Magic squares/Lua

Lua

---

<lang lua> function makeArray( s )

   local q = {}
   for j = 1, s do
       table.insert( q, {} )
       for i = 1, s do
           table.insert( q[j], 0 )
       end
   end
   return q

end

-- odd magic square -- function buildOMS( s )

   if s % 2 == 0 then s = s + 1 end
   local q, p = makeArray( s ), 1
   local i, j, ti, tj = 1 + math.floor( s / 2 ), 1
   while( p <= s * s ) do
       q[i][j] = p
       ti = i + 1; if ti > s then ti = 1 end
       tj = j - 1; if tj < 1 then tj = s end
       if q[ti][tj] ~= 0 then
           ti = i; tj = j + 1
       end
       i = ti; j = tj; p = p + 1;
   end
   return q, s

end

-- singly even magic square -- function buildSEMS( s )

   if s % 2 == 1 then s = s + 1 end
   while( s % 4 == 0 ) do s = s + 2 end

   local q, z, o = makeArray( s ), math.floor( s / 2 )
   local b, c, d, a = z * z; c = 2 * b; d = 3 * b

   o = buildOMS( z )
   for j = 1, z do
       for i = 1, z do
           a = o[i][j]
           q[i][j] = a
           q[i + z][j + z] = a + b
           q[i + z][j] = a + c
           q[i][j + z] = a + d
       end
   end

   local lc = math.floor( z / 2 )
   local rc, t = lc - 1 
   for j = 1, z do
       for i = 1, s do  
           if i <= lc or i > s - rc or ( i == lc + 1 and j == lc + 1 ) then
               if not( i == 1 and j == lc+ 1 ) then
                   t = q[i][j]
                   q[i][j] = q[i][j + z]
                   q[i][j + z] = t
               end
           end
       end
   end
   return q, s

end

-- doubly even magic square -- function buildDEMS( s )

   while( s % 4 > 0 ) do s = s + 1 end
   local q = makeArray( s )
   local temp, n, tot, sx, sy = {{1,0,0,1}, {0,1,1,0}, {0,1,1,0}, {1,0,0,1}}, 
         0, s * s
   for j = 1, s do
       for i = 1, s do
           sx = i % 4; if sx < 1 then sx = 4 end
           sy = j % 4; if sy < 1 then sy = 4 end
           if temp[sy][sx] == 1 then q[i][j] = n + 1
           else q[i][j] = tot - n end
           n = n + 1
       end
   end
   return q, s

end

function myFormat( s, l )

   for i = 1, l - #s do
       s = "0" .. s
   end
   return s .. " "

end

LOG_10 = 2.302585092994 function display( q, s )

   io.write( string.format( " - %d x %d\n", s, s ) )
   local k = 1 + math.floor( math.log( s * s ) / LOG_10 )
   for j = 1, s do
       for i = 1, s do
           io.write( myFormat( string.format( "%d", q[i][j] ), k ) )
       end
       print()
   end
   io.write( string.format( "Magic sum: %d\n", s * ( ( s * s ) + 1 ) / 2 ) )

end

--entry point -- io.write( "\nOdd Magic Square" ) display( buildOMS( 9 ) )

io.write( "\nSingly Even Magic Square" ) display( buildSEMS( 6 ) )

io.write( "\nDoubly Even Magic Square" ) display( buildDEMS( 8 ) )

</lang>

Output:

Odd Magic Square - 9 x 9
47 58 69 80 01 12 23 34 45
57 68 79 09 11 22 33 44 46
67 78 08 10 21 32 43 54 56
77 07 18 20 31 42 53 55 66
06 17 19 30 41 52 63 65 76
16 27 29 40 51 62 64 75 05
26 28 39 50 61 72 74 04 15
36 38 49 60 71 73 03 14 25
37 48 59 70 81 02 13 24 35
Magic sum: 369
Singly Even Magic Square - 6 x 6
35 01 06 26 19 24
03 32 07 21 23 25
31 09 02 22 27 20
08 28 33 17 10 15
30 05 34 12 14 16
04 36 29 13 18 11
Magic sum: 111
Doubly Even Magic Square - 8 x 8
01 63 62 04 05 59 58 08
56 10 11 53 52 14 15 49
48 18 19 45 44 22 23 41
25 39 38 28 29 35 34 32
33 31 30 36 37 27 26 40
24 42 43 21 20 46 47 17
16 50 51 13 12 54 55 09
57 07 06 60 61 03 02 64
Magic sum: 260