Minimum number of cells after, before, above and below NxN squares
- 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
As with the Algol W version, the cells are printed as they are calculated. <lang algol68>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 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 ) ) ), 0 ), " " ) ) OD; print( ( newline ) ) OD END # print min cells # ; []INT tests = ( 10, 9, 2, 1 ); FOR i FROM LWB tests TO UPB tests DO print min cells( tests[ i ] ); print( ( newline ) ) OD
END</lang>
- 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
ALGOL W
This version avoids generating an explicit list of elements for each row in the matrix and just prints the elements as they are calculated. <lang algolw>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 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 := 1, 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.</lang>
- 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
Factor
<lang factor>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</lang>
- 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
<lang go>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) 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", cells) }
}
func main() {
for _, n := range []int{10, 9, 2, 1} { printMinCells(n) fmt.Println() }
}</lang>
- 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]
Julia
Set up the upper left quadrant and then mirror it. <lang julia>function printNbyN(sizes)
for N in sizes println("\nMinimum number of cells after, before, above and below $N x $N square:") mat = zeros(Int, N, N) for xy in CartesianIndices(mat) mat[xy] = minimum(Tuple(xy)) - 1 end for (rownum, row) in enumerate(eachrow(mat)) rownum > N ÷ 2 && (row .= mat[N - rownum + 1, :]) row[(N+2)÷2:end] .= reverse(row[begin:(N+1)÷2]) println(join(row, " ")) end end
end
printNbyN([10, 9, 2, 1])
</lang>
- 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
Nim
<lang Nim>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()</lang>
- 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
REXX
This REXX version automatically adjusts the width of each (cell) number displayed so that all displayed numbers are aligned. <lang rexx>/*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. */</lang>
- 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
<lang ring> 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 </lang>
- 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
<lang ecmascript>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:") 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", cells) }
}
for (n in [10, 9, 2, 1]) {
printMinCells.call(n) System.print()
}</lang>
- 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