Minimum number of cells after, before, above and below NxN squares: Difference between revisions
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Find and show on this page the minimum number of cells after, before, above and below '''N×N''' squares, where '''N = 10'''. |
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Revision as of 14:41, 2 August 2021
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.
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 square simple-table. nl 9 square simple-table.</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
Julia
Set up the upper left quadrant and then mirror it. <lang julia>function printNbyN(N)
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])
for n in row
print(rpad(n, 2))
end
println()
end
end
function testNbyN(sizes)
for n in sizes
println("\nSquare of size $n:")
printNbyN(n)
end
end
testNbyN([10, 9, 2, 1])
</lang>
- Output:
Square of size 10: 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 Square of size 9: 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 Square of size 2: 0 0 0 0 Square of size 1: 0
REXX
<lang rexx>/*REXX pgm finds/shows the minimum # of cells after, before, above, and below NxN square*/ parse arg $ /*obtain optional arguments from the CL*/ if $= | $="," then $= 10 9 2 1 /*Not specified? Then use the default.*/
do j=1 for words($) /*process each of the squares specified*/
x= word($, j) /*obtain the next square to process. */
w= length( (x-1) % 2) /*calculate the width of the largest #.*/
title= 'the minimum number of cells after, before, above, and below a ' x "x" x 'square'
say center(' 'title" ", 79) /*center title of output to be shown. */
say center(, 79, '─') /*display a separator line below title.*/
do r=0 for x /*process output for a N x N square. */
_= left(, max(1, 77%2 ) - x ) /*compute indentation output centering.*/
do c=0 for x
_= _ right( min(r, c, x-r-1, x-c-1), w) /*construct a row of the output square.*/
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 mimimum number of cells after, before, above, and below a 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
the mimimum number of cells after, before, above, and below a 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
the mimimum number of cells after, before, above, and below a 2 x 2 square
───────────────────────────────────────────────────────────────────────────────
0 0
0 0
the mimimum number of cells after, before, above, and below a 1 x 1 square
───────────────────────────────────────────────────────────────────────────────
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