9 billion names of God the integer
To save a bunch of memory, this algorithm throws away all the numbers that it knows it's not going to use again, on the assumption that the function will only be called with increasing values of $n. (It could easily be made to recalculate if it notices a regression.)
my @todo = $[1];
my @sums = 0;
sub nextrow($n) {
for +@todo .. $n -> $l {
my $r = [];
for reverse ^$l -> $x {
my @x := @todo[$x];
if @x {
$r.push: @sums[$x] += @x.shift;
}
else {
$r.push: @sums[$x];
}
}
@todo.push($r);
}
@todo[$n];
}
say "rows:";
say .fmt('%2d'), ": ", nextrow($_)[] for 1..25;
my @names-of-God = 1, { partition-sum ++$ } … *;
my @names-of-God-adder = lazy [\+] flat 1, ( (1 .. *) Z (1 .. *).map: * × 2 + 1 );
sub partition-sum ($n) {
sum @names-of-God[$n X- @names-of-God-adder[^(@names-of-God-adder.first: * > $n, :k)]]
Z× (flat (1, 1, -1, -1) xx *)
}
say "\nsums:";
for 23, 123, 1234, 12345 {
put $_, "\t", @names-of-God[$_];
}Output:
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