http://qs321.pair.com?node_id=341489

Kozz has asked for the wisdom of the Perl Monks concerning the following question:

Esteemed monks:

I've got data in an n-by-n two-dimensional array. Assuming that my n is divisible by two, I need to be able to iterate over the items in sub-matrices. Let me explain, and see if you can help me with this algorithm. I've tried, but can't quite wrap my head around it, and the code I DO make always tends to be far uglier than I'd expect it to be.

Disclosure: This is homework related. However, iterating over the data in this manner is not the main thrust of it. My "work" was done in the assignment of the 2-dim array elements' values. I just chose to break up the output into more manageable blocks (perhaps badly?).

Supposing n = 4, then I've got 4 "rows" of indices 0..3, each row having a "column" with indices 0..3, like this (vertical bars and dashed line to represent a line dividing matrix into quadrants):

```[ 00 01 | 02 03 ]
[ 10 11 | 12 13 ]
-----------------
[ 20 21 | 22 23 ]
[ 30 31 | 32 33 ]
I want to output the four elements in the upper-left quadrant of the matrix (00, 01, 10, 11, in that order), then upper right, lower left, lower right.

What trips me up is that I iterate over the first two cols of the first row, then increment row but reset cols. Then row gets reset and cols adjusted.... it's just a very awkward traversal of the matrix.

I know this is more of an algorithms question than a perl question, so smack me down with a -- if you must. But I know that there are monks that can likely whip up a very elegant solution for this.

Thanks for any insight you can provide.

Update: Code per request. This script was made just for a "simple" (ha-ha) base case to see if I could figure out how to iterate over pairs of indices in this manner. I know I've got an infinite loop, too, while I'm trying to figure out when to increment/decrement my rows & columns.

```#!/usr/bin/perl

my \$n = 2;
my \$max_exp = 1;

use strict;

my \$max_part = 2**\$max_exp;

my \$size = 2**\$n;

print "Matrix is \$size by \$size.\n";
print "Max size I'm allowed to print is \$max_part at a time.\n";

my \$max_part_tiles = \$max_part**2;

my \$total_tiles = (\$size)**2;
my \$tiles_counted = 0;
my \$part_tiles_counted = 0;

my (\$row_num, \$col_num, \$end_col) = (0, 0);
my (\$cols_displayed, \$rows_displayed) = (0, 0);

while(\$tiles_counted < \$total_tiles){

\$col_num=0;
\$end_col=\$max_part;
while(\$row_num < \$size){
while(\$col_num < \$end_col){
print "\$row_num \$col_num\n";
\$col_num++;
\$part_tiles_counted++;
}
if(\$col_num < (\$size-1) && ((\$row_num + 1) % \$size > 0
+) ){
\$row_num++;
\$col_num-=\$max_part;
}
if(\$col_num < (\$max_part-1) && \$row_num == (\$size-1)){
# \$col_num++;
\$row_num-=\$max_part;
\$end_col+=\$max_part;
}
if(\$col_num == (\$size-1) && \$row_num < (\$size-1)){
\$row_num++;
\$col_num-=\$max_part;
}
if(\$col_num == (\$max_part-1) && \$row_num == (\$size-1))
+{
\$row_num++;
\$col_num=0;
\$end_col=\$max_part;
}
\$tiles_counted += \$part_tiles_counted;
}

}