Rosetta Code

Magic squares of doubly even order: Difference between revisions

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Magic squares of doubly even order (view source)

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magic constant = 870
</pre>
 
=={{header|Amazing Hopper}}==
{{Trans|C++}}
<syntaxhighlight lang="c">
/*
Magic squares of doubly even order. Rosettacode.org
By Mr. Dalien.
*/
 
#include <basico.h>
 
#proto cuadradomágico(_X_)
#synon _cuadradomágico generarcuadradomágico
 
principal {
decimales '0', fijar separador 'NULO'
malla de bits(bits,'1;0;0;1','0;1;1;0','0;1;1;0','1;0;0;1')
borrar pantalla
iterar para( i=1; n=4, #(i<=3), ++i; #(n=4*i) )
dim( #(n*n) ) matriz de ceros 'sqr'
generar cuadrado mágico (n);
ir a sub ( meter en tabla, sqr, #(n+1) ), para 'sqr'
imprimir '"Magic square order ",n,\
"\nMagic constant : ",#((n * n + 1) * n / 2),\
NL,sqr,NL,NL'
luego limpiar 'sqr'
siguiente
terminar
}
 
subrutinas
 
sub( meter en tabla, s, n ) {
i=n,rareti(i, 'i')
retener 'n', insertar columnas en 's'
insertar filas en 's'
#basic{
s[1:2:2*n-1,1:_end_] = "---"
s[1:_end_, 1:2:2*n-1] = "|"
s[1:2:_end_,1:2:_end_] = "+"
}
retornar 's'
}
 
cuadrado mágico ( n )
iterar para ( cr=0;i=0, #(cr<n), ++cr )
iterar para ( cc=0, #(cc<n), ++cc;++i )
#( sqr[ (cc+n*cr)+1 ] = (bits[(cr%4+1),(cc%4+1)]) ? (i+1) : (n^2-i); )
siguiente
siguiente
#( sqr = lpad(" ",3,string(sqr)))
redim ( sqr, n, n )
retornar
</syntaxhighlight>
{{out}}
<pre>
Magic square order 4
Magic constant : 34
+---+---+---+---+
| 1| 15| 14| 4|
+---+---+---+---+
| 12| 6| 7| 9|
+---+---+---+---+
| 8| 10| 11| 5|
+---+---+---+---+
| 13| 3| 2| 16|
+---+---+---+---+
 
 
Magic square order 8
Magic constant : 260
+---+---+---+---+---+---+---+---+
| 1| 63| 62| 4| 5| 59| 58| 8|
+---+---+---+---+---+---+---+---+
| 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| 9|
+---+---+---+---+---+---+---+---+
| 57| 7| 6| 60| 61| 3| 2| 64|
+---+---+---+---+---+---+---+---+
 
 
Magic square order 12
Magic constant : 870
+---+---+---+---+---+---+---+---+---+---+---+---+
| 1|143|142| 4| 5|139|138| 8| 9|135|134| 12|
+---+---+---+---+---+---+---+---+---+---+---+---+
|132| 14| 15|129|128| 18| 19|125|124| 22| 23|121|
+---+---+---+---+---+---+---+---+---+---+---+---+
|120| 26| 27|117|116| 30| 31|113|112| 34| 35|109|
+---+---+---+---+---+---+---+---+---+---+---+---+
| 37|107|106| 40| 41|103|102| 44| 45| 99| 98| 48|
+---+---+---+---+---+---+---+---+---+---+---+---+
| 49| 95| 94| 52| 53| 91| 90| 56| 57| 87| 86| 60|
+---+---+---+---+---+---+---+---+---+---+---+---+
| 84| 62| 63| 81| 80| 66| 67| 77| 76| 70| 71| 73|
+---+---+---+---+---+---+---+---+---+---+---+---+
| 72| 74| 75| 69| 68| 78| 79| 65| 64| 82| 83| 61|
+---+---+---+---+---+---+---+---+---+---+---+---+
| 85| 59| 58| 88| 89| 55| 54| 92| 93| 51| 50| 96|
+---+---+---+---+---+---+---+---+---+---+---+---+
| 97| 47| 46|100|101| 43| 42|104|105| 39| 38|108|
+---+---+---+---+---+---+---+---+---+---+---+---+
| 36|110|111| 33| 32|114|115| 29| 28|118|119| 25|
+---+---+---+---+---+---+---+---+---+---+---+---+
| 24|122|123| 21| 20|126|127| 17| 16|130|131| 13|
+---+---+---+---+---+---+---+---+---+---+---+---+
|133| 11| 10|136|137| 7| 6|140|141| 3| 2|144|
+---+---+---+---+---+---+---+---+---+---+---+---+
 
</pre>
 
Line 888 ⟶ 1,009:
 
Magic constant: 260</pre>
 
=={{header|EDSAC order code}}==
<syntaxhighlight lang="edsac">
[Magic squares of doubly even order, for Rosetta Code.
EDSAC program, Initial Orders 2.]
[====================================================================================
Certain cells in the square are marked, such that if a cell is marked then so is
its reflection in the centre point of the square. Cells are numbered 1, 2, 3 ...
from left to right and top to bottom, but if a cell is marked it is swapped with its
reflection. Two marking methods are used, illustrated below for an 8x8 square.
+ o o + + o o + + + o o o o + +
o + + o o + + o + + o o o o + +
o + + o o + + o o o + + + + o o
+ o o + + o o + o o + + + + o o o = unmarked
+ o o + + o o + o o + + + + o o + = marked
o + + o o + + o o o + + + + o o
o + + o o + + o + + o o o o + +
+ o o + + o o + + + o o o o + +
Diagonal method Rectangle method
====================================================================================]
[Arrange the storage]
T45K P56F [H parameter: subroutine to print string]
T46K P100F [N parameter: subroutine to print number]
T47K P204F [M parameter: main routine]
T54K P200F [C parameter: constants read by subroutine R2]
 
[Library subroutine R2: reads integers from tape and can then be overwritten.]
GK T20F VD L8F A40D UD TF I40F A40F S39F G@ S2F G23F A5@ T5@ E4@ E13Z
T#C [tell R2 where to store values]
13743895347F8589934592#TZ
[C parameter: masks read in by subroutine R2, not by the regular loader]
[0] PF PF [diagonal method, binary 01100110011001100110011001100110011]
[2] PF PF [rectangle method, binary 01000000000000000000000000000000000]
 
[M parameter Main routine + high-level subroutine]
E25K TM GK
[35-bit values, must be at even address]
[0] PF PF [initial value of x mask]
[2] PF [x-mask, low 17 bits]
[3] PF [x-mask, high 17 bits]
[4] PF [y-mask, low 17 bits]
[5] PF [y-mask, high 17 bits]
[17-bit values]
[6] PF [sign bit from y mask]
[7] PF [m, input by user]
[8] PF [n = 4*m = order of magic square]
[9] PF [n^2 + 1]
[10] PF [negative counter for x-values (columns)]
[11] PF [negative counter for y-values (rows)]
[12] PF [current entry 1, 2, 3, ...]
[13] PD [constant 1]
[14] K4096F [null]
[15] !F [space]
[16] @F [carriage return]
[17] &F [line feed]
[18] P10F [to check for user dialling '0']
[Strings to be printed]
[19] K2048FMFAFGFIFCF!FSFQFUFAFRFEF!FOFFF!FOFRFDFEFRF!F#FRF*FMF@F&FK4096F
[49] K2048FDFIFAFLF!FMF!F#FKFPF!F*FTFOF!FCFAFNFCFEFLF#FLF!FK4096F
[75] K2048FDFIFAFGFOFNFAFLF!FMFEFTFHFOFDF#FCF@F&FK4096F
[96] K2048FRFEFCFTFAFNFGFLFEF!FMFEFTFHFOFDF#FCF@F&FK4096F
 
[Enter with acc = 0]
[118] A118@ GH A19@ [print 'MAGIC SQUARE OF ORDER 4M']
[121] A121@ GH A49@ [print 'DIAL M (0 TO CANCEL)']
ZF [halt machine; restarts when user dials a number]
[Here acc holds number of pulses in address field]
S18@ E175@ [exit if dialled '0' (10 pulses)]
A18@ [restore acc after test; m is in address field]
L512F [shift 11 left for printing]
UF [temp to 0F]
OF O16@ O17@ [print m followed by CR, LF]
R1024F [shift 12 right, m is now right-justified]
U7@ [store m]
L1F T8@ [shift 2 left and store n = 4*m]
H8@ V8@ [acc := n^2]
L64F L64F [shift 16 left to adjust scaling after mult]
A13@ T9@ [store n^2 + 1 = sum of a cell and its reflection]
[143] A143@ GH A75@ [print 'DIAGONAL METHOD:']
A#C [acc := diagonal mask]
U#@ [store as x-mask at start of each row]
T4#@ [also as initial value of y-mask]
[149] A149@ G177@ [call subroutine to print magic square]
[151] A151@ GH A96@ [print 'RECTANGLE METHOD:']
A2#C U4D T6D [copy rectangke mask to 4D and 6D]
S7@ [initialize negative counter to -m]
[158] TF [loop: update negative counter in 0F]
A4D RD T4D [shift 4D 1 right]
A6D R2F T6D [shift 6D 3 right]
AF A13@ [inc negative counter]
G158@ [loop back till done m times]
A4D S6D L1F [acc := 4D - 6D, then 2 left]
[Mask in binary is now 0 (m times) 1 (2*m times) 0...0]
U#@ [store as x-mask at start of each row]
T4#@ [also as initial value of y-mask]
[173] A173@ G177@ [call subroutine to print magic square]
[175] O14@ [done; print null to flush teleprinter buffer]
ZF [halt machine]
 
[Subroutine to print magic square after x- and y-mask have been initialized.]
[It's assumed that strings printed by caller leave teleprinter in figures mode.]
[177] A3F T220@ [plant return link as usual]
A15@ T1F [space replaces leading 0 when printing]
T12@ [initialize cell entry to 0]
S8@ [initialize negative counter of rows to -n]
[Start of row]
[183] T11@ [update negative counter of rows]
A#@ T2#@ [reset x-mask for start of row]
H14@ C5@ T6@ [isolate sign bit of y-mask]
S8@ [initialize negative counter of columns to -n]
[Next cell in this row.
Cell is considered marked if sign bits in x- and y-masks are equal.
Or could say marked if sign bits are unequal; would also give a magic square.]
[190] T10@ [update negative counter of columns]
A12@ A13@ T12@ [inc cell entry]
A3@ A6@ [compare signs in x- and y-masks]
E200@ [jump if equal (or could replace E by G)]
TF [clear acc]
A12@ [acc := entry]
E203@ [join common code]
[200] TF [clear acc]
A9@ S12@ [acc := complement of entry]
[203] TF [to 0F for printing]
[204] A204@ GN [print number]
A2#@ LD T2#@ [shift x-mask 1 left]
A10@ A13@ [inc negative counter of cells]
G190@ [loop till row is complete]
[End of row]
O16@ O17@ [print CR, LF]
A4#@ LD T4#@ [shift y-mask 1 left]
A11@ A13@ [inc negative counter of rows]
G183@ [loop till magic square is complete]
[220] ZF [(planted) jump back to caller]
 
[H parameter: Subroutine to print a string.]
E25K TH
[Input: A order for first character must follow subroutine call (G order)
String is terminated with EDSAC null, which is sent to the teleprinter.]
GKA18@U17@S19@T4@AFT6@AFUFOFE12@A20@G16@TFA6@A2FG5@TFZFU3FU1FK2048F
 
[N parameter: Subroutine to print non-negative 17-bit integer.]
E25K TN
[Parameters: 0F = integer to be printed (not preserved)
1F = character for leading zero (preserved)
Workspace: 4F..7F, 38 locations]
GKA3FT34@A1FT7FS35@T6FT4#FAFT4FH36@V4FRDA4#FR1024FH37@E23@O7FA2F
T6FT5FV4#FYFL8FT4#FA5FL1024FUFA6FG16@OFTFT7FA6FG17@ZFP4FZ219DTF
 
[M parameter again]
E25K TM GK
E118Z [define entry point]
PF [acc = 0 on entry]
 
</syntaxhighlight>
{{out}}
<pre>
MAGIC SQUARE OF ORDER 4M
DIAL M (0 TO CANCEL) 2
DIAGONAL METHOD:
64 2 3 61 60 6 7 57
9 55 54 12 13 51 50 16
17 47 46 20 21 43 42 24
40 26 27 37 36 30 31 33
32 34 35 29 28 38 39 25
41 23 22 44 45 19 18 48
49 15 14 52 53 11 10 56
8 58 59 5 4 62 63 1
RECTANGLE METHOD:
64 63 3 4 5 6 58 57
56 55 11 12 13 14 50 49
17 18 46 45 44 43 23 24
25 26 38 37 36 35 31 32
33 34 30 29 28 27 39 40
41 42 22 21 20 19 47 48
16 15 51 52 53 54 10 9
8 7 59 60 61 62 2 1
</pre>
 
=={{header|Elena}}==
Line 899 ⟶ 1,197:
{
if(n < 4 || n.mod(4) != 0)
{ InvalidArgumentException.new:("base must be a positive multiple of 4").raise() };
int bits := 09669h;
Line 907 ⟶ 1,205:
var result := IntMatrix.allocate(n,n);
int i := 0;
for (int r := 0,; r < n,; r += 1)
{
for(int c := 0,; c < n,; c += 1,; i += 1)
{
int bitPos := c / mult + (r / mult) * 4;
Line 2,764 ⟶ 3,062:
{{trans|Kotlin}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascriptwren">import "./fmt" for Conv, Fmt
 
var magicSquareDoublyEven = Fn.new { |n|
Anonymous user
Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/352928...352934"