Minimum number of cells after, before, above and below NxN squares: Difference between revisions
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(→{{header|Python}}: Added a variant which disengages model from display.) |
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</lang>{{out}} |
</lang>{{out}} |
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Same as Wren version. |
Same as Wren version. |
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Or, disentangling computation from IO (separating model from display), and composing from generics: |
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<lang python>'''Distance to edge of matrix''' |
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from itertools import product |
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from functools import reduce |
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# distancesToEdge :: Int -> [[Int]] |
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def distancesToEdge(n): |
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'''A square matrix of dimension n, in which each |
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value is the minimum distance from the matrix |
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position to the edge of the matrix. |
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''' |
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axis = range(0, n) |
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return chunksOf(n)([ |
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min(x, y, n - x - 1, n - y - 1) |
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for (x, y) in product(axis, axis) |
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]) |
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# ------------------------- TEST ------------------------- |
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# main :: IO () |
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def main(): |
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'''Square matrices of distances to the matrix edge. |
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Sample matrices of dimensions [10, 9, 2, 1]. |
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''' |
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print('\n\n'.join([ |
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showMatrix(distancesToEdge(n)) for n |
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in [10, 9, 2, 1] |
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])) |
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# ----------------------- DISPLAY ------------------------ |
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# showMatrix :: [[a]] -> String |
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def showMatrix(rows): |
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'''A string representation of the given matrix. |
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''' |
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return reduce( |
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lambda a, row: a + "\n" + str(row), |
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rows, |
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"" |
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) |
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# ----------------------- GENERIC ------------------------ |
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# chunksOf :: Int -> [a] -> [[a]] |
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def chunksOf(n): |
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'''A series of lists of length n, subdividing the |
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contents of xs. Where the length of xs is not evenly |
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divisible, the final list will be shorter than n. |
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''' |
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def go(xs): |
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return [ |
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xs[i:n + i] for i in range(0, len(xs), n) |
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] if 0 < n else None |
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return go |
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# MAIN --- |
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if __name__ == '__main__': |
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main()</lang> |
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{{Out}} |
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<pre>[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] |
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[0, 1, 1, 1, 1, 1, 1, 1, 1, 0] |
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[0, 1, 2, 2, 2, 2, 2, 2, 1, 0] |
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[0, 1, 2, 3, 3, 3, 3, 2, 1, 0] |
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[0, 1, 2, 3, 4, 4, 3, 2, 1, 0] |
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[0, 1, 2, 3, 4, 4, 3, 2, 1, 0] |
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[0, 1, 2, 3, 3, 3, 3, 2, 1, 0] |
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[0, 1, 2, 2, 2, 2, 2, 2, 1, 0] |
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[0, 1, 1, 1, 1, 1, 1, 1, 1, 0] |
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[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] |
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[0, 0, 0, 0, 0, 0, 0, 0, 0] |
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[0, 1, 1, 1, 1, 1, 1, 1, 0] |
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[0, 1, 2, 2, 2, 2, 2, 1, 0] |
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[0, 1, 2, 3, 3, 3, 2, 1, 0] |
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[0, 1, 2, 3, 4, 3, 2, 1, 0] |
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[0, 1, 2, 3, 3, 3, 2, 1, 0] |
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[0, 1, 2, 2, 2, 2, 2, 1, 0] |
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[0, 1, 1, 1, 1, 1, 1, 1, 0] |
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[0, 0, 0, 0, 0, 0, 0, 0, 0] |
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[0, 0] |
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[0, 0] |
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[0]</pre> |
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=={{header|Raku}}== |
=={{header|Raku}}== |
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Revision as of 23:14, 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.
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
<lang julia>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])
</lang>
- 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
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
Perl
<lang perl>#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Minimum_number_of_cells_after,_before,_above_and_below_NxN_squares use warnings; use List::Util qw( max min );
my $N = 10;
for my $row ( 0 .. $N - 1 )
{
my @cols = map { min $_, $row, $N-1 - max $_, $row } 0 .. $N-1;
print "@cols\n";
}</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
Python
<lang python>def printMinCells(siz):
print(f"\nMinimum number of cells after, before, above and below {siz} x {siz} square:")
for row in range(siz):
cells = [min(row, cel, siz - row - 1, row, siz - cel - 1) for cel in range(siz)]
print(" ".join([str(n) for n in cells]))
for gridsize in [10, 9, 2, 1]:
printMinCells(gridsize)
</lang>
- Output:
Same as Wren version.
Or, disentangling computation from IO (separating model from display), and composing from generics:
<lang python>Distance to edge of matrix
from itertools import product from functools import reduce
- 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.
axis = range(0, n)
return chunksOf(n)([
min(x, y, n - x - 1, n - y - 1)
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 :: a -> String
def showMatrix(rows):
A string representation of the given matrix.
return reduce(
lambda a, row: a + "\n" + str(row),
rows,
""
)
- ----------------------- 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()</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]
Raku
<lang perl6>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;
}</lang>
- 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
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
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0 0
0 0
the minimum number of cells after, before, above, and below a 1x1 square matrix
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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