/
next_palindrome_from_non-palindrome.pl
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/
next_palindrome_from_non-palindrome.pl
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#!/usr/bin/perl
# Generate the next palindrome in a given base, where the input number may not be a palindrome.
# Algorithm by David A. Corneth (Jun 06 2014), with extensions by Daniel Suteu (Jun 06 2020).
# See also:
# https://oeis.org/A002113
# https://en.wikipedia.org/wiki/Palindromic_number
use 5.020;
use strict;
use warnings;
use ntheory qw(:all);
use experimental qw(signatures);
use Test::More tests => 41;
sub next_palindrome ($n, $base = 10) {
my @d = todigits($n, $base);
my $l = $#d;
my $i = ((scalar(@d) + 1) >> 1) - 1;
my $is_palindrome = 1;
foreach my $j (0 .. $i) {
if ($d[$j] != $d[$l - $j]) {
$is_palindrome = 0;
last;
}
}
if (!$is_palindrome) {
my @copy = @d;
foreach my $i (0 .. $i) {
$d[$l - $i] = $d[$i];
}
my $is_greater = 1;
foreach my $j (0 .. $i) {
my $cmp = $d[$i + $j + 1] <=> $copy[$i + $j + 1];
if ($cmp > 0) {
last;
}
if ($cmp < 0) {
$is_greater = 0;
last;
}
}
if ($is_greater) {
return fromdigits(\@d, $base);
}
}
while ($i >= 0 and $d[$i] == $base - 1) {
$d[$i] = 0;
$d[$l - $i] = 0;
$i--;
}
if ($i >= 0) {
$d[$i]++;
$d[$l - $i] = $d[$i];
}
else {
@d = (0) x (scalar(@d) + 1);
$d[0] = 1;
$d[-1] = 1;
}
fromdigits(\@d, $base);
}
#
## Run some tests
#
my @palindromes = do {
my $x = 0;
my @list;
for (1 .. 61) {
push @list, $x;
$x = next_palindrome($x);
}
@list;
};
is_deeply(
\@palindromes,
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121,
131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343,
353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515
]
);
is(next_palindrome(10), 11);
is(next_palindrome(11), 22);
is(next_palindrome(12), 22);
is(next_palindrome(110), 111);
is(next_palindrome(111), 121);
is(next_palindrome(112), 121);
is(next_palindrome(120), 121);
is(next_palindrome(121), 131);
is(next_palindrome(1234), 1331);
is(next_palindrome(12345), 12421);
is(next_palindrome(8887), 8888);
is(next_palindrome(8888), 8998);
is(next_palindrome(8889), 8998);
is(next_palindrome(88887), 88888);
is(next_palindrome(88888), 88988);
is(next_palindrome(88889), 88988);
is(next_palindrome(9998), 9999);
is(next_palindrome(99998), 99999);
is(next_palindrome(9999), 10001);
is(next_palindrome(99999), 100001);
is(next_palindrome(12311), 12321);
is(next_palindrome(1321), 1331);
is(next_palindrome(1331), 1441);
is(next_palindrome(13530), 13531);
is(next_palindrome(13520), 13531);
is(next_palindrome(13521), 13531);
is(next_palindrome(13530), 13531);
is(next_palindrome(13531), 13631);
is(next_palindrome(13540), 13631);
is(next_palindrome(13532), 13631);
is(next_palindrome(1234, 2), 1241);
is(next_palindrome(1234, 3), 1249);
is(next_palindrome(1234, 4), 1265);
is(next_palindrome(1234, 5), 1246);
is(next_palindrome(1234, 6), 1253);
is(next_palindrome(12345, 2), 12483);
is(next_palindrome(12345, 3), 12382);
is(next_palindrome(12345, 4), 12355);
is(next_palindrome(12345, 5), 12348);
is(next_palindrome(12345, 6), 12439);