9 20 /* x[i,j,k] = 1 means that cell (i,j) contains integer k */
alpar@9 21
alpar@9 22 s.t. a{i in 1..n, j in 1..n}: sum{k in N} x[i,j,k] = 1;
alpar@9 23 /* each cell must be assigned exactly one integer */
alpar@9 24
alpar@9 25 s.t. b{k in N}: sum{i in 1..n, j in 1..n} x[i,j,k] = 1;
alpar@9 26 /* each integer must be assigned exactly to one cell */
alpar@9 27
alpar@9 28 var s;
alpar@9 29 /* the magic sum */
alpar@9 30
alpar@9 31 s.t. r{i in 1..n}: sum{j in 1..n, k in N} k * x[i,j,k] = s;
alpar@9 32 /* the sum in each row must be the magic sum */
alpar@9 33
alpar@9 34 s.t. c{j in 1..n}: sum{i in 1..n, k in N} k * x[i,j,k] = s;
alpar@9 35 /* the sum in each column must be the magic sum */
alpar@9 36
alpar@9 37 s.t. d: sum{i in 1..n, k in N} k * x[i,i,k] = s;
alpar@9 38 /* the sum in the diagonal must be the magic sum */
alpar@9 39
alpar@9 40 s.t. e: sum{i in 1..n, k in N} k * x[i,n-i+1,k] = s;
alpar@9 41 /* the sum in the co-diagonal must be the magic sum */
alpar@9 42
alpar@9 43 solve;
alpar@9 44
alpar@9 45 printf "\n";
alpar@9 46 printf "Magic sum is %d\n", s;
alpar@9 47 printf "\n";
alpar@9 48 for{i in 1..n}
alpar@9 49 { printf{j in 1..n} "%3d", sum{k in N} k * x[i,j,k];
alpar@9 50 printf "\n";
alpar@9 51 }
alpar@9 52 printf "\n";
alpar@9 53
alpar@9 54 end;