Matrix with two diagonals
- Task
Draw a square matrix which has 1's on both diagonals but 0's elsewhere.
If you can please use GUI
AppleScript
<lang applescript>on twoDiagonalMatrix(n)
if (n < 2) then error "twoDiagonalMatrix() handler: parameter must be > 1."
set digits to {}
set oddness to n mod 2
repeat (n - 1 + oddness) times
set end of digits to 0
end repeat
set m to n div 2 + oddness -- Middle index of digit source list.
set item m of digits to 1
set matrix to {}
set leftLen to m - 1 -- Length of left end of each row - 1.
set rightLen to leftLen - oddness -- Length of right end ditto.
-- Assemble the first m rows from the relevant sections of 'digits'.
repeat with i from m to 1 by -1
set end of matrix to items i thru (i + leftLen) of digits & items -(i + rightLen) thru -i of digits
end repeat
-- The remaining rows are the reverse of these, not repeating the mth where n is odd.
return matrix & reverse of items 1 thru (m - oddness) of matrix
end twoDiagonalMatrix
-- Task code. on matrixToText(matrix, separator)
copy matrix to matrix
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to separator
repeat with thisLine in matrix
set thisLine's contents to thisLine as text
end repeat
set AppleScript's text item delimiters to linefeed
set matrix to matrix as text
set AppleScript's text item delimiters to astid
return matrix
end matrixToText
return linefeed & matrixToText(twoDiagonalMatrix(7), space) & ¬
(linefeed & linefeed & matrixToText(twoDiagonalMatrix(8), space))</lang>
- Output:
<lang applescript>" 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1
1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1"</lang>
C
<lang c>#include <stdio.h>
void specialMatrix(unsigned int n) {
int i, j;
for (i = 0; i < n; ++i) {
for (j = 0; j < n; ++j) {
if (i == j || i + j == n - 1) {
printf("%d ", 1);
} else {
printf("%d ", 0);
}
}
printf("\n");
}
}
int main() {
specialMatrix(10); // even n
printf("\n");
specialMatrix(11); // odd n
return 0;
}</lang>
- Output:
1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1
F#
<lang fsharp> // Matrix with two diagonals. Nigel Galloway: February 17th., 2022 let m11 m=Array2D.init m m (fun n g->if n=g || n+g=m-1 then 1 else 0) printfn "%A\n\n%A" (m11 5) (m11 6) </lang>
- Output:
[[1; 0; 0; 0; 1] [0; 1; 0; 1; 0] [0; 0; 1; 0; 0] [0; 1; 0; 1; 0] [1; 0; 0; 0; 1]] [[1; 0; 0; 0; 0; 1] [0; 1; 0; 0; 1; 0] [0; 0; 1; 1; 0; 0] [0; 0; 1; 1; 0; 0] [0; 1; 0; 0; 1; 0] [1; 0; 0; 0; 0; 1]]
Factor
<lang factor>USING: io kernel math math.matrices prettyprint ;
- <x-matrix> ( n -- matrix )
dup dup 1 - '[ 2dup = -rot + _ = or 1 0 ? ] <matrix-by-indices> ;
6 <x-matrix> simple-table. nl 7 <x-matrix> simple-table.</lang>
- Output:
1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1
Go
<lang go>package main
import "fmt"
func specialMatrix(n uint) {
for i := uint(0); i < n; i++ {
for j := uint(0); j < n; j++ {
if i == j || i+j == n-1 {
fmt.Printf("%d ", 1)
} else {
fmt.Printf("%d ", 0)
}
}
fmt.Println()
}
}
func main() {
specialMatrix(8) // even n fmt.Println() specialMatrix(9) // odd n
}</lang>
- Output:
1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1
Haskell
<lang haskell>---------------- MATRIX WITH TWO DIAGONALS ---------------
twoDiagonalMatrix :: Int -> Int twoDiagonalMatrix n = flip (fmap . go) xs <$> xs
where
xs = [1 .. n]
go x y
| y == x = 1
| y == succ (subtract x n) = 1
| otherwise = 0
TEST -------------------------
main :: IO () main =
mapM_ putStrLn $
unlines . fmap (((' ' :) . show) =<<)
. twoDiagonalMatrix
<$> [7, 8]</lang>
Or, in the form of a list comprehension:
<lang haskell>-------------- MATRIX WITH TWO DIAGONALS ---------------
twoDiagonalMatrix :: Int -> Int twoDiagonalMatrix n =
let xs = [1 .. n]
in [ [ fromEnum $ x `elem` [y, succ (n - y)]
| x <- xs
]
| y <- xs
]
TEST -------------------------
main :: IO () main =
mapM_ putStrLn $
unlines . fmap (((' ' :) . show) =<<)
. twoDiagonalMatrix
<$> [7, 8]</lang>
- Output:
1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1
J
Implementation:
<lang J>task=: Template:(+.</lang>
In other words, generate an order n identity matrix, flip it and (treating it as a bit matrix) OR the two matrices.
Some examples:
<lang J> task 2 1 1 1 1
task 3
1 0 1 0 1 0 1 0 1
task 4
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1
task 5
1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1
task 6
1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1</lang>
JavaScript
<lang javascript>(() => {
"use strict";
// ------------ MATRIX WITH TWO DIAGONALS ------------
// doubleDiagonal :: Int -> Int const doubleDiagonal = n => { // A square matrix of dimension n with ones // along both diagonals, and zeros elsewhere. const xs = enumFromTo(1)(n);
return xs.map(
y => xs.map(
x => Number(
[y, 1 + n - y].includes(x)
)
)
);
};
// ---------------------- TEST -----------------------
const main = () => [7, 8].map(
n => showMatrix(
doubleDiagonal(n)
)
).join("\n\n");
// --------------------- GENERIC ---------------------
// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m =>
n => Array.from({
length: 1 + n - m
}, (_, i) => m + i);
// showMatrix :: a -> String const showMatrix = rows => // String representation of a matrix. rows.map( row => row.map(String).join(" ") ).join("\n");
// MAIN -- return main();
})();</lang>
- Output:
1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1
Perl
Strings
<lang perl>#!/usr/bin/perl
use strict; #https://rosettacode.org/wiki/Matrix_with_two_diagonals use warnings;
print diagonal($_), "\n" for 10, 11;
sub diagonal
{
my $n = shift() - 1;
local $_ = 1 . 0 x ($n - 1) . 2 . "\n" . (0 . 0 x $n . "\n") x $n;
1 while s/(?<=1...{$n})0/1/s or s/(?<=2.{$n})[01]/2/s;
return tr/2/1/r =~ s/\B/ /gr;
}</lang>
- Output:
1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1
Numbers
<lang perl>use strict; use warnings; use feature 'say';
sub dual_diagonal {
my($n) = shift() - 1;
my @m;
for (0..$n) {
my @rr = reverse my @r = ( (0) x $_, 1, (0) x ($n-$_) );
push @m, [ map { $r[$_] or $rr[$_] } 0..$n ]
}
@m
}
say join ' ', @$_ for dual_diagonal(4); say ; say join ' ', @$_ for dual_diagonal(5); </lang>
- Output:
1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1
Phix
Tee hee, pick the bones out of this one. Lovely.
with javascript_semantics for n=6 to 7 do pp(apply(true,reinstate,{repeat(repeat(0,n),n),apply(true,sq_mul,{tagset(n),{{1,-1}}}),{{1,1}}}),{pp_Nest,1}) end for
- Output:
{{1,0,0,0,0,1},
{0,1,0,0,1,0},
{0,0,1,1,0,0},
{0,0,1,1,0,0},
{0,1,0,0,1,0},
{1,0,0,0,0,1}}
{{1,0,0,0,0,0,1},
{0,1,0,0,0,1,0},
{0,0,1,0,1,0,0},
{0,0,0,1,0,0,0},
{0,0,1,0,1,0,0},
{0,1,0,0,0,1,0},
{1,0,0,0,0,0,1}}
Slightly saner, shows sackly same stuff:
with javascript_semantics for n=6 to 7 do sequence s = repeat(repeat(0,n),n) for i=1 to n do s[i][i] = 1 s[i][-i] = 1 end for pp(s,{pp_Nest,1}) end for
Python
<lang python>Matrix with two diagonals
- twoDiagonalMatrix :: Int -> Int
def twoDiagonalMatrix(n):
A square matrix of dimension n with ones
along both diagonals, and zeros elsewhere.
xs = range(1, 1 + n)
return [
[
int(x in (y, 1 + (n - y)))
for x in xs
]
for y in xs
]
- ------------------------- TEST -------------------------
- main :: IO ()
def main():
Matrices of dimension 7 and 8
for n in [7, 8]:
print(
showMatrix(
twoDiagonalMatrix(n)
) + '\n'
)
- ----------------------- GENERIC ------------------------
- showMatrix :: Int -> String
def showMatrix(rows):
String representation of a matrix
return '\n'.join([
' '.join([str(x) for x in y]) for y in rows
])
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1
Raku
<lang perl6>sub dual-diagonal($n) { ([1, |(0 xx $n-1)], *.rotate(-1) … *[*-1]).map: { [$_ Z|| .reverse] } }
.say for dual-diagonal(6); say ; .say for dual-diagonal(7);</lang>
- Output:
[1 0 0 0 0 1] [0 1 0 0 1 0] [0 0 1 1 0 0] [0 0 1 1 0 0] [0 1 0 0 1 0] [1 0 0 0 0 1] [1 0 0 0 0 0 1] [0 1 0 0 0 1 0] [0 0 1 0 1 0 0] [0 0 0 1 0 0 0] [0 0 1 0 1 0 0] [0 1 0 0 0 1 0] [1 0 0 0 0 0 1]
Red
<lang rebol>Red[]
x-matrix: function [size][
repeat i size [
repeat j size [
prin either any [i = j i + j = (size + 1)] [1] [0]
prin sp
]
prin newline
]
]
x-matrix 6 prin newline x-matrix 7</lang>
- Output:
1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1
Ring
<lang ring>
- Project : Identity Matrix
- Date : 2022/16/02
- Author : Gal Zsolt (~ CalmoSoft ~)
- Email : <calmosoft@gmail.com>
load "stdlib.ring" load "guilib.ring"
size = 8 C_Spacing = 1
C_ButtonBlueStyle = 'border-radius:6px;color:black; background-color: blue' C_ButtonOrangeStyle = 'border-radius:6px;color:black; background-color: orange'
Button = newlist(size,size) LayoutButtonRow = list(size)
app = new qApp {
win = new qWidget() {
setWindowTitle('Identity Matrix') move(500,100) reSize(600,600) winheight = win.height() fontSize = 18 + (winheight / 100)
LayoutButtonMain = new QVBoxLayout()
LayoutButtonMain.setSpacing(C_Spacing) LayoutButtonMain.setContentsmargins(0,0,0,0)
for Row = 1 to size LayoutButtonRow[Row] = new QHBoxLayout() { setSpacing(C_Spacing) setContentsmargins(0,0,0,0) }
for Col = 1 to size
Button[Row][Col] = new QPushButton(win) {
setSizePolicy(1,1)
}
LayoutButtonRow[Row].AddWidget(Button[Row][Col]) next LayoutButtonMain.AddLayout(LayoutButtonRow[Row]) next
LayoutDataRow1 = new QHBoxLayout() { setSpacing(C_Spacing) setContentsMargins(0,0,0,0) }
LayoutButtonMain.AddLayout(LayoutDataRow1)
setLayout(LayoutButtonMain)
show()
}
pBegin()
exec()
}
func pBegin()
for Row = 1 to size
for Col = 1 to size
if Row = Col or Row + Col = 9
Button[Row][Col].setStyleSheet(C_ButtonOrangeStyle)
Button[Row][Col].settext("1")
else
Button[Row][Col].setStyleSheet(C_ButtonBlueStyle)
Button[Row][Col].settext("0")
ok
next
next
score = 0
</lang>
Outpu image:
Special identity matrix with two diagonals
Wren
A terminal based solution as I don't like asking people to view external images. <lang ecmascript>var specialMatrix = Fn.new { |n|
for (i in 0...n) {
for (j in 0...n) {
System.write((i == j || i + j == n - 1) ? "1 " : "0 ")
}
System.print()
}
}
specialMatrix.call(6) // even n System.print() specialMatrix.call(7) // odd n</lang>
- Output:
1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1
XPL0
<lang XPL0>proc DrawMat(S); int S, I, J; [for I:= 0 to S-1 do
[for J:= 0 to S-1 do
Text(0, if J=I or J=S-1-I then "1 " else "0 ");
CrLf(0);
];
]; [DrawMat(6); CrLf(0);
DrawMat(7); CrLf(0);
]</lang>
- Output:
1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1