Added recursive solutions

diff --git a/09-resolving-the-bill/interleaving.ipynb b/09-resolving-the-bill/interleaving.ipynb
index 26ebb46c2253b83bbad5e3a53407f766a58f8e45..c1c4bed9a63315a351d0716f4fd2dd9e0cddee53 100644 (file)
--- a/09-resolving-the-bill/interleaving.ipynb
+++ b/09-resolving-the-bill/interleaving.ipynb
@@ -651,7 +651,7 @@
     {
      "data": {
       "text/plain": [
-       "'gbbdffedehgebaaeghbggcfeegfaccdhaaaachhdhhchfcfdfb'"
+       "'fgcebagebfhfbadbgggacgeebbfceffhbhbgdfhhbahgbchbhe'"
       ]
      },
      "execution_count": 18,
@@ -713,51 +713,54 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0 0 0 adding u\n",
+      "0 0 0 adding y\n",
       "0 1 -1 adding a\n",
-      "1 1 0 adding c\n",
-      "2 1 1 adding v\n",
-      "2 2 0 adding h\n",
-      "3 2 1 adding e\n",
-      "4 2 2 adding v\n",
-      "4 3 1 adding e\n",
-      "5 3 2 adding u\n",
-      "5 4 1 adding f\n",
-      "6 4 2 adding u\n",
-      "6 5 1 adding v\n",
+      "1 1 0 adding z\n",
+      "1 2 -1 adding v\n",
+      "1 3 -2 adding x\n",
+      "1 4 -3 adding z\n",
+      "1 5 -4 adding w\n",
+      "1 6 -5 adding e\n",
+      "2 6 -4 adding h\n",
+      "3 6 -3 adding b\n",
+      "4 6 -2 adding a\n",
+      "5 6 -1 adding b\n",
       "6 6 0 adding u\n",
       "6 7 -1 adding x\n",
-      "6 8 -2 adding z\n",
-      "6 9 -3 adding u\n",
-      "6 10 -4 adding a\n",
-      "7 10 -3 adding e\n",
-      "8 10 -2 adding d\n",
-      "9 10 -1 adding h\n",
-      "10 10 0 adding v\n",
-      "10 11 -1 adding u\n",
-      "10 12 -2 adding h\n",
-      "11 12 -1 adding g\n",
-      "12 12 0 adding x\n",
-      "12 13 -1 adding e\n",
-      "13 13 0 adding f\n",
-      "14 13 1 adding w\n",
-      "14 14 0 adding y\n",
-      "14 15 -1 adding u\n",
-      "14 16 -2 adding d\n",
-      "15 16 -1 adding g\n",
-      "16 16 0 adding h\n",
-      "17 16 1 adding g\n",
-      "18 16 2 adding g\n",
-      "19 16 3 adding g\n",
-      "20 16 4 remaining s2 yyuz\n"
+      "6 8 -2 adding e\n",
+      "7 8 -1 adding y\n",
+      "7 9 -2 adding x\n",
+      "7 10 -3 adding x\n",
+      "7 11 -4 adding x\n",
+      "7 12 -5 adding e\n",
+      "8 12 -4 adding e\n",
+      "9 12 -3 adding z\n",
+      "9 13 -4 adding z\n",
+      "9 14 -5 adding a\n",
+      "10 14 -4 adding c\n",
+      "11 14 -3 adding y\n",
+      "11 15 -4 adding d\n",
+      "12 15 -3 adding g\n",
+      "13 15 -2 adding g\n",
+      "14 15 -1 adding c\n",
+      "15 15 0 adding x\n",
+      "15 16 -1 adding e\n",
+      "16 16 0 adding f\n",
+      "17 16 1 adding w\n",
+      "17 17 0 adding w\n",
+      "17 18 -1 adding v\n",
+      "17 19 -2 adding f\n",
+      "18 19 -1 adding a\n",
+      "19 19 0 adding g\n",
+      "20 19 1 remaining s2 z\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "('acheefaedhhgefdghggg',\n",
-       " 'uvvuuvuxzuvuxwyuyyuz',\n",
-       " 'uacvheveufuvuxzuaedhvuhgxefwyudghgggyyuz',\n",
+       "('aehbabeeeacdggceffag',\n",
+       " 'yzvxzwuxyxxxzzyxwwvz',\n",
+       " 'yazvxzwehbabuxeyxxxeezzacydggcxefwwvfagz',\n",
        " 40)"
       ]
      },
@@ -783,466 +786,472 @@
      "output_type": "stream",
      "text": [
       "xxxx 0 0 ! ! ! True\n",
-      "seq2 0 1 ! a u False\n",
-      "seq2 0 2 ! c a False\n",
-      "seq2 0 3 ! h c False\n",
-      "seq2 0 4 ! e v False\n",
-      "seq2 0 5 ! e h False\n",
-      "seq2 0 6 ! f e False\n",
-      "seq2 0 7 ! a v False\n",
+      "seq2 0 1 ! a y False\n",
+      "seq2 0 2 ! e a False\n",
+      "seq2 0 3 ! h z False\n",
+      "seq2 0 4 ! b v False\n",
+      "seq2 0 5 ! a x False\n",
+      "seq2 0 6 ! b z False\n",
+      "seq2 0 7 ! e w False\n",
       "seq2 0 8 ! e e False\n",
-      "seq2 0 9 ! d u False\n",
-      "seq2 0 10 ! h f False\n",
-      "seq2 0 11 ! h u False\n",
-      "seq2 0 12 ! g v False\n",
-      "seq2 0 13 ! e u False\n",
-      "seq2 0 14 ! f x False\n",
-      "seq2 0 15 ! d z False\n",
-      "seq2 0 16 ! g u False\n",
-      "seq2 0 17 ! h a False\n",
-      "seq2 0 18 ! g e False\n",
-      "seq2 0 19 ! g d False\n",
-      "seq2 0 20 ! g h False\n",
-      "seq1 1 0 u ! u True\n",
-      "seq2 1 1 u a a True\n",
-      "seq2 1 2 u c c True\n",
-      "xxxx 1 3 u h v False\n",
-      "xxxx 1 4 u e h False\n",
-      "xxxx 1 5 u e e False\n",
-      "xxxx 1 6 u f v False\n",
-      "xxxx 1 7 u a e False\n",
-      "xxxx 1 8 u e u False\n",
-      "xxxx 1 9 u d f False\n",
-      "xxxx 1 10 u h u False\n",
-      "xxxx 1 11 u h v False\n",
-      "xxxx 1 12 u g u False\n",
-      "xxxx 1 13 u e x False\n",
-      "xxxx 1 14 u f z False\n",
-      "xxxx 1 15 u d u False\n",
-      "xxxx 1 16 u g a False\n",
-      "xxxx 1 17 u h e False\n",
-      "xxxx 1 18 u g d False\n",
-      "xxxx 1 19 u g h False\n",
-      "xxxx 1 20 u g v False\n",
-      "seq1 2 0 v ! a False\n",
-      "xxxx 2 1 v a c False\n",
-      "seq1 2 2 v c v True\n",
-      "seq2 2 3 v h h True\n",
-      "seq2 2 4 v e e True\n",
-      "xxxx 2 5 v e v False\n",
-      "xxxx 2 6 v f e False\n",
-      "xxxx 2 7 v a u False\n",
-      "xxxx 2 8 v e f False\n",
-      "xxxx 2 9 v d u False\n",
-      "xxxx 2 10 v h v False\n",
-      "xxxx 2 11 v h u False\n",
-      "xxxx 2 12 v g x False\n",
-      "xxxx 2 13 v e z False\n",
-      "xxxx 2 14 v f u False\n",
-      "xxxx 2 15 v d a False\n",
-      "xxxx 2 16 v g e False\n",
-      "xxxx 2 17 v h d False\n",
-      "xxxx 2 18 v g h False\n",
-      "xxxx 2 19 v g v False\n",
-      "xxxx 2 20 v g u False\n",
-      "seq1 3 0 v ! c False\n",
-      "xxxx 3 1 v a v False\n",
-      "xxxx 3 2 v c h False\n",
-      "xxxx 3 3 v h e False\n",
-      "seq1 3 4 v e v True\n",
-      "seq2 3 5 v e e True\n",
-      "xxxx 3 6 v f u False\n",
-      "xxxx 3 7 v a f False\n",
-      "xxxx 3 8 v e u False\n",
-      "xxxx 3 9 v d v False\n",
-      "xxxx 3 10 v h u False\n",
-      "xxxx 3 11 v h x False\n",
-      "xxxx 3 12 v g z False\n",
-      "xxxx 3 13 v e u False\n",
-      "xxxx 3 14 v f a False\n",
-      "xxxx 3 15 v d e False\n",
-      "xxxx 3 16 v g d False\n",
-      "xxxx 3 17 v h h False\n",
-      "xxxx 3 18 v g v False\n",
-      "xxxx 3 19 v g u False\n",
-      "xxxx 3 20 v g h False\n",
-      "seq1 4 0 u ! v False\n",
-      "xxxx 4 1 u a h False\n",
-      "xxxx 4 2 u c e False\n",
-      "xxxx 4 3 u h v False\n",
-      "xxxx 4 4 u e e False\n",
-      "seq1 4 5 u e u True\n",
-      "seq2 4 6 u f f True\n",
-      "xxxx 4 7 u a u False\n",
-      "xxxx 4 8 u e v False\n",
-      "xxxx 4 9 u d u False\n",
-      "xxxx 4 10 u h x False\n",
-      "xxxx 4 11 u h z False\n",
-      "xxxx 4 12 u g u False\n",
-      "xxxx 4 13 u e a False\n",
-      "xxxx 4 14 u f e False\n",
-      "xxxx 4 15 u d d False\n",
-      "xxxx 4 16 u g h False\n",
-      "xxxx 4 17 u h v False\n",
-      "xxxx 4 18 u g u False\n",
-      "xxxx 4 19 u g h False\n",
-      "xxxx 4 20 u g g False\n",
-      "seq1 5 0 u ! h False\n",
-      "xxxx 5 1 u a e False\n",
-      "xxxx 5 2 u c v False\n",
-      "xxxx 5 3 u h e False\n",
-      "xxxx 5 4 u e u False\n",
-      "xxxx 5 5 u e f False\n",
-      "seq1 5 6 u f u True\n",
-      "xxxx 5 7 u a v False\n",
-      "xxxx 5 8 u e u False\n",
-      "xxxx 5 9 u d x False\n",
-      "xxxx 5 10 u h z False\n",
-      "xxxx 5 11 u h u False\n",
-      "xxxx 5 12 u g a False\n",
-      "xxxx 5 13 u e e False\n",
-      "xxxx 5 14 u f d False\n",
-      "xxxx 5 15 u d h False\n",
-      "xxxx 5 16 u g v False\n",
-      "xxxx 5 17 u h u False\n",
-      "xxxx 5 18 u g h False\n",
-      "xxxx 5 19 u g g False\n",
-      "xxxx 5 20 u g x False\n",
-      "seq1 6 0 v ! e False\n",
-      "xxxx 6 1 v a v False\n",
-      "xxxx 6 2 v c e False\n",
-      "xxxx 6 3 v h u False\n",
-      "xxxx 6 4 v e f False\n",
-      "xxxx 6 5 v e u False\n",
-      "seq1 6 6 v f v True\n",
-      "xxxx 6 7 v a u False\n",
-      "xxxx 6 8 v e x False\n",
-      "xxxx 6 9 v d z False\n",
-      "xxxx 6 10 v h u False\n",
-      "xxxx 6 11 v h a False\n",
-      "xxxx 6 12 v g e False\n",
-      "xxxx 6 13 v e d False\n",
-      "xxxx 6 14 v f h False\n",
-      "xxxx 6 15 v d v False\n",
-      "xxxx 6 16 v g u False\n",
-      "xxxx 6 17 v h h False\n",
-      "xxxx 6 18 v g g False\n",
-      "xxxx 6 19 v g x False\n",
-      "xxxx 6 20 v g e False\n",
-      "seq1 7 0 u ! v False\n",
+      "seq2 0 9 ! e h False\n",
+      "seq2 0 10 ! a b False\n",
+      "seq2 0 11 ! c a False\n",
+      "seq2 0 12 ! d b False\n",
+      "seq2 0 13 ! g u False\n",
+      "seq2 0 14 ! g x False\n",
+      "seq2 0 15 ! c e False\n",
+      "seq2 0 16 ! e y False\n",
+      "seq2 0 17 ! f x False\n",
+      "seq2 0 18 ! f x False\n",
+      "seq2 0 19 ! a x False\n",
+      "seq2 0 20 ! g e False\n",
+      "seq1 1 0 y ! y True\n",
+      "seq2 1 1 y a a True\n",
+      "xxxx 1 2 y e z False\n",
+      "xxxx 1 3 y h v False\n",
+      "xxxx 1 4 y b x False\n",
+      "xxxx 1 5 y a z False\n",
+      "xxxx 1 6 y b w False\n",
+      "xxxx 1 7 y e e False\n",
+      "xxxx 1 8 y e h False\n",
+      "xxxx 1 9 y e b False\n",
+      "xxxx 1 10 y a a False\n",
+      "xxxx 1 11 y c b False\n",
+      "xxxx 1 12 y d u False\n",
+      "xxxx 1 13 y g x False\n",
+      "xxxx 1 14 y g e False\n",
+      "xxxx 1 15 y c y False\n",
+      "xxxx 1 16 y e x False\n",
+      "xxxx 1 17 y f x False\n",
+      "xxxx 1 18 y f x False\n",
+      "xxxx 1 19 y a e False\n",
+      "xxxx 1 20 y g e False\n",
+      "seq1 2 0 z ! a False\n",
+      "seq1 2 1 z a z True\n",
+      "xxxx 2 2 z e v False\n",
+      "xxxx 2 3 z h x False\n",
+      "xxxx 2 4 z b z False\n",
+      "xxxx 2 5 z a w False\n",
+      "xxxx 2 6 z b e False\n",
+      "xxxx 2 7 z e h False\n",
+      "xxxx 2 8 z e b False\n",
+      "xxxx 2 9 z e a False\n",
+      "xxxx 2 10 z a b False\n",
+      "xxxx 2 11 z c u False\n",
+      "xxxx 2 12 z d x False\n",
+      "xxxx 2 13 z g e False\n",
+      "xxxx 2 14 z g y False\n",
+      "xxxx 2 15 z c x False\n",
+      "xxxx 2 16 z e x False\n",
+      "xxxx 2 17 z f x False\n",
+      "xxxx 2 18 z f e False\n",
+      "xxxx 2 19 z a e False\n",
+      "xxxx 2 20 z g z False\n",
+      "seq1 3 0 v ! z False\n",
+      "seq1 3 1 v a v True\n",
+      "xxxx 3 2 v e x False\n",
+      "xxxx 3 3 v h z False\n",
+      "xxxx 3 4 v b w False\n",
+      "xxxx 3 5 v a e False\n",
+      "xxxx 3 6 v b h False\n",
+      "xxxx 3 7 v e b False\n",
+      "xxxx 3 8 v e a False\n",
+      "xxxx 3 9 v e b False\n",
+      "xxxx 3 10 v a u False\n",
+      "xxxx 3 11 v c x False\n",
+      "xxxx 3 12 v d e False\n",
+      "xxxx 3 13 v g y False\n",
+      "xxxx 3 14 v g x False\n",
+      "xxxx 3 15 v c x False\n",
+      "xxxx 3 16 v e x False\n",
+      "xxxx 3 17 v f e False\n",
+      "xxxx 3 18 v f e False\n",
+      "xxxx 3 19 v a z False\n",
+      "xxxx 3 20 v g z False\n",
+      "seq1 4 0 x ! v False\n",
+      "seq1 4 1 x a x True\n",
+      "xxxx 4 2 x e z False\n",
+      "xxxx 4 3 x h w False\n",
+      "xxxx 4 4 x b e False\n",
+      "xxxx 4 5 x a h False\n",
+      "xxxx 4 6 x b b False\n",
+      "xxxx 4 7 x e a False\n",
+      "xxxx 4 8 x e b False\n",
+      "xxxx 4 9 x e u False\n",
+      "xxxx 4 10 x a x False\n",
+      "xxxx 4 11 x c e False\n",
+      "xxxx 4 12 x d y False\n",
+      "xxxx 4 13 x g x False\n",
+      "xxxx 4 14 x g x False\n",
+      "xxxx 4 15 x c x False\n",
+      "xxxx 4 16 x e e False\n",
+      "xxxx 4 17 x f e False\n",
+      "xxxx 4 18 x f z False\n",
+      "xxxx 4 19 x a z False\n",
+      "xxxx 4 20 x g a False\n",
+      "seq1 5 0 z ! x False\n",
+      "seq1 5 1 z a z True\n",
+      "xxxx 5 2 z e w False\n",
+      "xxxx 5 3 z h e False\n",
+      "xxxx 5 4 z b h False\n",
+      "xxxx 5 5 z a b False\n",
+      "xxxx 5 6 z b a False\n",
+      "xxxx 5 7 z e b False\n",
+      "xxxx 5 8 z e u False\n",
+      "xxxx 5 9 z e x False\n",
+      "xxxx 5 10 z a e False\n",
+      "xxxx 5 11 z c y False\n",
+      "xxxx 5 12 z d x False\n",
+      "xxxx 5 13 z g x False\n",
+      "xxxx 5 14 z g x False\n",
+      "xxxx 5 15 z c e False\n",
+      "xxxx 5 16 z e e False\n",
+      "xxxx 5 17 z f z False\n",
+      "xxxx 5 18 z f z False\n",
+      "xxxx 5 19 z a a False\n",
+      "xxxx 5 20 z g c False\n",
+      "seq1 6 0 w ! z False\n",
+      "seq1 6 1 w a w True\n",
+      "seq2 6 2 w e e True\n",
+      "seq2 6 3 w h h True\n",
+      "seq2 6 4 w b b True\n",
+      "seq2 6 5 w a a True\n",
+      "seq2 6 6 w b b True\n",
+      "xxxx 6 7 w e u False\n",
+      "xxxx 6 8 w e x False\n",
+      "xxxx 6 9 w e e False\n",
+      "xxxx 6 10 w a y False\n",
+      "xxxx 6 11 w c x False\n",
+      "xxxx 6 12 w d x False\n",
+      "xxxx 6 13 w g x False\n",
+      "xxxx 6 14 w g e False\n",
+      "xxxx 6 15 w c e False\n",
+      "xxxx 6 16 w e z False\n",
+      "xxxx 6 17 w f z False\n",
+      "xxxx 6 18 w f a False\n",
+      "xxxx 6 19 w a c False\n",
+      "xxxx 6 20 w g y False\n",
+      "seq1 7 0 u ! w False\n",
       "xxxx 7 1 u a e False\n",
-      "xxxx 7 2 u c u False\n",
-      "xxxx 7 3 u h f False\n",
-      "xxxx 7 4 u e u False\n",
-      "xxxx 7 5 u e v False\n",
-      "seq1 7 6 u f u True\n",
-      "xxxx 7 7 u a x False\n",
-      "xxxx 7 8 u e z False\n",
-      "xxxx 7 9 u d u False\n",
-      "xxxx 7 10 u h a False\n",
-      "xxxx 7 11 u h e False\n",
-      "xxxx 7 12 u g d False\n",
-      "xxxx 7 13 u e h False\n",
-      "xxxx 7 14 u f v False\n",
-      "xxxx 7 15 u d u False\n",
-      "xxxx 7 16 u g h False\n",
-      "xxxx 7 17 u h g False\n",
-      "xxxx 7 18 u g x False\n",
-      "xxxx 7 19 u g e False\n",
-      "xxxx 7 20 u g f False\n",
+      "xxxx 7 2 u e h False\n",
+      "xxxx 7 3 u h b False\n",
+      "xxxx 7 4 u b a False\n",
+      "xxxx 7 5 u a b False\n",
+      "seq1 7 6 u b u True\n",
+      "xxxx 7 7 u e x False\n",
+      "xxxx 7 8 u e e False\n",
+      "xxxx 7 9 u e y False\n",
+      "xxxx 7 10 u a x False\n",
+      "xxxx 7 11 u c x False\n",
+      "xxxx 7 12 u d x False\n",
+      "xxxx 7 13 u g e False\n",
+      "xxxx 7 14 u g e False\n",
+      "xxxx 7 15 u c z False\n",
+      "xxxx 7 16 u e z False\n",
+      "xxxx 7 17 u f a False\n",
+      "xxxx 7 18 u f c False\n",
+      "xxxx 7 19 u a y False\n",
+      "xxxx 7 20 u g d False\n",
       "seq1 8 0 x ! e False\n",
-      "xxxx 8 1 x a u False\n",
-      "xxxx 8 2 x c f False\n",
-      "xxxx 8 3 x h u False\n",
-      "xxxx 8 4 x e v False\n",
-      "xxxx 8 5 x e u False\n",
-      "seq1 8 6 x f x True\n",
-      "xxxx 8 7 x a z False\n",
-      "xxxx 8 8 x e u False\n",
-      "xxxx 8 9 x d a False\n",
-      "xxxx 8 10 x h e False\n",
-      "xxxx 8 11 x h d False\n",
-      "xxxx 8 12 x g h False\n",
-      "xxxx 8 13 x e v False\n",
-      "xxxx 8 14 x f u False\n",
-      "xxxx 8 15 x d h False\n",
-      "xxxx 8 16 x g g False\n",
-      "xxxx 8 17 x h x False\n",
-      "xxxx 8 18 x g e False\n",
-      "xxxx 8 19 x g f False\n",
-      "xxxx 8 20 x g w False\n",
-      "seq1 9 0 z ! u False\n",
-      "xxxx 9 1 z a f False\n",
-      "xxxx 9 2 z c u False\n",
-      "xxxx 9 3 z h v False\n",
-      "xxxx 9 4 z e u False\n",
-      "xxxx 9 5 z e x False\n",
-      "seq1 9 6 z f z True\n",
-      "xxxx 9 7 z a u False\n",
-      "xxxx 9 8 z e a False\n",
-      "xxxx 9 9 z d e False\n",
-      "xxxx 9 10 z h d False\n",
-      "xxxx 9 11 z h h False\n",
-      "xxxx 9 12 z g v False\n",
-      "xxxx 9 13 z e u False\n",
-      "xxxx 9 14 z f h False\n",
-      "xxxx 9 15 z d g False\n",
-      "xxxx 9 16 z g x False\n",
-      "xxxx 9 17 z h e False\n",
-      "xxxx 9 18 z g f False\n",
-      "xxxx 9 19 z g w False\n",
-      "xxxx 9 20 z g y False\n",
-      "seq1 10 0 u ! f False\n",
-      "xxxx 10 1 u a u False\n",
-      "xxxx 10 2 u c v False\n",
-      "xxxx 10 3 u h u False\n",
-      "xxxx 10 4 u e x False\n",
-      "xxxx 10 5 u e z False\n",
-      "seq1 10 6 u f u True\n",
-      "seq2 10 7 u a a True\n",
-      "seq2 10 8 u e e True\n",
-      "seq2 10 9 u d d True\n",
-      "seq2 10 10 u h h True\n",
-      "xxxx 10 11 u h v False\n",
-      "xxxx 10 12 u g u False\n",
-      "xxxx 10 13 u e h False\n",
-      "xxxx 10 14 u f g False\n",
-      "xxxx 10 15 u d x False\n",
-      "xxxx 10 16 u g e False\n",
-      "xxxx 10 17 u h f False\n",
-      "xxxx 10 18 u g w False\n",
-      "xxxx 10 19 u g y False\n",
-      "xxxx 10 20 u g u False\n",
-      "seq1 11 0 v ! u False\n",
-      "xxxx 11 1 v a v False\n",
-      "xxxx 11 2 v c u False\n",
-      "xxxx 11 3 v h x False\n",
-      "xxxx 11 4 v e z False\n",
-      "xxxx 11 5 v e u False\n",
-      "xxxx 11 6 v f a False\n",
-      "xxxx 11 7 v a e False\n",
-      "xxxx 11 8 v e d False\n",
-      "xxxx 11 9 v d h False\n",
-      "seq1 11 10 v h v True\n",
-      "xxxx 11 11 v h u False\n",
-      "xxxx 11 12 v g h False\n",
-      "xxxx 11 13 v e g False\n",
-      "xxxx 11 14 v f x False\n",
-      "xxxx 11 15 v d e False\n",
-      "xxxx 11 16 v g f False\n",
-      "xxxx 11 17 v h w False\n",
-      "xxxx 11 18 v g y False\n",
-      "xxxx 11 19 v g u False\n",
-      "xxxx 11 20 v g d False\n",
-      "seq1 12 0 u ! v False\n",
-      "xxxx 12 1 u a u False\n",
-      "xxxx 12 2 u c x False\n",
-      "xxxx 12 3 u h z False\n",
-      "xxxx 12 4 u e u False\n",
-      "xxxx 12 5 u e a False\n",
-      "xxxx 12 6 u f e False\n",
-      "xxxx 12 7 u a d False\n",
-      "xxxx 12 8 u e h False\n",
-      "xxxx 12 9 u d v False\n",
-      "seq1 12 10 u h u True\n",
-      "seq2 12 11 u h h True\n",
-      "seq2 12 12 u g g True\n",
-      "xxxx 12 13 u e x False\n",
-      "xxxx 12 14 u f e False\n",
-      "xxxx 12 15 u d f False\n",
-      "xxxx 12 16 u g w False\n",
-      "xxxx 12 17 u h y False\n",
-      "xxxx 12 18 u g u False\n",
-      "xxxx 12 19 u g d False\n",
-      "xxxx 12 20 u g g False\n",
-      "seq1 13 0 x ! u False\n",
-      "xxxx 13 1 x a x False\n",
-      "xxxx 13 2 x c z False\n",
-      "xxxx 13 3 x h u False\n",
-      "xxxx 13 4 x e a False\n",
-      "xxxx 13 5 x e e False\n",
-      "xxxx 13 6 x f d False\n",
-      "xxxx 13 7 x a h False\n",
-      "xxxx 13 8 x e v False\n",
-      "xxxx 13 9 x d u False\n",
-      "xxxx 13 10 x h h False\n",
-      "xxxx 13 11 x h g False\n",
-      "seq1 13 12 x g x True\n",
-      "seq2 13 13 x e e True\n",
-      "seq2 13 14 x f f True\n",
-      "xxxx 13 15 x d w False\n",
-      "xxxx 13 16 x g y False\n",
-      "xxxx 13 17 x h u False\n",
-      "xxxx 13 18 x g d False\n",
-      "xxxx 13 19 x g g False\n",
-      "xxxx 13 20 x g h False\n",
-      "seq1 14 0 w ! x False\n",
-      "xxxx 14 1 w a z False\n",
-      "xxxx 14 2 w c u False\n",
-      "xxxx 14 3 w h a False\n",
-      "xxxx 14 4 w e e False\n",
-      "xxxx 14 5 w e d False\n",
-      "xxxx 14 6 w f h False\n",
-      "xxxx 14 7 w a v False\n",
-      "xxxx 14 8 w e u False\n",
-      "xxxx 14 9 w d h False\n",
-      "xxxx 14 10 w h g False\n",
-      "xxxx 14 11 w h x False\n",
-      "xxxx 14 12 w g e False\n",
-      "xxxx 14 13 w e f False\n",
-      "seq1 14 14 w f w True\n",
-      "xxxx 14 15 w d y False\n",
-      "xxxx 14 16 w g u False\n",
-      "xxxx 14 17 w h d False\n",
-      "xxxx 14 18 w g g False\n",
-      "xxxx 14 19 w g h False\n",
-      "xxxx 14 20 w g g False\n",
-      "seq1 15 0 y ! z False\n",
-      "xxxx 15 1 y a u False\n",
-      "xxxx 15 2 y c a False\n",
-      "xxxx 15 3 y h e False\n",
-      "xxxx 15 4 y e d False\n",
-      "xxxx 15 5 y e h False\n",
-      "xxxx 15 6 y f v False\n",
-      "xxxx 15 7 y a u False\n",
-      "xxxx 15 8 y e h False\n",
-      "xxxx 15 9 y d g False\n",
-      "xxxx 15 10 y h x False\n",
-      "xxxx 15 11 y h e False\n",
-      "xxxx 15 12 y g f False\n",
-      "xxxx 15 13 y e w False\n",
-      "seq1 15 14 y f y True\n",
-      "xxxx 15 15 y d u False\n",
-      "xxxx 15 16 y g d False\n",
-      "xxxx 15 17 y h g False\n",
-      "xxxx 15 18 y g h False\n",
-      "xxxx 15 19 y g g False\n",
-      "xxxx 15 20 y g g False\n",
-      "seq1 16 0 u ! u False\n",
-      "xxxx 16 1 u a a False\n",
-      "xxxx 16 2 u c e False\n",
-      "xxxx 16 3 u h d False\n",
-      "xxxx 16 4 u e h False\n",
-      "xxxx 16 5 u e v False\n",
-      "xxxx 16 6 u f u False\n",
-      "xxxx 16 7 u a h False\n",
-      "xxxx 16 8 u e g False\n",
-      "xxxx 16 9 u d x False\n",
-      "xxxx 16 10 u h e False\n",
-      "xxxx 16 11 u h f False\n",
-      "xxxx 16 12 u g w False\n",
-      "xxxx 16 13 u e y False\n",
-      "seq1 16 14 u f u True\n",
-      "seq2 16 15 u d d True\n",
-      "seq2 16 16 u g g True\n",
-      "seq2 16 17 u h h True\n",
-      "seq2 16 18 u g g True\n",
-      "seq2 16 19 u g g True\n",
-      "seq2 16 20 u g g True\n",
-      "seq1 17 0 y ! a False\n",
-      "xxxx 17 1 y a e False\n",
-      "xxxx 17 2 y c d False\n",
-      "xxxx 17 3 y h h False\n",
-      "xxxx 17 4 y e v False\n",
-      "xxxx 17 5 y e u False\n",
-      "xxxx 17 6 y f h False\n",
-      "xxxx 17 7 y a g False\n",
-      "xxxx 17 8 y e x False\n",
-      "xxxx 17 9 y d e False\n",
-      "xxxx 17 10 y h f False\n",
-      "xxxx 17 11 y h w False\n",
-      "xxxx 17 12 y g y False\n",
-      "xxxx 17 13 y e u False\n",
-      "xxxx 17 14 y f d False\n",
-      "xxxx 17 15 y d g False\n",
-      "xxxx 17 16 y g h False\n",
-      "xxxx 17 17 y h g False\n",
-      "xxxx 17 18 y g g False\n",
-      "xxxx 17 19 y g g False\n",
-      "seq1 17 20 y g y True\n",
-      "seq1 18 0 y ! e False\n",
-      "xxxx 18 1 y a d False\n",
-      "xxxx 18 2 y c h False\n",
-      "xxxx 18 3 y h v False\n",
-      "xxxx 18 4 y e u False\n",
-      "xxxx 18 5 y e h False\n",
-      "xxxx 18 6 y f g False\n",
-      "xxxx 18 7 y a x False\n",
-      "xxxx 18 8 y e e False\n",
-      "xxxx 18 9 y d f False\n",
-      "xxxx 18 10 y h w False\n",
-      "xxxx 18 11 y h y False\n",
-      "xxxx 18 12 y g u False\n",
-      "xxxx 18 13 y e d False\n",
-      "xxxx 18 14 y f g False\n",
-      "xxxx 18 15 y d h False\n",
-      "xxxx 18 16 y g g False\n",
-      "xxxx 18 17 y h g False\n",
-      "xxxx 18 18 y g g False\n",
-      "xxxx 18 19 y g y False\n",
-      "seq1 18 20 y g y True\n",
-      "seq1 19 0 u ! d False\n",
-      "xxxx 19 1 u a h False\n",
-      "xxxx 19 2 u c v False\n",
-      "xxxx 19 3 u h u False\n",
-      "xxxx 19 4 u e h False\n",
-      "xxxx 19 5 u e g False\n",
-      "xxxx 19 6 u f x False\n",
-      "xxxx 19 7 u a e False\n",
-      "xxxx 19 8 u e f False\n",
-      "xxxx 19 9 u d w False\n",
-      "xxxx 19 10 u h y False\n",
-      "xxxx 19 11 u h u False\n",
-      "xxxx 19 12 u g d False\n",
-      "xxxx 19 13 u e g False\n",
-      "xxxx 19 14 u f h False\n",
-      "xxxx 19 15 u d g False\n",
-      "xxxx 19 16 u g g False\n",
-      "xxxx 19 17 u h g False\n",
-      "xxxx 19 18 u g y False\n",
-      "xxxx 19 19 u g y False\n",
-      "seq1 19 20 u g u True\n",
-      "seq1 20 0 z ! h False\n",
-      "xxxx 20 1 z a v False\n",
-      "xxxx 20 2 z c u False\n",
-      "xxxx 20 3 z h h False\n",
-      "xxxx 20 4 z e g False\n",
-      "xxxx 20 5 z e x False\n",
-      "xxxx 20 6 z f e False\n",
-      "xxxx 20 7 z a f False\n",
-      "xxxx 20 8 z e w False\n",
-      "xxxx 20 9 z d y False\n",
-      "xxxx 20 10 z h u False\n",
-      "xxxx 20 11 z h d False\n",
-      "xxxx 20 12 z g g False\n",
-      "xxxx 20 13 z e h False\n",
-      "xxxx 20 14 z f g False\n",
-      "xxxx 20 15 z d g False\n",
-      "xxxx 20 16 z g g False\n",
-      "xxxx 20 17 z h y False\n",
-      "xxxx 20 18 z g y False\n",
-      "xxxx 20 19 z g u False\n",
+      "xxxx 8 1 x a h False\n",
+      "xxxx 8 2 x e b False\n",
+      "xxxx 8 3 x h a False\n",
+      "xxxx 8 4 x b b False\n",
+      "xxxx 8 5 x a u False\n",
+      "seq1 8 6 x b x True\n",
+      "seq2 8 7 x e e True\n",
+      "xxxx 8 8 x e y False\n",
+      "xxxx 8 9 x e x False\n",
+      "xxxx 8 10 x a x False\n",
+      "xxxx 8 11 x c x False\n",
+      "xxxx 8 12 x d e False\n",
+      "xxxx 8 13 x g e False\n",
+      "xxxx 8 14 x g z False\n",
+      "xxxx 8 15 x c z False\n",
+      "xxxx 8 16 x e a False\n",
+      "xxxx 8 17 x f c False\n",
+      "xxxx 8 18 x f y False\n",
+      "xxxx 8 19 x a d False\n",
+      "xxxx 8 20 x g g False\n",
+      "seq1 9 0 y ! h False\n",
+      "xxxx 9 1 y a b False\n",
+      "xxxx 9 2 y e a False\n",
+      "xxxx 9 3 y h b False\n",
+      "xxxx 9 4 y b u False\n",
+      "xxxx 9 5 y a x False\n",
+      "xxxx 9 6 y b e False\n",
+      "seq1 9 7 y e y True\n",
+      "xxxx 9 8 y e x False\n",
+      "xxxx 9 9 y e x False\n",
+      "xxxx 9 10 y a x False\n",
+      "xxxx 9 11 y c e False\n",
+      "xxxx 9 12 y d e False\n",
+      "xxxx 9 13 y g z False\n",
+      "xxxx 9 14 y g z False\n",
+      "xxxx 9 15 y c a False\n",
+      "xxxx 9 16 y e c False\n",
+      "xxxx 9 17 y f y False\n",
+      "xxxx 9 18 y f d False\n",
+      "xxxx 9 19 y a g False\n",
+      "xxxx 9 20 y g g False\n",
+      "seq1 10 0 x ! b False\n",
+      "xxxx 10 1 x a a False\n",
+      "xxxx 10 2 x e b False\n",
+      "xxxx 10 3 x h u False\n",
+      "xxxx 10 4 x b x False\n",
+      "xxxx 10 5 x a e False\n",
+      "xxxx 10 6 x b y False\n",
+      "seq1 10 7 x e x True\n",
+      "xxxx 10 8 x e x False\n",
+      "xxxx 10 9 x e x False\n",
+      "xxxx 10 10 x a e False\n",
+      "xxxx 10 11 x c e False\n",
+      "xxxx 10 12 x d z False\n",
+      "xxxx 10 13 x g z False\n",
+      "xxxx 10 14 x g a False\n",
+      "xxxx 10 15 x c c False\n",
+      "xxxx 10 16 x e y False\n",
+      "xxxx 10 17 x f d False\n",
+      "xxxx 10 18 x f g False\n",
+      "xxxx 10 19 x a g False\n",
+      "xxxx 10 20 x g c False\n",
+      "seq1 11 0 x ! a False\n",
+      "xxxx 11 1 x a b False\n",
+      "xxxx 11 2 x e u False\n",
+      "xxxx 11 3 x h x False\n",
+      "xxxx 11 4 x b e False\n",
+      "xxxx 11 5 x a y False\n",
+      "xxxx 11 6 x b x False\n",
+      "seq1 11 7 x e x True\n",
+      "xxxx 11 8 x e x False\n",
+      "xxxx 11 9 x e e False\n",
+      "xxxx 11 10 x a e False\n",
+      "xxxx 11 11 x c z False\n",
+      "xxxx 11 12 x d z False\n",
+      "xxxx 11 13 x g a False\n",
+      "xxxx 11 14 x g c False\n",
+      "xxxx 11 15 x c y False\n",
+      "xxxx 11 16 x e d False\n",
+      "xxxx 11 17 x f g False\n",
+      "xxxx 11 18 x f g False\n",
+      "xxxx 11 19 x a c False\n",
+      "xxxx 11 20 x g x False\n",
+      "seq1 12 0 x ! b False\n",
+      "xxxx 12 1 x a u False\n",
+      "xxxx 12 2 x e x False\n",
+      "xxxx 12 3 x h e False\n",
+      "xxxx 12 4 x b y False\n",
+      "xxxx 12 5 x a x False\n",
+      "xxxx 12 6 x b x False\n",
+      "seq1 12 7 x e x True\n",
+      "seq2 12 8 x e e True\n",
+      "seq2 12 9 x e e True\n",
+      "xxxx 12 10 x a z False\n",
+      "xxxx 12 11 x c z False\n",
+      "xxxx 12 12 x d a False\n",
+      "xxxx 12 13 x g c False\n",
+      "xxxx 12 14 x g y False\n",
+      "xxxx 12 15 x c d False\n",
+      "xxxx 12 16 x e g False\n",
+      "xxxx 12 17 x f g False\n",
+      "xxxx 12 18 x f c False\n",
+      "xxxx 12 19 x a x False\n",
+      "xxxx 12 20 x g e False\n",
+      "seq1 13 0 z ! u False\n",
+      "xxxx 13 1 z a x False\n",
+      "xxxx 13 2 z e e False\n",
+      "xxxx 13 3 z h y False\n",
+      "xxxx 13 4 z b x False\n",
+      "xxxx 13 5 z a x False\n",
+      "xxxx 13 6 z b x False\n",
+      "xxxx 13 7 z e e False\n",
+      "xxxx 13 8 z e e False\n",
+      "seq1 13 9 z e z True\n",
+      "xxxx 13 10 z a z False\n",
+      "xxxx 13 11 z c a False\n",
+      "xxxx 13 12 z d c False\n",
+      "xxxx 13 13 z g y False\n",
+      "xxxx 13 14 z g d False\n",
+      "xxxx 13 15 z c g False\n",
+      "xxxx 13 16 z e g False\n",
+      "xxxx 13 17 z f c False\n",
+      "xxxx 13 18 z f x False\n",
+      "xxxx 13 19 z a e False\n",
+      "xxxx 13 20 z g f False\n",
+      "seq1 14 0 z ! x False\n",
+      "xxxx 14 1 z a e False\n",
+      "xxxx 14 2 z e y False\n",
+      "xxxx 14 3 z h x False\n",
+      "xxxx 14 4 z b x False\n",
+      "xxxx 14 5 z a x False\n",
+      "xxxx 14 6 z b e False\n",
+      "xxxx 14 7 z e e False\n",
+      "xxxx 14 8 z e z False\n",
+      "seq1 14 9 z e z True\n",
+      "seq2 14 10 z a a True\n",
+      "seq2 14 11 z c c True\n",
+      "xxxx 14 12 z d y False\n",
+      "xxxx 14 13 z g d False\n",
+      "xxxx 14 14 z g g False\n",
+      "xxxx 14 15 z c g False\n",
+      "xxxx 14 16 z e c False\n",
+      "xxxx 14 17 z f x False\n",
+      "xxxx 14 18 z f e False\n",
+      "xxxx 14 19 z a f False\n",
+      "xxxx 14 20 z g w False\n",
+      "seq1 15 0 y ! e False\n",
+      "xxxx 15 1 y a y False\n",
+      "xxxx 15 2 y e x False\n",
+      "xxxx 15 3 y h x False\n",
+      "xxxx 15 4 y b x False\n",
+      "xxxx 15 5 y a e False\n",
+      "xxxx 15 6 y b e False\n",
+      "xxxx 15 7 y e z False\n",
+      "xxxx 15 8 y e z False\n",
+      "xxxx 15 9 y e a False\n",
+      "xxxx 15 10 y a c False\n",
+      "seq1 15 11 y c y True\n",
+      "seq2 15 12 y d d True\n",
+      "seq2 15 13 y g g True\n",
+      "seq2 15 14 y g g True\n",
+      "seq2 15 15 y c c True\n",
+      "xxxx 15 16 y e x False\n",
+      "xxxx 15 17 y f e False\n",
+      "xxxx 15 18 y f f False\n",
+      "xxxx 15 19 y a w False\n",
+      "xxxx 15 20 y g w False\n",
+      "seq1 16 0 x ! y False\n",
+      "xxxx 16 1 x a x False\n",
+      "xxxx 16 2 x e x False\n",
+      "xxxx 16 3 x h x False\n",
+      "xxxx 16 4 x b e False\n",
+      "xxxx 16 5 x a e False\n",
+      "xxxx 16 6 x b z False\n",
+      "xxxx 16 7 x e z False\n",
+      "xxxx 16 8 x e a False\n",
+      "xxxx 16 9 x e c False\n",
+      "xxxx 16 10 x a y False\n",
+      "xxxx 16 11 x c d False\n",
+      "xxxx 16 12 x d g False\n",
+      "xxxx 16 13 x g g False\n",
+      "xxxx 16 14 x g c False\n",
+      "seq1 16 15 x c x True\n",
+      "seq2 16 16 x e e True\n",
+      "seq2 16 17 x f f True\n",
+      "xxxx 16 18 x f w False\n",
+      "xxxx 16 19 x a w False\n",
+      "xxxx 16 20 x g v False\n",
+      "seq1 17 0 w ! x False\n",
+      "xxxx 17 1 w a x False\n",
+      "xxxx 17 2 w e x False\n",
+      "xxxx 17 3 w h e False\n",
+      "xxxx 17 4 w b e False\n",
+      "xxxx 17 5 w a z False\n",
+      "xxxx 17 6 w b z False\n",
+      "xxxx 17 7 w e a False\n",
+      "xxxx 17 8 w e c False\n",
+      "xxxx 17 9 w e y False\n",
+      "xxxx 17 10 w a d False\n",
+      "xxxx 17 11 w c g False\n",
+      "xxxx 17 12 w d g False\n",
+      "xxxx 17 13 w g c False\n",
+      "xxxx 17 14 w g x False\n",
+      "xxxx 17 15 w c e False\n",
+      "xxxx 17 16 w e f False\n",
+      "seq1 17 17 w f w True\n",
+      "xxxx 17 18 w f w False\n",
+      "xxxx 17 19 w a v False\n",
+      "xxxx 17 20 w g f False\n",
+      "seq1 18 0 w ! x False\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "xxxx 18 1 w a x False\n",
+      "xxxx 18 2 w e e False\n",
+      "xxxx 18 3 w h e False\n",
+      "xxxx 18 4 w b z False\n",
+      "xxxx 18 5 w a z False\n",
+      "xxxx 18 6 w b a False\n",
+      "xxxx 18 7 w e c False\n",
+      "xxxx 18 8 w e y False\n",
+      "xxxx 18 9 w e d False\n",
+      "xxxx 18 10 w a g False\n",
+      "xxxx 18 11 w c g False\n",
+      "xxxx 18 12 w d c False\n",
+      "xxxx 18 13 w g x False\n",
+      "xxxx 18 14 w g e False\n",
+      "xxxx 18 15 w c f False\n",
+      "xxxx 18 16 w e w False\n",
+      "seq1 18 17 w f w True\n",
+      "xxxx 18 18 w f v False\n",
+      "xxxx 18 19 w a f False\n",
+      "xxxx 18 20 w g a False\n",
+      "seq1 19 0 v ! x False\n",
+      "xxxx 19 1 v a e False\n",
+      "xxxx 19 2 v e e False\n",
+      "xxxx 19 3 v h z False\n",
+      "xxxx 19 4 v b z False\n",
+      "xxxx 19 5 v a a False\n",
+      "xxxx 19 6 v b c False\n",
+      "xxxx 19 7 v e y False\n",
+      "xxxx 19 8 v e d False\n",
+      "xxxx 19 9 v e g False\n",
+      "xxxx 19 10 v a g False\n",
+      "xxxx 19 11 v c c False\n",
+      "xxxx 19 12 v d x False\n",
+      "xxxx 19 13 v g e False\n",
+      "xxxx 19 14 v g f False\n",
+      "xxxx 19 15 v c w False\n",
+      "xxxx 19 16 v e w False\n",
+      "seq1 19 17 v f v True\n",
+      "seq2 19 18 v f f True\n",
+      "seq2 19 19 v a a True\n",
+      "seq2 19 20 v g g True\n",
+      "seq1 20 0 z ! e False\n",
+      "xxxx 20 1 z a e False\n",
+      "xxxx 20 2 z e z False\n",
+      "xxxx 20 3 z h z False\n",
+      "xxxx 20 4 z b a False\n",
+      "xxxx 20 5 z a c False\n",
+      "xxxx 20 6 z b y False\n",
+      "xxxx 20 7 z e d False\n",
+      "xxxx 20 8 z e g False\n",
+      "xxxx 20 9 z e g False\n",
+      "xxxx 20 10 z a c False\n",
+      "xxxx 20 11 z c x False\n",
+      "xxxx 20 12 z d e False\n",
+      "xxxx 20 13 z g f False\n",
+      "xxxx 20 14 z g w False\n",
+      "xxxx 20 15 z c w False\n",
+      "xxxx 20 16 z e v False\n",
+      "xxxx 20 17 z f f False\n",
+      "xxxx 20 18 z f a False\n",
+      "xxxx 20 19 z a g False\n",
       "seq1 20 20 z g z True\n",
       "T . . . . . . . . . . . . . . . . . . . .\n",
-      "T T T . . . . . . . . . . . . . . . . . .\n",
-      ". . T T T . . . . . . . . . . . . . . . .\n",
-      ". . . . T T . . . . . . . . . . . . . . .\n",
-      ". . . . . T T . . . . . . . . . . . . . .\n",
+      "T T . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . .\n",
+      ". T T T T T T . . . . . . . . . . . . . .\n",
       ". . . . . . T . . . . . . . . . . . . . .\n",
-      ". . . . . . T . . . . . . . . . . . . . .\n",
-      ". . . . . . T . . . . . . . . . . . . . .\n",
-      ". . . . . . T . . . . . . . . . . . . . .\n",
-      ". . . . . . T . . . . . . . . . . . . . .\n",
-      ". . . . . . T T T T T . . . . . . . . . .\n",
-      ". . . . . . . . . . T . . . . . . . . . .\n",
-      ". . . . . . . . . . T T T . . . . . . . .\n",
-      ". . . . . . . . . . . . T T T . . . . . .\n",
-      ". . . . . . . . . . . . . . T . . . . . .\n",
-      ". . . . . . . . . . . . . . T . . . . . .\n",
-      ". . . . . . . . . . . . . . T T T T T T T\n",
-      ". . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . T T . . . . . . . . . . . . .\n",
+      ". . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . T T T . . . . . . . . . . .\n",
+      ". . . . . . . . . T . . . . . . . . . . .\n",
+      ". . . . . . . . . T T T . . . . . . . . .\n",
+      ". . . . . . . . . . . T T T T T . . . . .\n",
+      ". . . . . . . . . . . . . . . T T T . . .\n",
+      ". . . . . . . . . . . . . . . . . T . . .\n",
+      ". . . . . . . . . . . . . . . . . T . . .\n",
+      ". . . . . . . . . . . . . . . . . T T T T\n",
       ". . . . . . . . . . . . . . . . . . . . T\n"
      ]
     }
@@ -1260,7 +1269,7 @@
     {
      "data": {
       "text/plain": [
-       "'UacVheVeUfUVUXZUaedhVUhgXefWYUdghgggYYUZ'"
+       "'YaZVXZWehbabUXeYXXXeeZZacYdggcXefWWVfagZ'"
       ]
      },
      "execution_count": 22,
@@ -1282,27 +1291,27 @@
      "output_type": "stream",
      "text": [
       "T . . . . . . . . . . . . . . . . . . . .\n",
-      "T T T . . . . . . . . . . . . . . . . . .\n",
-      ". . T T T . . . . . . . . . . . . . . . .\n",
-      ". . . . T T . . . . . . . . . . . . . . .\n",
-      ". . . . . T T . . . . . . . . . . . . . .\n",
-      ". . . . . . T . . . . . . . . . . . . . .\n",
-      ". . . . . . T . . . . . . . . . . . . . .\n",
-      ". . . . . . T . . . . . . . . . . . . . .\n",
+      "T T . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . .\n",
+      ". T T T T T T . . . . . . . . . . . . . .\n",
       ". . . . . . T . . . . . . . . . . . . . .\n",
-      ". . . . . . T . . . . . . . . . . . . . .\n",
-      ". . . . . . T T T T T . . . . . . . . . .\n",
-      ". . . . . . . . . . T . . . . . . . . . .\n",
-      ". . . . . . . . . . T T T . . . . . . . .\n",
-      ". . . . . . . . . . . . T T T . . . . . .\n",
-      ". . . . . . . . . . . . . . T . . . . . .\n",
-      ". . . . . . . . . . . . . . T . . . . . .\n",
-      ". . . . . . . . . . . . . . T T T T T T T\n",
-      ". . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . T T . . . . . . . . . . . . .\n",
+      ". . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . T T T . . . . . . . . . . .\n",
+      ". . . . . . . . . T . . . . . . . . . . .\n",
+      ". . . . . . . . . T T T . . . . . . . . .\n",
+      ". . . . . . . . . . . T T T T T . . . . .\n",
+      ". . . . . . . . . . . . . . . T T T . . .\n",
+      ". . . . . . . . . . . . . . . . . T . . .\n",
+      ". . . . . . . . . . . . . . . . . T . . .\n",
+      ". . . . . . . . . . . . . . . . . T T T T\n",
       ". . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . T\n",
-      "UacVheVeUfUVUXZUaedhVUhgXefWYUdghgggYYUZ\n"
+      "YaZVXZWehbabUXeYXXXeeZZacYdggcXefWWVfagZ\n"
      ]
     },
     {
@@ -1331,9 +1340,9 @@
     {
      "data": {
       "text/plain": [
-       "('gfccbgegegaccfcgeehbgcafchgbfdfbggbcachfdfaccfbffb',\n",
-       " 'accfcfbdaabcabbbegdfffhcgcefbddegghgfdgcgdcffcfdcd',\n",
-       " 'acgcfcffbdcacbabcagbbbegegegadcfcffcgfeehbgchacfchggcbefbfddfbdggbegcgachhfgfdfdgcgdacccfbffcffbfdcd',\n",
+       "('ehcceddeafddffefgffdfbbedabhbadebdchfabhhbfghdggcd',\n",
+       " 'hdahagaefhadaaaeehdhfaeafgcgcdfbegehdfchbfecgbgfbe',\n",
+       " 'hehcdahceddageaaefddfffefgfhafddaafaebbehedhdfabaeahbadfgcgecbddcfbhfegeahbhdhbfcfhgbfhdgecgbgcgdfbe',\n",
        " 100)"
       ]
      },
@@ -1359,57 +1368,57 @@
      "output_type": "stream",
      "text": [
       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . T . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . T . . T T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . T . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . T T T T . . . . . . . . . . . . . . .\n",
+      "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T . . T T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      "ACgCFCfFBDcAcbABCAgBBBegegEGaDcFcfFcgFeehbgcHaCfchgGCbEFBfdDfbDggbEGcGachHfGFdfDGCGDaccCfbFFCffbFDCD\n"
+      "HehcDAHceddAGeaAEfddffFefgfHAfdDAAfAEbbEHeDHdFabAEAhbadFGCGeCbdDcFBhfEGEaHbhDhbFCfHgBFhdgECGBgcGdFBE\n"
      ]
     },
     {
@@ -1457,58 +1466,58 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . T . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . T T . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . T T . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . T . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T\n",
-      "acGcfcfFbdCaCBabcaGbbbegEGEGAdCfCfFCGfEEHBGChAcFCHgGcBefbFdDFBdGGBegCgAChHFgfDFdgcgdAcCCFBffcFFBfdcd\n"
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T\n",
+      "hEHCdahCEDDagEaAeFDDfFFEFGFhaFdDaaFaeBBehEdhDfABaeaHBADfgcgEcBdDCfbHFegeAhBHdHBfcFhGbfHDGecgbGCgDfbe\n"
      ]
     },
     {
@@ -1557,7 +1566,7 @@
     {
      "data": {
       "text/plain": [
-       "('adadhfgacgbahfchffghdfffcfcdccchedahggdffhgbacghbe', False, False)"
+       "('ahgafgaagdgccegafedggefddeaabhffchdgeabcfaacahcgge', False, False)"
       ]
      },
      "execution_count": 29,
@@ -1579,7 +1588,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
@@ -1630,7 +1639,7 @@
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      "a\n"
+      "\n"
      ]
     },
     {
@@ -1651,6 +1660,85 @@
     "v"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def is_interleave_recursive(s1, s2, s3):\n",
+    "    if not s1:\n",
+    "        return s2 == s3\n",
+    "    elif not s2:\n",
+    "        return s1 == s3\n",
+    "    else:\n",
+    "        if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
+    "            return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n",
+    "        elif s1[-1] == s3[-1]:\n",
+    "            return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
+    "        elif s2[-1] == s3[-1]:\n",
+    "            return is_interleave(s1, s2[:-1], s3[:-1])\n",
+    "        else:\n",
+    "            return False"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "s1 = make_string(500)\n",
+    "s2 = make_string(500)\n",
+    "s3 = make_string(500)\n",
+    "s12 = interleave(s1, s2)\n",
+    "s23 = interleave(s2, s3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 49,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "is_interleave_recursive(s1, s2, s12)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "False"
+      ]
+     },
+     "execution_count": 50,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "is_interleave_recursive(s1, s2, s23)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1660,7 +1748,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 32,
    "metadata": {
     "collapsed": true
    },
@@ -1673,7 +1761,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 33,
    "metadata": {
     "collapsed": true
    },
@@ -1699,16 +1787,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "('badbbdcadc', 'bdaadcadab', 'bdabaadbdcbadcaddacb', 20)"
+       "('acabcbccaa', 'cabcadddca', 'acabcbcccaaabcadddca', 20)"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 34,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1723,27 +1811,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 35,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* b d a . . . . . . .\n",
-      "b . . b a . . . . . .\n",
-      ". . . a a d . . . . .\n",
-      ". . . . d . . . . . .\n",
-      ". . . . b d c . . . .\n",
-      ". . . . . . b a d . .\n",
-      ". . . . . . . d . . .\n",
-      ". . . . . . . c . . .\n",
-      ". . . . . . . a d . .\n",
-      ". . . . . . . d d a .\n",
-      ". . . . . . . . . c b\n",
-      "bdaBaADBdcBaDCAdDaCb\n",
-      "bdabaadbdcbadcaddacb\n",
-      "   * ***  * *** * * \n"
+      "* . . . . . . . . . .\n",
+      "a c a b c . . . . . .\n",
+      "c . . c . . . . . . .\n",
+      "a . . . . . . . . . .\n",
+      "b c . . . . . . . . .\n",
+      "c . . . . . . . . . .\n",
+      "b c . . . . . . . . .\n",
+      "c c . . . . . . . . .\n",
+      "c c a . . . . . . . .\n",
+      ". a a . . . . . . . .\n",
+      ". a a b c a d d d c a\n",
+      "ACABCBcCCaAAbcadddca\n",
+      "acabcbcccaaabcadddca\n",
+      "****** ** **        \n"
      ]
     },
     {
@@ -1752,7 +1840,7 @@
        "True"
       ]
      },
-     "execution_count": 34,
+     "execution_count": 35,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1767,27 +1855,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 36,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* b . . . . . . . . .\n",
-      "b . . . . . . . . . .\n",
-      "d . . . . . . . . . .\n",
-      "a b a . . . . . . . .\n",
-      ". a a d b . . . . . .\n",
-      ". . d . d . . . . . .\n",
-      ". . . . c b . . . . .\n",
-      ". . . . . a d c a d .\n",
-      ". . . . . d . . d d .\n",
-      ". . . . . . . . . a c\n",
-      ". . . . . . . . . . b\n",
-      "BDAbaAdbDCbAdcadDAcB\n",
-      "bdabaadbdcbadcaddacb\n",
-      "***  *  ** *    ** *\n"
+      "* a c a b c b c c . .\n",
+      ". c . . c . c c c a a\n",
+      ". a . . . . . . a a a\n",
+      ". b c . . . . . . . b\n",
+      ". c . . . . . . . . c\n",
+      ". . . . . . . . . . a\n",
+      ". . . . . . . . . . d\n",
+      ". . . . . . . . . . d\n",
+      ". . . . . . . . . . d\n",
+      ". . . . . . . . . . c\n",
+      ". . . . . . . . . . a\n",
+      "acabcbccCaaABCADDDCA\n",
+      "acabcbcccaaabcadddca\n",
+      "        *  *********\n"
      ]
     },
     {
@@ -1796,7 +1884,7 @@
        "True"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 36,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1811,27 +1899,26 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 37,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* . . . . . . . . . .\n",
+      "* a . . . . . . . . .\n",
+      "a . . . . . . . . . .\n",
+      "c a . . . . . . . . .\n",
+      "a . . . . . . . . . .\n",
       "b . . . . . . . . . .\n",
+      "c . . . . . . . . . .\n",
+      "b . . . . . . . . . .\n",
+      "c . . . . . . . . . .\n",
+      "c . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      "B\n",
-      "b\n",
-      "*\n"
+      "\n",
+      "\n"
      ]
     },
     {
@@ -1840,7 +1927,7 @@
        "False"
       ]
      },
-     "execution_count": 36,
+     "execution_count": 37,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1855,26 +1942,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 38,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* . . . . . . . . . .\n",
-      "b . . . . . . . . . .\n",
-      "d a . . . . . . . . .\n",
-      "a . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
+      "* a . . . . . . . . .\n",
+      ". c . . . . . . . . .\n",
+      ". a . . . . . . . . .\n",
+      ". b . . . . . . . . .\n",
+      ". c . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
-      "\n",
-      "\n"
+      "aCABC\n",
+      "acabc\n",
+      " ****\n"
      ]
     },
     {
@@ -1883,7 +1971,7 @@
        "False"
       ]
      },
-     "execution_count": 37,
+     "execution_count": 38,
      "metadata": {},
      "output_type": "execute_result"
     }

diff --git a/09-resolving-the-bill/subsequence.ipynb b/09-resolving-the-bill/subsequence.ipynb
index 4484bfb6c6a1fa5fe979607ccc7d6c4c086d1b26..79d837f8f830cff9c312a37eefd447148c31ceeb 100644 (file)
--- a/09-resolving-the-bill/subsequence.ipynb
+++ b/09-resolving-the-bill/subsequence.ipynb
@@ -19,7 +19,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import random"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
    "metadata": {
     "collapsed": true
    },
@@ -41,7 +52,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 4,
    "metadata": {
     "scrolled": true
    },
@@ -117,7 +128,7 @@
        " (5, 10): False}"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -131,7 +142,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 5,
    "metadata": {
     "collapsed": true
    },
@@ -145,7 +156,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -167,7 +178,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -244,7 +255,7 @@
        " (4, 7): (4, 6, 'b', 's2')}"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -288,7 +299,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 8,
    "metadata": {
     "collapsed": true
    },
@@ -312,7 +323,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -321,7 +332,7 @@
        "'AAAbAbb'"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -332,8 +343,67 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def is_subseq(seq1, seq2, return_backpointers=False, return_table=False, debug=False):\n",
+    "    \"\"\"Return true if seq1 is a subsequence of seq2.\n",
+    "    If return_backpointers, also return the set of backpointers to\n",
+    "    reconstruct the subsequence\"\"\"\n",
+    "    \n",
+    "    # dp_table[i, j] is True if first i characters of seq1 can\n",
+    "    # be found in the first j characters of seq2\n",
+    "  \n",
+    "    dp_table = {(i, j): False\n",
+    "               for i in range(len(seq1)+1)\n",
+    "               for j in range(len(seq2)+1)}\n",
+    "\n",
+    "    backpointers = {}\n",
+    "    \n",
+    "    for i in range(len(seq1)+1):\n",
+    "        for j in range(i, len(seq2)+1):\n",
+    "            if i == 0 or j == 0:\n",
+    "                dp_table[i, j] = True\n",
+    "                if debug: print('aa', i, j, '!', '!', dp_table[i, j])\n",
+    "            else:\n",
+    "                # extend by character from s2\n",
+    "                if dp_table[i, j-1]:\n",
+    "                    dp_table[i, j] = True\n",
+    "                    backpointers[i, j] = (i, j-1, seq2[j-1], 's2')\n",
+    "                    if debug: print('s2', i, j, seq1[i-1], seq2[j-1], dp_table[i, j])                \n",
+    "                # extend by character from s1\n",
+    "                if dp_table[i-1, j-1] and seq1[i-1] == seq2[j-1]:\n",
+    "                    dp_table[i, j] = True\n",
+    "                    backpointers[i, j] = (i-1, j-1, seq1[i-1], 's1')                \n",
+    "                    if debug: print('s1', i, j, seq1[i-1], seq2[j-1], dp_table[i, j])\n",
+    "                if not dp_table[i, j]:\n",
+    "                    if debug: print('xx', i, j, seq1[i-1], seq2[j-1], dp_table[i, j]) \n",
+    "   \n",
+    "#     if return_backpointers:\n",
+    "#         return dp_table[len(seq1), len(seq2)], backpointers\n",
+    "#     else:\n",
+    "#         return dp_table[len(seq1), len(seq2)]\n",
+    "    \n",
+    "    if return_backpointers or return_table:\n",
+    "        retval = [dp_table[len(seq1), len(seq2)]]\n",
+    "        if return_backpointers:\n",
+    "            retval += [backpointers]\n",
+    "        if return_table:\n",
+    "            retval += [dp_table]\n",
+    "        return tuple(retval)\n",
+    "    else:\n",
+    "        return dp_table[len(seq1), len(seq2)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -398,7 +468,7 @@
        "True"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -409,64 +479,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def is_subseq(seq1, seq2, return_backpointers=False, return_table=False, debug=False):\n",
-    "    \"\"\"Return true if seq1 is a subsequence of seq2.\n",
-    "    If return_backpointers, also return the set of backpointers to\n",
-    "    reconstruct the subsequence\"\"\"\n",
-    "    \n",
-    "    # dp_table[i, j] is True if first i characters of seq1 can\n",
-    "    # be found in the first j characters of seq2\n",
-    "  \n",
-    "    dp_table = {(i, j): False\n",
-    "               for i in range(len(seq1)+1)\n",
-    "               for j in range(len(seq2)+1)}\n",
-    "\n",
-    "    backpointers = {}\n",
-    "    \n",
-    "    for i in range(len(seq1)+1):\n",
-    "        for j in range(i, len(seq2)+1):\n",
-    "            if i == 0 or j == 0:\n",
-    "                dp_table[i, j] = True\n",
-    "                if debug: print('aa', i, j, '!', '!', dp_table[i, j])\n",
-    "            else:\n",
-    "                # extend by character from s2\n",
-    "                if dp_table[i, j-1]:\n",
-    "                    dp_table[i, j] = True\n",
-    "                    backpointers[i, j] = (i, j-1, seq2[j-1], 's2')\n",
-    "                    if debug: print('s2', i, j, seq1[i-1], seq2[j-1], dp_table[i, j])                \n",
-    "                # extend by character from s1\n",
-    "                if dp_table[i-1, j-1] and seq1[i-1] == seq2[j-1]:\n",
-    "                    dp_table[i, j] = True\n",
-    "                    backpointers[i, j] = (i-1, j-1, seq1[i-1], 's1')                \n",
-    "                    if debug: print('s1', i, j, seq1[i-1], seq2[j-1], dp_table[i, j])\n",
-    "                if not dp_table[i, j]:\n",
-    "                    if debug: print('xx', i, j, seq1[i-1], seq2[j-1], dp_table[i, j]) \n",
-    "   \n",
-    "#     if return_backpointers:\n",
-    "#         return dp_table[len(seq1), len(seq2)], backpointers\n",
-    "#     else:\n",
-    "#         return dp_table[len(seq1), len(seq2)]\n",
-    "    \n",
-    "    if return_backpointers or return_table:\n",
-    "        retval = [dp_table[len(seq1), len(seq2)]]\n",
-    "        if return_backpointers:\n",
-    "            retval += [backpointers]\n",
-    "        if return_table:\n",
-    "            retval += [dp_table]\n",
-    "        return tuple(retval)\n",
-    "    else:\n",
-    "        return dp_table[len(seq1), len(seq2)]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 13,
    "metadata": {
     "collapsed": true
    },
@@ -479,7 +492,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -488,7 +501,7 @@
        "True"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -500,7 +513,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
@@ -509,7 +522,7 @@
        "'AbAAbcAcb'"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -520,7 +533,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -541,7 +554,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
@@ -562,7 +575,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -571,7 +584,7 @@
        "False"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -582,7 +595,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
@@ -591,7 +604,7 @@
        "('aaaa', 'dabaabcacb')"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -602,7 +615,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
@@ -635,7 +648,7 @@
        " (4, 10): (4, 9, 'b', 's2')}"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 20,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -646,20 +659,265 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "False"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "is_subseq(s1, s2f)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "aa 0 0 ! ! True\n",
+      "aa 0 1 ! ! True\n",
+      "aa 0 2 ! ! True\n",
+      "aa 0 3 ! ! True\n",
+      "aa 0 4 ! ! True\n",
+      "aa 0 5 ! ! True\n",
+      "aa 0 6 ! ! True\n",
+      "aa 0 7 ! ! True\n",
+      "s1 1 1 a a True\n",
+      "s2 1 2 a a True\n",
+      "s1 1 2 a a True\n",
+      "s2 1 3 a a True\n",
+      "s1 1 3 a a True\n",
+      "s2 1 4 a b True\n",
+      "s2 1 5 a a True\n",
+      "s1 1 5 a a True\n",
+      "s2 1 6 a b True\n",
+      "s2 1 7 a b True\n",
+      "s1 2 2 a a True\n",
+      "s2 2 3 a a True\n",
+      "s1 2 3 a a True\n",
+      "s2 2 4 a b True\n",
+      "s2 2 5 a a True\n",
+      "s1 2 5 a a True\n",
+      "s2 2 6 a b True\n",
+      "s2 2 7 a b True\n",
+      "s1 3 3 a a True\n",
+      "s2 3 4 a b True\n",
+      "s2 3 5 a a True\n",
+      "s1 3 5 a a True\n",
+      "s2 3 6 a b True\n",
+      "s2 3 7 a b True\n",
+      "xx 4 4 a b False\n",
+      "s1 4 5 a a True\n",
+      "s2 4 6 a b True\n",
+      "s2 4 7 a b True\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(True,\n",
+       " {(1, 1): (0, 0, 'a', 's1'),\n",
+       "  (1, 2): (0, 1, 'a', 's1'),\n",
+       "  (1, 3): (0, 2, 'a', 's1'),\n",
+       "  (1, 4): (1, 3, 'b', 's2'),\n",
+       "  (1, 5): (0, 4, 'a', 's1'),\n",
+       "  (1, 6): (1, 5, 'b', 's2'),\n",
+       "  (1, 7): (1, 6, 'b', 's2'),\n",
+       "  (2, 2): (1, 1, 'a', 's1'),\n",
+       "  (2, 3): (1, 2, 'a', 's1'),\n",
+       "  (2, 4): (2, 3, 'b', 's2'),\n",
+       "  (2, 5): (1, 4, 'a', 's1'),\n",
+       "  (2, 6): (2, 5, 'b', 's2'),\n",
+       "  (2, 7): (2, 6, 'b', 's2'),\n",
+       "  (3, 3): (2, 2, 'a', 's1'),\n",
+       "  (3, 4): (3, 3, 'b', 's2'),\n",
+       "  (3, 5): (2, 4, 'a', 's1'),\n",
+       "  (3, 6): (3, 5, 'b', 's2'),\n",
+       "  (3, 7): (3, 6, 'b', 's2'),\n",
+       "  (4, 5): (3, 4, 'a', 's1'),\n",
+       "  (4, 6): (4, 5, 'b', 's2'),\n",
+       "  (4, 7): (4, 6, 'b', 's2')})"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "is_subseq('aaaa', 'aaababb', return_backpointers=True, debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def is_subseq_recursive(s1, s2):\n",
+    "    if not s1:\n",
+    "        return True\n",
+    "    elif len(s1) > len(s2):\n",
+    "        return False\n",
+    "    else:\n",
+    "        if s1[-1] == s2[-1]:\n",
+    "            return is_subseq_recursive(s1[:-1], s2[:-1]) or is_subseq_recursive(s1, s2[:-1])\n",
+    "        else:\n",
+    "            return is_subseq_recursive(s1, s2[:-1])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "is_subseq_recursive(s1, s2t)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "False"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "is_subseq_recursive(s1, s2f)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def make_string(length, alphabet=None):\n",
+    "    if not alphabet:\n",
+    "        alphabet = 'abcdefgh'\n",
+    "    return ''.join(random.choice(alphabet) for _ in range(length)) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def interleave(s1, s2, wander_limit=10, debug=False):\n",
+    "    i1 = i2 = wander = 0\n",
+    "    interleaved = []\n",
+    "    while i1 <= len(s1) and i2 <= len(s2):\n",
+    "        if i1 == len(s1):\n",
+    "            if debug: print(i1, i2, wander, 'remaining s2', s2[i2:])\n",
+    "            interleaved += s2[i2:]\n",
+    "            i2 = len(s2) + 1\n",
+    "        elif i2 == len(s2):\n",
+    "            if debug: print(i1, i2, wander, 'remaining s1', s1[i1:])\n",
+    "            interleaved += s1[i1:]\n",
+    "            i1 = len(s1) + 1\n",
+    "        else:\n",
+    "            if wander == wander_limit:\n",
+    "                step = -1\n",
+    "            elif wander == -wander_limit:\n",
+    "                step = +1\n",
+    "            else:\n",
+    "                step = random.choice([+1, -1])\n",
+    "            if step == +1:\n",
+    "                if debug: print(i1, i2, wander, 'adding', s1[i1])\n",
+    "                interleaved += s1[i1]\n",
+    "                i1 += 1\n",
+    "                wander += 1\n",
+    "            else:\n",
+    "                if debug: print(i1, i2, wander, 'adding', s2[i2])\n",
+    "                interleaved += s2[i2]\n",
+    "                i2 += 1\n",
+    "                wander -= 1\n",
+    "    return ''.join(interleaved)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "sl1 = make_string(200)\n",
+    "sl2 = make_string(200)\n",
+    "sl3 = make_string(200)\n",
+    "sl12 = interleave(sl1, sl2)\n",
+    "sl23 = interleave(sl2, sl3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(True, False)"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "is_subseq(sl1, sl12), is_subseq(sl1, sl23)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
-    "is_subseq('aaaa', 'aaababb', return_backpointers=True, debug=True)"
+    "is_subseq_recursive(sl1, sl12), is_subseq_recursive(sl1, sl23)"
    ]
   },
   {