Add euler#220 .

Based on
https://github.com/shlomif/project-euler/tree/master/project-euler/220 .

perl6-benchmarks/benchmark.pl

@@ -19,7 +19,9 @@
 
 sub _bench
 {
-    my ( $DIR, $TESTS ) = @_;
+    my ( $DIR, $TESTS, $times ) = @_;
+
+    $times //= 1;
 
     if ( $DIR !~ /$FILTER/ )
     {
@@ -29,7 +31,7 @@ sub _bench
     print "Benchmarking $DIR\n";
 
     chdir($DIR);
-    timethese( 1, $TESTS, );
+    timethese( $times, $TESTS, );
     chdir($PWD);
 
     return;
@@ -52,6 +54,15 @@ sub _bench
         'p6' => sub { system( "perl6", "euler_189-2.p6" ); },
     }
 );
+_bench(
+    "./euler220/",
+    {
+        'cpy3' => sub { system( "python3", "220-v1.py" ); },
+        'pypy' => sub { system( "pypy",    "220-v1.py" ); },
+        'p6'   => sub { system( "perl6",   "220-v1.p6" ); },
+    },
+    50
+);
 _bench(
     "./euler287/",
     {

perl6-benchmarks/euler220/220-v1.p6

@@ -0,0 +1,104 @@
+#!/usr/bin/env perl6
+
+# The Expat License
+#
+# Copyright ($c) 2018, Shlomi Fish
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in
+# all copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+class XY { has $.x = 0; has $.y = 0; };
+multi infix:<+> (XY \a, XY \o) {
+    a.clone: |([«+»] (a, o)».Capture».hash)
+};
+multi infix:<-> (XY \a, XY \o) {
+    a.clone: |([«-»] (a, o)».Capture».hash)
+};
+class State {
+    has $.cur is rw = XY.new;
+    has $.dir1 is rw = 0;
+    has $.n is rw = 0;
+};
+multi infix:<+> (State \a, State \o) {
+    a.clone: |([«+»] (a, o)».Capture».hash)
+};
+multi infix:<-> (State \a, State \o) {
+    a.clone: |([«-»] (a, o)».Capture».hash)
+};
+
+sub master($maxdepth, $mn)
+{
+my $s1 = State.new;
+my %Cache;
+my @dirs = [XY.new(x=> 0, y=> 1), XY.new(x=> 1, y=> 0), XY.new(x=> 0, y=> -1), XY.new(x=> -1, y=> 0) ];
+my $printed = False;
+
+sub dragon($depth, $seq)
+{
+    my $init = $s1.clone;
+    my $key = ($depth, $seq, ($s1.dir1 +& 3));
+    if ( %Cache{$key}:exists ) {
+        my $val = %Cache{$key};
+        if $val.n + $s1.n < $mn {
+            $s1 = $s1 + $val;
+            return;
+        }
+    }
+    for $seq.comb() -> $c {
+        if $c eq 'a' {
+            if $depth < $maxdepth {
+                dragon($depth+1, 'aRbFR')
+            }
+        }
+        elsif $c eq 'b' {
+            if $depth < $maxdepth {
+                dragon($depth+1, 'LFaLb')
+            }
+        }
+        elsif $c eq 'R' {
+            ++$s1.dir1;
+        }
+        elsif $c eq 'L' {
+            --$s1.dir1;
+        }
+        elsif $c eq 'F' {
+            ++$s1.n;
+            $s1.cur = $s1.cur + @dirs[$s1.dir1 +& 3];
+        }
+        else {
+            die $c;
+            ...;
+        }
+        if $s1.n >= $mn {
+            if $s1.n == $mn {
+                if not $printed {
+                    printf("cur = %d,%d\n", $s1.cur.x, $s1.cur.y);
+                    $printed = True
+                }
+            }
+            return;
+        }
+    }
+    %Cache{$key} = $s1 - $init;
+}
+dragon(0, 'Fa');
+return;
+}
+
+master(10, 500);
+master(50, 1000000000000);

perl6-benchmarks/euler220/220-v1.py

@@ -0,0 +1,111 @@
+#!/usr/bin/env python
+
+# The Expat License
+#
+# Copyright (c) 2018, Shlomi Fish
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in
+# all copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+from six import print_
+
+
+class State:
+    """docstring for State"""
+
+    def __init__(self):
+        self.cur = [0, 0]
+        self.dir1 = 0
+        self.n = 0
+
+    def dup(self):
+        ret = State()
+        ret.cur = [x for x in self.cur]
+        ret.dir1 = self.dir1
+        ret.n = self.n
+        return ret
+
+    def delta(self, o):
+        ret = self.dup()
+        ret.cur[0] -= o.cur[0]
+        ret.cur[1] -= o.cur[1]
+        ret.dir1 -= o.dir1
+        ret.n -= o.n
+        return ret
+
+    def apply_delta(self, o):
+        ret = self.dup()
+        ret.cur[0] += o.cur[0]
+        ret.cur[1] += o.cur[1]
+        ret.dir1 += o.dir1
+        ret.n += o.n
+        return ret
+
+
+s = State()
+Cache = {}
+dirs = [(0, 1), (1, 0), (0, -1), (-1, 0)]
+maxdepth = 10
+mn = 500
+STEP = 100000000
+printed = False
+
+
+def dragon(depth, seq):
+    global Cache, maxdepth, s
+    init = s.dup()
+    key = (depth, seq, (s.dir1 & 3))
+    if key in Cache:
+        val = Cache[key]
+        if val.n + s.n < mn:
+            s = s.apply_delta(val)
+            return
+    for c in seq:
+        if c == 'a':
+            if depth < maxdepth:
+                dragon(depth+1, 'aRbFR')
+        elif c == 'b':
+            if depth < maxdepth:
+                dragon(depth+1, 'LFaLb')
+        elif c == 'R':
+            s.dir1 += 1
+        elif c == 'L':
+            s.dir1 -= 1
+        elif c == 'F':
+            s.n += 1
+            s.cur[0] += dirs[s.dir1 & 3][0]
+            s.cur[1] += dirs[s.dir1 & 3][1]
+        else:
+            raise BaseException("unknown")
+        if s.n >= mn:
+            if s.n == mn:
+                global printed
+                if not printed:
+                    print_("cur = %d,%d" % (s.cur[0], s.cur[1]))
+                    printed = True
+            return
+    Cache[key] = s.delta(init)
+
+
+dragon(0, 'Fa')
+maxdepth = 50
+mn = 1000000000000
+s = State()
+Cache = {}
+printed = False
+dragon(0, 'Fa')