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Minimum number of cells after, before, above and below NxN squares

From Rosetta Code
Minimum number of cells after, before, above and below NxN squares is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Task

Find and show on this page the minimum number of cells after, before, above and below   N×N   squares,   where   N = 10.

ALGOL 68[edit]

Translation of: Wren

As with the Algol W version, the cells are printed as they are calculated. Ensures the counts are shown in the same width.

BEGIN # show the minimum number of cells above, below, before and after each #
# cell in a suare matrix #
 
PROC min = ( INT a, b )INT: IF a < b THEN a ELSE b FI;
 
PROC print min cells = ( INT n )VOID:
BEGIN
# deduce how many digits we need to show so the counts are all #
# the same width #
INT w = BEGIN
INT width := 1, v := ( ( n - ( ABS NOT ODD n ) ) OVER 2 );
WHILE v > 9 DO v OVERAB 10; width +:= 1 OD;
width
END;
print( ( "Minimum number of cells after, before, above and below "
, whole( n, 0 )
, " x "
, whole( n, 0 )
, " square:"
, newline
)
);
FOR r FROM 0 TO n - 1 DO
FOR c FROM 0 TO n - 1 DO print( ( whole( min( n-r-1, min( r, min( c, n-c-1 ) ) ), -w ), " " ) ) OD;
print( ( newline ) )
OD
END # print min cells # ;
 
[]INT tests = ( 10, 9, 2, 1, 21 );
FOR i FROM LWB tests TO UPB tests DO
print min cells( tests[ i ] );
print( ( newline ) )
OD
 
END
Output:
Minimum number of cells after, before, above and below 10 x 10 square:
0 0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 9 x 9 square:
0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 3 4 3 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 2 x 2 square:
0 0
0 0

Minimum number of cells after, before, above and below 1 x 1 square:
0

Minimum number of cells after, before, above and below 21 x 21 square:
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
 0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
 0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
 0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
 0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
 0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  7  7  7  7  7  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  8  8  8  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  9  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9 10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  9  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  8  8  8  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  7  7  7  7  7  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
 0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
 0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
 0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
 0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
 0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

ALGOL W[edit]

Translation of: Wren

This version avoids generating an explicit list of elements for each row in the matrix and just prints the elements as they are calculated. The elements are all shown in the same field width.

begin % show the minimum number of cells above, below, before and after each %
 % cell in a square matrix  %
 
integer procedure min4( integer value a, b, c, d ) ;
begin
integer m;
m := a;
if b < m then m := b;
if c < m then m := c;
if d < m then m := d;
m
end min4 ;
 
procedure printMinCells ( integer value n ) ;
begin
integer w, v;
w := 1; v := ( ( n - ( if odd( n ) then 1 else 0 ) ) div 2 );
while v > 9 do begin v := v div 10; w := w + 1 end;
write( i_w := 1, s_w := 0, "Minimum number of cells after, before, above and below ", n, " x ", n, " square:" );
write();
for r := 0 until n - 1 do begin
for c := 0 until n - 1 do writeon( i_w := w, s_w := 1, min4( n-r-1, r, c, n-c-1 ) );
write()
end for_r
end printMinCells ;
 
for n := 10, 9, 2, 1 do printMinCells( n )
 
end.
Output:
Minimum number of cells after, before, above and below 10 x 10 square:
0 0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 9 x 9 square:
0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 3 4 3 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 2 x 2 square:
0 0
0 0

Minimum number of cells after, before, above and below 1 x 1 square:
0

Minimum number of cells after, before, above and below 21 x 21 square:
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
 0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
 0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
 0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
 0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
 0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  7  7  7  7  7  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  8  8  8  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  9  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9 10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  9  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  8  8  8  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  7  7  7  7  7  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
 0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
 0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
 0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
 0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
 0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

Excel[edit]

LAMBDA[edit]

Binding the name distancesToEdge to the following lambda expression in the Name Manager of the Excel WorkBook:

(See LAMBDA: The ultimate Excel worksheet function)

=LAMBDA(n,
LET(
lastIndex, n - 1,
LAMBDA(i,
LET(
x, MOD(i, n),
y, QUOTIENT(i, n),
 
evaluate(
"MIN({" &
TEXT(x, "0") & "," &
TEXT(y, "0") & "," &
TEXT(lastIndex - x, "0") & "," &
TEXT(lastIndex - y, "0") &
"})"
)
)
)(SEQUENCE(n, n, 0, 1))
)
)
Output:

The single formula in the cell B2 defines the whole matrix value which spills out to column K and row 11:

fx =distancesToEdge(A2)
A B C D E F G H I J K
1 Dimension
2 10 0 0 0 0 0 0 0 0 0 0
3 0 1 1 1 1 1 1 1 1 0
4 0 1 2 2 2 2 2 2 1 0
5 0 1 2 3 3 3 3 2 1 0
6 0 1 2 3 4 4 3 2 1 0
7 0 1 2 3 4 4 3 2 1 0
8 0 1 2 3 3 3 3 2 1 0
9 0 1 2 2 2 2 2 2 1 0
10 0 1 1 1 1 1 1 1 1 0
11 0 0 0 0 0 0 0 0 0 0
12
13 9 0 0 0 0 0 0 0 0 0
14 0 1 1 1 1 1 1 1 0
15 0 1 2 2 2 2 2 1 0
16 0 1 2 3 3 3 2 1 0
17 0 1 2 3 4 3 2 1 0
18 0 1 2 3 3 3 2 1 0
19 0 1 2 2 2 2 2 1 0
20 0 1 1 1 1 1 1 1 0
21 0 0 0 0 0 0 0 0 0
22
23 2 0 0
24 0 0
25
26 1 0

F#[edit]

 
// Minimum number of cells after, before, above and below NxN squares. Nigel Galloway: August 1st., 2021
printfn "%A" (Array2D.init 10 10 (fun n g->List.min [n;g;9-n;9-g]))
printfn "\n%A" (Array2D.init 9 9 (fun n g->List.min [n;g;8-n;8-g]))
 
Output:
[[0; 0; 0; 0; 0; 0; 0; 0; 0; 0]
 [0; 1; 1; 1; 1; 1; 1; 1; 1; 0]
 [0; 1; 2; 2; 2; 2; 2; 2; 1; 0]
 [0; 1; 2; 3; 3; 3; 3; 2; 1; 0]
 [0; 1; 2; 3; 4; 4; 3; 2; 1; 0]
 [0; 1; 2; 3; 4; 4; 3; 2; 1; 0]
 [0; 1; 2; 3; 3; 3; 3; 2; 1; 0]
 [0; 1; 2; 2; 2; 2; 2; 2; 1; 0]
 [0; 1; 1; 1; 1; 1; 1; 1; 1; 0]
 [0; 0; 0; 0; 0; 0; 0; 0; 0; 0]]

[[0; 0; 0; 0; 0; 0; 0; 0; 0]
 [0; 1; 1; 1; 1; 1; 1; 1; 0]
 [0; 1; 2; 2; 2; 2; 2; 1; 0]
 [0; 1; 2; 3; 3; 3; 2; 1; 0]
 [0; 1; 2; 3; 4; 3; 2; 1; 0]
 [0; 1; 2; 3; 3; 3; 2; 1; 0]
 [0; 1; 2; 2; 2; 2; 2; 1; 0]
 [0; 1; 1; 1; 1; 1; 1; 1; 0]
 [0; 0; 0; 0; 0; 0; 0; 0; 0]]

Factor[edit]

Works with: Factor version 0.99 2021-06-02
USING: io kernel math math.matrices math.vectors prettyprint
sequences ;
 
: square ( n -- matrix )
[ <cartesian-square-indices> ] keep 1 - dup
'[ dup sum _ > [ _ v-n vabs ] when infimum ] matrix-map ;
 
{ 10 9 2 1 } [ square simple-table. nl ] each
Output:
0 0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 3 4 3 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0

0 0
0 0

0

Go[edit]

Translation of: Wren
package main
 
import "fmt"
 
func printMinCells(n int) {
fmt.Printf("Minimum number of cells after, before, above and below %d x %d square:\n", n, n)
p := 1
if n > 20 {
p = 2
}
for r := 0; r < n; r++ {
cells := make([]int, n)
for c := 0; c < n; c++ {
nums := []int{n - r - 1, r, c, n - c - 1}
min := n
for _, num := range nums {
if num < min {
min = num
}
}
cells[c] = min
}
fmt.Printf("%*d \n", p, cells)
}
}
 
func main() {
for _, n := range []int{23, 10, 9, 2, 1} {
printMinCells(n)
fmt.Println()
}
}
Output:
Minimum number of cells after, before, above and below 23 x 23 square:
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0] 
[ 0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0] 
[ 0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0] 
[ 0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0] 
[ 0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0] 
[ 0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  7  8  9 10 11 10  9  8  7  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0] 
[ 0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0] 
[ 0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0] 
[ 0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0] 
[ 0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0] 
[ 0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0] 
[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0] 

Minimum number of cells after, before, above and below 10 x 10 square:
[0 0 0 0 0 0 0 0 0 0] 
[0 1 1 1 1 1 1 1 1 0] 
[0 1 2 2 2 2 2 2 1 0] 
[0 1 2 3 3 3 3 2 1 0] 
[0 1 2 3 4 4 3 2 1 0] 
[0 1 2 3 4 4 3 2 1 0] 
[0 1 2 3 3 3 3 2 1 0] 
[0 1 2 2 2 2 2 2 1 0] 
[0 1 1 1 1 1 1 1 1 0] 
[0 0 0 0 0 0 0 0 0 0] 

Minimum number of cells after, before, above and below 9 x 9 square:
[0 0 0 0 0 0 0 0 0] 
[0 1 1 1 1 1 1 1 0] 
[0 1 2 2 2 2 2 1 0] 
[0 1 2 3 3 3 2 1 0] 
[0 1 2 3 4 3 2 1 0] 
[0 1 2 3 3 3 2 1 0] 
[0 1 2 2 2 2 2 1 0] 
[0 1 1 1 1 1 1 1 0] 
[0 0 0 0 0 0 0 0 0] 

Minimum number of cells after, before, above and below 2 x 2 square:
[0 0] 
[0 0] 

Minimum number of cells after, before, above and below 1 x 1 square:
[0] 

Haskell[edit]

import Data.List.Split (chunksOf)
 
----------- SHORTEST DISTANCES TO EDGE OF MATRIX ---------
 
distancesToEdge :: Int -> [[Int]]
distancesToEdge n =
( \i ->
chunksOf n $
(\(x, y) -> minimum [x, y, i - x, i - y])
<$> (fmap (,) >>= (<*>)) [0 .. i]
)
$ pred n
 
--------------------------- TEST -------------------------
main :: IO ()
main =
mapM_ putStrLn $
showMatrix . distancesToEdge <$> [10, 9, 2, 1]
 
------------------------- DISPLAY ------------------------
 
showMatrix :: Show a => [[a]] -> String
showMatrix m =
let w = (succ . maximum) $ fmap (length . show) =<< m
rjust n c = (drop . length) <*> (replicate n c <>)
in unlines (unwords . fmap (rjust w ' ' . show) <$> m)
Output:
 0  0  0  0  0  0  0  0  0  0
 0  1  1  1  1  1  1  1  1  0
 0  1  2  2  2  2  2  2  1  0
 0  1  2  3  3  3  3  2  1  0
 0  1  2  3  4  4  3  2  1  0
 0  1  2  3  4  4  3  2  1  0
 0  1  2  3  3  3  3  2  1  0
 0  1  2  2  2  2  2  2  1  0
 0  1  1  1  1  1  1  1  1  0
 0  0  0  0  0  0  0  0  0  0

 0  0  0  0  0  0  0  0  0
 0  1  1  1  1  1  1  1  0
 0  1  2  2  2  2  2  1  0
 0  1  2  3  3  3  2  1  0
 0  1  2  3  4  3  2  1  0
 0  1  2  3  3  3  2  1  0
 0  1  2  2  2  2  2  1  0
 0  1  1  1  1  1  1  1  0
 0  0  0  0  0  0  0  0  0

 0  0
 0  0

 0

Julia[edit]

function printNbyN(sizes)
for N in sizes
mat = zeros(Int, N, N)
println("\n\nMinimum number of cells after, before, above and below $N x $N square:")
for r in 1:N, c in 1:N
mat[r, c] = min(r - 1, c - 1, N - r, N - c)
end
display(mat)
end
end
 
printNbyN([23, 10, 9, 2, 1])
 
 
Output:
  
Minimum number of cells after, before, above and below 23 x 23 square:
23×23 Matrix{Int64}:
 0  0  0  0  0  0  0  0  0  0   0   0   0  0  0  0  0  0  0  0  0  0  0
 0  1  1  1  1  1  1  1  1  1   1   1   1  1  1  1  1  1  1  1  1  1  0
 0  1  2  2  2  2  2  2  2  2   2   2   2  2  2  2  2  2  2  2  2  1  0
 0  1  2  3  3  3  3  3  3  3   3   3   3  3  3  3  3  3  3  3  2  1  0
 0  1  2  3  4  4  4  4  4  4   4   4   4  4  4  4  4  4  4  3  2  1  0
 0  1  2  3  4  5  5  5  5  5   5   5   5  5  5  5  5  5  4  3  2  1  0
 0  1  2  3  4  5  6  6  6  6   6   6   6  6  6  6  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  7  7   7   7   7  7  7  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  8   8   8   8  8  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9   9   9   9  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  10  10  10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  10  11  10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  10  10  10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9   9   9   9  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  8   8   8   8  8  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  7  7   7   7   7  7  7  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  6  6  6   6   6   6  6  6  6  6  5  4  3  2  1  0
 0  1  2  3  4  5  5  5  5  5   5   5   5  5  5  5  5  5  4  3  2  1  0
 0  1  2  3  4  4  4  4  4  4   4   4   4  4  4  4  4  4  4  3  2  1  0
 0  1  2  3  3  3  3  3  3  3   3   3   3  3  3  3  3  3  3  3  2  1  0
 0  1  2  2  2  2  2  2  2  2   2   2   2  2  2  2  2  2  2  2  2  1  0
 0  1  1  1  1  1  1  1  1  1   1   1   1  1  1  1  1  1  1  1  1  1  0
 0  0  0  0  0  0  0  0  0  0   0   0   0  0  0  0  0  0  0  0  0  0  0

Minimum number of cells after, before, above and below 10 x 10 square:
10×10 Matrix{Int64}:
 0  0  0  0  0  0  0  0  0  0
 0  1  1  1  1  1  1  1  1  0
 0  1  2  2  2  2  2  2  1  0
 0  1  2  3  3  3  3  2  1  0
 0  1  2  3  4  4  3  2  1  0
 0  1  2  3  4  4  3  2  1  0
 0  1  2  3  3  3  3  2  1  0
 0  1  2  2  2  2  2  2  1  0
 0  1  1  1  1  1  1  1  1  0
 0  0  0  0  0  0  0  0  0  0

Minimum number of cells after, before, above and below 9 x 9 square:
9×9 Matrix{Int64}:
 0  0  0  0  0  0  0  0  0
 0  1  1  1  1  1  1  1  0
 0  1  2  2  2  2  2  1  0
 0  1  2  3  3  3  2  1  0
 0  1  2  3  4  3  2  1  0
 0  1  2  3  3  3  2  1  0
 0  1  2  2  2  2  2  1  0
 0  1  1  1  1  1  1  1  0
 0  0  0  0  0  0  0  0  0

Minimum number of cells after, before, above and below 2 x 2 square:
2×2 Matrix{Int64}:
 0  0
 0  0

Minimum number of cells after, before, above and below 1 x 1 square:
1×1 Matrix{Int64}:
 0

MiniZinc[edit]

 
%Minimum number of cells after, before, above and below NxN squares. Nigel Galloway, August 3rd., 2021
int: Size=10; int: S=Size-1; set of int: N=0..S;
array[N,N] of var int: G = array2d(N,N,[min([n,g,S-n,S-g])|n,g in N]);
output([show2d(G)])
 
Output:
[| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
   0, 1, 1, 1, 1, 1, 1, 1, 1, 0 |
   0, 1, 2, 2, 2, 2, 2, 2, 1, 0 |
   0, 1, 2, 3, 3, 3, 3, 2, 1, 0 |
   0, 1, 2, 3, 4, 4, 3, 2, 1, 0 |
   0, 1, 2, 3, 4, 4, 3, 2, 1, 0 |
   0, 1, 2, 3, 3, 3, 3, 2, 1, 0 |
   0, 1, 2, 2, 2, 2, 2, 2, 1, 0 |
   0, 1, 1, 1, 1, 1, 1, 1, 1, 0 |
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |]
----------
Finished in 209msec

Nim[edit]

Translation of: Go
import strutils
 
proc printMinCells(n: Positive) =
echo "Minimum number of cells after, before, above and below $1 x $1 square:".format(n)
var cells = newSeq[int](n)
for r in 0..<n:
for c in 0..<n:
cells[c] = min([n - r - 1, r, c, n - c - 1])
echo cells.join(" ")
 
when isMainModule:
for n in [10, 9, 2, 1]:
printMinCells(n)
echo()
Output:
Minimum number of cells after, before, above and below 10 x 10 square:
0 0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 9 x 9 square:
0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 3 4 3 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 2 x 2 square:
0 0
0 0

Minimum number of cells after, before, above and below 1 x 1 square:
0

Pascal[edit]

Using symmetry within row and col.Fill only the middle and let the values before in place.

program mindistance;
{$IFDEF FPC} //used fpc 3.2.1
{$MODE DELPHI} {$OPTIMIZATION ON,ALL} {$COPERATORS ON}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF}
uses
sysutils
{$IFDEF WINDOWS},Windows{$ENDIF}
;
 
type
tMinDist = array of Uint32;
tpMinDist= pUint32;
var
dgtwidth : NativeUint;
OneRowElems : tMinDist;
 
function CalcDigitWidth(n: NativeUint):NativeUint;
begin
result:= 2;
while n>= 10 do
Begin
inc(result);
n := n DIV 10;
end;
end;
 
procedure OutOneRow(var OneRowElems:tMinDist);
var
one_digit,one_row :string;
i : NativeInt;
begin
one_row:= '';
For i := low(OneRowElems) to High(OneRowElems) do
begin
str(OneRowElems[i]:dgtwidth,one_digit);
one_row += one_digit;
end;
writeln(one_row);
end;
 
procedure OutSquareDist(MaxCoor : NativeUInt);
var
pRes : tpMinDist;
min_dist,row : NativeInt;
begin
//iniated with 0
setlength(OneRowElems,MaxCoor);
MaxCoor -= 1;//= High(OneRowElems);
pRes := @OneRowElems[0];
 
row := MaxCoor;
repeat
min_dist := MaxCoor-row;
if min_dist > row then
min_dist := row;
//fill the inner rest with min_dist
FillDWord(pRes[min_dist],(MaxCoor-2*min_dist+1),min_dist);
 
OutOneRow(OneRowElems);
 
dec(row);
until row < 0;
writeln;
setlength(OneRowElems,0);
end;
 
procedure Test(MaxCoor:NativeInt);
begin
if MaxCoor<= 0 then
EXIT;
write('Minimum number of cells after, before, above and below ');
writeln(MaxCoor,' x ',MaxCoor,' square:');
dgtwidth := CalcDigitWidth(NativeUint(MaxCoor) DIV 2);
OutSquareDist(MaxCoor);
end;
 
Begin
// Test(200*1000);// without output TIO.RUN Real time: 4.152 s CPU share: 97.70 %
Test(23);
Test(10);
Test(9);
Test(1);
end.
 
Output:
TIO.RUN
Minimum number of cells after, before, above and below 23 x 23 square:
  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
  0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
  0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
  0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
  0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
  0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9 10 11 10  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
  0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
  0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
  0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
  0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

Minimum number of cells after, before, above and below 10 x 10 square:
 0 0 0 0 0 0 0 0 0 0
 0 1 1 1 1 1 1 1 1 0
 0 1 2 2 2 2 2 2 1 0
 0 1 2 3 3 3 3 2 1 0
 0 1 2 3 4 4 3 2 1 0
 0 1 2 3 4 4 3 2 1 0
 0 1 2 3 3 3 3 2 1 0
 0 1 2 2 2 2 2 2 1 0
 0 1 1 1 1 1 1 1 1 0
 0 0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 9 x 9 square:
 0 0 0 0 0 0 0 0 0
 0 1 1 1 1 1 1 1 0
 0 1 2 2 2 2 2 1 0
 0 1 2 3 3 3 2 1 0
 0 1 2 3 4 3 2 1 0
 0 1 2 3 3 3 2 1 0
 0 1 2 2 2 2 2 1 0
 0 1 1 1 1 1 1 1 0
 0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 1 x 1 square:
 0

Perl[edit]

use strict;
use warnings;
use List::Util qw( max min );
 
for my $N (0, 1, 2, 6, 9, 23) {
my $fmt = ('%' . (1+length int $N/2) . 'd') x $N . "\n";
print "$N x $N distance to nearest edge:\n";
for my $row ( 0 .. $N-1 ) {
my @cols = map { min $_, $row, $N-1 - max $_, $row } 0 .. $N-1;
printf $fmt, @cols;
}
print "\n";
}
Output:
0 x 0 distance to nearest edge:

1 x 1 distance to nearest edge:
 0

2 x 2 distance to nearest edge:
 0 0
 0 0

6 x 6 distance to nearest edge:
 0 0 0 0 0 0
 0 1 1 1 1 0
 0 1 2 2 1 0
 0 1 2 2 1 0
 0 1 1 1 1 0
 0 0 0 0 0 0

9 x 9 distance to nearest edge:
 0 0 0 0 0 0 0 0 0
 0 1 1 1 1 1 1 1 0
 0 1 2 2 2 2 2 1 0
 0 1 2 3 3 3 2 1 0
 0 1 2 3 4 3 2 1 0
 0 1 2 3 3 3 2 1 0
 0 1 2 2 2 2 2 1 0
 0 1 1 1 1 1 1 1 0
 0 0 0 0 0 0 0 0 0

23 x 23 distance to nearest edge:
  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
  0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
  0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
  0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
  0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
  0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9 10 11 10  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
  0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
  0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
  0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
  0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

Phix[edit]

with javascript_semantics
procedure distance_to_edge(integer n)
    printf(1,"Minimum number of cells after, before, above and below %d x %d square:\n",n)
    for r=1 to n do
        for c=1 to n do
            printf(1,"%2d",min({r-1,c-1,n-r,n-c}))
        end for
        printf(1,"\n")
    end for 
end procedure
papply({23,10,9,2,1},distance_to_edge)
Output:
Minimum number of cells after, before, above and below 23 x 23 square:
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
 0 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 0
 0 1 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 1 0
 0 1 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 1 0
 0 1 2 3 4 5 5 5 5 5 5 5 5 5 5 5 5 5 4 3 2 1 0
 0 1 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 5 4 3 2 1 0
 0 1 2 3 4 5 6 7 7 7 7 7 7 7 7 7 6 5 4 3 2 1 0
 0 1 2 3 4 5 6 7 8 8 8 8 8 8 8 7 6 5 4 3 2 1 0
 0 1 2 3 4 5 6 7 8 9 9 9 9 9 8 7 6 5 4 3 2 1 0
 0 1 2 3 4 5 6 7 8 9101010 9 8 7 6 5 4 3 2 1 0
 0 1 2 3 4 5 6 7 8 9101110 9 8 7 6 5 4 3 2 1 0
 0 1 2 3 4 5 6 7 8 9101010 9 8 7 6 5 4 3 2 1 0
 0 1 2 3 4 5 6 7 8 9 9 9 9 9 8 7 6 5 4 3 2 1 0
 0 1 2 3 4 5 6 7 8 8 8 8 8 8 8 7 6 5 4 3 2 1 0
 0 1 2 3 4 5 6 7 7 7 7 7 7 7 7 7 6 5 4 3 2 1 0
 0 1 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 5 4 3 2 1 0
 0 1 2 3 4 5 5 5 5 5 5 5 5 5 5 5 5 5 4 3 2 1 0
 0 1 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 1 0
 0 1 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 1 0
 0 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 0
 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Minimum number of cells after, before, above and below 10 x 10 square:
 0 0 0 0 0 0 0 0 0 0
 0 1 1 1 1 1 1 1 1 0
 0 1 2 2 2 2 2 2 1 0
 0 1 2 3 3 3 3 2 1 0
 0 1 2 3 4 4 3 2 1 0
 0 1 2 3 4 4 3 2 1 0
 0 1 2 3 3 3 3 2 1 0
 0 1 2 2 2 2 2 2 1 0
 0 1 1 1 1 1 1 1 1 0
 0 0 0 0 0 0 0 0 0 0
Minimum number of cells after, before, above and below 9 x 9 square:
 0 0 0 0 0 0 0 0 0
 0 1 1 1 1 1 1 1 0
 0 1 2 2 2 2 2 1 0
 0 1 2 3 3 3 2 1 0
 0 1 2 3 4 3 2 1 0
 0 1 2 3 3 3 2 1 0
 0 1 2 2 2 2 2 1 0
 0 1 1 1 1 1 1 1 0
 0 0 0 0 0 0 0 0 0
Minimum number of cells after, before, above and below 2 x 2 square:
 0 0
 0 0
Minimum number of cells after, before, above and below 1 x 1 square:
 0

Although I rather like it the way it is, you could argue there should be more spacing on the 23x23, if you insist do this before the loops and use fmt on the innermost line:

    string fmt = sprintf("%%%dd",length(sprint(floor((n-1)/2)))+1)

or maybe just (good for n<=200 whereas the above goes on and on to "%4d", etc.)

    string fmt = iff(n<=20?"%2d":"%3d")

Python[edit]

def min_cells_matrix(siz):
return [[min(row, col, siz - row - 1, siz - col - 1) for col in range(siz)] for row in range(siz)]
 
def display_matrix(mat):
siz = len(mat)
spaces = 2 if siz < 20 else 3 if siz < 200 else 4
print(f"\nMinimum number of cells after, before, above and below {siz} x {siz} square:")
for row in range(siz):
print("".join([f"{n:{spaces}}" for n in mat[row]]))
 
def test_min_mat():
for siz in [23, 10, 9, 2, 1]:
display_matrix(min_cells_matrix(siz))
 
if __name__ == "__main__":
test_min_mat()
 
Output:
Minimum number of cells after, before, above and below 23 x 23 square:
  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
  0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
  0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
  0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
  0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
  0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9 10 11 10  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0
  0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
  0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
  0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
  0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
  0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

Minimum number of cells after, before, above and below 10 x 10 square:
 0 0 0 0 0 0 0 0 0 0
 0 1 1 1 1 1 1 1 1 0
 0 1 2 2 2 2 2 2 1 0
 0 1 2 3 3 3 3 2 1 0
 0 1 2 3 4 4 3 2 1 0
 0 1 2 3 4 4 3 2 1 0
 0 1 2 3 3 3 3 2 1 0
 0 1 2 2 2 2 2 2 1 0
 0 1 1 1 1 1 1 1 1 0
 0 0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 9 x 9 square:
 0 0 0 0 0 0 0 0 0
 0 1 1 1 1 1 1 1 0
 0 1 2 2 2 2 2 1 0
 0 1 2 3 3 3 2 1 0
 0 1 2 3 4 3 2 1 0
 0 1 2 3 3 3 2 1 0
 0 1 2 2 2 2 2 1 0
 0 1 1 1 1 1 1 1 0
 0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 2 x 2 square:
 0 0
 0 0

Minimum number of cells after, before, above and below 1 x 1 square:
 0

Or, disentangling computation from IO (separating model from display), and composing from generics:

'''Distance to edge of matrix'''
 
from itertools import chain, product
 
 
# distancesToEdge :: Int -> [[Int]]
def distancesToEdge(n):
'''A square matrix of dimension n, in which each
value is the minimum distance from the matrix
position to the edge of the matrix.
'''

lastIndex = n - 1
axis = range(0, n)
return chunksOf(n)([
min(x, y, lastIndex - x, lastIndex - y)
for (x, y) in product(axis, axis)
])
 
 
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Square matrices of distances to the matrix edge.
Sample matrices of dimensions [10, 9, 2, 1].
'''

print('\n\n'.join([
showMatrix(distancesToEdge(n)) for n
in [10, 9, 2, 1]
]))
 
 
# ----------------------- DISPLAY ------------------------
 
# showMatrix :: [[Int]] -> String
def showMatrix(xs):
'''String representation of xs
as a matrix.
'''

def go():
rows = [[str(x) for x in row] for row in xs]
w = max(map(len, chain.from_iterable(rows)))
return "\n".join(
" ".join(k.rjust(w, ' ') for k in row)
for row in rows
)
return go() if xs else ''
 
 
# ----------------------- GENERIC ------------------------
 
# chunksOf :: Int -> [a] -> [[a]]
def chunksOf(n):
'''A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
divisible, the final list will be shorter than n.
'''

def go(xs):
return [
xs[i:n + i] for i in range(0, len(xs), n)
] if 0 < n else None
return go
 
 
# MAIN ---
if __name__ == '__main__':
main()
Output:
0 0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 3 4 3 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0

0 0
0 0

0

Raku[edit]

sub distance-to-edge (\N) {
my $c = ceiling N / 2;
my $f = floor N / 2;
my @ul = ^$c .map: -> $x { [ ^$c .map: { min($x, $_) } ] }
@ul[$_].append: reverse @ul[$_; ^$f] for ^$c;
@ul.push: [ reverse @ul[$_] ] for reverse ^$f;
@ul
}
 
for 0, 1, 2, 6, 9, 23 {
my @dte = .&distance-to-edge;
my $max = chars max flat @dte».Slip;
 
say "\n$_ x $_ distance to nearest edge:";
.fmt("%{$max}d").say for @dte;
}
Output:
0 x 0 distance to nearest edge:

1 x 1 distance to nearest edge:
0

2 x 2 distance to nearest edge:
0 0
0 0

6 x 6 distance to nearest edge:
0 0 0 0 0 0
0 1 1 1 1 0
0 1 2 2 1 0
0 1 2 2 1 0
0 1 1 1 1 0
0 0 0 0 0 0

9 x 9 distance to nearest edge:
0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 3 4 3 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0

23 x 23 distance to nearest edge:
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
 0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
 0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
 0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
 0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
 0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9 10 11 10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
 0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
 0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
 0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
 0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
 0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

REXX[edit]

This REXX version automatically adjusts the width of each (cell) number displayed so that all displayed numbers are aligned.

/*REXX pgm finds the minimum# of cells after, before, above, & below a NxN square matrix*/
parse arg $ /*obtain optional arguments from the CL*/
if $='' | $="," then $= 21 10 9 2 1 /*Not specified? Then use the default.*/
@title= ' the minimum number of cells after, before, above, and below a '
do j=1 for words($); g= word($, j) /*process each of the squares specified*/
w= length( (g-1) % 2) /*width of largest number to be shown. */
say center(@title g"x"g ' square matrix ', 86) /*center title of output to be shown. */
say center('', 86, '─') /*display a separator line below title.*/
 
do r=0 for g /*process output for a NxN sq. matrix*/
_= left('', max(0, 85%(w+1) -g ) ) /*compute indentation output centering.*/
do c=0 for g
_= _ right( min(r, c, g-r-1, g-c-1), w) /*construct a row of the output matrix.*/
end /*c*/
say _ /*display a row of the output square. */
end /*r*/
 
say; say /*display 2 blank lines between outputs*/
end /*j*/ /*stick a fork in it, we're all done. */
output   when using the default inputs:
 the minimum number of cells after, before, above, and below a  21x21  square matrix
──────────────────────────────────────────────────────────────────────────────────────
         0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
         0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
         0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
         0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
         0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
         0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
         0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
         0  1  2  3  4  5  6  7  7  7  7  7  7  7  6  5  4  3  2  1  0
         0  1  2  3  4  5  6  7  8  8  8  8  8  7  6  5  4  3  2  1  0
         0  1  2  3  4  5  6  7  8  9  9  9  8  7  6  5  4  3  2  1  0
         0  1  2  3  4  5  6  7  8  9 10  9  8  7  6  5  4  3  2  1  0
         0  1  2  3  4  5  6  7  8  9  9  9  8  7  6  5  4  3  2  1  0
         0  1  2  3  4  5  6  7  8  8  8  8  8  7  6  5  4  3  2  1  0
         0  1  2  3  4  5  6  7  7  7  7  7  7  7  6  5  4  3  2  1  0
         0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
         0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
         0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
         0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
         0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
         0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
         0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0


 the minimum number of cells after, before, above, and below a  10x10  square matrix
──────────────────────────────────────────────────────────────────────────────────────
                                 0 0 0 0 0 0 0 0 0 0
                                 0 1 1 1 1 1 1 1 1 0
                                 0 1 2 2 2 2 2 2 1 0
                                 0 1 2 3 3 3 3 2 1 0
                                 0 1 2 3 4 4 3 2 1 0
                                 0 1 2 3 4 4 3 2 1 0
                                 0 1 2 3 3 3 3 2 1 0
                                 0 1 2 2 2 2 2 2 1 0
                                 0 1 1 1 1 1 1 1 1 0
                                 0 0 0 0 0 0 0 0 0 0


  the minimum number of cells after, before, above, and below a  9x9  square matrix
──────────────────────────────────────────────────────────────────────────────────────
                                  0 0 0 0 0 0 0 0 0
                                  0 1 1 1 1 1 1 1 0
                                  0 1 2 2 2 2 2 1 0
                                  0 1 2 3 3 3 2 1 0
                                  0 1 2 3 4 3 2 1 0
                                  0 1 2 3 3 3 2 1 0
                                  0 1 2 2 2 2 2 1 0
                                  0 1 1 1 1 1 1 1 0
                                  0 0 0 0 0 0 0 0 0


  the minimum number of cells after, before, above, and below a  2x2  square matrix
──────────────────────────────────────────────────────────────────────────────────────
                                         0 0
                                         0 0


  the minimum number of cells after, before, above, and below a  1x1  square matrix
──────────────────────────────────────────────────────────────────────────────────────
                                          0

Ring[edit]

 
see "working..." + nl
see "Minimum number of cells after, before, above and below NxN squares:" + nl
row = 0
cellsMin = []
 
for n = 1 to 10
for m = 1 to 10
cells = []
add(cells,m-1)
add(cells,10-m)
add(cells,n-1)
add(cells,10-n)
min = min(cells)
add(cellsMin,min)
next
next
 
ind = 100
for n = 1 to ind
row++
see "" + cellsMin[n] + " "
if row%10 = 0
see nl
ok
next
 
see "done..." + nl
 
Output:
working...
Minimum number of cells after, before, above and below NxN squares:
0 0 0 0 0 0 0 0 0 0 
0 1 1 1 1 1 1 1 1 0 
0 1 2 2 2 2 2 2 1 0 
0 1 2 3 3 3 3 2 1 0 
0 1 2 3 4 4 3 2 1 0 
0 1 2 3 4 4 3 2 1 0 
0 1 2 3 3 3 3 2 1 0 
0 1 2 2 2 2 2 2 1 0 
0 1 1 1 1 1 1 1 1 0 
0 0 0 0 0 0 0 0 0 0 
done...

Wren[edit]

Library: Wren-math
Library: Wren-fmt
import "/math" for Nums
import "/fmt" for Fmt
 
var printMinCells = Fn.new { |n|
System.print("Minimum number of cells after, before, above and below %(n) x %(n) square:")
var p = (n < 21) ? 1 : 2
for (r in 0...n) {
var cells = List.filled(n, 0)
for (c in 0...n) cells[c] = Nums.min([n-r-1, r, c, n-c-1])
Fmt.print("$*d", p, cells)
}
}
 
for (n in [23, 10, 9, 2, 1]) {
printMinCells.call(n)
System.print()
}
Output:
Minimum number of cells after, before, above and below 23 x 23 square:
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
 0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
 0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
 0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
 0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
 0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9 10 11 10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9 10 10 10  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  9  9  9  9  9  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  8  8  8  8  8  8  8  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  7  7  7  7  7  7  7  7  7  6  5  4  3  2  1  0
 0  1  2  3  4  5  6  6  6  6  6  6  6  6  6  6  6  5  4  3  2  1  0
 0  1  2  3  4  5  5  5  5  5  5  5  5  5  5  5  5  5  4  3  2  1  0
 0  1  2  3  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  3  2  1  0
 0  1  2  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  2  1  0
 0  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  0
 0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

Minimum number of cells after, before, above and below 10 x 10 square:
0 0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 4 4 3 2 1 0
0 1 2 3 3 3 3 2 1 0
0 1 2 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 9 x 9 square:
0 0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1 0
0 1 2 2 2 2 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 3 4 3 2 1 0
0 1 2 3 3 3 2 1 0
0 1 2 2 2 2 2 1 0
0 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0

Minimum number of cells after, before, above and below 2 x 2 square:
0 0
0 0

Minimum number of cells after, before, above and below 1 x 1 square:
0