Diagonal array input

Question

I have a 2D array (StartingArray) NxN (for example 3x3). I would like my 2 other arrays (LRotateArray and RRotateArray) to be StartingArray rotated by 45 degrees left and right (each line in LRotateArray and RRotateArray are diagonals in StartingArray):

StartingArray:
1 2 3
4 5 6
7 8 9

LRotateArray:
1
4 2
7 5 3
8 6
9

RRotateArray:
7
4 8
1 5 9 
2 6
3

I want to edit LRotateArray and RRotateArray while getting input to StartingArray.

I found a formula allowing me to generate LRotateArray:

if StartingArray[i][j]=k then L_j=i+j
if j>(N-1-i) then  L_i=N-i-j else L_i=i
LRotateArray[L_i][L_j]=k

Is there any easy way to transform LRotateArray into RRotateArray, or do I have to find another formula like the one above?

Getting RRotateArray from the StartingArray is a lot easier than getting it from LRotateArray. So I suggest you find another formula for this. However regarding your current formula, I have no idea how it would work and some of it (L_i=N=i-j) just does not make any sense at all. — Avo Muromägi
– Avo Muromägi, Commented Nov 19, 2013 at 12:20

Avo Muromägi · Accepted Answer · 2013-11-19 12:28:44Z

1

IMHO building RRotateArray from StartingArray is easier than building it from LRotateArray. This is how I would implement both rotations:

for Row := 0 to N - 1 do
begin
  for Col := 0 to N - 1 do
  begin
    LeftRow := Col + Row;
    LeftCol := Min(Col, N - 1 - Row);
    LRotateArray[LeftCol, LeftRow] := StartingArray [Col, Row];

    RightRow := Col + (N - Row - 1);
    RightCol := Min(Col, Row);
    RRotateArray[RightCol, RightRow] := StartingArray [Col, Row];
  end;
end;

answered Nov 19, 2013 at 12:28

Avo Muromägi

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