Count number of times an item is placed within a cell - perl

I am randomly populating a grid where the cartesian coordinates are normalized from 0 to 100 (100x100x100 grid) and the "intensity" of each data point within is normalized from 0 to 256. Here is an excerpt from my code in perl:
open(FILE,$file);
while(sysread(FILE,$data,16)) {
#row=unpack("f>4",$data); # input file is binary so I had to convert here
$x=int((($row[0] - $xmin)/($xmax - $xmin)*10) + 0.5); # max and min variables
$y=int((($row[1] - $ymin)/($ymax - $ymin)*10) + 0.5); # are previously defined
$z=int((($row[2] - $zmin)/($zmax - $zmin)*10) + 0.5);
$i=int(($row[3]/62*256) + 0.5);
$i=255 if ($i>255);
$out[$x][$y][$z]=$i; # simply assigns an intensity for each data
# point (in random order), only 1 point can be
# added to each 1x1x1 cell
}
Some points are too close together and are being placed in the same 1x1x1 cell. When this happens, each intensity added overwrites the previous one. How can I count the number of times that more than one point is placed in a cell?
Thanks in advance!

You can do this pretty easily with another hash, just join all of your keys ($x,$y,$z) together into a single key and set the hash value to true whenever you insert a value.
my %visited_points;
open(FILE,$file);
while(sysread(FILE,$data,16)) {
#row=unpack("f>4",$data); # input file is binary so I had to convert here
$x=int((($row[0] - $xmin)/($xmax - $xmin)*10) + 0.5); # max and min variables
$y=int((($row[1] - $ymin)/($ymax - $ymin)*10) + 0.5); # are
$z=int((($row[2] - $zmin)/($zmax - $zmin)*10) + 0.5);
$i=int(($row[3]/62*256) + 0.5);
$i=255 if ($i>255);
my $key = "$x$y$z";
# check if something already occupies this cell
if( exists( $visited_points{$key} ) ) {
# take some other action
}
$out[$x][$y][$z]=$i; # simply assigns an intensity for each data
# point (in random order), only 1 point can be
# added to each 1x1x1 cell
# mark that there is something in this cell
$visited_points{$key} = 1;
}
If you wanted to count you count easily just increment the value as well.

To make it more hpc(high performance computing)-friendly, I found that instead of the $key and if-loop, simply putting in a count like this works too.
open(FILE,$file);
while(sysread(FILE,$data,16)) {
#row=unpack("f>4",$data); # input file is binary so I had to convert here
$x=int((($row[0] - $xmin)/($xmax - $xmin)*10) + 0.5); # max and min variables
$y=int((($row[1] - $ymin)/($ymax - $ymin)*10) + 0.5); # are previously defined
$z=int((($row[2] - $zmin)/($zmax - $zmin)*10) + 0.5);
$i=int(($row[3]/62*256) + 0.5);
$i=255 if ($i>255);
$count[$x][$y][$z]+=1;
$out[$x][$y][$z]=$i; # simply assigns an intensity for each data
# point (in random order), only 1 point can be
# added to each 1x1x1 cell
}
Then, if $count[$x][$y][$z] is greater than 1, it means more than one point was put in that bin. If it equals 1, only one point was put there, and if it is less than one, then the bin is empty.

Another version of Hunter's solution replaces a hash (with encoded key); with an array (with an encoded index).
Pros: possibly very slightly improving performance. More likely than not, not by a great enough margin to matter, in all honesty, but do your own benchmarking to be sure.
Cons: sacrifice of memory. If your grid is populated sparsely - say 1000 points out of 1 million - you would store 1000 elements in a hash but 1,000,000 elements in the array.
# my #visited_points;
my $key = $x * 10000 + $y * 100 + $z;
# Mark as visited
$visited_points[$key]++;
# Check if visited:
if (defined $visited_points[$key]) {
# Bail out?
}
# Check how many times visited?
# Use trinary ?: operator to gracefully convert undef to 0
my $count = $visited_points[$key] ? $visited_points[$key] : 0;

Related

Libreoffice calc - how to write a same value into a range

I know how to 'select' a range in LO (7.2.4.1) Calc BASIC ....
ThisComponent.CurrentController.ActiveSheet.getCellRangeByName("D1:H6")
But how to write a value, e.g. "1", into that range using BASIC?
myRange = ThisComponent.CurrentController.ActiveSheet.getCellRangeByName("D1:H6")
myRange.Value = 1
Gives an "property or method not found" error. But I can't find any properties or values to go after Range to allow me to do what I want. Flailing around and trying
myRange.setValue = 1
myRange.writeValue = 1
myRange.setString = "1"
and numerous other variants don't work either.
Would really appreciate the solution. Thanks.
You can edit the value of an individual cell, but not the entire range. You will have to iterate over all the cells in the range one at a time, changing the value of each of them.
Sub Set1ToD1H6
myRange = ThisComponent.CurrentController.ActiveSheet.getCellRangeByName("D1:H6")
For i = 0 To myRange.getRows().getCount()-1
For j = 0 To myRange.getColumns().getCount()-1
myRange.getCellByPosition(j, i).setValue(1)
Next j
Next i
End Sub
But since the read-write operation to a cell is comparable in time to the read-write operation to a whole range, it is preferable to use another method - to prepare data in an array and write from it to a range in one operation:
Sub Set1ToRange
myRange = ThisComponent.CurrentController.ActiveSheet.getCellRangeByName("D1:H6")
dataOfRange = myRange.getData()
For i = LBound(dataOfRange) To UBound(dataOfRange)
For j = LBound(dataOfRange(i)) To UBound(dataOfRange(i))
dataOfRange(i)(j) = 1
Next j
Next i
myRange.setData(dataOfRange)
End Sub
(For your example, this will be approximately 30 times faster, for a larger range the time winnings will be even more significant)
The .getData() and .setData() methods work on numeric range values. To work with text strings (and numbers), use .getDataArray() and .setDataArray(), for working with cell formulas use .getFormulaArray() and .setFormulaArray()

Hash an 8 digit number that contains non repetitive digits from 1 to 8 only

Given that a number can contain only digits from 1 to 8 (with no repetition), and is of length 8, how can we hash such numbers without using a hashSet?
We can't just directly use the value of the number of the hashing value, as the stack size of the program is limited. (By this, I mean that we can't directly make the index of an array, represent our number).
Therefore, this 8 digit number needs to be mapped to, at maximum, a 5 digit number.
I saw this answer. The hash function returns a 8-digit number, for a input that is an 8-digit number.
So, what can I do here?
There's a few things you can do. You could subtract 1 from each digit and parse it as an octal number, which will map one-to-one every number from your domain to the range [0,16777216) with no gaps. The resulting number can be used as an index into a very large array. An example of this could work as below:
function hash(num) {
return parseInt(num
.toString()
.split('')
.map(x => x - 1), 8);
}
const set = new Array(8**8);
set[hash(12345678)] = true;
// 12345678 is in the set
Or if you wanna conserve some space and grow the data structure as you add elements. You can use a tree structure with 8 branches at every node and a maximum depth of 8. I'll leave that up to you to figure out if you think it's worth the trouble.
Edit:
After seeing the updated question, I began thinking about how you could probably map the number to its position in a lexicographically sorted list of the permutations of the digits 1-8. That would be optimal because it gives you the theoretical 5-digit hash you want (under 40320). I had some trouble formulating the algorithm to do this on my own, so I did some digging. I found this example implementation that does just what you're looking for. I've taken inspiration from this to implement the algorithm in JavaScript for you.
function hash(num) {
const digits = num
.toString()
.split('')
.map(x => x - 1);
const len = digits.length;
const seen = new Array(len);
let rank = 0;
for(let i = 0; i < len; i++) {
seen[digits[i]] = true;
rank += numsBelowUnseen(digits[i], seen) * fact(len - i - 1);
}
return rank;
}
// count unseen digits less than n
function numsBelowUnseen(n, seen) {
let count = 0;
for(let i = 0; i < n; i++) {
if(!seen[i]) count++;
}
return count;
}
// factorial fuction
function fact(x) {
return x <= 0 ? 1 : x * fact(x - 1);
}
kamoroso94 gave me the idea of representing the number in octal. The number remains unique if we remove the first digit from it. So, we can make an array of length 8^7=2097152, and thus use the 7-digit octal version as index.
If this array size is bigger than the stack, then we can use only 6 digits of the input, convert them to their octal values. So, 8^6=262144, that is pretty small. We can make a 2D array of length 8^6. So, total space used will be in the order of 2*(8^6). The first index of the second dimension represents that the number starts from the smaller number, and the second index represents that the number starts from the bigger number.

Perl: getting count for range of values

I want to perform a count for a range of values, i.e, I have 900 values of X between 1 to 75x10^6. I need to count the number of times these X's fall in range like 1-1000000, 1000001-2000000, 2000001-3000000 ... 750 ranges, then return the counts of these ranges.
I have the values of X stored in an array so I could have done it with for loop and if..else, but giving 750 if-else's is no solution and I don't know how to implement value range in hash-keys. Please help
Thank you in advance :)
For each value, you can subtract 1, divide by 1000000, and cut off any decimals. That gives you the index of the range as a number between 0 and 749 (inclusive).
Example:
use strict;
use warnings;
my #values = (...); # filled from somewhere
my #range_count;
for my $value (#values) {
my $x = int(($value - 1) / 1e6);
$range_count[$x]++;
}
Now $range_count[0] contains the number of values in the first range, $range_count[1] the number of values in the second range, etc.
However, if there were no values in some range, the count will be undef, not 0. If this difference is important, define #range_count as
my #range_count = (0) x 750;
instead.

How can I take n elements at random from a Perl array?

I have an array, A = [a1,a2,a3,...aP] with size P. I have to sample q elements from array A.
I plan to use a loop with q iterations, and randomly pick a element from A at each iteration. But how can I make sure that the picked number will be different at each iteration?
The other answers all involve shuffling the array, which is O(n).
It means modifying the original array (destructive) or copying the original array (memory intensive).
The first way to make it more memory efficient is not to shuffle the original array but to shuffle an array of indexes.
# Shuffled list of indexes into #deck
my #shuffled_indexes = shuffle(0..$#deck);
# Get just N of them.
my #pick_indexes = #shuffled_indexes[ 0 .. $num_picks - 1 ];
# Pick cards from #deck
my #picks = #deck[ #pick_indexes ];
It is at least independent of the content of the #deck, but its still O(nlogn) performance and O(n) memory.
A more efficient algorithm (not necessarily faster, depends on now big your array is) is to look at each element of the array and decide if it's going to make it into the array. This is similar to how you select a random line from a file without reading the whole file into memory, each line has a 1/N chance of being picked where N is the line number. So the first line has a 1/1 chance (it's always picked). The next has a 1/2. Then 1/3 and so on. Each pick will overwrite the previous pick. This results in each line having a 1/total_lines chance.
You can work it out for yourself. A one line file has a 1/1 chance so the first one is always picked. A two line file... the first line has a 1/1 then a 1/2 chance of surviving, which is 1/2, and the second line has a 1/2 chance. For a three line file... the first line has a 1/1 chance of being picked, then a 1/2 * 2/3 chance of surviving which is 2/6 or 1/3. And so on.
The algorithm is O(n) for speed, it iterates through an unordered array once, and does not consume any more memory than is needed to store the picks.
With a little modification, this works for multiple picks. Instead of a 1/$position chance, it's $picks_left / $position. Each time a pick is successful, you decrement $picks_left. You work from the high position to the low one. Unlike before, you don't overwrite.
my $picks_left = $picks;
my $num_left = #$deck;
my #picks;
my $idx = 0;
while($picks_left > 0 ) { # when we have all our picks, stop
# random number from 0..$num_left-1
my $rand = int(rand($num_left));
# pick successful
if( $rand < $picks_left ) {
push #picks, $deck->[$idx];
$picks_left--;
}
$num_left--;
$idx++;
}
This is how perl5i implements its pick method (coming next release).
To understand viscerally why this works, take the example of picking 2 from a 4 element list. Each should have a 1/2 chance of being picked.
1. (2 picks, 4 items): 2/4 = 1/2
Simple enough. Next element has a 1/2 chance that an element will already have been picked, in which case it's chances are 1/3. Otherwise its chances are 2/3. Doing the math...
2. (1 or 2 picks, 3 items): (1/3 * 1/2) + (2/3 * 1/2) = 3/6 = 1/2
Next has a 1/4 chance that both elements will already be picked (1/2 * 1/2), then it has no chance; 1/2 chance that only one will be picked, then it has 1/2; and the remaining 1/4 that no items will be picked in which case it's 2/2.
3. (0, 1 or 2 picks, 2 items): (0/2 * 1/4) + (1/2 * 2/4) + (2/2 * 1/4) = 2/8 + 1/4 = 1/2
Finally, for the last item, there's a 1/2 the previous took the last pick.
4. (0 or 1 pick, 1 items): (0/1 * 2/4) + (1/1 * 2/4) = 1/2
Not exactly a proof, but good for convincing yourself it works.
From perldoc perlfaq4:
How do I shuffle an array randomly?
If you either have Perl 5.8.0 or later installed, or if you have
Scalar-List-Utils 1.03 or later installed, you can say:
use List::Util 'shuffle';
#shuffled = shuffle(#list);
If not, you can use a Fisher-Yates shuffle.
sub fisher_yates_shuffle {
my $deck = shift; # $deck is a reference to an array
return unless #$deck; # must not be empty!
my $i = #$deck;
while (--$i) {
my $j = int rand ($i+1);
#$deck[$i,$j] = #$deck[$j,$i];
}
}
# shuffle my mpeg collection
#
my #mpeg = <audio/*/*.mp3>;
fisher_yates_shuffle( \#mpeg ); # randomize #mpeg in place
print #mpeg;
You could also use List::Gen:
my $gen = <1..10>;
print "$_\n" for $gen->pick(5); # prints five random numbers
You can suse the Fisher-Yates shuffle algorithm to randomly permute your array and then use a slice of the first q elements. Here's code from PerlMonks:
# randomly permutate #array in place
sub fisher_yates_shuffle
{
my $array = shift;
my $i = #$array;
while ( --$i )
{
my $j = int rand( $i+1 );
#$array[$i,$j] = #$array[$j,$i];
}
}
fisher_yates_shuffle( \#array ); # permutes #array in place
You can probably optimize this by having the shuffle stop after it has q random elements selected. (The way this is written, you'd want the last q elements.)
You may construct second array, boolean with size P and store true for picked numbers. And when the numer is picked, check second table; in case "true" you must pick next one.

Randomize matrix in perl, keeping row and column totals the same

I have a matrix that I want to randomize a couple of thousand times, while keeping the row and column totals the same:
1 2 3
A 0 0 1
B 1 1 0
C 1 0 0
An example of a valid random matrix would be:
1 2 3
A 1 0 0
B 1 1 0
C 0 0 1
My actual matrix is a lot bigger (about 600x600 items), so I really need an approach that is computationally efficient.
My initial (inefficient) approach consisted of shuffling arrays using the Perl Cookbook shuffle
I pasted my current code below. I've got extra code in place to start with a new shuffled list of numbers, if no solution is found in the while loop. The algorithm works fine for a small matrix, but as soon as I start scaling up it takes forever to find a random matrix that fits the requirements.
Is there a more efficient way to accomplish what I'm searching for?
Thanks a lot!
#!/usr/bin/perl -w
use strict;
my %matrix = ( 'A' => {'3' => 1 },
'B' => {'1' => 1,
'2' => 1 },
'C' => {'1' => 1 }
);
my #letters = ();
my #numbers = ();
foreach my $letter (keys %matrix){
foreach my $number (keys %{$matrix{$letter}}){
push (#letters, $letter);
push (#numbers, $number);
}
}
my %random_matrix = ();
&shuffle(\#numbers);
foreach my $letter (#letters){
while (exists($random_matrix{$letter}{$numbers[0]})){
&shuffle (\#numbers);
}
my $chosen_number = shift (#numbers);
$random_matrix{$letter}{$chosen_number} = 1;
}
sub shuffle {
my $array = shift;
my $i = scalar(#$array);
my $j;
foreach my $item (#$array )
{
--$i;
$j = int rand ($i+1);
next if $i == $j;
#$array [$i,$j] = #$array[$j,$i];
}
return #$array;
}
The problem with your current algorithm is that you are trying to shuffle your way out of dead ends -- specifically, when your #letters and #numbers arrays (after the initial shuffle of #numbers) yield the same cell more than once. That approach works when the matrix is small, because it doesn't take too many tries to find a viable re-shuffle. However, it's a killer when the lists are big. Even if you could hunt for alternatives more efficiently -- for example, trying permutations rather than random shuffling -- the approach is probably doomed.
Rather than shuffling entire lists, you might tackle the problem by making small modifications to an existing matrix.
For example, let's start with your example matrix (call it M1). Randomly pick one cell to change (say, A1). At this point the matrix is in an illegal state. Our goal will be to fix it in the minimum number of edits -- specifically 3 more edits. You implement these 3 additional edits by "walking" around the matrix, with each repair of a row or column yielding another problem to be solved, until you have walked full circle (err ... full rectangle).
For example, after changing A1 from 0 to 1, there are 3 ways to walk for the next repair: A3, B1, and C1. Let's decide that the 1st edit should fix rows. So we pick A3. On the second edit, we will fix the column, so we have choices: B3 or C3 (say, C3). The final repair offers only one choice (C1), because we need to return to the column of our original edit. The end result is a new, valid matrix.
Orig Change A1 Change A3 Change C3 Change C1
M1 M2
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
----- ----- ----- ----- -----
A | 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0
B | 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0
C | 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1
If an editing path leads to a dead end, you backtrack. If all of the repair paths fail, the initial edit can be rejected.
This approach will generate new, valid matrixes quickly. It will not necessarily produce random outcomes: M1 and M2 will still be highly correlated with each other, a point that will become more directly evident as the size of the matrix grows.
How do you increase the randomness? You mentioned that most cells (99% or more) are zeros. One idea would be to proceed like this: for each 1 in the matrix, set its value to 0 and then repair the matrix using the 4-edit method outlined above. In effect, you would be moving all of the ones to new, random locations.
Here is an illustration. There are probably further speed optimizations in here, but this approach yielded 10 new 600x600 matrixes, at 0.5% density, in 30 seconds or so on my Windows box. Don't know if that's fast enough.
use strict;
use warnings;
# Args: N rows, N columns, density, N iterations.
main(#ARGV);
sub main {
my $n_iter = pop;
my $matrix = init_matrix(#_);
print_matrix($matrix);
for my $n (1 .. $n_iter){
warn $n, "\n"; # Show progress.
edit_matrix($matrix);
print_matrix($matrix);
}
}
sub init_matrix {
# Generate initial matrix, given N of rows, N of cols, and density.
my ($rows, $cols, $density) = #_;
my #matrix;
for my $r (1 .. $rows){
push #matrix, [ map { rand() < $density ? 1 : 0 } 1 .. $cols ];
}
return \#matrix;
}
sub print_matrix {
# Dump out a matrix for checking.
my $matrix = shift;
print "\n";
for my $row (#$matrix){
my #vals = map { $_ ? 1 : ''} #$row;
print join("\t", #vals), "\n";
}
}
sub edit_matrix {
# Takes a matrix and moves all of the non-empty cells somewhere else.
my $matrix = shift;
my $move_these = cells_to_move($matrix);
for my $cell (#$move_these){
my ($i, $j) = #$cell;
# Move the cell, provided that the cell hasn't been moved
# already and the subsequent edits don't lead to a dead end.
$matrix->[$i][$j] = 0
if $matrix->[$i][$j]
and other_edits($matrix, $cell, 0, $j);
}
}
sub cells_to_move {
# Returns a list of non-empty cells.
my $matrix = shift;
my $i = -1;
my #cells = ();
for my $row (#$matrix){
$i ++;
for my $j (0 .. #$row - 1){
push #cells, [$i, $j] if $matrix->[$i][$j];
}
}
return \#cells;
}
sub other_edits {
my ($matrix, $cell, $step, $last_j) = #_;
# We have succeeded if we've already made 3 edits.
$step ++;
return 1 if $step > 3;
# Determine the roster of next edits to fix the row or
# column total upset by our prior edit.
my ($i, $j) = #$cell;
my #fixes;
if ($step == 1){
#fixes =
map { [$i, $_] }
grep { $_ != $j and not $matrix->[$i][$_] }
0 .. #{$matrix->[0]} - 1
;
shuffle(\#fixes);
}
elsif ($step == 2) {
#fixes =
map { [$_, $j] }
grep { $_ != $i and $matrix->[$_][$j] }
0 .. #$matrix - 1
;
shuffle(\#fixes);
}
else {
# On the last edit, the column of the fix must be
# the same as the column of the initial edit.
#fixes = ([$i, $last_j]) unless $matrix->[$i][$last_j];
}
for my $f (#fixes){
# If all subsequent fixes succeed, we are golden: make
# the current fix and return true.
if ( other_edits($matrix, [#$f], $step, $last_j) ){
$matrix->[$f->[0]][$f->[1]] = $step == 2 ? 0 : 1;
return 1;
}
}
# Failure if we get here.
return;
}
sub shuffle {
my $array = shift;
my $i = scalar(#$array);
my $j;
for (#$array ){
$i --;
$j = int rand($i + 1);
#$array[$i, $j] = #$array[$j, $i] unless $i == $j;
}
}
Step 1: First I would initialize the matrix to zeros and calculate the required row and column totals.
Step 2: Now pick a random row, weighted by the count of 1s that must be in that row (so a row with count 300 is more likely to be picked than a row with weight 5).
Step 3: For this row, pick a random column, weighted by the count of 1s in that column (except ignore any cells that may already contain a 1 - more on this later).
Step 4: Place a one in this cell and reduce both the row and column count for the appropriate row and column.
Step 5: Go back to step 2 until no rows have non-zero count.
The problem though is that this algorithm can fail to terminate because you may have a row where you need to place a one, and a column that needs a one, but you've already placed a one in that cell, so you get 'stuck'. I'm not sure how likely this is to happen, but I wouldn't be surprised if it happened very frequently - enough to make the algorithm unusable. If this is a problem I can think of two ways to fix it:
a) Construct the above algorithm recursively and allow backtracking on failure.
b) Allow a cell to contain a value greater than 1 if there is no other option and keep going. Then at the end you have a correct row and column count but some cells may contain numbers greater than 1. You can fix this by finding a grouping that looks like this:
2 . . . . 0
. . . . . .
. . . . . .
0 . . . . 1
and changing it to:
1 . . . . 1
. . . . . .
. . . . . .
1 . . . . 0
It should be easy to find such a grouping if you have many zeros. I think b) is likely to be faster.
I'm not sure it's the best way, but it's probably faster than shuffling arrays. I'll be tracking this question to see what other people come up with.
I'm not a mathematician, but I figure that if you need to keep the same column and row totals, then random versions of the matrix will have the same quantity of ones and zeros.
Correct me if I'm wrong, but that would mean that making subsequent versions of the matrix would only require you to shuffle around the rows and columns.
Randomly shuffling columns won't change your totals for rows and columns, and randomly shuffling rows won't either. So, what I would do, is first shuffle rows, and then shuffle columns.
That should be pretty fast.
Not sure if it will help, but you can try going from one corner and for each column and row you should track the total and actual sum. Instead of trying to hit a good matrix, try to see the total as amount and split it. For each element, find the smaller number of row total - actual row total and column total - actual column total. Now you have the upper bound for your random number.
Is it clear? Sorry I don't know Perl, so I cannot show any code.
Like #Gabriel I'm not a Perl programmer so it's possible that this is what your code already does ...
You've only posted one example. It's not clear whether you want a random matrix which has the same number of 1s in each row and column as your start matrix, or one which has the same rows and columns but shuffled. If the latter is good enough you could create an array of row (or column, it doesn't matter) indexes and randomly permute that. You can then read your original array in the order specified by the randomised index. No need to modify the original array or create a copy.
Of course, this might not meet aspects of your requirements which are not explicit.
Thank the Perl code of FMc. Based on this solution, I rewrite it in Python (for my own use and share here for more clarity) as shown below:
matrix = numpy.array(
[[0, 0, 1],
[1, 1, 0],
[1, 0, 0]]
)
def shuffle(array):
i = len(array)
j = 0
for _ in (array):
i -= 1;
j = random.randrange(0, i+1) #int rand($i + 1);
#print('arrary:', array)
#print(f'len(array)={len(array)}, (i, j)=({i}, {j})')
if i != j:
tmp = array[i]
array[i] = array[j]
array[j] = tmp
return array
def other_edits(matrix, cell, step, last_j):
# We have succeeded if we've already made 3 edits.
step += 1
if step > 3:
return True
# Determine the roster of next edits to fix the row or
# column total upset by our prior edit.
(i, j) = cell
fixes = []
if (step == 1):
fixes = [[i, x] for x in range(len(matrix[0])) if x != j and not matrix[i][x] ]
fixes = shuffle(fixes)
elif (step == 2):
fixes = [[x, j] for x in range(len(matrix)) if x != i and matrix[x][j]]
fixes = shuffle(fixes)
else:
# On the last edit, the column of the fix must be
# the same as the column of the initial edit.
if not matrix[i][last_j]: fixes = [[i, last_j]]
for f in (fixes):
# If all subsequent fixes succeed, we are golden: make
# the current fix and return true.
if ( other_edits(matrix, f, step, last_j) ):
matrix[f[0]][f[1]] = 0 if step == 2 else 1
return True
# Failure if we get here.
return False # return False
def cells_to_move(matrix):
# Returns a list of non-empty cells.
i = -1
cells = []
for row in matrix:
i += 1;
for j in range(len(row)):
if matrix[i][j]: cells.append([i, j])
return cells
def edit_matrix(matrix):
# Takes a matrix and moves all of the non-empty cells somewhere else.
move_these = cells_to_move(matrix)
for cell in move_these:
(i, j) = cell
# Move the cell, provided that the cell hasn't been moved
# already and the subsequent edits don't lead to a dead end.
if matrix[i][j] and other_edits(matrix, cell, 0, j):
matrix[i][j] = 0
return matrix
def Shuffle_Matrix(matrix, N, M, n_iter):
for n in range(n_iter):
print(f'iteration: {n+1}') # Show progress.
matrix = edit_matrix(matrix)
#print('matrix:\n', matrix)
return matrix
print(matrix.shape[0], matrix.shape[1])
# Args: N rows, N columns, N iterations.
matrix2 = Shuffle_Matrix(matrix, matrix.shape[0], matrix.shape[1], 1)
print("The resulting matrix:\n", matrix2)