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.

11l[edit]

Translation of: Python
F min_cells_matrix(siz)
   R (0 .< siz).map(row -> (0 .< @siz).map(col -> min(@row, col, @@siz - @row - 1, @@siz - col - 1)))

F display_matrix(mat)
   V siz = mat.len
   V spaces = I siz < 20 {2} E I siz < 200 {3} E 4
   print("\nMinimum number of cells after, before, above and below "siz‘ x ’siz‘ square:’)
   L(row) 0 .< siz
      print(mat[row].map(n -> String(n).rjust(@spaces)).join(‘’))

L(siz) [23, 10, 9, 2, 1]
   display_matrix(min_cells_matrix(siz))
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

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

APL[edit]

Works with: Dyalog APL
n_by_n  (⌽⌊⊖)(∘.¯1+⍳)
n_by_n¨ 2 3 9 10
Output:
┌───┬─────┬─────────────────┬───────────────────┐
│0 0│0 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 0│0 1 1 1 1 1 1 1 0│0 1 1 1 1 1 1 1 1 0│
│   │0 0 0│0 1 2 2 2 2 2 1 0│0 1 2 2 2 2 2 2 1 0│
│   │     │0 1 2 3 3 3 2 1 0│0 1 2 3 3 3 3 2 1 0│
│   │     │0 1 2 3 4 3 2 1 0│0 1 2 3 4 4 3 2 1 0│
│   │     │0 1 2 3 3 3 2 1 0│0 1 2 3 4 4 3 2 1 0│
│   │     │0 1 2 2 2 2 2 1 0│0 1 2 3 3 3 3 2 1 0│
│   │     │0 1 1 1 1 1 1 1 0│0 1 2 2 2 2 2 2 1 0│
│   │     │0 0 0 0 0 0 0 0 0│0 1 1 1 1 1 1 1 1 0│
│   │     │                 │0 0 0 0 0 0 0 0 0 0│
└───┴─────┴─────────────────┴───────────────────┘

AutoHotkey[edit]

gridSize := 10

grid := []
loop % gridSize {
    row := A_Index
    loop % gridSize {
        col := A_Index
        grid[row, col] := Min(row, col, gridSize+1-row, gridSize+1-col) - 1
    }
}

for row, obj in Grid {
    for col, v in obj
        result .= v "  "
    result .= "`n"
}
MsgBox % result
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  

AWK[edit]

# syntax: GAWK -f MINIMUM_NUMBER_OF_CELLS_AFTER_BEFORE_ABOVE_AND_BELOW_NXN_SQUARES.AWK
BEGIN {
    leng = split("3,4,9,10,23",arr,",")
    for (k=1; k<=leng; k++) {
      n = arr[k]
      printf("\nDistance to nearest edge: %dx%d\n",n,n)
      for (i=1; i<=n; i++) {
        for (j=1; j<=n; j++) {
          printf("%2d ",min(min(i-1,n-i),min(j-1,n-j)))
        }
        printf("\n")
      }
    }
    exit(0)
}
function min(x,y) { return((x < y) ? x : y) }
Output:
Distance to nearest edge: 3x3
 0  0  0
 0  1  0
 0  0  0

Distance to nearest edge: 4x4
 0  0  0  0
 0  1  1  0
 0  1  1  0
 0  0  0  0

Distance to nearest edge: 9x9
 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

Distance to nearest edge: 10x10
 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

Distance to nearest edge: 23x23
 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


BASIC[edit]

BASIC256[edit]

Translation of: FreeBASIC
function min(a, b)
	if a<=b then return a else return b
end function

subroutine minab(n)
	for i = 1 to n
		for j = 1 to n
			print min(min(i-1, n-i), min(j-1, n-j)); "  ";
		next j
		print
	next i
end subroutine

call minab(10)
end
Output:
Igual que la entrada de FreeBASIC.

QBasic[edit]

Works with: QBasic
Works with: QuickBasic
Translation of: FreeBASIC
DECLARE FUNCTION min! (a!, b!)
DECLARE SUB minab (n!)

CLS
minab (10)
END

FUNCTION min (a, b)
	IF a <= b THEN min = a ELSE min = b
END FUNCTION

SUB minab (n)
	FOR i = 1 TO n
		FOR j = 1 TO n
			PRINT USING "## "; min(min(i - 1, n - i), min(j - 1, n - j));
		NEXT j
		PRINT
	NEXT i
END SUB
Output:
Igual que la entrada de FreeBASIC.

True BASIC[edit]

Translation of: QBasic
FUNCTION min (a, b)
    IF a <= b THEN LET min = a ELSE LET min = b
END FUNCTION

SUB minab (n)
    FOR i = 1 TO n
        FOR j = 1 TO n
            PRINT USING "## ": min(min(i - 1, n - i), min(j - 1, n - j));
        NEXT j
        PRINT
    NEXT i
END SUB

CALL minab (10)
END
Output:
Igual que la entrada de QBasic.

Yabasic[edit]

Translation of: FreeBASIC
minab(10)
end

sub minab(n)
	for i = 1 to n
		for j = 1 to n
			print min(min(i-1, n-i), min(j-1, n-j)) using ("##");
		next j
		print
	next i
end sub
Output:
Igual que la entrada de FreeBASIC.


BCPL[edit]

get "libhdr"

let min(a,b) = a<b -> a, b

let minNbyN(n, cw) be
    for y=0 to n-1
    $(  for x=0 to n-1 do
            writed(min(x, min(n-x-1, min(y, n-y-1))), cw)
        wrch('*N')
    $)
    
let start() be minNbyN(10, 3)
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

BQN[edit]

NByN ← ⌊⌜˜ ⌽⊸⌊∘↕
NByN¨ 2‿3‿9‿10
Output:
┌─                                                                 
· ┌─      ┌─        ┌─                    ┌─                       
  ╵ 0 0   ╵ 0 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 0     0 1 1 1 1 1 1 1 0     0 1 1 1 1 1 1 1 1 0    
        ┘   0 0 0     0 1 2 2 2 2 2 1 0     0 1 2 2 2 2 2 2 1 0    
                  ┘   0 1 2 3 3 3 2 1 0     0 1 2 3 3 3 3 2 1 0    
                      0 1 2 3 4 3 2 1 0     0 1 2 3 4 4 3 2 1 0    
                      0 1 2 3 3 3 2 1 0     0 1 2 3 4 4 3 2 1 0    
                      0 1 2 2 2 2 2 1 0     0 1 2 3 3 3 3 2 1 0    
                      0 1 1 1 1 1 1 1 0     0 1 2 2 2 2 2 2 1 0    
                      0 0 0 0 0 0 0 0 0     0 1 1 1 1 1 1 1 1 0    
                                        ┘   0 0 0 0 0 0 0 0 0 0    
                                                                ┘  
                                                                  ┘

C[edit]

Translation of: FreeBASIC
#include<stdio.h>
#include<stdlib.h>

#define min(a, b) (a<=b?a:b)

void minab( unsigned int n ) {
    int i, j;
    for(i=0;i<n;i++) {
        for(j=0;j<n;j++) {
            printf( "%2d  ", min( min(i, n-1-i), min(j, n-1-j) ));
        }
        printf( "\n" );
    }
    return;
}

int main(void) {
    minab(10);
    return 0;
}
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

CLU[edit]

min = proc [T: type] (a, b: T) returns (T)
      where T has lt: proctype (T,T) returns (bool)
    if a<b
        then return(a)
        else return(b)
    end
end min

min_n_by_n = proc (n: int) returns (array[array[int]])
    ai = array[int]
    aai = array[ai]
    t: aai := aai$[]
    for y: int in int$from_to(0, n-1) do
        aai$addh(t, ai$[])
        for x: int in int$from_to(0, n-1) do
            i: int := min[int](x, min[int](n-x-1, min[int](y, n-y-1)))
            ai$addh(aai$top(t), i)
        end
    end
    return(t)
end min_n_by_n

print_table = proc (s: stream, table: array[array[int]])
    ai = array[int]
    aai = array[ai]
    for line: ai in aai$elements(table) do
        for item: int in ai$elements(line) do 
            stream$puts(s, int$unparse(item) || " ")
        end
        stream$putl(s, "")
    end
end print_table

start_up = proc ()
    print_table(stream$primary_output(), min_n_by_n(10))
end start_up
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

COBOL[edit]

       IDENTIFICATION DIVISION.
       PROGRAM-ID. MINIMUM-CELLS-N-BY-N.
       
       DATA DIVISION.
       WORKING-STORAGE SECTION.
       01 TABLE-SIZE        PIC 99 VALUE 10.
       01 X                 PIC 99.
       01 Y                 PIC 99.
       01 ITEM              PIC 99.
       01 MIN               PIC 99.
       
       01 FMT               PIC ZZ9.
       01 TABLE-LINE        PIC X(72).
       01 LINE-PTR          PIC 99.
       
       PROCEDURE DIVISION.
       BEGIN.
           PERFORM MAKE-LINE VARYING Y FROM 0 BY 1 
               UNTIL Y IS EQUAL TO TABLE-SIZE.
           STOP RUN.
       
       MAKE-LINE.
           MOVE SPACES TO TABLE-LINE.
           MOVE 1 TO LINE-PTR.
           PERFORM ADD-ITEM VARYING X FROM 0 BY 1
               UNTIL X IS EQUAL TO TABLE-SIZE.
           DISPLAY TABLE-LINE.
           
       ADD-ITEM.
           PERFORM FIND-MINIMUM-VALUE.
           MOVE MIN TO FMT.
           STRING FMT DELIMITED BY SIZE INTO TABLE-LINE 
               WITH POINTER LINE-PTR.
       
       FIND-MINIMUM-VALUE.
           MOVE X TO MIN.
           MOVE Y TO ITEM.
           PERFORM CHECK-MINIMUM.
           COMPUTE ITEM = TABLE-SIZE - Y - 1.
           PERFORM CHECK-MINIMUM.
           COMPUTE ITEM = TABLE-SIZE - X - 1.
           PERFORM CHECK-MINIMUM.
       
       CHECK-MINIMUM.
           IF ITEM IS LESS THAN MIN, MOVE ITEM TO MIN.
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

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

Fermat[edit]

Func Min(a, b) = if a<=b then a else b fi.;
n:=10;
Array x[n, n];
[x]:= [<i=1,n> <j=1,n> Min(Min(i-1,n-i),Min(j-1,n-j))];
[x];
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   ]]

FreeBASIC[edit]

#define min(a, b) Iif(a<=b,a,b)

sub minab( n as uinteger )
    for i as uinteger = 1 to n
        for j as uinteger = 1 to n
            print using "## ";min( min(i-1, n-i), min(j-1, n-j) );
        next j
        print
    next i
end sub

minab(10)
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

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] 

GW-BASIC[edit]

10 N = 10
20 FOR I = 0 TO N - 1
30 IF I < N - 1 - I THEN DI = I ELSE DI = N - 1 - I
40 FOR J = 0 TO N - 1
50 IF J < N - 1 - J THEN DJ = J ELSE DJ = N - 1 - J
60 IF DI < DJ THEN M = DI ELSE M = DJ
70 PRINT USING "##  ";M;
80 NEXT J
90 PRINT
100 NEXT I

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

or in terms of Data.Matrix:

import Data.Matrix ( matrix, Matrix )

distanceToEdge :: Int -> Matrix Int
distanceToEdge n =
  matrix
    n
    n
    (\(a, b) -> minimum [pred a, pred b, n - a, n - b])

main :: IO ()
main =
  mapM_ print $ distanceToEdge <$> [10, 9, 2, 1]
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 │
└   ┘

J[edit]

nByN=: (|."1<.|.)@(<./~@i.)
nByN each 2 3 9 10
Output:
┌───┬─────┬─────────────────┬───────────────────┐
│0 0│0 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 0│0 1 1 1 1 1 1 1 0│0 1 1 1 1 1 1 1 1 0│
│   │0 0 0│0 1 2 2 2 2 2 1 0│0 1 2 2 2 2 2 2 1 0│
│   │     │0 1 2 3 3 3 2 1 0│0 1 2 3 3 3 3 2 1 0│
│   │     │0 1 2 3 4 3 2 1 0│0 1 2 3 4 4 3 2 1 0│
│   │     │0 1 2 3 3 3 2 1 0│0 1 2 3 4 4 3 2 1 0│
│   │     │0 1 2 2 2 2 2 1 0│0 1 2 3 3 3 3 2 1 0│
│   │     │0 1 1 1 1 1 1 1 0│0 1 2 2 2 2 2 2 1 0│
│   │     │0 0 0 0 0 0 0 0 0│0 1 1 1 1 1 1 1 1 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

Modula-2[edit]

MODULE MinNByN;
FROM InOut IMPORT WriteCard, WriteLn;

PROCEDURE minNbyN(n, cellwidth: CARDINAL);
    VAR x, y: CARDINAL;
    
    PROCEDURE min(a, b: CARDINAL): CARDINAL;
    BEGIN
        IF a < b THEN RETURN a;
        ELSE RETURN b;
        END;
    END min;
BEGIN
    FOR y := 0 TO n-1 DO
        FOR x := 0 TO n-1 DO
            WriteCard(min(x, min(n-x-1, min(y, n-y-1))), cellwidth);
        END;
        WriteLn();
    END;
END minNbyN;

BEGIN
    minNbyN(10, 3);
END MinNByN.
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

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

PARI/GP[edit]

n=10
matrix(n,n,i,j,min(min(i-1,n-i),min(j-1,n-j)))
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]

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")

PILOT[edit]

C :size=10
  :y=0
*line
C :$l=
  :x=0
*item
C :sy=(size-y)-1
  :sx=(size-x)-1
  :i=x
C (y<i):i=y
C (sy<i):i=sy
C (sx<i):i=sx
  :$l=$l #i
  :x=x+1
J (x<size):*item
T :$l
C :y=y+1
J (y<size):*line
E :
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

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

and in terms of a generalized matrix function:

'''Minimum distances to edge of matrix'''

from itertools import chain


# distanceFromEdge :: Int -> [[Int]]
def distanceFromEdge(n):
    '''A matrix of minimum distances to the
       edge of the matrix.
    '''
    return matrix(n)(n)(
        lambda row, col: min([
            row - 1, col - 1,
            n - row, n - col
        ])
    )


# ------------------------- TEST -------------------------
# main :: IO ()
def main():
    '''Test'''
    for n in [10, 9, 2, 1]:
        print(
            showMatrix(
                distanceFromEdge(n)
            ) + "\n"
        )


# ----------------------- GENERIC ------------------------

# matrix :: Int -> Int -> ((Int, Int) -> a) -> [[a]]
def matrix(nRows):
    '''A matrix of a given number of columns and rows,
       in which each value is a given function over the
       tuple of its (one-based) row and column indices.
    '''
    def go(nCols):
        def g(f):
            return [
                [f(y, x) for x in range(1, 1 + nCols)]
                for y in range(1, 1 + nRows)
            ]
        return g
    return go


# 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 ''


# 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...

Ruby[edit]

def dist2edge(n)
  width = (n/2).to_s.size+1
  m = n-1
  (0..m).map do |x|
    (0..m).map{|y| [x, y, m-x, m-y].min.to_s.center(width) }.join
  end
end
    
puts dist2edge(10)
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 

Vlang[edit]

Translation of: Go
fn print_min_cells(n int) {
    println("Minimum number of cells after, before, above and below $n x $n square:")
    for r in 0..n {
        mut cells := []int{len: n}
        for c in 0..n {
            nums := [n - r - 1, r, c, n - c - 1]
            mut min := n
            for num in nums {
                if num < min {
                    min = num
                }
            }
            cells[c] = min
        }
        println(cells)
    }
}
 
fn main() {
    for n in [23, 10, 9, 2, 1] {
        print_min_cells(n)
        println('')
    }
}
Output:
Same as Go entry

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

XPL0[edit]

func Min(A, B);
int  A, B;
return if A<B then A else B;

def N=10, M=N-1, C=M/2;
int X, Y, VX, VY;
[for Y:= 0 to M do
    [for X:= 0 to M do
        [VX:= if X <= C then X else M-X;
         VY:= if Y <= C then Y else M-Y;
         IntOut(0, Min(VX, VY));  ChOut(0, ^ );
        ];
    CrLf(0);
    ];
]
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