4 "cell_type": "markdown",
7 "# Interleaved strings\n",
9 "Given two strings a and b and a target c, could c be formed form some interleaving/merge of a and b?\n",
16 "When s3 = \"aadbbcbcac\", return true.\n",
17 "When s3 = \"aadbbbaccc\", return false."
43 "s3t = \"aadbbcbcac\"\n",
44 "s3f = \"aadbbbaccc\""
55 "[(0, ''), (1, 'a'), (2, 'aa'), (3, 'aab'), (4, 'aabc'), (5, 'aabcc')]"
60 "output_type": "execute_result"
64 "[(i, s1[:i]) for i in range(len(s1)+1)]"
68 "cell_type": "markdown",
71 "`dp_table[i, j]` is True if first `i` + `j` characters of `s3` can be formed from interleaving of first `i` characters of `s1` and first `j` characters of `s2`."
82 "[[True, False, False, False, False, False],\n",
83 " [False, False, False, False, False, False],\n",
84 " [False, False, False, False, False, False],\n",
85 " [False, False, False, False, False, False],\n",
86 " [False, False, False, False, False, False],\n",
87 " [False, False, False, False, False, False]]"
92 "output_type": "execute_result"
96 "dp_table = [[False] * (len(s1) + 1) for _ in range(len(s2) + 1)]\n",
97 "dp_table[0][0] = True\n",
103 "execution_count": 4,
149 "execution_count": 4,
151 "output_type": "execute_result"
155 "dp_table = {(i, j): False\n",
156 " for i in range(len(s1)+1)\n",
157 " for j in range(len(s2)+1)}\n",
163 "execution_count": 5,
169 "def show_table(table):\n",
170 " return '\\n'.join(\n",
171 " ' '.join(str(table[i, j])[0] for j in sorted(set([k[1] for k in table])))\n",
172 " for i in sorted(set([k[0] for k in table]))) "
177 "execution_count": 6,
183 "def show_table(table):\n",
184 " return '\\n'.join(\n",
185 " ' '.join('T' if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n",
186 " for i in sorted(set([k[0] for k in table]))) "
191 "execution_count": 7,
196 "output_type": "stream",
208 "print(show_table(dp_table))"
213 "execution_count": 8,
218 "output_type": "stream",
220 "aabcc dbbca aadbbcbcac\n",
221 "aa 0 0 ! ! ! True\n",
222 "s2 0 1 ! d a False\n",
223 "s2 0 2 ! b a False\n",
224 "s2 0 3 ! b d False\n",
225 "s2 0 4 ! c b False\n",
226 "s2 0 5 ! a b False\n",
227 "s1 1 0 a ! a True\n",
228 "xx 1 1 a d a False\n",
229 "xx 1 2 a b d False\n",
230 "xx 1 3 a b b False\n",
231 "xx 1 4 a c b False\n",
232 "xx 1 5 a a c False\n",
233 "s1 2 0 a ! a True\n",
234 "s2 2 1 a d d True\n",
235 "s2 2 2 a b b True\n",
236 "s2 2 3 a b b True\n",
237 "s2 2 4 a c c True\n",
238 "xx 2 5 a a b False\n",
239 "s1 3 0 b ! d False\n",
240 "s1 3 1 b d b True\n",
241 "s2 3 2 b b b True\n",
242 "s1 3 2 b b b True\n",
243 "xx 3 3 b b c False\n",
244 "s1 3 4 b c b True\n",
245 "xx 3 5 b a c False\n",
246 "s1 4 0 c ! b False\n",
247 "xx 4 1 c d b False\n",
248 "s1 4 2 c b c True\n",
249 "s2 4 3 c b b True\n",
250 "s2 4 4 c c c True\n",
251 "s1 4 4 c c c True\n",
252 "s2 4 5 c a a True\n",
253 "s1 5 0 c ! b False\n",
254 "xx 5 1 c d c False\n",
255 "xx 5 2 c b b False\n",
256 "s1 5 3 c b c True\n",
257 "xx 5 4 c c a False\n",
258 "s1 5 5 c a c True\n",
270 "{(1, 0): (0, 0, 'a', 's1'),\n",
271 " (2, 0): (1, 0, 'a', 's1'),\n",
272 " (2, 1): (2, 0, 'd', 's2'),\n",
273 " (2, 2): (2, 1, 'b', 's2'),\n",
274 " (2, 3): (2, 2, 'b', 's2'),\n",
275 " (2, 4): (2, 3, 'c', 's2'),\n",
276 " (3, 1): (2, 1, 'b', 's1'),\n",
277 " (3, 2): (2, 2, 'b', 's1'),\n",
278 " (3, 4): (2, 4, 'b', 's1'),\n",
279 " (4, 2): (3, 2, 'c', 's1'),\n",
280 " (4, 3): (4, 2, 'b', 's2'),\n",
281 " (4, 4): (3, 4, 'c', 's1'),\n",
282 " (4, 5): (4, 4, 'a', 's2'),\n",
283 " (5, 3): (4, 3, 'c', 's1'),\n",
284 " (5, 5): (4, 5, 'c', 's1')}"
287 "execution_count": 8,
289 "output_type": "execute_result"
295 "print(s1, s2, s3)\n",
297 "dp_table = {(i, j): False\n",
298 " for i in range(len(s1)+1)\n",
299 " for j in range(len(s2)+1)}\n",
301 "backpointers = {}\n",
303 "for i in range(len(s1)+1):\n",
304 " for j in range(len(s2)+1):\n",
305 " if i == 0 and j == 0:\n",
306 " dp_table[i, j] = True\n",
307 " print('aa', i, j, '!', '!', '!', dp_table[i, j])\n",
309 " # extend by character from s2\n",
310 " if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
311 " dp_table[i, j] = True\n",
312 " backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
313 " print('s2', i, j, '!', s2[j-1], s3[i+j-1], dp_table[i, j])\n",
315 " # extend by character from s1\n",
316 " if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
317 " dp_table[i, j] = True\n",
318 " backpointers[i, j] = (i-1, j, s1[i-1], 's1')\n",
319 " print('s1', i, j, s1[i-1], '!', s3[i+j-1], dp_table[i, j])\n",
321 " # extend by character from s2\n",
322 " if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
323 " dp_table[i, j] = True\n",
324 " backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
325 " print('s2', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j]) \n",
326 " # extend by character from s1\n",
327 " if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
328 " dp_table[i, j] = True\n",
329 " backpointers[i, j] = (i-1, j, s1[i-1], 's1') \n",
330 " print('s1', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
331 " if not dp_table[i, j]:\n",
332 " print('xx', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
334 "print(show_table(dp_table))\n",
340 "execution_count": 11,
346 "def is_interleave(seq1, seq2, seq3, return_backpointers=False, return_table=False, debug=False):\n",
347 " \"\"\"Return true if seq3 is some interleaved merge of seq1 and seq2.\n",
348 " If return_backpointers, also return the set of backpointers to\n",
349 " reconstruct the interleaving\"\"\"\n",
351 " # dp_table[i, j] is True if first i+j characters of seq is made up of \n",
352 " # an interleaving of the first i characters of seq1 and the \n",
353 " # first j characters of seq2\n",
355 " if len(seq1) + len(seq2) != len(seq3):\n",
356 " if return_backpointers or return_table:\n",
357 " retval = [False]\n",
358 " if return_backpointers:\n",
360 " if return_table:\n",
362 " return tuple(retval)\n",
366 " dp_table = {(i, j): False\n",
367 " for i in range(len(seq1)+1)\n",
368 " for j in range(len(seq2)+1)}\n",
370 " backpointers = {}\n",
372 " for i in range(len(seq1)+1):\n",
373 " for j in range(len(seq2)+1):\n",
374 " if i == 0 and j == 0:\n",
375 " dp_table[i, j] = True\n",
376 " if debug: print('xxxx', i, j, '!', '!', '!', dp_table[i, j])\n",
378 " # extend by character from seq2\n",
379 " if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
380 " dp_table[i, j] = True\n",
381 " backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
382 " if debug: print('seq2', i, j, '!', seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
384 " # extend by character from seq1\n",
385 " if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
386 " dp_table[i, j] = True\n",
387 " backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')\n",
388 " if debug: print('seq1', i, j, seq1[i-1], '!', seq3[i+j-1], dp_table[i, j])\n",
390 " # extend by character from seq2\n",
391 " if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
392 " dp_table[i, j] = True\n",
393 " backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
394 " if debug: print('seq2', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j]) \n",
395 " # extend by character from seq1\n",
396 " if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
397 " dp_table[i, j] = True\n",
398 " backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1') \n",
399 " if debug: print('seq1', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
400 " if not dp_table[i, j]:\n",
401 " if debug: print('xxxx', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
403 " if return_backpointers or return_table:\n",
404 " retval = [dp_table[len(seq1), len(seq2)]]\n",
405 " if return_backpointers:\n",
406 " retval += [backpointers]\n",
407 " if return_table:\n",
408 " retval += [dp_table]\n",
409 " return tuple(retval)\n",
411 " return dp_table[len(seq1), len(seq2)]"
416 "execution_count": 12,
425 "execution_count": 12,
427 "output_type": "execute_result"
431 "is_interleave(s1, s2, s3t)"
436 "execution_count": 13,
443 " {(1, 0): (0, 0, 'a', 'seq1'),\n",
444 " (2, 0): (1, 0, 'a', 'seq1'),\n",
445 " (2, 1): (2, 0, 'd', 'seq2'),\n",
446 " (2, 2): (2, 1, 'b', 'seq2'),\n",
447 " (2, 3): (2, 2, 'b', 'seq2'),\n",
448 " (2, 4): (2, 3, 'c', 'seq2'),\n",
449 " (3, 1): (2, 1, 'b', 'seq1'),\n",
450 " (3, 2): (2, 2, 'b', 'seq1'),\n",
451 " (3, 4): (2, 4, 'b', 'seq1'),\n",
452 " (4, 2): (3, 2, 'c', 'seq1'),\n",
453 " (4, 3): (4, 2, 'b', 'seq2'),\n",
454 " (4, 4): (3, 4, 'c', 'seq1'),\n",
455 " (4, 5): (4, 4, 'a', 'seq2'),\n",
456 " (5, 3): (4, 3, 'c', 'seq1'),\n",
457 " (5, 5): (4, 5, 'c', 'seq1')})"
460 "execution_count": 13,
462 "output_type": "execute_result"
466 "is_interleave(s1, s2, s3t, return_backpointers=True)"
471 "execution_count": 14,
480 " {(1, 0): (0, 0, 'a', 'seq1'),\n",
481 " (2, 0): (1, 0, 'a', 'seq1'),\n",
482 " (2, 1): (2, 0, 'd', 'seq2'),\n",
483 " (2, 2): (2, 1, 'b', 'seq2'),\n",
484 " (2, 3): (2, 2, 'b', 'seq2'),\n",
485 " (2, 4): (2, 3, 'c', 'seq2'),\n",
486 " (3, 1): (2, 1, 'b', 'seq1'),\n",
487 " (3, 2): (2, 2, 'b', 'seq1'),\n",
488 " (3, 4): (2, 4, 'b', 'seq1'),\n",
489 " (4, 2): (3, 2, 'c', 'seq1'),\n",
490 " (4, 3): (4, 2, 'b', 'seq2'),\n",
491 " (4, 4): (3, 4, 'c', 'seq1'),\n",
492 " (4, 5): (4, 4, 'a', 'seq2'),\n",
493 " (5, 3): (4, 3, 'c', 'seq1'),\n",
494 " (5, 5): (4, 5, 'c', 'seq1')},\n",
533 "execution_count": 14,
535 "output_type": "execute_result"
539 "is_interleave(s1, s2, s3t, return_backpointers=True, return_table=True)"
544 "execution_count": 15,
553 "execution_count": 15,
555 "output_type": "execute_result"
559 "is_interleave(s1, s2, s3f)"
564 "execution_count": 16,
569 "output_type": "stream",
571 "xxxx 0 0 ! ! ! True\n",
572 "seq2 0 1 ! b a False\n",
573 "seq2 0 2 ! b a False\n",
574 "seq2 0 3 ! b a False\n",
575 "seq1 1 0 a ! a True\n",
576 "xxxx 1 1 a b a False\n",
577 "xxxx 1 2 a b a False\n",
578 "xxxx 1 3 a b b False\n",
579 "seq1 2 0 a ! a True\n",
580 "xxxx 2 1 a b a False\n",
581 "xxxx 2 2 a b b False\n",
582 "xxxx 2 3 a b a False\n",
583 "seq1 3 0 a ! a True\n",
584 "seq2 3 1 a b b True\n",
585 "xxxx 3 2 a b a False\n",
586 "xxxx 3 3 a b b False\n",
587 "seq1 4 0 a ! b False\n",
588 "seq1 4 1 a b a True\n",
589 "seq2 4 2 a b b True\n",
590 "seq2 4 3 a b b True\n"
597 " {(1, 0): (0, 0, 'a', 'seq1'),\n",
598 " (2, 0): (1, 0, 'a', 'seq1'),\n",
599 " (3, 0): (2, 0, 'a', 'seq1'),\n",
600 " (3, 1): (3, 0, 'b', 'seq2'),\n",
601 " (4, 1): (3, 1, 'a', 'seq1'),\n",
602 " (4, 2): (4, 1, 'b', 'seq2'),\n",
603 " (4, 3): (4, 2, 'b', 'seq2')})"
606 "execution_count": 16,
608 "output_type": "execute_result"
612 "is_interleave('aaaa', 'bbb', 'aaababb', return_backpointers=True, debug=True)"
617 "execution_count": 17,
623 "def show_backtrace(bps):\n",
624 " i = max([0] + [k[0] for k in bps])\n",
625 " j = max([0] + [k[1] for k in bps])\n",
627 " if (i, j) in bps:\n",
628 " while i != 0 or j != 0:\n",
629 " if bps[i, j][3] == 'seq1':\n",
630 " chars += bps[i, j][2].upper()\n",
632 " chars += bps[i, j][2]\n",
633 " i, j = bps[i, j][0], bps[i, j][1] \n",
634 " return ''.join(list(reversed(chars)))\n",
641 "execution_count": 18,
647 "def make_string(length, alphabet=None):\n",
648 " if not alphabet:\n",
649 " alphabet = 'abcdefgh'\n",
650 " return ''.join(random.choice(alphabet) for _ in range(length)) "
655 "execution_count": 19,
661 "'fddagfdacgbdggabhgcgfddecffbghccebhefghbchhhbfdfgc'"
664 "execution_count": 19,
666 "output_type": "execute_result"
675 "execution_count": 20,
681 "def interleave(s1, s2, wander_limit=10, debug=False):\n",
682 " i1 = i2 = wander = 0\n",
683 " interleaved = []\n",
684 " while i1 <= len(s1) and i2 <= len(s2):\n",
685 " if i1 == len(s1):\n",
686 " if debug: print(i1, i2, wander, 'remaining s2', s2[i2:])\n",
687 " interleaved += s2[i2:]\n",
688 " i2 = len(s2) + 1\n",
689 " elif i2 == len(s2):\n",
690 " if debug: print(i1, i2, wander, 'remaining s1', s1[i1:])\n",
691 " interleaved += s1[i1:]\n",
692 " i1 = len(s1) + 1\n",
694 " if wander == wander_limit:\n",
696 " elif wander == -wander_limit:\n",
699 " step = random.choice([+1, -1])\n",
701 " if debug: print(i1, i2, wander, 'adding', s1[i1])\n",
702 " interleaved += s1[i1]\n",
706 " if debug: print(i1, i2, wander, 'adding', s2[i2])\n",
707 " interleaved += s2[i2]\n",
710 " return ''.join(interleaved)\n",
716 "execution_count": 21,
721 "output_type": "stream",
740 "7 10 -3 adding x\n",
741 "7 11 -4 adding e\n",
742 "8 11 -3 adding d\n",
743 "9 11 -2 adding w\n",
744 "9 12 -3 adding c\n",
745 "10 12 -2 adding z\n",
746 "10 13 -3 adding y\n",
747 "10 14 -4 adding h\n",
748 "11 14 -3 adding g\n",
749 "12 14 -2 adding z\n",
750 "12 15 -3 adding x\n",
751 "12 16 -4 adding w\n",
752 "12 17 -5 adding e\n",
753 "13 17 -4 adding w\n",
754 "13 18 -5 adding f\n",
755 "14 18 -4 adding z\n",
756 "14 19 -5 adding f\n",
757 "15 19 -4 adding b\n",
758 "16 19 -3 adding u\n",
759 "16 20 -4 remaining s1 gchd\n"
765 "('ghddageedchgeffbgchd',\n",
766 " 'xyxvxvwvuwxwzyzxwwzu',\n",
767 " 'xyxghdvxdvagwveuwxedwczyhgzxwewfzfbugchd',\n",
771 "execution_count": 21,
773 "output_type": "execute_result"
777 "s1 = make_string(20)\n",
778 "s2 = make_string(20, alphabet='uvwxyz')\n",
779 "il = interleave(s1, s2, wander_limit=5, debug=True)\n",
780 "s1, s2, il, len(il)"
785 "execution_count": 22,
790 "output_type": "stream",
792 "xxxx 0 0 ! ! ! True\n",
793 "seq2 0 1 ! g x False\n",
794 "seq2 0 2 ! h y False\n",
795 "seq2 0 3 ! d x False\n",
796 "seq2 0 4 ! d g False\n",
797 "seq2 0 5 ! a h False\n",
798 "seq2 0 6 ! g d False\n",
799 "seq2 0 7 ! e v False\n",
800 "seq2 0 8 ! e x False\n",
801 "seq2 0 9 ! d d False\n",
802 "seq2 0 10 ! c v False\n",
803 "seq2 0 11 ! h a False\n",
804 "seq2 0 12 ! g g False\n",
805 "seq2 0 13 ! e w False\n",
806 "seq2 0 14 ! f v False\n",
807 "seq2 0 15 ! f e False\n",
808 "seq2 0 16 ! b u False\n",
809 "seq2 0 17 ! g w False\n",
810 "seq2 0 18 ! c x False\n",
811 "seq2 0 19 ! h e False\n",
812 "seq2 0 20 ! d d False\n",
813 "seq1 1 0 x ! x True\n",
814 "xxxx 1 1 x g y False\n",
815 "xxxx 1 2 x h x False\n",
816 "xxxx 1 3 x d g False\n",
817 "xxxx 1 4 x d h False\n",
818 "xxxx 1 5 x a d False\n",
819 "xxxx 1 6 x g v False\n",
820 "xxxx 1 7 x e x False\n",
821 "xxxx 1 8 x e d False\n",
822 "xxxx 1 9 x d v False\n",
823 "xxxx 1 10 x c a False\n",
824 "xxxx 1 11 x h g False\n",
825 "xxxx 1 12 x g w False\n",
826 "xxxx 1 13 x e v False\n",
827 "xxxx 1 14 x f e False\n",
828 "xxxx 1 15 x f u False\n",
829 "xxxx 1 16 x b w False\n",
830 "xxxx 1 17 x g x False\n",
831 "xxxx 1 18 x c e False\n",
832 "xxxx 1 19 x h d False\n",
833 "xxxx 1 20 x d w False\n",
834 "seq1 2 0 y ! y True\n",
835 "xxxx 2 1 y g x False\n",
836 "xxxx 2 2 y h g False\n",
837 "xxxx 2 3 y d h False\n",
838 "xxxx 2 4 y d d False\n",
839 "xxxx 2 5 y a v False\n",
840 "xxxx 2 6 y g x False\n",
841 "xxxx 2 7 y e d False\n",
842 "xxxx 2 8 y e v False\n",
843 "xxxx 2 9 y d a False\n",
844 "xxxx 2 10 y c g False\n",
845 "xxxx 2 11 y h w False\n",
846 "xxxx 2 12 y g v False\n",
847 "xxxx 2 13 y e e False\n",
848 "xxxx 2 14 y f u False\n",
849 "xxxx 2 15 y f w False\n",
850 "xxxx 2 16 y b x False\n",
851 "xxxx 2 17 y g e False\n",
852 "xxxx 2 18 y c d False\n",
853 "xxxx 2 19 y h w False\n",
854 "xxxx 2 20 y d c False\n",
855 "seq1 3 0 x ! x True\n",
856 "seq2 3 1 x g g True\n",
857 "seq2 3 2 x h h True\n",
858 "seq2 3 3 x d d True\n",
859 "xxxx 3 4 x d v False\n",
860 "xxxx 3 5 x a x False\n",
861 "xxxx 3 6 x g d False\n",
862 "xxxx 3 7 x e v False\n",
863 "xxxx 3 8 x e a False\n",
864 "xxxx 3 9 x d g False\n",
865 "xxxx 3 10 x c w False\n",
866 "xxxx 3 11 x h v False\n",
867 "xxxx 3 12 x g e False\n",
868 "xxxx 3 13 x e u False\n",
869 "xxxx 3 14 x f w False\n",
870 "xxxx 3 15 x f x False\n",
871 "xxxx 3 16 x b e False\n",
872 "xxxx 3 17 x g d False\n",
873 "xxxx 3 18 x c w False\n",
874 "xxxx 3 19 x h c False\n",
875 "xxxx 3 20 x d z False\n",
876 "seq1 4 0 v ! g False\n",
877 "xxxx 4 1 v g h False\n",
878 "xxxx 4 2 v h d False\n",
879 "seq1 4 3 v d v True\n",
880 "xxxx 4 4 v d x False\n",
881 "xxxx 4 5 v a d False\n",
882 "xxxx 4 6 v g v False\n",
883 "xxxx 4 7 v e a False\n",
884 "xxxx 4 8 v e g False\n",
885 "xxxx 4 9 v d w False\n",
886 "xxxx 4 10 v c v False\n",
887 "xxxx 4 11 v h e False\n",
888 "xxxx 4 12 v g u False\n",
889 "xxxx 4 13 v e w False\n",
890 "xxxx 4 14 v f x False\n",
891 "xxxx 4 15 v f e False\n",
892 "xxxx 4 16 v b d False\n",
893 "xxxx 4 17 v g w False\n",
894 "xxxx 4 18 v c c False\n",
895 "xxxx 4 19 v h z False\n",
896 "xxxx 4 20 v d y False\n",
897 "seq1 5 0 x ! h False\n",
898 "xxxx 5 1 x g d False\n",
899 "xxxx 5 2 x h v False\n",
900 "seq1 5 3 x d x True\n",
901 "seq2 5 4 x d d True\n",
902 "xxxx 5 5 x a v False\n",
903 "xxxx 5 6 x g a False\n",
904 "xxxx 5 7 x e g False\n",
905 "xxxx 5 8 x e w False\n",
906 "xxxx 5 9 x d v False\n",
907 "xxxx 5 10 x c e False\n",
908 "xxxx 5 11 x h u False\n",
909 "xxxx 5 12 x g w False\n",
910 "xxxx 5 13 x e x False\n",
911 "xxxx 5 14 x f e False\n",
912 "xxxx 5 15 x f d False\n",
913 "xxxx 5 16 x b w False\n",
914 "xxxx 5 17 x g c False\n",
915 "xxxx 5 18 x c z False\n",
916 "xxxx 5 19 x h y False\n",
917 "xxxx 5 20 x d h False\n",
918 "seq1 6 0 v ! d False\n",
919 "xxxx 6 1 v g v False\n",
920 "xxxx 6 2 v h x False\n",
921 "xxxx 6 3 v d d False\n",
922 "seq1 6 4 v d v True\n",
923 "seq2 6 5 v a a True\n",
924 "seq2 6 6 v g g True\n",
925 "xxxx 6 7 v e w False\n",
926 "xxxx 6 8 v e v False\n",
927 "xxxx 6 9 v d e False\n",
928 "xxxx 6 10 v c u False\n",
929 "xxxx 6 11 v h w False\n",
930 "xxxx 6 12 v g x False\n",
931 "xxxx 6 13 v e e False\n",
932 "xxxx 6 14 v f d False\n",
933 "xxxx 6 15 v f w False\n",
934 "xxxx 6 16 v b c False\n",
935 "xxxx 6 17 v g z False\n",
936 "xxxx 6 18 v c y False\n",
937 "xxxx 6 19 v h h False\n",
938 "xxxx 6 20 v d g False\n",
939 "seq1 7 0 w ! v False\n",
940 "xxxx 7 1 w g x False\n",
941 "xxxx 7 2 w h d False\n",
942 "xxxx 7 3 w d v False\n",
943 "xxxx 7 4 w d a False\n",
944 "xxxx 7 5 w a g False\n",
945 "seq1 7 6 w g w True\n",
946 "xxxx 7 7 w e v False\n",
947 "xxxx 7 8 w e e False\n",
948 "xxxx 7 9 w d u False\n",
949 "xxxx 7 10 w c w False\n",
950 "xxxx 7 11 w h x False\n",
951 "xxxx 7 12 w g e False\n",
952 "xxxx 7 13 w e d False\n",
953 "xxxx 7 14 w f w False\n",
954 "xxxx 7 15 w f c False\n",
955 "xxxx 7 16 w b z False\n",
956 "xxxx 7 17 w g y False\n",
957 "xxxx 7 18 w c h False\n",
958 "xxxx 7 19 w h g False\n",
959 "xxxx 7 20 w d z False\n",
960 "seq1 8 0 v ! x False\n",
961 "xxxx 8 1 v g d False\n",
962 "xxxx 8 2 v h v False\n",
963 "xxxx 8 3 v d a False\n",
964 "xxxx 8 4 v d g False\n",
965 "xxxx 8 5 v a w False\n",
966 "seq1 8 6 v g v True\n",
967 "seq2 8 7 v e e True\n",
968 "xxxx 8 8 v e u False\n",
969 "xxxx 8 9 v d w False\n",
970 "xxxx 8 10 v c x False\n",
971 "xxxx 8 11 v h e False\n",
972 "xxxx 8 12 v g d False\n",
973 "xxxx 8 13 v e w False\n",
974 "xxxx 8 14 v f c False\n",
975 "xxxx 8 15 v f z False\n",
976 "xxxx 8 16 v b y False\n",
977 "xxxx 8 17 v g h False\n",
978 "xxxx 8 18 v c g False\n",
979 "xxxx 8 19 v h z False\n",
980 "xxxx 8 20 v d x False\n",
981 "seq1 9 0 u ! d False\n",
982 "xxxx 9 1 u g v False\n",
983 "xxxx 9 2 u h a False\n",
984 "xxxx 9 3 u d g False\n",
985 "xxxx 9 4 u d w False\n",
986 "xxxx 9 5 u a v False\n",
987 "xxxx 9 6 u g e False\n",
988 "seq1 9 7 u e u True\n",
989 "xxxx 9 8 u e w False\n",
990 "xxxx 9 9 u d x False\n",
991 "xxxx 9 10 u c e False\n",
992 "xxxx 9 11 u h d False\n",
993 "xxxx 9 12 u g w False\n",
994 "xxxx 9 13 u e c False\n",
995 "xxxx 9 14 u f z False\n",
996 "xxxx 9 15 u f y False\n",
997 "xxxx 9 16 u b h False\n",
998 "xxxx 9 17 u g g False\n",
999 "xxxx 9 18 u c z False\n",
1000 "xxxx 9 19 u h x False\n",
1001 "xxxx 9 20 u d w False\n",
1002 "seq1 10 0 w ! v False\n",
1003 "xxxx 10 1 w g a False\n",
1004 "xxxx 10 2 w h g False\n",
1005 "xxxx 10 3 w d w False\n",
1006 "xxxx 10 4 w d v False\n",
1007 "xxxx 10 5 w a e False\n",
1008 "xxxx 10 6 w g u False\n",
1009 "seq1 10 7 w e w True\n",
1010 "xxxx 10 8 w e x False\n",
1011 "xxxx 10 9 w d e False\n",
1012 "xxxx 10 10 w c d False\n",
1013 "xxxx 10 11 w h w False\n",
1014 "xxxx 10 12 w g c False\n",
1015 "xxxx 10 13 w e z False\n",
1016 "xxxx 10 14 w f y False\n",
1017 "xxxx 10 15 w f h False\n",
1018 "xxxx 10 16 w b g False\n",
1019 "xxxx 10 17 w g z False\n",
1020 "xxxx 10 18 w c x False\n",
1021 "xxxx 10 19 w h w False\n",
1022 "xxxx 10 20 w d e False\n",
1023 "seq1 11 0 x ! a False\n",
1024 "xxxx 11 1 x g g False\n",
1025 "xxxx 11 2 x h w False\n",
1026 "xxxx 11 3 x d v False\n",
1027 "xxxx 11 4 x d e False\n",
1028 "xxxx 11 5 x a u False\n",
1029 "xxxx 11 6 x g w False\n",
1030 "seq1 11 7 x e x True\n",
1031 "seq2 11 8 x e e True\n",
1032 "seq2 11 9 x d d True\n",
1033 "xxxx 11 10 x c w False\n",
1034 "xxxx 11 11 x h c False\n",
1035 "xxxx 11 12 x g z False\n",
1036 "xxxx 11 13 x e y False\n",
1037 "xxxx 11 14 x f h False\n",
1038 "xxxx 11 15 x f g False\n",
1039 "xxxx 11 16 x b z False\n",
1040 "xxxx 11 17 x g x False\n",
1041 "xxxx 11 18 x c w False\n",
1042 "xxxx 11 19 x h e False\n",
1043 "xxxx 11 20 x d w False\n",
1044 "seq1 12 0 w ! g False\n",
1045 "xxxx 12 1 w g w False\n",
1046 "xxxx 12 2 w h v False\n",
1047 "xxxx 12 3 w d e False\n",
1048 "xxxx 12 4 w d u False\n",
1049 "xxxx 12 5 w a w False\n",
1050 "xxxx 12 6 w g x False\n",
1051 "xxxx 12 7 w e e False\n",
1052 "xxxx 12 8 w e d False\n",
1053 "seq1 12 9 w d w True\n",
1054 "seq2 12 10 w c c True\n",
1055 "xxxx 12 11 w h z False\n",
1056 "xxxx 12 12 w g y False\n",
1057 "xxxx 12 13 w e h False\n",
1058 "xxxx 12 14 w f g False\n",
1059 "xxxx 12 15 w f z False\n",
1060 "xxxx 12 16 w b x False\n",
1061 "xxxx 12 17 w g w False\n",
1062 "xxxx 12 18 w c e False\n",
1063 "xxxx 12 19 w h w False\n",
1064 "xxxx 12 20 w d f False\n",
1065 "seq1 13 0 z ! w False\n",
1066 "xxxx 13 1 z g v False\n",
1067 "xxxx 13 2 z h e False\n",
1068 "xxxx 13 3 z d u False\n",
1069 "xxxx 13 4 z d w False\n",
1070 "xxxx 13 5 z a x False\n",
1071 "xxxx 13 6 z g e False\n",
1072 "xxxx 13 7 z e d False\n",
1073 "xxxx 13 8 z e w False\n",
1074 "xxxx 13 9 z d c False\n",
1075 "seq1 13 10 z c z True\n",
1076 "xxxx 13 11 z h y False\n",
1077 "xxxx 13 12 z g h False\n",
1078 "xxxx 13 13 z e g False\n",
1079 "xxxx 13 14 z f z False\n",
1080 "xxxx 13 15 z f x False\n",
1081 "xxxx 13 16 z b w False\n",
1082 "xxxx 13 17 z g e False\n",
1083 "xxxx 13 18 z c w False\n",
1084 "xxxx 13 19 z h f False\n",
1085 "xxxx 13 20 z d z False\n",
1086 "seq1 14 0 y ! v False\n",
1087 "xxxx 14 1 y g e False\n",
1088 "xxxx 14 2 y h u False\n",
1089 "xxxx 14 3 y d w False\n",
1090 "xxxx 14 4 y d x False\n",
1091 "xxxx 14 5 y a e False\n",
1092 "xxxx 14 6 y g d False\n",
1093 "xxxx 14 7 y e w False\n",
1094 "xxxx 14 8 y e c False\n",
1095 "xxxx 14 9 y d z False\n",
1096 "seq1 14 10 y c y True\n",
1097 "seq2 14 11 y h h True\n",
1098 "seq2 14 12 y g g True\n",
1099 "xxxx 14 13 y e z False\n",
1100 "xxxx 14 14 y f x False\n",
1101 "xxxx 14 15 y f w False\n",
1102 "xxxx 14 16 y b e False\n",
1103 "xxxx 14 17 y g w False\n",
1104 "xxxx 14 18 y c f False\n",
1105 "xxxx 14 19 y h z False\n",
1106 "xxxx 14 20 y d f False\n",
1107 "seq1 15 0 z ! e False\n",
1108 "xxxx 15 1 z g u False\n",
1109 "xxxx 15 2 z h w False\n",
1110 "xxxx 15 3 z d x False\n",
1111 "xxxx 15 4 z d e False\n",
1112 "xxxx 15 5 z a d False\n",
1113 "xxxx 15 6 z g w False\n",
1114 "xxxx 15 7 z e c False\n",
1115 "xxxx 15 8 z e z False\n",
1116 "xxxx 15 9 z d y False\n",
1117 "xxxx 15 10 z c h False\n",
1118 "xxxx 15 11 z h g False\n",
1119 "seq1 15 12 z g z True\n",
1120 "xxxx 15 13 z e x False\n",
1121 "xxxx 15 14 z f w False\n",
1122 "xxxx 15 15 z f e False\n",
1123 "xxxx 15 16 z b w False\n",
1124 "xxxx 15 17 z g f False\n",
1125 "xxxx 15 18 z c z False\n",
1126 "xxxx 15 19 z h f False\n",
1127 "xxxx 15 20 z d b False\n",
1128 "seq1 16 0 x ! u False\n",
1129 "xxxx 16 1 x g w False\n",
1130 "xxxx 16 2 x h x False\n",
1131 "xxxx 16 3 x d e False\n",
1132 "xxxx 16 4 x d d False\n",
1133 "xxxx 16 5 x a w False\n",
1134 "xxxx 16 6 x g c False\n",
1135 "xxxx 16 7 x e z False\n",
1136 "xxxx 16 8 x e y False\n",
1137 "xxxx 16 9 x d h False\n",
1138 "xxxx 16 10 x c g False\n",
1139 "xxxx 16 11 x h z False\n",
1140 "seq1 16 12 x g x True\n",
1141 "xxxx 16 13 x e w False\n",
1142 "xxxx 16 14 x f e False\n",
1143 "xxxx 16 15 x f w False\n",
1144 "xxxx 16 16 x b f False\n",
1145 "xxxx 16 17 x g z False\n",
1146 "xxxx 16 18 x c f False\n",
1147 "xxxx 16 19 x h b False\n",
1148 "xxxx 16 20 x d u False\n",
1149 "seq1 17 0 w ! w False\n",
1150 "xxxx 17 1 w g x False\n",
1151 "xxxx 17 2 w h e False\n",
1152 "xxxx 17 3 w d d False\n",
1153 "xxxx 17 4 w d w False\n",
1154 "xxxx 17 5 w a c False\n",
1155 "xxxx 17 6 w g z False\n",
1156 "xxxx 17 7 w e y False\n",
1157 "xxxx 17 8 w e h False\n",
1158 "xxxx 17 9 w d g False\n",
1159 "xxxx 17 10 w c z False\n",
1160 "xxxx 17 11 w h x False\n",
1161 "seq1 17 12 w g w True\n",
1162 "seq2 17 13 w e e True\n",
1163 "xxxx 17 14 w f w False\n",
1164 "xxxx 17 15 w f f False\n",
1165 "xxxx 17 16 w b z False\n",
1166 "xxxx 17 17 w g f False\n",
1167 "xxxx 17 18 w c b False\n",
1168 "xxxx 17 19 w h u False\n",
1169 "xxxx 17 20 w d g False\n",
1170 "seq1 18 0 w ! x False\n",
1171 "xxxx 18 1 w g e False\n",
1172 "xxxx 18 2 w h d False\n",
1173 "xxxx 18 3 w d w False\n",
1174 "xxxx 18 4 w d c False\n",
1175 "xxxx 18 5 w a z False\n",
1176 "xxxx 18 6 w g y False\n",
1177 "xxxx 18 7 w e h False\n",
1178 "xxxx 18 8 w e g False\n",
1179 "xxxx 18 9 w d z False\n",
1180 "xxxx 18 10 w c x False\n",
1181 "xxxx 18 11 w h w False\n",
1182 "xxxx 18 12 w g e False\n",
1183 "seq1 18 13 w e w True\n",
1184 "seq2 18 14 w f f True\n",
1185 "xxxx 18 15 w f z False\n",
1186 "xxxx 18 16 w b f False\n",
1187 "xxxx 18 17 w g b False\n",
1188 "xxxx 18 18 w c u False\n",
1189 "xxxx 18 19 w h g False\n",
1190 "xxxx 18 20 w d c False\n",
1191 "seq1 19 0 z ! e False\n",
1192 "xxxx 19 1 z g d False\n",
1193 "xxxx 19 2 z h w False\n",
1194 "xxxx 19 3 z d c False\n",
1195 "xxxx 19 4 z d z False\n",
1196 "xxxx 19 5 z a y False\n",
1197 "xxxx 19 6 z g h False\n",
1198 "xxxx 19 7 z e g False\n",
1199 "xxxx 19 8 z e z False\n",
1200 "xxxx 19 9 z d x False\n",
1201 "xxxx 19 10 z c w False\n",
1202 "xxxx 19 11 z h e False\n",
1203 "xxxx 19 12 z g w False\n",
1204 "xxxx 19 13 z e f False\n",
1205 "seq1 19 14 z f z True\n",
1206 "seq2 19 15 z f f True\n",
1207 "seq2 19 16 z b b True\n",
1208 "xxxx 19 17 z g u False\n",
1209 "xxxx 19 18 z c g False\n",
1210 "xxxx 19 19 z h c False\n",
1211 "xxxx 19 20 z d h False\n",
1212 "seq1 20 0 u ! d False\n",
1213 "xxxx 20 1 u g w False\n",
1214 "xxxx 20 2 u h c False\n",
1215 "xxxx 20 3 u d z False\n",
1216 "xxxx 20 4 u d y False\n",
1217 "xxxx 20 5 u a h False\n",
1218 "xxxx 20 6 u g g False\n",
1219 "xxxx 20 7 u e z False\n",
1220 "xxxx 20 8 u e x False\n",
1221 "xxxx 20 9 u d w False\n",
1222 "xxxx 20 10 u c e False\n",
1223 "xxxx 20 11 u h w False\n",
1224 "xxxx 20 12 u g f False\n",
1225 "xxxx 20 13 u e z False\n",
1226 "xxxx 20 14 u f f False\n",
1227 "xxxx 20 15 u f b False\n",
1228 "seq1 20 16 u b u True\n",
1229 "seq2 20 17 u g g True\n",
1230 "seq2 20 18 u c c True\n",
1231 "seq2 20 19 u h h True\n",
1232 "seq2 20 20 u d d True\n",
1233 "T . . . . . . . . . . . . . . . . . . . .\n",
1234 "T . . . . . . . . . . . . . . . . . . . .\n",
1235 "T . . . . . . . . . . . . . . . . . . . .\n",
1236 "T T T T . . . . . . . . . . . . . . . . .\n",
1237 ". . . T . . . . . . . . . . . . . . . . .\n",
1238 ". . . T T . . . . . . . . . . . . . . . .\n",
1239 ". . . . T T T . . . . . . . . . . . . . .\n",
1240 ". . . . . . T . . . . . . . . . . . . . .\n",
1241 ". . . . . . T T . . . . . . . . . . . . .\n",
1242 ". . . . . . . T . . . . . . . . . . . . .\n",
1243 ". . . . . . . T . . . . . . . . . . . . .\n",
1244 ". . . . . . . T T T . . . . . . . . . . .\n",
1245 ". . . . . . . . . T T . . . . . . . . . .\n",
1246 ". . . . . . . . . . T . . . . . . . . . .\n",
1247 ". . . . . . . . . . T T T . . . . . . . .\n",
1248 ". . . . . . . . . . . . T . . . . . . . .\n",
1249 ". . . . . . . . . . . . T . . . . . . . .\n",
1250 ". . . . . . . . . . . . T T . . . . . . .\n",
1251 ". . . . . . . . . . . . . T T . . . . . .\n",
1252 ". . . . . . . . . . . . . . T T T . . . .\n",
1253 ". . . . . . . . . . . . . . . . T T T T T\n"
1258 "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True, debug=True)\n",
1259 "print(show_table(t))"
1263 "cell_type": "code",
1264 "execution_count": 23,
1270 "'XYXghdVXdVagWVeUWXedWcZYhgZXWeWfZfbUgchd'"
1273 "execution_count": 23,
1275 "output_type": "execute_result"
1279 "show_backtrace(bp)"
1283 "cell_type": "code",
1284 "execution_count": 24,
1289 "output_type": "stream",
1291 "T . . . . . . . . . . . . . . . . . . . .\n",
1292 "T . . . . . . . . . . . . . . . . . . . .\n",
1293 "T . . . . . . . . . . . . . . . . . . . .\n",
1294 "T T T T . . . . . . . . . . . . . . . . .\n",
1295 ". . . T . . . . . . . . . . . . . . . . .\n",
1296 ". . . T T . . . . . . . . . . . . . . . .\n",
1297 ". . . . T T T . . . . . . . . . . . . . .\n",
1298 ". . . . . . T . . . . . . . . . . . . . .\n",
1299 ". . . . . . T T . . . . . . . . . . . . .\n",
1300 ". . . . . . . T . . . . . . . . . . . . .\n",
1301 ". . . . . . . T . . . . . . . . . . . . .\n",
1302 ". . . . . . . T T T . . . . . . . . . . .\n",
1303 ". . . . . . . . . T T . . . . . . . . . .\n",
1304 ". . . . . . . . . . T . . . . . . . . . .\n",
1305 ". . . . . . . . . . T T T . . . . . . . .\n",
1306 ". . . . . . . . . . . . T . . . . . . . .\n",
1307 ". . . . . . . . . . . . T . . . . . . . .\n",
1308 ". . . . . . . . . . . . T T . . . . . . .\n",
1309 ". . . . . . . . . . . . . T T . . . . . .\n",
1310 ". . . . . . . . . . . . . . T T T . . . .\n",
1311 ". . . . . . . . . . . . . . . . T T T T T\n",
1312 "XYXghdVXdVagWVeUWXedWcZYhgZXWeWfZfbUgchd\n"
1321 "execution_count": 24,
1323 "output_type": "execute_result"
1327 "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1328 "print(show_table(t))\n",
1329 "print(show_backtrace(bp))\n",
1334 "cell_type": "code",
1335 "execution_count": 25,
1341 "('fahfgbdechbafcbcadcfchhccffhfgeagdhdceebccbhgdefgd',\n",
1342 " 'badbgfaachhhhgghhebahhcbgabcfafeehfcabhbaaccgbcfae',\n",
1343 " 'badfbgfahfgbadecahcbahfhchbchagghhdcefchbahhhcbcgacfbcffhafefgeaegdhfcabhhbdcaaccgebcfebcaecbhgdefgd',\n",
1347 "execution_count": 25,
1349 "output_type": "execute_result"
1353 "s1 = make_string(50)\n",
1354 "s2 = make_string(50)\n",
1355 "il = interleave(s1, s2)\n",
1356 "s1, s2, il, len(il)"
1360 "cell_type": "code",
1361 "execution_count": 26,
1366 "output_type": "stream",
1368 "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1369 "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1370 "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1371 "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1372 ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1373 ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1374 ". T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1375 ". T . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1376 ". . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1377 ". . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1378 ". . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1379 ". . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1380 ". . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1381 ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1382 ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1383 ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1384 ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1385 ". . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1386 ". . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1387 ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1388 ". . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1389 ". . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1390 ". . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1391 ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1392 ". . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1393 ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1394 ". . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1395 ". . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1396 ". . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1397 ". . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . .\n",
1398 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
1399 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . .\n",
1400 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . .\n",
1401 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T T T . . . . . . . . . . . . . . .\n",
1402 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1403 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1404 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1405 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1406 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
1407 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
1408 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . .\n",
1409 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1410 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1411 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1412 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1413 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
1414 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
1415 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
1416 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . .\n",
1417 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . .\n",
1418 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T T T T\n",
1419 "BADfBGFahfgbAdecAhCbaHfHcHbcHaGGHHdcEfchBAhHHCBcGAcfBCfFhAFEfgeaEgdHFCABhHBdcAACCGeBCFebcAEcbhgdefgd\n"
1428 "execution_count": 26,
1430 "output_type": "execute_result"
1434 "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1435 "print(show_table(t))\n",
1436 "print(show_backtrace(bp))\n",
1441 "cell_type": "code",
1442 "execution_count": 27,
1447 "output_type": "stream",
1449 "1000 loops, best of 3: 1.24 ms per loop\n"
1455 "is_interleave(s2, s1, il)"
1459 "cell_type": "code",
1460 "execution_count": 28,
1465 "output_type": "stream",
1467 "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1468 ". . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1469 ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1470 ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1471 ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1472 ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1473 ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1474 ". . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1475 ". . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1476 ". . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1477 ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1478 ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1479 ". . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1480 ". . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1481 ". . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1482 ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1483 ". . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1484 ". . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1485 ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1486 ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1487 ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1488 ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1489 ". . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1490 ". . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1491 ". . . . . . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1492 ". . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1493 ". . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . .\n",
1494 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
1495 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n",
1496 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . .\n",
1497 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . .\n",
1498 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . .\n",
1499 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . .\n",
1500 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . .\n",
1501 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T . . . . . . . . . . .\n",
1502 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . T T T . . . . . . . . . .\n",
1503 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . .\n",
1504 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . .\n",
1505 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . .\n",
1506 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . .\n",
1507 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . .\n",
1508 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T\n",
1509 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1510 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1511 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1512 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1513 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1514 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1515 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1516 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1517 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1518 "badFbgfAHFGBaDECaHcBAhFhChBChAgghhDCeFCHbahhHcbCgaCFbcfFHafeFGEAeGDhfcabhHbDCaaccgEbcfEBCaeCBHGDEFGD\n"
1527 "execution_count": 28,
1529 "output_type": "execute_result"
1533 "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1534 "print(show_table(t))\n",
1535 "print(show_backtrace(bp))\n",
1540 "cell_type": "code",
1541 "execution_count": 29,
1550 "execution_count": 29,
1552 "output_type": "execute_result"
1556 "show_backtrace(bp).lower() == il"
1560 "cell_type": "code",
1561 "execution_count": 30,
1567 "('gbaehdacgdebgaebecfbefcbehfgcheaccdehbfdfadebhcehd', False, False)"
1570 "execution_count": 30,
1572 "output_type": "execute_result"
1576 "s3 = make_string(50)\n",
1577 "s3, is_interleave(s1, s3, il), is_interleave(s2, s3, il)"
1581 "cell_type": "code",
1582 "execution_count": 31,
1587 "output_type": "stream",
1589 "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1590 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1591 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1592 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1593 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1594 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1595 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1596 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1597 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1598 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1599 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1600 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1601 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1602 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1603 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1604 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1605 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1606 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1607 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1608 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1609 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1610 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1611 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1612 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1613 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1614 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1615 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1616 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1617 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1618 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1619 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1620 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1621 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1622 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1623 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1624 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1625 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1626 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1627 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1628 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1629 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1630 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1631 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1632 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1633 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1634 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1635 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1636 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1637 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1638 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1639 ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1649 "execution_count": 31,
1651 "output_type": "execute_result"
1655 "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1656 "print(show_table(t))\n",
1657 "print(show_backtrace(bp))\n",
1662 "cell_type": "code",
1663 "execution_count": 32,
1669 "def is_interleave_recursive(s1, s2, s3):\n",
1671 " return s2 == s3\n",
1673 " return s1 == s3\n",
1675 " if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
1676 " return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n",
1677 " elif s1[-1] == s3[-1]:\n",
1678 " return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
1679 " elif s2[-1] == s3[-1]:\n",
1680 " return is_interleave(s1, s2[:-1], s3[:-1])\n",
1686 "cell_type": "code",
1687 "execution_count": 33,
1693 "s1 = make_string(500)\n",
1694 "s2 = make_string(500)\n",
1695 "s3 = make_string(500)\n",
1696 "s12 = interleave(s1, s2)\n",
1697 "s23 = interleave(s2, s3)"
1701 "cell_type": "code",
1702 "execution_count": 34,
1711 "execution_count": 34,
1713 "output_type": "execute_result"
1717 "is_interleave_recursive(s1, s2, s12)"
1721 "cell_type": "code",
1722 "execution_count": 35,
1731 "execution_count": 35,
1733 "output_type": "execute_result"
1737 "is_interleave_recursive(s1, s2, s23)"
1741 "cell_type": "markdown",
1748 "cell_type": "code",
1749 "execution_count": 36,
1755 "def show_annotated_table(table, bps):\n",
1756 " return '\\n'.join(' '.join('*' if (i, j) == (0, 0) else bps[i, j][2] if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n",
1757 " for i in sorted(set([k[0] for k in table])))"
1761 "cell_type": "code",
1762 "execution_count": 37,
1768 "def show_backtrace_star(bps):\n",
1769 " i = max([0] + [k[0] for k in bps])\n",
1770 " j = max([0] + [k[1] for k in bps])\n",
1773 " if (i, j) in bps:\n",
1774 " while i != 0 or j != 0:\n",
1775 " chars += bps[i, j][2]\n",
1776 " if bps[i, j][3] == 'seq1':\n",
1780 " i, j = bps[i, j][0], bps[i, j][1] \n",
1781 " return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n",
1787 "cell_type": "code",
1788 "execution_count": 73,
1793 "output_type": "stream",
1797 "2: cdaacacadcddbccacdab\n",
1798 "3: bbcdabbaaabcbcadcaac\n",
1799 "4: accbbabbdbaaabadaadc\n",
1801 "6: aacccabaddcdaddaabdc\n"
1807 "['accbbabbdbaaabadaadc']"
1810 "execution_count": 73,
1812 "output_type": "execute_result"
1816 "s1 = make_string(10, alphabet='abcd')\n",
1817 "s2 = make_string(10, alphabet='abcd')\n",
1818 "s3 = make_string(10, alphabet='abcd')\n",
1819 "s4 = make_string(10, alphabet='abcd')\n",
1820 "il = interleave(s1, s2)\n",
1821 "bs = [s3, il, interleave(s3, s4), interleave(s2, s4), interleave(s1, s3)]\n",
1822 "random.shuffle(bs)\n",
1823 "bs = [s1, s2] + bs\n",
1824 "tg = [l for l in bs if is_interleave(s1, s2, l)]\n",
1825 "print('\\n'.join(['{}: {}'.format(i, s) for i, s in enumerate(bs)]))\n",
1830 "cell_type": "code",
1831 "execution_count": 74,
1836 "output_type": "stream",
1838 "* . . . . . . . . . .\n",
1839 "a . . . . . . . . . .\n",
1840 "c . . . . . . . . . .\n",
1841 "c b b . . . . . . . .\n",
1842 "b b . . . . . . . . .\n",
1843 ". a b b . . . . . . .\n",
1844 ". . . d b a a . . . .\n",
1845 ". . . . a a a b a d a\n",
1846 ". . . . a a . a . a a\n",
1847 ". . . . . . . d a . d\n",
1848 ". . . . . . . . . . c\n",
1849 "ACCbBAbbDbaaAbadaADC\n",
1850 "accbbabbdbaaabadaadc\n",
1860 "execution_count": 74,
1862 "output_type": "execute_result"
1866 "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1867 "print(show_annotated_table(t, bp))\n",
1868 "print(show_backtrace(bp))\n",
1869 "print(show_backtrace_star(bp))\n",
1874 "cell_type": "code",
1875 "execution_count": 75,
1880 "output_type": "stream",
1882 "aacccabaddcdaddaabdc\n",
1883 " * ** ** * * * **\n"
1892 "execution_count": 75,
1894 "output_type": "execute_result"
1898 "ind = [i for i, b in enumerate(bs) if is_interleave(s1, s3, b)][0]\n",
1899 "v, bp = is_interleave(s1, s3, bs[ind], return_backpointers=True)\n",
1900 "print(show_backtrace_star(bp))\n",
1905 "cell_type": "code",
1906 "execution_count": 39,
1911 "output_type": "stream",
1913 "* . . . . . . . . . .\n",
1914 "b d . . . . . . . . .\n",
1915 ". b c c . . . . . . .\n",
1916 ". . . d . . . . . . .\n",
1917 ". . . c a a . . . . .\n",
1918 ". . . a a a . . . . .\n",
1919 ". . . a a a d a . . .\n",
1920 ". . . a a . a a b a c\n",
1921 ". . . . d a . . . . d\n",
1922 ". . . . . . . . . . d\n",
1923 ". . . . . . . . . . c\n",
1924 "BdBccDCaaAAdaAbacDDC\n",
1925 "bdbccdcaaaadaabacddc\n",
1935 "execution_count": 39,
1937 "output_type": "execute_result"
1941 "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1942 "print(show_annotated_table(t, bp))\n",
1943 "print(show_backtrace(bp))\n",
1944 "print(show_backtrace_star(bp))\n",
1949 "cell_type": "code",
1950 "execution_count": 40,
1955 "output_type": "stream",
1957 "* . . . . . . . . . .\n",
1958 ". . . . . . . . . . .\n",
1959 ". . . . . . . . . . .\n",
1960 ". . . . . . . . . . .\n",
1961 ". . . . . . . . . . .\n",
1962 ". . . . . . . . . . .\n",
1963 ". . . . . . . . . . .\n",
1964 ". . . . . . . . . . .\n",
1965 ". . . . . . . . . . .\n",
1966 ". . . . . . . . . . .\n",
1967 ". . . . . . . . . . .\n",
1978 "execution_count": 40,
1980 "output_type": "execute_result"
1984 "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1985 "print(show_annotated_table(t, bp))\n",
1986 "print(show_backtrace(bp))\n",
1987 "print(show_backtrace_star(bp))\n",
1992 "cell_type": "code",
1993 "execution_count": 41,
1998 "output_type": "stream",
2000 "* . . . . . . . . . .\n",
2001 "b . . . . . . . . . .\n",
2002 ". . . . . . . . . . .\n",
2003 ". . . . . . . . . . .\n",
2004 ". . . . . . . . . . .\n",
2005 ". . . . . . . . . . .\n",
2006 ". . . . . . . . . . .\n",
2007 ". . . . . . . . . . .\n",
2008 ". . . . . . . . . . .\n",
2009 ". . . . . . . . . . .\n",
2010 ". . . . . . . . . . .\n",
2022 "execution_count": 41,
2024 "output_type": "execute_result"
2028 "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n",
2029 "print(show_annotated_table(t, bp))\n",
2030 "print(show_backtrace(bp))\n",
2031 "print(show_backtrace_star(bp))\n",
2036 "cell_type": "markdown",
2041 "# Make puzzle data"
2045 "cell_type": "code",
2046 "execution_count": 47,
2052 "my_bill = make_string(200)\n",
2053 "friend_bill = make_string(200)\n",
2054 "other_bills = [make_string(200) for _ in range(98)]\n",
2056 "target_interleaved = interleave(my_bill, friend_bill)\n",
2057 "mine_interleaved = [interleave(my_bill, o) for o in random.sample(other_bills, 21)]\n",
2058 "friend_interleaved = [interleave(friend_bill, o) for o in random.sample(other_bills, 13)]\n",
2059 "other_interleaved = []\n",
2060 "for _ in range(103):\n",
2061 " s1, s2 = random.sample(other_bills, 2)\n",
2062 " other_interleaved += [interleave(s1, s2)]"
2066 "cell_type": "code",
2067 "execution_count": 48,
2073 "all_targets = [target_interleaved] + mine_interleaved + friend_interleaved + other_interleaved"
2077 "cell_type": "code",
2078 "execution_count": 49,
2083 "output_type": "stream",
2085 "CPU times: user 3.16 s, sys: 8 ms, total: 3.16 s\n",
2086 "Wall time: 3.17 s\n"
2095 "execution_count": 49,
2097 "output_type": "execute_result"
2101 "%time [i for i, s12 in enumerate(all_targets) if is_interleave(my_bill, friend_bill, s12)]"
2105 "cell_type": "code",
2106 "execution_count": 50,
2111 "output_type": "stream",
2113 "CPU times: user 788 ms, sys: 0 ns, total: 788 ms\n",
2114 "Wall time: 789 ms\n"
2123 "execution_count": 50,
2125 "output_type": "execute_result"
2129 "%time [i for i, s12 in enumerate(all_targets) if is_interleave_recursive(my_bill, friend_bill, s12)]"
2133 "cell_type": "code",
2134 "execution_count": 51,
2140 "bill_set = all_targets + random.sample(other_bills, 8)\n",
2141 "random.shuffle(bill_set)\n",
2142 "bill_set = [my_bill, friend_bill] + bill_set\n",
2144 "# with open('09-bills.txt', 'w') as f:\n",
2145 "# for i, b in enumerate(bill_set):\n",
2146 "# f.write('{}: {}\\n'.format(i, b))"
2150 "cell_type": "code",
2151 "execution_count": null,
2161 "display_name": "Python 3",
2162 "language": "python",
2166 "codemirror_mode": {
2170 "file_extension": ".py",
2171 "mimetype": "text/x-python",
2173 "nbconvert_exporter": "python",
2174 "pygments_lexer": "ipython3",