In trying to write a script to permute values in a list, I'm getting an uninitialized value warning - perl

Question

I'm very unsure what is happening. For various lengths of #depths, the code generally works. However, throughout the output, at certain points the program barfs up complaints about use of an uninitialized value.
The errors blame line 20: print $chars[$depths[$y]];
I apologize ahead of time if it's something obvious, but I'm definitely missing the issue. I've googled for about an hour with no luck so any nudges in the right direction would be very appreciated!
Complete code:
#! /usr/bin/perl -w
use strict;
use warnings;
#my #chars = ("0" .. "9");
#my #depths = (0) x 4;
my #chars = ("0" .. "1");
my #depths = (0) x 3;
my ($i, $x, $y);
for ($i = 0; $i < #chars ** #depths; $i++) {
for ($y = 0; $y < #depths; $y++) {
print $chars[$depths[$y]];
}
print"\n";
$depths[$#depths]++;
for($x = 0; $x < #depths; $x++) {
if($depths[$x] == #chars) {
$depths[$x-1]++;
while($x < #depths) {
$depths[$x++] = 0;
}
}
}
}
Output:
000
001
010
011
Use of uninitialized value in print at a.pl line 15.
00
100
101
110

Answer 1

I added some print statements to your code, and the problem becomes apparent.
#! /usr/bin/perl -w
use strict;
use warnings;
my #chars = ("0".."1");
my #depths = (0) x 3;
my $i;
my $x;
my $y;
for ($i = 0; $i < #chars**#depths; $i++)
{
printf "m = %d\n", scalar(#depths);
for ($y = 0; $y < #depths; $y++)
{
print "y:$y; d[y] = $depths[$y]\n";
print " :$chars[$depths[$y]]:\n";
}
print"\n";
printf "b[%d] ", $depths[$#depths];
$depths[$#depths]++;
printf "a[%d]\n", $depths[$#depths];
for($x = 0; $x < #depths; $x++){
if($depths[$x] == #chars){
$depths[$x-1]++;
while($x < #depths){
$depths[$x++] = 0;
}
}
}
}
The output was:
m = 3
y:0; d[y] = 0
:0:
y:1; d[y] = 0
:0:
y:2; d[y] = 0
:0:
b[0] a[1]
m = 3
y:0; d[y] = 0
:0:
y:1; d[y] = 0
:0:
y:2; d[y] = 1
:1:
b[1] a[2]
m = 3
y:0; d[y] = 0
:0:
y:1; d[y] = 1
:1:
y:2; d[y] = 0
:0:
b[0] a[1]
m = 3
y:0; d[y] = 0
:0:
y:1; d[y] = 1
:1:
y:2; d[y] = 1
:1:
b[1] a[2]
m = 3
y:0; d[y] = 0
:0:
y:1; d[y] = 2
Use of uninitialized value within #chars in concatenation (.) or string at perm.pl line 18.
::
y:2; d[y] = 0
:0:
b[0] a[1]
m = 3
y:0; d[y] = 1
:1:
y:1; d[y] = 0
:0:
y:2; d[y] = 0
:0:
b[0] a[1]
m = 3
y:0; d[y] = 1
:1:
y:1; d[y] = 0
:0:
y:2; d[y] = 1
:1:
b[1] a[2]
m = 3
y:0; d[y] = 1
:1:
y:1; d[y] = 1
:1:
y:2; d[y] = 0
:0:
b[0] a[1]
The line immediately before the error report shows that $depths[$y] is 2, but the array #chars only contains elements with indexes 0 and 1, so the warning is accurate.

Answer 2

Think of #depths as a base N number (where N is the number of #chars), and each element of #depths is a digit. You're trying to add one to that number, but you're failing.
A carry propagates from the least significant digit to the most significant, so you should be the loop than handles the carry should loop from the least significant digit to the most significant, but you're doing it in the opposite order. $x should start at $#depth and decrease as the loop advances.
Let's look at an example. Say there are 10 symbols (#chars == 10):
456999 <- #depth
+ 1
-------
457000
So you want to increment the right-most digit that's not equal to $#chars, and set to zero all the right-most digits that are equal to $#chars. Here's how I coded that:
#!/usr/bin/perl -w
use strict;
use warnings;
my #chars = ("0".."2");
my #depths = (0) x 3;
OUTER: while (1) {
print #chars[#depths], "\n";
my $x = $#depths;
while ($depths[$x] == $#chars) {
$depths[$x] = 0;
last OUTER if $x == 0;
--$x;
}
++$depths[$x];
}