Add solution to Euler #612.

categories/euler/prob612-shlomif.p6

@@ -0,0 +1,133 @@
+my @FACTS = (1);
+for 1 .. 100 -> $n
+{
+    @FACTS.push(@FACTS[*-1] * $n);
+}
+
+say @FACTS[10];
+
+
+
+sub calc_count($l, $w_zero, $num_nat_digits)
+{
+    my $num_digits = $num_nat_digits + ($w_zero ?? 1 !! 0);
+    if $num_digits > $l
+    {
+        return 0;
+    }
+    if ! $w_zero
+    {
+        sub rec(@counts, $s)
+        {
+            if $s > $l
+            {
+                return 0;
+            }
+            if @counts == $num_digits
+            {
+                if $s != $l
+                {
+                    return 0;
+                }
+                my $ret = @FACTS[$l] * @FACTS[$num_digits];
+                my %repeats;
+                for @counts -> $x
+                {
+                    $ret /= @FACTS[$x];
+                    ++%repeats{$x};
+                }
+                for %repeats.values() -> $v
+                {
+                    $ret /= @FACTS[$v];
+                }
+                # say('ret = ', $ret, ' ',$s, ' ', $l, ' ', $num_digits, @counts);
+                return $ret;
+            }
+            my $ret = 0;
+            for 1 .. (+@counts ?? @counts[*-1] !! $l - $num_digits + 1) -> $nxt
+            {
+                $ret += rec([|@counts, $nxt], $s + $nxt);
+            }
+            return $ret;
+        }
+        return rec([], 0);
+    }
+    else
+    {
+        my $ret = 0;
+        # Choose a pivot for the first place and go for it
+        for 0 .. $l-2 -> $cnt
+        {
+            $ret += @FACTS[$l-1]/@FACTS[$cnt]/@FACTS[$l-1-$cnt] *
+                   calc_count($l - 1 - $cnt, False, $num_nat_digits);
+        }
+        return $ret * $num_nat_digits;
+        # raise BaseException("unimplemented")
+    }
+}
+
+sub solve($myl)
+{
+    my @counts;
+    for [False, True] -> $z
+    {
+        for 0 .. 9 -> $n
+        {
+            my $v = sum(map sub ($l) { calc_count($l, $z, $n) }, 0 .. $myl);
+            if $v > 0
+            {
+                @counts.push([$z, $n, $v]);
+            }
+        }
+    }
+    say(@counts);
+    my $ret = 0;
+    for 0 ..^@counts -> $ik
+    {
+        my ($zi, $ni, $vi) = |@counts[$ik];
+        for $ik ..^@counts -> $jk
+        {
+            my ($zj, $nj, $vj) = |@counts[$jk];
+            for 0 .. min($ni, $nj) -> $num_common
+            {
+                if ($num_common == 0 and (!$zi or !$zj))
+                {
+                    next;
+                }
+                my $i_num_diff = $ni - $num_common;
+                my $j_num_diff = $nj - $num_common;
+
+                my $digs = $num_common + $i_num_diff + $j_num_diff;
+                if $digs > 9
+                {
+                    next;
+                }
+                my $r = ($vi * $vj) * @FACTS[9] /
+                    @FACTS[$num_common] / @FACTS[$i_num_diff] /
+                    @FACTS[$j_num_diff] / @FACTS[9 - $digs];
+                if $ik == $jk
+                {
+                    if $num_common == $ni
+                    {
+                        $r -= $vi * @FACTS[9] / @FACTS[$ni] / @FACTS[9 - $ni];
+                    }
+                }
+                else
+                {
+                    $r *= 2;
+                }
+
+                say ("num_common=", $num_common, "i=", $ik, "j=", $jk,
+                       "r=", $r);
+                $ret += $r;
+            }
+        }
+    }
+    return $ret +> 1;
+}
+
+say ("s[fast] = ", solve(2));
+my $my_solution = solve(18);
+printf("solution = %d ( MOD = %d )\n", $my_solution, $my_solution % 1000267129);
+
+=finish