Add a working solution of #463.

categories/euler/prob463-shlomif.p6

@@ -1,5 +1,10 @@
 use v6;
 
+# Dedicated to the memory of Christina Grimmie (
+# https://en.wikipedia.org/wiki/Christina_Grimmie ), see:
+# https://www.youtube.com/watch?v=kYX8sjIzjGw .
+#   -- shlomif
+
 class Poly
 {
     has $.mult;
@@ -104,10 +109,136 @@ sub lookup($mult)
     return @($ret).map({ .mult });
 }
 
-my $mult = 4;
-while (1)
+if (False)
+{
+    my $mult = 4;
+    while (1)
+    {
+        say lookup($mult);
+        $mult +<= 1;
+    }
+}
+
+my $MOD = 1_000_000_000;
+
+sub _cache(%h, $key, $promise)
+{
+    my $ret = %h{$key};
+
+    if (!defined($ret))
+    {
+        $ret = ($promise.() % $MOD);
+        %h{$key} = $ret;
+    }
+
+    return $ret;
+}
+
+my %f_cache;
+
+sub f_mod($n)
+{
+    if ($n < 1)
+    {
+        die "Foo";
+    }
+
+    return _cache(%f_cache, $n, sub {
+        if ($n == 1)
+        {
+            return 1;
+        }
+        elsif ($n == 3)
+        {
+            return 3;
+        }
+        elsif (($n +& 1) == 0)
+        {
+            return f_mod($n +> 1);
+        }
+        elsif (($n +& 3) == 1)
+        {
+            return (2 * f_mod(($n +> 1) + 1) - f_mod($n +> 2));
+        }
+        else
+        {
+            return (3 * f_mod(($n +> 1)) - 2 * f_mod($n +> 2));
+        }
+        }
+    );
+}
+
+sub s_bruteforce
 {
-    say lookup($mult);
-    $mult +<= 1;
+    my ($n) = @_;
+
+    my $s = 0;
+
+    for 1 .. $n -> $i
+    {
+        ($s += f_mod($i)) %= $MOD;
+    }
+
+    return $s;
 }
 
+sub s_smart($start, $end)
+{
+    state %s_cache;
+
+    # say "s->e : $start->$end";
+    return _cache(%s_cache, "$start|$end", sub {
+        if ($start > $end)
+        {
+            return 0;
+        }
+        if ($start == $end)
+        {
+            return f_mod($start);
+        }
+        if ($end <= 8)
+        {
+            return s_bruteforce($end) - s_bruteforce($start - 1);
+        }
+        if (($start +& 0b11) != 0)
+        {
+            return (f_mod($start) + s_smart($start+1, $end));
+        }
+        if (($end +& 0b11) != 0b11)
+        {
+            return (f_mod($end) + s_smart($start, $end-1));
+        }
+        my $power2 = ((($start +& ($start-1)) != 0) ?? 1+(($start-1)+^$start) !! $start);
+        my $new_end = $start + $power2 - 1;
+        while ($new_end > $end)
+        {
+            $new_end = $start + ($power2 +>= 1) - 1;
+        }
+        my @c = lookup($power2);
+        my $m = $start / $power2;
+        return (@c[0] * f_mod($m*2+1) + @c[1] * f_mod($m) + s_smart($new_end+1, $end));
+    },
+);
+    }
+
+if (False)
+{
+    my $want = 0;
+    for 1 .. 100_000 -> $n
+    {
+        if ($n % 1_000 == 0)
+        {
+            say "Reached n=$n";
+        }
+        ($want += f_mod($n)) %= $MOD;
+        my $have = s_smart(1, $n);
+        if ($want != $have)
+        {
+            die "want=$want have=$have n=$n!";
+        }
+    }
+}
+
+{
+    say "S(3 ** 37) = ", s_smart(1, 3 ** 37);
+}