09-resolving-the-bill/interleaving.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "markdown",
   5    "metadata": {},
   6    "source": [
   7     "# Interleaved strings\n",
   8     "\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",
  10     "\n",
  11     "For example,\n",
  12     "Given:\n",
  13     "s1 = \"aabcc\",\n",
  14     "s2 = \"dbbca\",\n",
  15     "\n",
  16     "When s3 = \"aadbbcbcac\", return true.\n",
  17     "When s3 = \"aadbbbaccc\", return false."
  18    ]
  19   },
  20   {
  21    "cell_type": "code",
  22    "execution_count": 2,
  23    "metadata": {
  24     "collapsed": true
  25    },
  26    "outputs": [],
  27    "source": [
  28     "import random\n",
  29     "import string"
  30    ]
  31   },
  32   {
  33    "cell_type": "code",
  34    "execution_count": 47,
  35    "metadata": {
  36     "collapsed": true
  37    },
  38    "outputs": [],
  39    "source": [
  40     "import sys\n",
  41     "sys.setrecursionlimit(10**6)"
  42    ]
  43   },
  44   {
  45    "cell_type": "code",
  46    "execution_count": 3,
  47    "metadata": {
  48     "collapsed": true
  49    },
  50    "outputs": [],
  51    "source": [
  52     "s1 = \"aabcc\"\n",
  53     "s2 = \"dbbca\"\n",
  54     "\n",
  55     "s3t = \"aadbbcbcac\"\n",
  56     "s3f = \"aadbbbaccc\""
  57    ]
  58   },
  59   {
  60    "cell_type": "code",
  61    "execution_count": 4,
  62    "metadata": {},
  63    "outputs": [
  64     {
  65      "data": {
  66       "text/plain": [
  67        "[(0, ''), (1, 'a'), (2, 'aa'), (3, 'aab'), (4, 'aabc'), (5, 'aabcc')]"
  68       ]
  69      },
  70      "execution_count": 4,
  71      "metadata": {},
  72      "output_type": "execute_result"
  73     }
  74    ],
  75    "source": [
  76     "[(i, s1[:i]) for i in range(len(s1)+1)]"
  77    ]
  78   },
  79   {
  80    "cell_type": "markdown",
  81    "metadata": {},
  82    "source": [
  83     "`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`."
  84    ]
  85   },
  86   {
  87    "cell_type": "code",
  88    "execution_count": 5,
  89    "metadata": {},
  90    "outputs": [
  91     {
  92      "data": {
  93       "text/plain": [
  94        "[[True, False, False, False, False, False],\n",
  95        " [False, False, False, False, False, False],\n",
  96        " [False, False, False, False, False, False],\n",
  97        " [False, False, False, False, False, False],\n",
  98        " [False, False, False, False, False, False],\n",
  99        " [False, False, False, False, False, False]]"
 100       ]
 101      },
 102      "execution_count": 5,
 103      "metadata": {},
 104      "output_type": "execute_result"
 105     }
 106    ],
 107    "source": [
 108     "dp_table = [[False] * (len(s1) + 1) for _ in range(len(s2) + 1)]\n",
 109     "dp_table[0][0] = True\n",
 110     "dp_table"
 111    ]
 112   },
 113   {
 114    "cell_type": "code",
 115    "execution_count": 6,
 116    "metadata": {
 117     "scrolled": true
 118    },
 119    "outputs": [
 120     {
 121      "data": {
 122       "text/plain": [
 123        "{(0, 0): False,\n",
 124        " (0, 1): False,\n",
 125        " (0, 2): False,\n",
 126        " (0, 3): False,\n",
 127        " (0, 4): False,\n",
 128        " (0, 5): False,\n",
 129        " (1, 0): False,\n",
 130        " (1, 1): False,\n",
 131        " (1, 2): False,\n",
 132        " (1, 3): False,\n",
 133        " (1, 4): False,\n",
 134        " (1, 5): False,\n",
 135        " (2, 0): False,\n",
 136        " (2, 1): False,\n",
 137        " (2, 2): False,\n",
 138        " (2, 3): False,\n",
 139        " (2, 4): False,\n",
 140        " (2, 5): False,\n",
 141        " (3, 0): False,\n",
 142        " (3, 1): False,\n",
 143        " (3, 2): False,\n",
 144        " (3, 3): False,\n",
 145        " (3, 4): False,\n",
 146        " (3, 5): False,\n",
 147        " (4, 0): False,\n",
 148        " (4, 1): False,\n",
 149        " (4, 2): False,\n",
 150        " (4, 3): False,\n",
 151        " (4, 4): False,\n",
 152        " (4, 5): False,\n",
 153        " (5, 0): False,\n",
 154        " (5, 1): False,\n",
 155        " (5, 2): False,\n",
 156        " (5, 3): False,\n",
 157        " (5, 4): False,\n",
 158        " (5, 5): False}"
 159       ]
 160      },
 161      "execution_count": 6,
 162      "metadata": {},
 163      "output_type": "execute_result"
 164     }
 165    ],
 166    "source": [
 167     "dp_table = {(i, j): False\n",
 168     "           for i in range(len(s1)+1)\n",
 169     "           for j in range(len(s2)+1)}\n",
 170     "dp_table"
 171    ]
 172   },
 173   {
 174    "cell_type": "code",
 175    "execution_count": 7,
 176    "metadata": {
 177     "collapsed": true
 178    },
 179    "outputs": [],
 180    "source": [
 181     "def show_table(table):\n",
 182     "    return '\\n'.join(\n",
 183     "        ' '.join(str(table[i, j])[0] for j in sorted(set([k[1] for k in table])))\n",
 184     "        for i in sorted(set([k[0] for k in table])))        "
 185    ]
 186   },
 187   {
 188    "cell_type": "code",
 189    "execution_count": 8,
 190    "metadata": {
 191     "collapsed": true
 192    },
 193    "outputs": [],
 194    "source": [
 195     "def show_table(table):\n",
 196     "    return '\\n'.join(\n",
 197     "        ' '.join('T' if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n",
 198     "        for i in sorted(set([k[0] for k in table])))        "
 199    ]
 200   },
 201   {
 202    "cell_type": "code",
 203    "execution_count": 9,
 204    "metadata": {},
 205    "outputs": [
 206     {
 207      "name": "stdout",
 208      "output_type": "stream",
 209      "text": [
 210       ". . . . . .\n",
 211       ". . . . . .\n",
 212       ". . . . . .\n",
 213       ". . . . . .\n",
 214       ". . . . . .\n",
 215       ". . . . . .\n"
 216      ]
 217     }
 218    ],
 219    "source": [
 220     "print(show_table(dp_table))"
 221    ]
 222   },
 223   {
 224    "cell_type": "code",
 225    "execution_count": 10,
 226    "metadata": {},
 227    "outputs": [
 228     {
 229      "name": "stdout",
 230      "output_type": "stream",
 231      "text": [
 232       "aabcc dbbca aadbbcbcac\n",
 233       "aa 0 0 ! ! ! True\n",
 234       "s2 0 1 ! d a False\n",
 235       "s2 0 2 ! b a False\n",
 236       "s2 0 3 ! b d False\n",
 237       "s2 0 4 ! c b False\n",
 238       "s2 0 5 ! a b False\n",
 239       "s1 1 0 a ! a True\n",
 240       "xx 1 1 a d a False\n",
 241       "xx 1 2 a b d False\n",
 242       "xx 1 3 a b b False\n",
 243       "xx 1 4 a c b False\n",
 244       "xx 1 5 a a c False\n",
 245       "s1 2 0 a ! a True\n",
 246       "s2 2 1 a d d True\n",
 247       "s2 2 2 a b b True\n",
 248       "s2 2 3 a b b True\n",
 249       "s2 2 4 a c c True\n",
 250       "xx 2 5 a a b False\n",
 251       "s1 3 0 b ! d False\n",
 252       "s1 3 1 b d b True\n",
 253       "s2 3 2 b b b True\n",
 254       "s1 3 2 b b b True\n",
 255       "xx 3 3 b b c False\n",
 256       "s1 3 4 b c b True\n",
 257       "xx 3 5 b a c False\n",
 258       "s1 4 0 c ! b False\n",
 259       "xx 4 1 c d b False\n",
 260       "s1 4 2 c b c True\n",
 261       "s2 4 3 c b b True\n",
 262       "s2 4 4 c c c True\n",
 263       "s1 4 4 c c c True\n",
 264       "s2 4 5 c a a True\n",
 265       "s1 5 0 c ! b False\n",
 266       "xx 5 1 c d c False\n",
 267       "xx 5 2 c b b False\n",
 268       "s1 5 3 c b c True\n",
 269       "xx 5 4 c c a False\n",
 270       "s1 5 5 c a c True\n",
 271       "T . . . . .\n",
 272       "T . . . . .\n",
 273       "T T T T T .\n",
 274       ". T T . T .\n",
 275       ". . T T T T\n",
 276       ". . . T . T\n"
 277      ]
 278     },
 279     {
 280      "data": {
 281       "text/plain": [
 282        "{(1, 0): (0, 0, 'a', 's1'),\n",
 283        " (2, 0): (1, 0, 'a', 's1'),\n",
 284        " (2, 1): (2, 0, 'd', 's2'),\n",
 285        " (2, 2): (2, 1, 'b', 's2'),\n",
 286        " (2, 3): (2, 2, 'b', 's2'),\n",
 287        " (2, 4): (2, 3, 'c', 's2'),\n",
 288        " (3, 1): (2, 1, 'b', 's1'),\n",
 289        " (3, 2): (2, 2, 'b', 's1'),\n",
 290        " (3, 4): (2, 4, 'b', 's1'),\n",
 291        " (4, 2): (3, 2, 'c', 's1'),\n",
 292        " (4, 3): (4, 2, 'b', 's2'),\n",
 293        " (4, 4): (3, 4, 'c', 's1'),\n",
 294        " (4, 5): (4, 4, 'a', 's2'),\n",
 295        " (5, 3): (4, 3, 'c', 's1'),\n",
 296        " (5, 5): (4, 5, 'c', 's1')}"
 297       ]
 298      },
 299      "execution_count": 10,
 300      "metadata": {},
 301      "output_type": "execute_result"
 302     }
 303    ],
 304    "source": [
 305     "s3 = s3t\n",
 306     "\n",
 307     "print(s1, s2, s3)\n",
 308     "\n",
 309     "dp_table = {(i, j): False\n",
 310     "           for i in range(len(s1)+1)\n",
 311     "           for j in range(len(s2)+1)}\n",
 312     "\n",
 313     "backpointers = {}\n",
 314     "\n",
 315     "for i in range(len(s1)+1):\n",
 316     "    for j in range(len(s2)+1):\n",
 317     "        if i == 0 and j == 0:\n",
 318     "            dp_table[i, j] = True\n",
 319     "            print('aa', i, j, '!', '!', '!', dp_table[i, j])\n",
 320     "        elif i == 0:\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, '!', s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 326     "        elif j == 0:\n",
 327     "            # extend by character from s1\n",
 328     "            if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
 329     "                dp_table[i, j] = True\n",
 330     "                backpointers[i, j] = (i-1, j, s1[i-1], 's1')\n",
 331     "            print('s1', i, j, s1[i-1], '!', s3[i+j-1], dp_table[i, j])\n",
 332     "        else:\n",
 333     "            # extend by character from s2\n",
 334     "            if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
 335     "                dp_table[i, j] = True\n",
 336     "                backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
 337     "                print('s2', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])                \n",
 338     "            # extend by character from s1\n",
 339     "            if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
 340     "                dp_table[i, j] = True\n",
 341     "                backpointers[i, j] = (i-1, j, s1[i-1], 's1')                \n",
 342     "                print('s1', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 343     "            if not dp_table[i, j]:\n",
 344     "                print('xx', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 345     "\n",
 346     "print(show_table(dp_table))\n",
 347     "backpointers"
 348    ]
 349   },
 350   {
 351    "cell_type": "code",
 352    "execution_count": 11,
 353    "metadata": {
 354     "collapsed": true
 355    },
 356    "outputs": [],
 357    "source": [
 358     "def is_interleave(seq1, seq2, seq3, return_backpointers=False, return_table=False, debug=False):\n",
 359     "    \"\"\"Return true if seq3 is some interleaved merge of seq1 and seq2.\n",
 360     "    If return_backpointers, also return the set of backpointers to\n",
 361     "    reconstruct the interleaving\"\"\"\n",
 362     "    \n",
 363     "    # dp_table[i, j] is True if first i+j characters of seq is made up of \n",
 364     "    # an interleaving of the first i characters of seq1 and the \n",
 365     "    # first j characters of seq2\n",
 366     "    \n",
 367     "    if len(seq1) + len(seq2) != len(seq3):\n",
 368     "        if return_backpointers or return_table:\n",
 369     "            retval = [False]\n",
 370     "            if return_backpointers:\n",
 371     "                retval += [{}]\n",
 372     "            if return_table:\n",
 373     "                retval += [{}]\n",
 374     "            return tuple(retval)\n",
 375     "        else:\n",
 376     "            return False\n",
 377     "    \n",
 378     "    dp_table = {(i, j): False\n",
 379     "               for i in range(len(seq1)+1)\n",
 380     "               for j in range(len(seq2)+1)}\n",
 381     "\n",
 382     "    backpointers = {}\n",
 383     "\n",
 384     "    for i in range(len(seq1)+1):\n",
 385     "        for j in range(len(seq2)+1):\n",
 386     "            if i == 0 and j == 0:\n",
 387     "                dp_table[i, j] = True\n",
 388     "                if debug: print('xxxx', i, j, '!', '!', '!', dp_table[i, j])\n",
 389     "            elif i == 0:\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, '!', seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 395     "            elif j == 0:\n",
 396     "                # extend by character from seq1\n",
 397     "                if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
 398     "                    dp_table[i, j] = True\n",
 399     "                    backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')\n",
 400     "                if debug: print('seq1', i, j, seq1[i-1], '!', seq3[i+j-1], dp_table[i, j])\n",
 401     "            else:\n",
 402     "                # extend by character from seq2\n",
 403     "                if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
 404     "                    dp_table[i, j] = True\n",
 405     "                    backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
 406     "                    if debug: print('seq2', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])                \n",
 407     "                # extend by character from seq1\n",
 408     "                if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
 409     "                    dp_table[i, j] = True\n",
 410     "                    backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')                \n",
 411     "                    if debug: print('seq1', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 412     "                if not dp_table[i, j]:\n",
 413     "                    if debug: print('xxxx', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 414     "\n",
 415     "    if return_backpointers or return_table:\n",
 416     "        retval = [dp_table[len(seq1), len(seq2)]]\n",
 417     "        if return_backpointers:\n",
 418     "            retval += [backpointers]\n",
 419     "        if return_table:\n",
 420     "            retval += [dp_table]\n",
 421     "        return tuple(retval)\n",
 422     "    else:\n",
 423     "        return dp_table[len(seq1), len(seq2)]"
 424    ]
 425   },
 426   {
 427    "cell_type": "code",
 428    "execution_count": 12,
 429    "metadata": {},
 430    "outputs": [
 431     {
 432      "data": {
 433       "text/plain": [
 434        "True"
 435       ]
 436      },
 437      "execution_count": 12,
 438      "metadata": {},
 439      "output_type": "execute_result"
 440     }
 441    ],
 442    "source": [
 443     "is_interleave(s1, s2, s3t)"
 444    ]
 445   },
 446   {
 447    "cell_type": "code",
 448    "execution_count": 13,
 449    "metadata": {},
 450    "outputs": [
 451     {
 452      "data": {
 453       "text/plain": [
 454        "(True,\n",
 455        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 456        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 457        "  (2, 1): (2, 0, 'd', 'seq2'),\n",
 458        "  (2, 2): (2, 1, 'b', 'seq2'),\n",
 459        "  (2, 3): (2, 2, 'b', 'seq2'),\n",
 460        "  (2, 4): (2, 3, 'c', 'seq2'),\n",
 461        "  (3, 1): (2, 1, 'b', 'seq1'),\n",
 462        "  (3, 2): (2, 2, 'b', 'seq1'),\n",
 463        "  (3, 4): (2, 4, 'b', 'seq1'),\n",
 464        "  (4, 2): (3, 2, 'c', 'seq1'),\n",
 465        "  (4, 3): (4, 2, 'b', 'seq2'),\n",
 466        "  (4, 4): (3, 4, 'c', 'seq1'),\n",
 467        "  (4, 5): (4, 4, 'a', 'seq2'),\n",
 468        "  (5, 3): (4, 3, 'c', 'seq1'),\n",
 469        "  (5, 5): (4, 5, 'c', 'seq1')})"
 470       ]
 471      },
 472      "execution_count": 13,
 473      "metadata": {},
 474      "output_type": "execute_result"
 475     }
 476    ],
 477    "source": [
 478     "is_interleave(s1, s2, s3t, return_backpointers=True)"
 479    ]
 480   },
 481   {
 482    "cell_type": "code",
 483    "execution_count": 14,
 484    "metadata": {
 485     "scrolled": true
 486    },
 487    "outputs": [
 488     {
 489      "data": {
 490       "text/plain": [
 491        "(True,\n",
 492        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 493        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 494        "  (2, 1): (2, 0, 'd', 'seq2'),\n",
 495        "  (2, 2): (2, 1, 'b', 'seq2'),\n",
 496        "  (2, 3): (2, 2, 'b', 'seq2'),\n",
 497        "  (2, 4): (2, 3, 'c', 'seq2'),\n",
 498        "  (3, 1): (2, 1, 'b', 'seq1'),\n",
 499        "  (3, 2): (2, 2, 'b', 'seq1'),\n",
 500        "  (3, 4): (2, 4, 'b', 'seq1'),\n",
 501        "  (4, 2): (3, 2, 'c', 'seq1'),\n",
 502        "  (4, 3): (4, 2, 'b', 'seq2'),\n",
 503        "  (4, 4): (3, 4, 'c', 'seq1'),\n",
 504        "  (4, 5): (4, 4, 'a', 'seq2'),\n",
 505        "  (5, 3): (4, 3, 'c', 'seq1'),\n",
 506        "  (5, 5): (4, 5, 'c', 'seq1')},\n",
 507        " {(0, 0): True,\n",
 508        "  (0, 1): False,\n",
 509        "  (0, 2): False,\n",
 510        "  (0, 3): False,\n",
 511        "  (0, 4): False,\n",
 512        "  (0, 5): False,\n",
 513        "  (1, 0): True,\n",
 514        "  (1, 1): False,\n",
 515        "  (1, 2): False,\n",
 516        "  (1, 3): False,\n",
 517        "  (1, 4): False,\n",
 518        "  (1, 5): False,\n",
 519        "  (2, 0): True,\n",
 520        "  (2, 1): True,\n",
 521        "  (2, 2): True,\n",
 522        "  (2, 3): True,\n",
 523        "  (2, 4): True,\n",
 524        "  (2, 5): False,\n",
 525        "  (3, 0): False,\n",
 526        "  (3, 1): True,\n",
 527        "  (3, 2): True,\n",
 528        "  (3, 3): False,\n",
 529        "  (3, 4): True,\n",
 530        "  (3, 5): False,\n",
 531        "  (4, 0): False,\n",
 532        "  (4, 1): False,\n",
 533        "  (4, 2): True,\n",
 534        "  (4, 3): True,\n",
 535        "  (4, 4): True,\n",
 536        "  (4, 5): True,\n",
 537        "  (5, 0): False,\n",
 538        "  (5, 1): False,\n",
 539        "  (5, 2): False,\n",
 540        "  (5, 3): True,\n",
 541        "  (5, 4): False,\n",
 542        "  (5, 5): True})"
 543       ]
 544      },
 545      "execution_count": 14,
 546      "metadata": {},
 547      "output_type": "execute_result"
 548     }
 549    ],
 550    "source": [
 551     "is_interleave(s1, s2, s3t, return_backpointers=True, return_table=True)"
 552    ]
 553   },
 554   {
 555    "cell_type": "code",
 556    "execution_count": 15,
 557    "metadata": {},
 558    "outputs": [
 559     {
 560      "data": {
 561       "text/plain": [
 562        "False"
 563       ]
 564      },
 565      "execution_count": 15,
 566      "metadata": {},
 567      "output_type": "execute_result"
 568     }
 569    ],
 570    "source": [
 571     "is_interleave(s1, s2, s3f)"
 572    ]
 573   },
 574   {
 575    "cell_type": "code",
 576    "execution_count": 16,
 577    "metadata": {},
 578    "outputs": [
 579     {
 580      "name": "stdout",
 581      "output_type": "stream",
 582      "text": [
 583       "xxxx 0 0 ! ! ! True\n",
 584       "seq2 0 1 ! b a False\n",
 585       "seq2 0 2 ! b a False\n",
 586       "seq2 0 3 ! b a False\n",
 587       "seq1 1 0 a ! a True\n",
 588       "xxxx 1 1 a b a False\n",
 589       "xxxx 1 2 a b a False\n",
 590       "xxxx 1 3 a b b False\n",
 591       "seq1 2 0 a ! a True\n",
 592       "xxxx 2 1 a b a False\n",
 593       "xxxx 2 2 a b b False\n",
 594       "xxxx 2 3 a b a False\n",
 595       "seq1 3 0 a ! a True\n",
 596       "seq2 3 1 a b b True\n",
 597       "xxxx 3 2 a b a False\n",
 598       "xxxx 3 3 a b b False\n",
 599       "seq1 4 0 a ! b False\n",
 600       "seq1 4 1 a b a True\n",
 601       "seq2 4 2 a b b True\n",
 602       "seq2 4 3 a b b True\n"
 603      ]
 604     },
 605     {
 606      "data": {
 607       "text/plain": [
 608        "(True,\n",
 609        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 610        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 611        "  (3, 0): (2, 0, 'a', 'seq1'),\n",
 612        "  (3, 1): (3, 0, 'b', 'seq2'),\n",
 613        "  (4, 1): (3, 1, 'a', 'seq1'),\n",
 614        "  (4, 2): (4, 1, 'b', 'seq2'),\n",
 615        "  (4, 3): (4, 2, 'b', 'seq2')})"
 616       ]
 617      },
 618      "execution_count": 16,
 619      "metadata": {},
 620      "output_type": "execute_result"
 621     }
 622    ],
 623    "source": [
 624     "is_interleave('aaaa', 'bbb', 'aaababb', return_backpointers=True, debug=True)"
 625    ]
 626   },
 627   {
 628    "cell_type": "code",
 629    "execution_count": 17,
 630    "metadata": {
 631     "collapsed": true
 632    },
 633    "outputs": [],
 634    "source": [
 635     "def show_backtrace(bps):\n",
 636     "    i = max([0] + [k[0] for k in bps])\n",
 637     "    j = max([0] + [k[1] for k in bps])\n",
 638     "    chars = ''\n",
 639     "    if (i, j) in bps:\n",
 640     "        while i != 0 or j != 0:\n",
 641     "            if bps[i, j][3] == 'seq1':\n",
 642     "                chars += bps[i, j][2].upper()\n",
 643     "            else:\n",
 644     "                chars += bps[i, j][2]\n",
 645     "            i, j = bps[i, j][0], bps[i, j][1] \n",
 646     "        return ''.join(list(reversed(chars)))\n",
 647     "    else:\n",
 648     "        return ''"
 649    ]
 650   },
 651   {
 652    "cell_type": "code",
 653    "execution_count": 18,
 654    "metadata": {
 655     "collapsed": true
 656    },
 657    "outputs": [],
 658    "source": [
 659     "def make_string(length, alphabet=None):\n",
 660     "    if not alphabet:\n",
 661     "        alphabet = 'abcdefgh'\n",
 662     "    return ''.join(random.choice(alphabet) for _ in range(length))    "
 663    ]
 664   },
 665   {
 666    "cell_type": "code",
 667    "execution_count": 19,
 668    "metadata": {},
 669    "outputs": [
 670     {
 671      "data": {
 672       "text/plain": [
 673        "'fcafghacdbdhegdbdfbbbghecebceaecbhbfgaedaggbbfefcd'"
 674       ]
 675      },
 676      "execution_count": 19,
 677      "metadata": {},
 678      "output_type": "execute_result"
 679     }
 680    ],
 681    "source": [
 682     "make_string(50)"
 683    ]
 684   },
 685   {
 686    "cell_type": "code",
 687    "execution_count": 20,
 688    "metadata": {
 689     "collapsed": true
 690    },
 691    "outputs": [],
 692    "source": [
 693     "def interleave(s1, s2, wander_limit=10, debug=False):\n",
 694     "    i1 = i2 = wander = 0\n",
 695     "    interleaved = []\n",
 696     "    while i1 <= len(s1) and i2 <= len(s2):\n",
 697     "        if i1 == len(s1):\n",
 698     "            if debug: print(i1, i2, wander, 'remaining s2', s2[i2:])\n",
 699     "            interleaved += s2[i2:]\n",
 700     "            i2 = len(s2) + 1\n",
 701     "        elif i2 == len(s2):\n",
 702     "            if debug: print(i1, i2, wander, 'remaining s1', s1[i1:])\n",
 703     "            interleaved += s1[i1:]\n",
 704     "            i1 = len(s1) + 1\n",
 705     "        else:\n",
 706     "            if wander == wander_limit:\n",
 707     "                step = -1\n",
 708     "            elif wander == -wander_limit:\n",
 709     "                step = +1\n",
 710     "            else:\n",
 711     "                step = random.choice([+1, -1])\n",
 712     "            if step == +1:\n",
 713     "                if debug: print(i1, i2, wander, 'adding', s1[i1])\n",
 714     "                interleaved += s1[i1]\n",
 715     "                i1 += 1\n",
 716     "                wander += 1\n",
 717     "            else:\n",
 718     "                if debug: print(i1, i2, wander, 'adding', s2[i2])\n",
 719     "                interleaved += s2[i2]\n",
 720     "                i2 += 1\n",
 721     "                wander -= 1\n",
 722     "    return ''.join(interleaved)\n",
 723     "            "
 724    ]
 725   },
 726   {
 727    "cell_type": "code",
 728    "execution_count": 21,
 729    "metadata": {},
 730    "outputs": [
 731     {
 732      "name": "stdout",
 733      "output_type": "stream",
 734      "text": [
 735       "0 0 0 adding g\n",
 736       "1 0 1 adding f\n",
 737       "2 0 2 adding z\n",
 738       "2 1 1 adding e\n",
 739       "3 1 2 adding y\n",
 740       "3 2 1 adding g\n",
 741       "4 2 2 adding f\n",
 742       "5 2 3 adding a\n",
 743       "6 2 4 adding z\n",
 744       "6 3 3 adding v\n",
 745       "6 4 2 adding y\n",
 746       "6 5 1 adding u\n",
 747       "6 6 0 adding z\n",
 748       "6 7 -1 adding h\n",
 749       "7 7 0 adding v\n",
 750       "7 8 -1 adding g\n",
 751       "8 8 0 adding d\n",
 752       "9 8 1 adding u\n",
 753       "9 9 0 adding z\n",
 754       "9 10 -1 adding a\n",
 755       "10 10 0 adding z\n",
 756       "10 11 -1 adding y\n",
 757       "10 12 -2 adding w\n",
 758       "10 13 -3 adding a\n",
 759       "11 13 -2 adding f\n",
 760       "12 13 -1 adding g\n",
 761       "13 13 0 adding g\n",
 762       "14 13 1 adding f\n",
 763       "15 13 2 adding h\n",
 764       "16 13 3 adding x\n",
 765       "16 14 2 adding w\n",
 766       "16 15 1 adding a\n",
 767       "17 15 2 adding e\n",
 768       "18 15 3 adding w\n",
 769       "18 16 2 adding d\n",
 770       "19 16 3 adding x\n",
 771       "19 17 2 adding u\n",
 772       "19 18 1 adding z\n",
 773       "19 19 0 adding x\n",
 774       "19 20 -1 remaining s1 g\n"
 775      ]
 776     },
 777     {
 778      "data": {
 779       "text/plain": [
 780        "('gfegfahgdaafggfhaedg',\n",
 781        " 'zyzvyuzvuzzywxwwxuzx',\n",
 782        " 'gfzeygfazvyuzhvgduzazywafggfhxwaewdxuzxg',\n",
 783        " 40)"
 784       ]
 785      },
 786      "execution_count": 21,
 787      "metadata": {},
 788      "output_type": "execute_result"
 789     }
 790    ],
 791    "source": [
 792     "s1 = make_string(20)\n",
 793     "s2 = make_string(20, alphabet='uvwxyz')\n",
 794     "il = interleave(s1, s2, wander_limit=5, debug=True)\n",
 795     "s1, s2, il, len(il)"
 796    ]
 797   },
 798   {
 799    "cell_type": "code",
 800    "execution_count": 22,
 801    "metadata": {},
 802    "outputs": [
 803     {
 804      "name": "stdout",
 805      "output_type": "stream",
 806      "text": [
 807       "xxxx 0 0 ! ! ! True\n",
 808       "seq2 0 1 ! g g True\n",
 809       "seq2 0 2 ! f f True\n",
 810       "seq2 0 3 ! e z False\n",
 811       "seq2 0 4 ! g e False\n",
 812       "seq2 0 5 ! f y False\n",
 813       "seq2 0 6 ! a g False\n",
 814       "seq2 0 7 ! h f False\n",
 815       "seq2 0 8 ! g a False\n",
 816       "seq2 0 9 ! d z False\n",
 817       "seq2 0 10 ! a v False\n",
 818       "seq2 0 11 ! a y False\n",
 819       "seq2 0 12 ! f u False\n",
 820       "seq2 0 13 ! g z False\n",
 821       "seq2 0 14 ! g h False\n",
 822       "seq2 0 15 ! f v False\n",
 823       "seq2 0 16 ! h g False\n",
 824       "seq2 0 17 ! a d False\n",
 825       "seq2 0 18 ! e u False\n",
 826       "seq2 0 19 ! d z False\n",
 827       "seq2 0 20 ! g a False\n",
 828       "seq1 1 0 z ! g False\n",
 829       "xxxx 1 1 z g f False\n",
 830       "seq1 1 2 z f z True\n",
 831       "seq2 1 3 z e e True\n",
 832       "xxxx 1 4 z g y False\n",
 833       "xxxx 1 5 z f g False\n",
 834       "xxxx 1 6 z a f False\n",
 835       "xxxx 1 7 z h a False\n",
 836       "xxxx 1 8 z g z False\n",
 837       "xxxx 1 9 z d v False\n",
 838       "xxxx 1 10 z a y False\n",
 839       "xxxx 1 11 z a u False\n",
 840       "xxxx 1 12 z f z False\n",
 841       "xxxx 1 13 z g h False\n",
 842       "xxxx 1 14 z g v False\n",
 843       "xxxx 1 15 z f g False\n",
 844       "xxxx 1 16 z h d False\n",
 845       "xxxx 1 17 z a u False\n",
 846       "xxxx 1 18 z e z False\n",
 847       "xxxx 1 19 z d a False\n",
 848       "xxxx 1 20 z g z False\n",
 849       "seq1 2 0 y ! f False\n",
 850       "xxxx 2 1 y g z False\n",
 851       "xxxx 2 2 y f e False\n",
 852       "seq1 2 3 y e y True\n",
 853       "seq2 2 4 y g g True\n",
 854       "seq2 2 5 y f f True\n",
 855       "seq2 2 6 y a a True\n",
 856       "xxxx 2 7 y h z False\n",
 857       "xxxx 2 8 y g v False\n",
 858       "xxxx 2 9 y d y False\n",
 859       "xxxx 2 10 y a u False\n",
 860       "xxxx 2 11 y a z False\n",
 861       "xxxx 2 12 y f h False\n",
 862       "xxxx 2 13 y g v False\n",
 863       "xxxx 2 14 y g g False\n",
 864       "xxxx 2 15 y f d False\n",
 865       "xxxx 2 16 y h u False\n",
 866       "xxxx 2 17 y a z False\n",
 867       "xxxx 2 18 y e a False\n",
 868       "xxxx 2 19 y d z False\n",
 869       "xxxx 2 20 y g y False\n",
 870       "seq1 3 0 z ! z False\n",
 871       "xxxx 3 1 z g e False\n",
 872       "xxxx 3 2 z f y False\n",
 873       "xxxx 3 3 z e g False\n",
 874       "xxxx 3 4 z g f False\n",
 875       "xxxx 3 5 z f a False\n",
 876       "seq1 3 6 z a z True\n",
 877       "xxxx 3 7 z h v False\n",
 878       "xxxx 3 8 z g y False\n",
 879       "xxxx 3 9 z d u False\n",
 880       "xxxx 3 10 z a z False\n",
 881       "xxxx 3 11 z a h False\n",
 882       "xxxx 3 12 z f v False\n",
 883       "xxxx 3 13 z g g False\n",
 884       "xxxx 3 14 z g d False\n",
 885       "xxxx 3 15 z f u False\n",
 886       "xxxx 3 16 z h z False\n",
 887       "xxxx 3 17 z a a False\n",
 888       "xxxx 3 18 z e z False\n",
 889       "xxxx 3 19 z d y False\n",
 890       "xxxx 3 20 z g w False\n",
 891       "seq1 4 0 v ! e False\n",
 892       "xxxx 4 1 v g y False\n",
 893       "xxxx 4 2 v f g False\n",
 894       "xxxx 4 3 v e f False\n",
 895       "xxxx 4 4 v g a False\n",
 896       "xxxx 4 5 v f z False\n",
 897       "seq1 4 6 v a v True\n",
 898       "xxxx 4 7 v h y False\n",
 899       "xxxx 4 8 v g u False\n",
 900       "xxxx 4 9 v d z False\n",
 901       "xxxx 4 10 v a h False\n",
 902       "xxxx 4 11 v a v False\n",
 903       "xxxx 4 12 v f g False\n",
 904       "xxxx 4 13 v g d False\n",
 905       "xxxx 4 14 v g u False\n",
 906       "xxxx 4 15 v f z False\n",
 907       "xxxx 4 16 v h a False\n",
 908       "xxxx 4 17 v a z False\n",
 909       "xxxx 4 18 v e y False\n",
 910       "xxxx 4 19 v d w False\n",
 911       "xxxx 4 20 v g a False\n",
 912       "seq1 5 0 y ! y False\n",
 913       "xxxx 5 1 y g g False\n",
 914       "xxxx 5 2 y f f False\n",
 915       "xxxx 5 3 y e a False\n",
 916       "xxxx 5 4 y g z False\n",
 917       "xxxx 5 5 y f v False\n",
 918       "seq1 5 6 y a y True\n",
 919       "xxxx 5 7 y h u False\n",
 920       "xxxx 5 8 y g z False\n",
 921       "xxxx 5 9 y d h False\n",
 922       "xxxx 5 10 y a v False\n",
 923       "xxxx 5 11 y a g False\n",
 924       "xxxx 5 12 y f d False\n",
 925       "xxxx 5 13 y g u False\n",
 926       "xxxx 5 14 y g z False\n",
 927       "xxxx 5 15 y f a False\n",
 928       "xxxx 5 16 y h z False\n",
 929       "xxxx 5 17 y a y False\n",
 930       "xxxx 5 18 y e w False\n",
 931       "xxxx 5 19 y d a False\n",
 932       "xxxx 5 20 y g f False\n",
 933       "seq1 6 0 u ! g False\n",
 934       "xxxx 6 1 u g f False\n",
 935       "xxxx 6 2 u f a False\n",
 936       "xxxx 6 3 u e z False\n",
 937       "xxxx 6 4 u g v False\n",
 938       "xxxx 6 5 u f y False\n",
 939       "seq1 6 6 u a u True\n",
 940       "xxxx 6 7 u h z False\n",
 941       "xxxx 6 8 u g h False\n",
 942       "xxxx 6 9 u d v False\n",
 943       "xxxx 6 10 u a g False\n",
 944       "xxxx 6 11 u a d False\n",
 945       "xxxx 6 12 u f u False\n",
 946       "xxxx 6 13 u g z False\n",
 947       "xxxx 6 14 u g a False\n",
 948       "xxxx 6 15 u f z False\n",
 949       "xxxx 6 16 u h y False\n",
 950       "xxxx 6 17 u a w False\n",
 951       "xxxx 6 18 u e a False\n",
 952       "xxxx 6 19 u d f False\n",
 953       "xxxx 6 20 u g g False\n",
 954       "seq1 7 0 z ! f False\n",
 955       "xxxx 7 1 z g a False\n",
 956       "xxxx 7 2 z f z False\n",
 957       "xxxx 7 3 z e v False\n",
 958       "xxxx 7 4 z g y False\n",
 959       "xxxx 7 5 z f u False\n",
 960       "seq1 7 6 z a z True\n",
 961       "seq2 7 7 z h h True\n",
 962       "xxxx 7 8 z g v False\n",
 963       "xxxx 7 9 z d g False\n",
 964       "xxxx 7 10 z a d False\n",
 965       "xxxx 7 11 z a u False\n",
 966       "xxxx 7 12 z f z False\n",
 967       "xxxx 7 13 z g a False\n",
 968       "xxxx 7 14 z g z False\n",
 969       "xxxx 7 15 z f y False\n",
 970       "xxxx 7 16 z h w False\n",
 971       "xxxx 7 17 z a a False\n",
 972       "xxxx 7 18 z e f False\n",
 973       "xxxx 7 19 z d g False\n",
 974       "xxxx 7 20 z g g False\n",
 975       "seq1 8 0 v ! a False\n",
 976       "xxxx 8 1 v g z False\n",
 977       "xxxx 8 2 v f v False\n",
 978       "xxxx 8 3 v e y False\n",
 979       "xxxx 8 4 v g u False\n",
 980       "xxxx 8 5 v f z False\n",
 981       "xxxx 8 6 v a h False\n",
 982       "seq1 8 7 v h v True\n",
 983       "seq2 8 8 v g g True\n",
 984       "seq2 8 9 v d d True\n",
 985       "xxxx 8 10 v a u False\n",
 986       "xxxx 8 11 v a z False\n",
 987       "xxxx 8 12 v f a False\n",
 988       "xxxx 8 13 v g z False\n",
 989       "xxxx 8 14 v g y False\n",
 990       "xxxx 8 15 v f w False\n",
 991       "xxxx 8 16 v h a False\n",
 992       "xxxx 8 17 v a f False\n",
 993       "xxxx 8 18 v e g False\n",
 994       "xxxx 8 19 v d g False\n",
 995       "xxxx 8 20 v g f False\n",
 996       "seq1 9 0 u ! z False\n",
 997       "xxxx 9 1 u g v False\n",
 998       "xxxx 9 2 u f y False\n",
 999       "xxxx 9 3 u e u False\n",
1000       "xxxx 9 4 u g z False\n",
1001       "xxxx 9 5 u f h False\n",
1002       "xxxx 9 6 u a v False\n",
1003       "xxxx 9 7 u h g False\n",
1004       "xxxx 9 8 u g d False\n",
1005       "seq1 9 9 u d u True\n",
1006       "xxxx 9 10 u a z False\n",
1007       "xxxx 9 11 u a a False\n",
1008       "xxxx 9 12 u f z False\n",
1009       "xxxx 9 13 u g y False\n",
1010       "xxxx 9 14 u g w False\n",
1011       "xxxx 9 15 u f a False\n",
1012       "xxxx 9 16 u h f False\n",
1013       "xxxx 9 17 u a g False\n",
1014       "xxxx 9 18 u e g False\n",
1015       "xxxx 9 19 u d f False\n",
1016       "xxxx 9 20 u g h False\n",
1017       "seq1 10 0 z ! v False\n",
1018       "xxxx 10 1 z g y False\n",
1019       "xxxx 10 2 z f u False\n",
1020       "xxxx 10 3 z e z False\n",
1021       "xxxx 10 4 z g h False\n",
1022       "xxxx 10 5 z f v False\n",
1023       "xxxx 10 6 z a g False\n",
1024       "xxxx 10 7 z h d False\n",
1025       "xxxx 10 8 z g u False\n",
1026       "seq1 10 9 z d z True\n",
1027       "seq2 10 10 z a a True\n",
1028       "xxxx 10 11 z a z False\n",
1029       "xxxx 10 12 z f y False\n",
1030       "xxxx 10 13 z g w False\n",
1031       "xxxx 10 14 z g a False\n",
1032       "xxxx 10 15 z f f False\n",
1033       "xxxx 10 16 z h g False\n",
1034       "xxxx 10 17 z a g False\n",
1035       "xxxx 10 18 z e f False\n",
1036       "xxxx 10 19 z d h False\n",
1037       "xxxx 10 20 z g x False\n",
1038       "seq1 11 0 z ! y False\n",
1039       "xxxx 11 1 z g u False\n",
1040       "xxxx 11 2 z f z False\n",
1041       "xxxx 11 3 z e h False\n",
1042       "xxxx 11 4 z g v False\n",
1043       "xxxx 11 5 z f g False\n",
1044       "xxxx 11 6 z a d False\n",
1045       "xxxx 11 7 z h u False\n",
1046       "xxxx 11 8 z g z False\n",
1047       "xxxx 11 9 z d a False\n",
1048       "seq1 11 10 z a z True\n",
1049       "xxxx 11 11 z a y False\n",
1050       "xxxx 11 12 z f w False\n",
1051       "xxxx 11 13 z g a False\n",
1052       "xxxx 11 14 z g f False\n",
1053       "xxxx 11 15 z f g False\n",
1054       "xxxx 11 16 z h g False\n",
1055       "xxxx 11 17 z a f False\n",
1056       "xxxx 11 18 z e h False\n",
1057       "xxxx 11 19 z d x False\n",
1058       "xxxx 11 20 z g w False\n",
1059       "seq1 12 0 y ! u False\n",
1060       "xxxx 12 1 y g z False\n",
1061       "xxxx 12 2 y f h False\n",
1062       "xxxx 12 3 y e v False\n",
1063       "xxxx 12 4 y g g False\n",
1064       "xxxx 12 5 y f d False\n",
1065       "xxxx 12 6 y a u False\n",
1066       "xxxx 12 7 y h z False\n",
1067       "xxxx 12 8 y g a False\n",
1068       "xxxx 12 9 y d z False\n",
1069       "seq1 12 10 y a y True\n",
1070       "xxxx 12 11 y a w False\n",
1071       "xxxx 12 12 y f a False\n",
1072       "xxxx 12 13 y g f False\n",
1073       "xxxx 12 14 y g g False\n",
1074       "xxxx 12 15 y f g False\n",
1075       "xxxx 12 16 y h f False\n",
1076       "xxxx 12 17 y a h False\n",
1077       "xxxx 12 18 y e x False\n",
1078       "xxxx 12 19 y d w False\n",
1079       "xxxx 12 20 y g a False\n",
1080       "seq1 13 0 w ! z False\n",
1081       "xxxx 13 1 w g h False\n",
1082       "xxxx 13 2 w f v False\n",
1083       "xxxx 13 3 w e g False\n",
1084       "xxxx 13 4 w g d False\n",
1085       "xxxx 13 5 w f u False\n",
1086       "xxxx 13 6 w a z False\n",
1087       "xxxx 13 7 w h a False\n",
1088       "xxxx 13 8 w g z False\n",
1089       "xxxx 13 9 w d y False\n",
1090       "seq1 13 10 w a w True\n",
1091       "seq2 13 11 w a a True\n",
1092       "seq2 13 12 w f f True\n",
1093       "seq2 13 13 w g g True\n",
1094       "seq2 13 14 w g g True\n",
1095       "seq2 13 15 w f f True\n",
1096       "seq2 13 16 w h h True\n",
1097       "xxxx 13 17 w a x False\n",
1098       "xxxx 13 18 w e w False\n",
1099       "xxxx 13 19 w d a False\n",
1100       "xxxx 13 20 w g e False\n",
1101       "seq1 14 0 x ! h False\n",
1102       "xxxx 14 1 x g v False\n",
1103       "xxxx 14 2 x f g False\n",
1104       "xxxx 14 3 x e d False\n",
1105       "xxxx 14 4 x g u False\n",
1106       "xxxx 14 5 x f z False\n",
1107       "xxxx 14 6 x a a False\n",
1108       "xxxx 14 7 x h z False\n",
1109       "xxxx 14 8 x g y False\n",
1110       "xxxx 14 9 x d w False\n",
1111       "xxxx 14 10 x a a False\n",
1112       "xxxx 14 11 x a f False\n",
1113       "xxxx 14 12 x f g False\n",
1114       "xxxx 14 13 x g g False\n",
1115       "xxxx 14 14 x g f False\n",
1116       "xxxx 14 15 x f h False\n",
1117       "seq1 14 16 x h x True\n",
1118       "xxxx 14 17 x a w False\n",
1119       "xxxx 14 18 x e a False\n",
1120       "xxxx 14 19 x d e False\n",
1121       "xxxx 14 20 x g w False\n",
1122       "seq1 15 0 w ! v False\n",
1123       "xxxx 15 1 w g g False\n",
1124       "xxxx 15 2 w f d False\n",
1125       "xxxx 15 3 w e u False\n",
1126       "xxxx 15 4 w g z False\n",
1127       "xxxx 15 5 w f a False\n",
1128       "xxxx 15 6 w a z False\n",
1129       "xxxx 15 7 w h y False\n",
1130       "xxxx 15 8 w g w False\n",
1131       "xxxx 15 9 w d a False\n",
1132       "xxxx 15 10 w a f False\n",
1133       "xxxx 15 11 w a g False\n",
1134       "xxxx 15 12 w f g False\n",
1135       "xxxx 15 13 w g f False\n",
1136       "xxxx 15 14 w g h False\n",
1137       "xxxx 15 15 w f x False\n",
1138       "seq1 15 16 w h w True\n",
1139       "seq2 15 17 w a a True\n",
1140       "seq2 15 18 w e e True\n",
1141       "xxxx 15 19 w d w False\n",
1142       "xxxx 15 20 w g d False\n",
1143       "seq1 16 0 w ! g False\n",
1144       "xxxx 16 1 w g d False\n",
1145       "xxxx 16 2 w f u False\n",
1146       "xxxx 16 3 w e z False\n",
1147       "xxxx 16 4 w g a False\n",
1148       "xxxx 16 5 w f z False\n",
1149       "xxxx 16 6 w a y False\n",
1150       "xxxx 16 7 w h w False\n",
1151       "xxxx 16 8 w g a False\n",
1152       "xxxx 16 9 w d f False\n",
1153       "xxxx 16 10 w a g False\n",
1154       "xxxx 16 11 w a g False\n",
1155       "xxxx 16 12 w f f False\n",
1156       "xxxx 16 13 w g h False\n",
1157       "xxxx 16 14 w g x False\n",
1158       "xxxx 16 15 w f w False\n",
1159       "xxxx 16 16 w h a False\n",
1160       "xxxx 16 17 w a e False\n",
1161       "seq1 16 18 w e w True\n",
1162       "seq2 16 19 w d d True\n",
1163       "xxxx 16 20 w g x False\n",
1164       "seq1 17 0 x ! d False\n",
1165       "xxxx 17 1 x g u False\n",
1166       "xxxx 17 2 x f z False\n",
1167       "xxxx 17 3 x e a False\n",
1168       "xxxx 17 4 x g z False\n",
1169       "xxxx 17 5 x f y False\n",
1170       "xxxx 17 6 x a w False\n",
1171       "xxxx 17 7 x h a False\n",
1172       "xxxx 17 8 x g f False\n",
1173       "xxxx 17 9 x d g False\n",
1174       "xxxx 17 10 x a g False\n",
1175       "xxxx 17 11 x a f False\n",
1176       "xxxx 17 12 x f h False\n",
1177       "xxxx 17 13 x g x False\n",
1178       "xxxx 17 14 x g w False\n",
1179       "xxxx 17 15 x f a False\n",
1180       "xxxx 17 16 x h e False\n",
1181       "xxxx 17 17 x a w False\n",
1182       "xxxx 17 18 x e d False\n",
1183       "seq1 17 19 x d x True\n",
1184       "xxxx 17 20 x g u False\n",
1185       "seq1 18 0 u ! u False\n",
1186       "xxxx 18 1 u g z False\n",
1187       "xxxx 18 2 u f a False\n",
1188       "xxxx 18 3 u e z False\n",
1189       "xxxx 18 4 u g y False\n",
1190       "xxxx 18 5 u f w False\n",
1191       "xxxx 18 6 u a a False\n",
1192       "xxxx 18 7 u h f False\n",
1193       "xxxx 18 8 u g g False\n",
1194       "xxxx 18 9 u d g False\n",
1195       "xxxx 18 10 u a f False\n",
1196       "xxxx 18 11 u a h False\n",
1197       "xxxx 18 12 u f x False\n",
1198       "xxxx 18 13 u g w False\n",
1199       "xxxx 18 14 u g a False\n",
1200       "xxxx 18 15 u f e False\n",
1201       "xxxx 18 16 u h w False\n",
1202       "xxxx 18 17 u a d False\n",
1203       "xxxx 18 18 u e x False\n",
1204       "seq1 18 19 u d u True\n",
1205       "xxxx 18 20 u g z False\n",
1206       "seq1 19 0 z ! z False\n",
1207       "xxxx 19 1 z g a False\n",
1208       "xxxx 19 2 z f z False\n",
1209       "xxxx 19 3 z e y False\n",
1210       "xxxx 19 4 z g w False\n",
1211       "xxxx 19 5 z f a False\n",
1212       "xxxx 19 6 z a f False\n",
1213       "xxxx 19 7 z h g False\n",
1214       "xxxx 19 8 z g g False\n",
1215       "xxxx 19 9 z d f False\n",
1216       "xxxx 19 10 z a h False\n",
1217       "xxxx 19 11 z a x False\n",
1218       "xxxx 19 12 z f w False\n",
1219       "xxxx 19 13 z g a False\n",
1220       "xxxx 19 14 z g e False\n",
1221       "xxxx 19 15 z f w False\n",
1222       "xxxx 19 16 z h d False\n",
1223       "xxxx 19 17 z a x False\n",
1224       "xxxx 19 18 z e u False\n",
1225       "seq1 19 19 z d z True\n",
1226       "xxxx 19 20 z g x False\n",
1227       "seq1 20 0 x ! a False\n",
1228       "xxxx 20 1 x g z False\n",
1229       "xxxx 20 2 x f y False\n",
1230       "xxxx 20 3 x e w False\n",
1231       "xxxx 20 4 x g a False\n",
1232       "xxxx 20 5 x f f False\n",
1233       "xxxx 20 6 x a g False\n",
1234       "xxxx 20 7 x h g False\n",
1235       "xxxx 20 8 x g f False\n",
1236       "xxxx 20 9 x d h False\n",
1237       "xxxx 20 10 x a x False\n",
1238       "xxxx 20 11 x a w False\n",
1239       "xxxx 20 12 x f a False\n",
1240       "xxxx 20 13 x g e False\n",
1241       "xxxx 20 14 x g w False\n",
1242       "xxxx 20 15 x f d False\n",
1243       "xxxx 20 16 x h x False\n",
1244       "xxxx 20 17 x a u False\n",
1245       "xxxx 20 18 x e z False\n",
1246       "seq1 20 19 x d x True\n",
1247       "seq2 20 20 x g g True\n",
1248       "T T T . . . . . . . . . . . . . . . . . .\n",
1249       ". . T T . . . . . . . . . . . . . . . . .\n",
1250       ". . . T T T T . . . . . . . . . . . . . .\n",
1251       ". . . . . . T . . . . . . . . . . . . . .\n",
1252       ". . . . . . T . . . . . . . . . . . . . .\n",
1253       ". . . . . . T . . . . . . . . . . . . . .\n",
1254       ". . . . . . T . . . . . . . . . . . . . .\n",
1255       ". . . . . . T T . . . . . . . . . . . . .\n",
1256       ". . . . . . . T T T . . . . . . . . . . .\n",
1257       ". . . . . . . . . T . . . . . . . . . . .\n",
1258       ". . . . . . . . . T T . . . . . . . . . .\n",
1259       ". . . . . . . . . . T . . . . . . . . . .\n",
1260       ". . . . . . . . . . T . . . . . . . . . .\n",
1261       ". . . . . . . . . . T T T T T T T . . . .\n",
1262       ". . . . . . . . . . . . . . . . T . . . .\n",
1263       ". . . . . . . . . . . . . . . . T T T . .\n",
1264       ". . . . . . . . . . . . . . . . . . T T .\n",
1265       ". . . . . . . . . . . . . . . . . . . T .\n",
1266       ". . . . . . . . . . . . . . . . . . . T .\n",
1267       ". . . . . . . . . . . . . . . . . . . T .\n",
1268       ". . . . . . . . . . . . . . . . . . . T T\n"
1269      ]
1270     }
1271    ],
1272    "source": [
1273     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True, debug=True)\n",
1274     "print(show_table(t))"
1275    ]
1276   },
1277   {
1278    "cell_type": "code",
1279    "execution_count": 23,
1280    "metadata": {},
1281    "outputs": [
1282     {
1283      "data": {
1284       "text/plain": [
1285        "'gfZeYgfaZVYUZhVgdUZaZYWafggfhXWaeWdXUZXg'"
1286       ]
1287      },
1288      "execution_count": 23,
1289      "metadata": {},
1290      "output_type": "execute_result"
1291     }
1292    ],
1293    "source": [
1294     "show_backtrace(bp)"
1295    ]
1296   },
1297   {
1298    "cell_type": "code",
1299    "execution_count": 24,
1300    "metadata": {},
1301    "outputs": [
1302     {
1303      "name": "stdout",
1304      "output_type": "stream",
1305      "text": [
1306       "T T T . . . . . . . . . . . . . . . . . .\n",
1307       ". . T T . . . . . . . . . . . . . . . . .\n",
1308       ". . . T T T T . . . . . . . . . . . . . .\n",
1309       ". . . . . . T . . . . . . . . . . . . . .\n",
1310       ". . . . . . T . . . . . . . . . . . . . .\n",
1311       ". . . . . . T . . . . . . . . . . . . . .\n",
1312       ". . . . . . T . . . . . . . . . . . . . .\n",
1313       ". . . . . . T T . . . . . . . . . . . . .\n",
1314       ". . . . . . . T T T . . . . . . . . . . .\n",
1315       ". . . . . . . . . T . . . . . . . . . . .\n",
1316       ". . . . . . . . . T T . . . . . . . . . .\n",
1317       ". . . . . . . . . . T . . . . . . . . . .\n",
1318       ". . . . . . . . . . T . . . . . . . . . .\n",
1319       ". . . . . . . . . . T T T T T T T . . . .\n",
1320       ". . . . . . . . . . . . . . . . T . . . .\n",
1321       ". . . . . . . . . . . . . . . . T T T . .\n",
1322       ". . . . . . . . . . . . . . . . . . T T .\n",
1323       ". . . . . . . . . . . . . . . . . . . T .\n",
1324       ". . . . . . . . . . . . . . . . . . . T .\n",
1325       ". . . . . . . . . . . . . . . . . . . T .\n",
1326       ". . . . . . . . . . . . . . . . . . . T T\n",
1327       "gfZeYgfaZVYUZhVgdUZaZYWafggfhXWaeWdXUZXg\n"
1328      ]
1329     },
1330     {
1331      "data": {
1332       "text/plain": [
1333        "True"
1334       ]
1335      },
1336      "execution_count": 24,
1337      "metadata": {},
1338      "output_type": "execute_result"
1339     }
1340    ],
1341    "source": [
1342     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1343     "print(show_table(t))\n",
1344     "print(show_backtrace(bp))\n",
1345     "v"
1346    ]
1347   },
1348   {
1349    "cell_type": "code",
1350    "execution_count": 25,
1351    "metadata": {},
1352    "outputs": [
1353     {
1354      "data": {
1355       "text/plain": [
1356        "('chcceahdchbdeahgacbfbfebfefacfebhhcdfgfgggfeahaadd',\n",
1357        " 'fbhafageadeedbcdfffaabefeeffaffgebdbchcgfcgggecbgh',\n",
1358        " 'chccfbehaahfdcagheabdedeaehgdabccbfdbfebffeffafacfaebefeebfhhcdfafffgebdgfgggbfchceahgaafdcgdggecbgh',\n",
1359        " 100)"
1360       ]
1361      },
1362      "execution_count": 25,
1363      "metadata": {},
1364      "output_type": "execute_result"
1365     }
1366    ],
1367    "source": [
1368     "s1 = make_string(50)\n",
1369     "s2 = make_string(50)\n",
1370     "il = interleave(s1, s2)\n",
1371     "s1, s2, il, len(il)"
1372    ]
1373   },
1374   {
1375    "cell_type": "code",
1376    "execution_count": 26,
1377    "metadata": {},
1378    "outputs": [
1379     {
1380      "name": "stdout",
1381      "output_type": "stream",
1382      "text": [
1383       "T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1384       ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1385       ". . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1386       ". . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1387       ". . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1388       ". . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1389       ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1390       ". . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1391       ". . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1392       ". . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1393       ". . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1394       ". . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1395       ". . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1396       ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1397       ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1398       ". . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1399       ". . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1400       ". . . . . . . . . . . . . . . . . . . . . T . . T T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1401       ". . . . . . . . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . .\n",
1402       ". . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . .\n",
1403       ". . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . .\n",
1404       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . T T T . . . . . . . . . . . . . . . . . .\n",
1405       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
1406       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
1407       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
1408       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
1409       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . .\n",
1410       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . .\n",
1411       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . .\n",
1412       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . .\n",
1413       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . .\n",
1414       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . .\n",
1415       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1416       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1417       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1418       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . .\n",
1419       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
1420       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . .\n",
1421       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . .\n",
1422       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . .\n",
1423       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . .\n",
1424       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T .\n",
1425       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T .\n",
1426       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T\n",
1427       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1428       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1429       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1430       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1431       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1432       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1433       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1434       "chccFBeHaAhFdcAGhEAbdeDEaEhgDaBcCbfDbfebfFefFaFAcfAeBEFEEbFhhcdFAfFFGEBDgfgggBfCHCeahGaaFdCGdGGECBGH\n"
1435      ]
1436     },
1437     {
1438      "data": {
1439       "text/plain": [
1440        "True"
1441       ]
1442      },
1443      "execution_count": 26,
1444      "metadata": {},
1445      "output_type": "execute_result"
1446     }
1447    ],
1448    "source": [
1449     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1450     "print(show_table(t))\n",
1451     "print(show_backtrace(bp))\n",
1452     "v"
1453    ]
1454   },
1455   {
1456    "cell_type": "code",
1457    "execution_count": 27,
1458    "metadata": {},
1459    "outputs": [
1460     {
1461      "name": "stdout",
1462      "output_type": "stream",
1463      "text": [
1464       "1000 loops, best of 3: 1.31 ms per loop\n"
1465      ]
1466     }
1467    ],
1468    "source": [
1469     "%%timeit\n",
1470     "is_interleave(s2, s1, il)"
1471    ]
1472   },
1473   {
1474    "cell_type": "code",
1475    "execution_count": 28,
1476    "metadata": {},
1477    "outputs": [
1478     {
1479      "name": "stdout",
1480      "output_type": "stream",
1481      "text": [
1482       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1483       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1484       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1485       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1486       "T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1487       ". . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1488       ". . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1489       ". . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1490       ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1491       ". . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1492       ". . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1493       ". . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1494       ". . . . . . . . . T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1495       ". . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1496       ". . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1497       ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1498       ". . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1499       ". . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1500       ". . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1501       ". . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1502       ". . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1503       ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1504       ". . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1505       ". . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1506       ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1507       ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1508       ". . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1509       ". . . . . . . . . . . . . . . . . T T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1510       ". . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1511       ". . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1512       ". . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1513       ". . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1514       ". . . . . . . . . . . . . . . . . . . . . T . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1515       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1516       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1517       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1518       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . .\n",
1519       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T T T T T T . . . . . . . . . . . . . . .\n",
1520       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . T . . . . . . . . . . . . . . .\n",
1521       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
1522       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
1523       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
1524       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
1525       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . .\n",
1526       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
1527       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
1528       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . .\n",
1529       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . .\n",
1530       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . .\n",
1531       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . .\n",
1532       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T T\n",
1533       "CHCCfbEhaAHfDCagHeaBdeDEAeHGdAbcCBFdBFEBfFEffaFACFaEbefeeBfHHCDfaffFgebdGFGGGbFchcEAHgAAfDcgDggecbgh\n"
1534      ]
1535     },
1536     {
1537      "data": {
1538       "text/plain": [
1539        "True"
1540       ]
1541      },
1542      "execution_count": 28,
1543      "metadata": {},
1544      "output_type": "execute_result"
1545     }
1546    ],
1547    "source": [
1548     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1549     "print(show_table(t))\n",
1550     "print(show_backtrace(bp))\n",
1551     "v"
1552    ]
1553   },
1554   {
1555    "cell_type": "code",
1556    "execution_count": 29,
1557    "metadata": {},
1558    "outputs": [
1559     {
1560      "data": {
1561       "text/plain": [
1562        "True"
1563       ]
1564      },
1565      "execution_count": 29,
1566      "metadata": {},
1567      "output_type": "execute_result"
1568     }
1569    ],
1570    "source": [
1571     "show_backtrace(bp).lower() == il"
1572    ]
1573   },
1574   {
1575    "cell_type": "code",
1576    "execution_count": 30,
1577    "metadata": {},
1578    "outputs": [
1579     {
1580      "data": {
1581       "text/plain": [
1582        "('cbchedabcadedhfafahdaacbhhhedfhgceafghceehaefaebcc', False, False)"
1583       ]
1584      },
1585      "execution_count": 30,
1586      "metadata": {},
1587      "output_type": "execute_result"
1588     }
1589    ],
1590    "source": [
1591     "s3 = make_string(50)\n",
1592     "s3, is_interleave(s1, s3, il), is_interleave(s2, s3, il)"
1593    ]
1594   },
1595   {
1596    "cell_type": "code",
1597    "execution_count": 31,
1598    "metadata": {},
1599    "outputs": [
1600     {
1601      "name": "stdout",
1602      "output_type": "stream",
1603      "text": [
1604       "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1605       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1606       "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1607       "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1608       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\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",
1640       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1641       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1642       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1643       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1644       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1645       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1646       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1647       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1648       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1649       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1650       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1651       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1652       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1653       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1654       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1655       "\n"
1656      ]
1657     },
1658     {
1659      "data": {
1660       "text/plain": [
1661        "False"
1662       ]
1663      },
1664      "execution_count": 31,
1665      "metadata": {},
1666      "output_type": "execute_result"
1667     }
1668    ],
1669    "source": [
1670     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1671     "print(show_table(t))\n",
1672     "print(show_backtrace(bp))\n",
1673     "v"
1674    ]
1675   },
1676   {
1677    "cell_type": "code",
1678    "execution_count": 32,
1679    "metadata": {
1680     "collapsed": true
1681    },
1682    "outputs": [],
1683    "source": [
1684     "def is_interleave_recursive(s1, s2, s3):\n",
1685     "    if not s1:\n",
1686     "        return s2 == s3\n",
1687     "    elif not s2:\n",
1688     "        return s1 == s3\n",
1689     "    elif len(s1) + len(s2) != len(s3):\n",
1690     "        return False\n",
1691     "    else:\n",
1692     "        if s1[-1] == s3[-1] and s2[-1] == s3[-1]:\n",
1693     "            return (is_interleave_recursive(s1[:-1], s2, s3[:-1]) \n",
1694     "                    or \n",
1695     "                    is_interleave_recursive(s1, s2[:-1], s3[:-1]) )\n",
1696     "        elif s1[-1] == s3[-1]:\n",
1697     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
1698     "        elif s2[-1] == s3[-1]:\n",
1699     "            return is_interleave_recursive(s1, s2[:-1], s3[:-1])\n",
1700     "        else:\n",
1701     "            return False"
1702    ]
1703   },
1704   {
1705    "cell_type": "code",
1706    "execution_count": 33,
1707    "metadata": {
1708     "collapsed": true
1709    },
1710    "outputs": [],
1711    "source": [
1712     "import uuid"
1713    ]
1714   },
1715   {
1716    "cell_type": "code",
1717    "execution_count": 34,
1718    "metadata": {
1719     "collapsed": true
1720    },
1721    "outputs": [],
1722    "source": [
1723     "def is_subseq_recursive_dot(s1, s2):\n",
1724     "    node_id = uuid.uuid4().hex\n",
1725     "    node_string = 'n{} [label=\"{}\\\\n{}\"];'.format(node_id, s1, s2)\n",
1726     "#     print(s1, s2, node_string)\n",
1727     "    if not s1:\n",
1728     "        return node_id, ['n{} [label=\"-\\\\n{}\\\\nTrue\"];'.format(node_id, s2)]\n",
1729     "    elif len(s1) > len(s2):\n",
1730     "        return node_id, ['n{} [label=\"{}\\\\n{}\\\\nFalse\"];'.format(node_id, s1, s2)]\n",
1731     "    else:\n",
1732     "        if s1[-1] == s2[-1]:\n",
1733     "            node1_id, node1_graph = is_subseq_recursive_dot(s1[:-1], s2[:-1])\n",
1734     "            node2_id, node2_graph = is_subseq_recursive_dot(s1, s2[:-1])\n",
1735     "            return node_id, ([node_string, \n",
1736     "                    'n{} -> n{};'.format(node_id, node1_id), \n",
1737     "                    'n{} -> n{};'.format(node_id, node2_id)] + \n",
1738     "                    node1_graph + node2_graph)\n",
1739     "        else:\n",
1740     "            node1_id, node1_graph = is_subseq_recursive_dot(s1, s2[:-1])\n",
1741     "            return node_id, ([node_string, \n",
1742     "                    'n{} -> n{};'.format(node_id, node1_id)] + \n",
1743     "                    node1_graph)"
1744    ]
1745   },
1746   {
1747    "cell_type": "code",
1748    "execution_count": 35,
1749    "metadata": {
1750     "collapsed": true
1751    },
1752    "outputs": [],
1753    "source": [
1754     "def is_interleave_recursive_dot(s1, s2, s3):\n",
1755     "    \n",
1756     "#     print(s1, s2, s3)\n",
1757     "    node_id = uuid.uuid4().hex\n",
1758     "    node_string = 'n{} [label=\"{}\\\\n{}\\\\n{}\"];'.format(node_id, s1, s2, s3)\n",
1759     "\n",
1760     "    if not s1:\n",
1761     "        if s2 == s3:\n",
1762     "            return node_id, ['n{} [label=\"-\\\\n{}\\\\n{}\\\\nTrue\"];'.format(node_id, s2, s3)]\n",
1763     "        else:\n",
1764     "            return node_id, ['n{} [label=\"-\\\\n{}\\\\n{}\\\\nFalse\"];'.format(node_id, s2, s3)]\n",
1765     "    elif not s2:\n",
1766     "        if s1 == s3:\n",
1767     "            return node_id, ['n{} [label=\"{}\\\\n-\\\\n{}\\\\nTrue\"];'.format(node_id, s1, s3)]\n",
1768     "        else:\n",
1769     "            return node_id, ['n{} [label=\"{}\\\\n-\\\\n{}\\\\nFalse\"];'.format(node_id, s1, s3)]\n",
1770     "    else:\n",
1771     "        if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
1772     "            node1_id, node1_graph = is_interleave_recursive_dot(s1[:-1], s2, s3[:-1])\n",
1773     "            node2_id, node2_graph = is_interleave_recursive_dot(s1, s2[:-1], s3[:-1])\n",
1774     "            return node_id, ([node_string, \n",
1775     "                    'n{} -> n{};'.format(node_id, node1_id), \n",
1776     "                    'n{} -> n{};'.format(node_id, node2_id)] + \n",
1777     "                    node1_graph + node2_graph)\n",
1778     "        elif s1[-1] == s3[-1]:\n",
1779     "            node1_id, node1_graph = is_interleave_recursive_dot(s1[:-1], s2, s3[:-1])\n",
1780     "            return node_id, ([node_string, \n",
1781     "                    'n{} -> n{};'.format(node_id, node1_id)] + \n",
1782     "                    node1_graph)\n",
1783     "        elif s2[-1] == s3[-1]:\n",
1784     "            node1_id, node1_graph = is_interleave_recursive_dot(s1, s2[:-1], s3[:-1])\n",
1785     "            return node_id, ([node_string, \n",
1786     "                    'n{} -> n{};'.format(node_id, node1_id)] + \n",
1787     "                    node1_graph)\n",
1788     "        else:\n",
1789     "            return node_id, ['n{} [label=\"{}\\\\n{}\\\\n{}\\\\nFalse\"];'.format(node_id, s1, s2, s3)]"
1790    ]
1791   },
1792   {
1793    "cell_type": "code",
1794    "execution_count": 36,
1795    "metadata": {
1796     "collapsed": true
1797    },
1798    "outputs": [],
1799    "source": [
1800     "s1 = \"aabcc\"\n",
1801     "s2 = \"dbbca\"\n",
1802     "\n",
1803     "s3t = \"aadbbcbcac\"\n",
1804     "s3f = \"aadbbbaccc\""
1805    ]
1806   },
1807   {
1808    "cell_type": "code",
1809    "execution_count": 37,
1810    "metadata": {},
1811    "outputs": [
1812     {
1813      "name": "stdout",
1814      "output_type": "stream",
1815      "text": [
1816       "T . . . . .\n",
1817       "T . . . . .\n",
1818       "T T T T T .\n",
1819       ". T T . T .\n",
1820       ". . T T T T\n",
1821       ". . . T . T\n",
1822       "AAdbbcBCaC\n"
1823      ]
1824     }
1825    ],
1826    "source": [
1827     "v, bp, t = is_interleave(s1, s2, s3t, return_backpointers=True, return_table=True)\n",
1828     "print(show_table(t))\n",
1829     "print(show_backtrace(bp))"
1830    ]
1831   },
1832   {
1833    "cell_type": "code",
1834    "execution_count": 38,
1835    "metadata": {
1836     "collapsed": true
1837    },
1838    "outputs": [],
1839    "source": [
1840     "def show_table_md(table, s1, s2, s3):\n",
1841     "    header = '|   |' + '|'.join('{}<br />{}'.format('<br />'.join(str(s2[:i])), i) for i in range(len(s2) + 1)) + '|'\n",
1842     "    separator = '|:---:' * (len(s2) + 2) + '|'\n",
1843     "    rows = []\n",
1844     "    columns = sorted(set(k[1] for k in table))\n",
1845     "    for r in range(len(s1) + 1):\n",
1846     "        row = '|**{}<br />{}**|'.format(r, s1[:r])\n",
1847     "        row += '|'.join('{}<br />T'.format(s3[:(r+c)]) if table[r, c] else '{}<br />.'.format(s3[:(r+c)]) for c in columns)\n",
1848     "        row += '|'\n",
1849     "        rows += [row]\n",
1850     "    return '\\n'.join([header] + [separator] + rows)"
1851    ]
1852   },
1853   {
1854    "cell_type": "code",
1855    "execution_count": 39,
1856    "metadata": {},
1857    "outputs": [
1858     {
1859      "name": "stdout",
1860      "output_type": "stream",
1861      "text": [
1862       "|   |<br />0|d<br />1|d<br />b<br />2|d<br />b<br />b<br />3|d<br />b<br />b<br />c<br />4|d<br />b<br />b<br />c<br />a<br />5|\n",
1863       "|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n",
1864       "|**0<br />**|<br />T|a<br />.|aa<br />.|aad<br />.|aadb<br />.|aadbb<br />.|\n",
1865       "|**1<br />a**|a<br />T|aa<br />.|aad<br />.|aadb<br />.|aadbb<br />.|aadbbc<br />.|\n",
1866       "|**2<br />aa**|aa<br />T|aad<br />T|aadb<br />T|aadbb<br />T|aadbbc<br />T|aadbbcb<br />.|\n",
1867       "|**3<br />aab**|aad<br />.|aadb<br />T|aadbb<br />T|aadbbc<br />.|aadbbcb<br />T|aadbbcbc<br />.|\n",
1868       "|**4<br />aabc**|aadb<br />.|aadbb<br />.|aadbbc<br />T|aadbbcb<br />T|aadbbcbc<br />T|aadbbcbca<br />T|\n",
1869       "|**5<br />aabcc**|aadbb<br />.|aadbbc<br />.|aadbbcb<br />.|aadbbcbc<br />T|aadbbcbca<br />.|aadbbcbcac<br />T|\n"
1870      ]
1871     }
1872    ],
1873    "source": [
1874     "print(show_table_md(t, s1, s2, s3t))"
1875    ]
1876   },
1877   {
1878    "cell_type": "markdown",
1879    "metadata": {},
1880    "source": [
1881     "|   |<br />0|d<br />1|d<br />b<br />2|d<br />b<br />b<br />3|d<br />b<br />b<br />c<br />4|d<br />b<br />b<br />c<br />a<br />5|\n",
1882     "|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n",
1883     "|**0<br />**|<br />T|a<br />.|aa<br />.|aad<br />.|aadb<br />.|aadbb<br />.|\n",
1884     "|**1<br />a**|a<br />T|aa<br />.|aad<br />.|aadb<br />.|aadbb<br />.|aadbbc<br />.|\n",
1885     "|**2<br />aa**|aa<br />T|aad<br />T|aadb<br />T|aadbb<br />T|aadbbc<br />T|aadbbcb<br />.|\n",
1886     "|**3<br />aab**|aad<br />.|aadb<br />T|aadbb<br />T|aadbbc<br />.|aadbbcb<br />T|aadbbcbc<br />.|\n",
1887     "|**4<br />aabc**|aadb<br />.|aadbb<br />.|aadbbc<br />T|aadbbcb<br />T|aadbbcbc<br />T|aadbbcbca<br />T|\n",
1888     "|**5<br />aabcc**|aadbb<br />.|aadbbc<br />.|aadbbcb<br />.|aadbbcbc<br />T|aadbbcbca<br />.|aadbbcbcac<br />T|"
1889    ]
1890   },
1891   {
1892    "cell_type": "code",
1893    "execution_count": 40,
1894    "metadata": {},
1895    "outputs": [
1896     {
1897      "name": "stdout",
1898      "output_type": "stream",
1899      "text": [
1900       "T T T T\n",
1901       "T . T .\n",
1902       ". . T T\n",
1903       ". . . T\n",
1904       "abACaB\n"
1905      ]
1906     }
1907    ],
1908    "source": [
1909     "e1 = 'acb'\n",
1910     "e2 = 'aba'\n",
1911     "e3 = 'abacab'\n",
1912     "v, bp, et = is_interleave(e1, e2, e3, return_backpointers=True, return_table=True)\n",
1913     "print(show_table(et))\n",
1914     "print(show_backtrace(bp))"
1915    ]
1916   },
1917   {
1918    "cell_type": "code",
1919    "execution_count": 41,
1920    "metadata": {},
1921    "outputs": [
1922     {
1923      "name": "stdout",
1924      "output_type": "stream",
1925      "text": [
1926       "|   |<br />0|a<br />1|a<br />b<br />2|a<br />b<br />a<br />3|\n",
1927       "|:---:|:---:|:---:|:---:|:---:|\n",
1928       "|**0<br />**|<br />T|a<br />T|ab<br />T|aba<br />T|\n",
1929       "|**1<br />a**|a<br />T|ab<br />.|aba<br />T|abac<br />.|\n",
1930       "|**2<br />ac**|ab<br />.|aba<br />.|abac<br />T|abaca<br />T|\n",
1931       "|**3<br />acb**|aba<br />.|abac<br />.|abaca<br />.|abacab<br />T|\n"
1932      ]
1933     }
1934    ],
1935    "source": [
1936     "print(show_table_md(et, e1, e2, e3))"
1937    ]
1938   },
1939   {
1940    "cell_type": "markdown",
1941    "metadata": {},
1942    "source": [
1943     "|   |<br />0|a<br />1|a<br />b<br />2|a<br />b<br />a<br />3|\n",
1944     "|:---:|:---:|:---:|:---:|:---:|\n",
1945     "|**0<br />**|<br />T|a<br />T|ab<br />T|aba<br />T|\n",
1946     "|**1<br />a**|a<br />T|ab<br />.|aba<br />T|abac<br />.|\n",
1947     "|**2<br />ac**|ab<br />.|aba<br />.|abac<br />T|abaca<br />T|\n",
1948     "|**3<br />acb**|aba<br />.|abac<br />.|abaca<br />.|abacab<br />T|"
1949    ]
1950   },
1951   {
1952    "cell_type": "code",
1953    "execution_count": 42,
1954    "metadata": {
1955     "scrolled": true
1956    },
1957    "outputs": [
1958     {
1959      "name": "stdout",
1960      "output_type": "stream",
1961      "text": [
1962       "ndf96f65c85de45ba814c3aebe4afed65 [label=\"aabcc\\ndbbca\\naadbbcbcac\"];\n",
1963       "ndf96f65c85de45ba814c3aebe4afed65 -> n0e6e480c9d664ba2af7e041445763b66;\n",
1964       "n0e6e480c9d664ba2af7e041445763b66 [label=\"aabc\\ndbbca\\naadbbcbca\"];\n",
1965       "n0e6e480c9d664ba2af7e041445763b66 -> nc7f25932eaf1431cb98430f8b1644221;\n",
1966       "nc7f25932eaf1431cb98430f8b1644221 [label=\"aabc\\ndbbc\\naadbbcbc\"];\n",
1967       "nc7f25932eaf1431cb98430f8b1644221 -> ncd2942f9e99443619c6ce1d72a10da75;\n",
1968       "nc7f25932eaf1431cb98430f8b1644221 -> n0e76b3b46aba4a8abdbd569a0762170a;\n",
1969       "ncd2942f9e99443619c6ce1d72a10da75 [label=\"aab\\ndbbc\\naadbbcb\"];\n",
1970       "ncd2942f9e99443619c6ce1d72a10da75 -> n4762ffa7e0c6426792438c6f84c9d2f9;\n",
1971       "n4762ffa7e0c6426792438c6f84c9d2f9 [label=\"aa\\ndbbc\\naadbbc\"];\n",
1972       "n4762ffa7e0c6426792438c6f84c9d2f9 -> n9434633af1674b45ae72a987932bcacc;\n",
1973       "n9434633af1674b45ae72a987932bcacc [label=\"aa\\ndbb\\naadbb\"];\n",
1974       "n9434633af1674b45ae72a987932bcacc -> n72dd6ed85e8d43d39b1c6b240f672815;\n",
1975       "n72dd6ed85e8d43d39b1c6b240f672815 [label=\"aa\\ndb\\naadb\"];\n",
1976       "n72dd6ed85e8d43d39b1c6b240f672815 -> nf904e4ea330a48028602500e910001ba;\n",
1977       "nf904e4ea330a48028602500e910001ba [label=\"aa\\nd\\naad\"];\n",
1978       "nf904e4ea330a48028602500e910001ba -> nc2246b72d95748f5984f7a9a922afafa;\n",
1979       "nc2246b72d95748f5984f7a9a922afafa [label=\"aa\\n-\\naa\\nTrue\"];\n",
1980       "n0e76b3b46aba4a8abdbd569a0762170a [label=\"aabc\\ndbb\\naadbbcb\"];\n",
1981       "n0e76b3b46aba4a8abdbd569a0762170a -> nde239312af534c47988db27094dc5e3b;\n",
1982       "nde239312af534c47988db27094dc5e3b [label=\"aabc\\ndb\\naadbbc\"];\n",
1983       "nde239312af534c47988db27094dc5e3b -> n0571e43544db4baea762dd9382a90eab;\n",
1984       "n0571e43544db4baea762dd9382a90eab [label=\"aab\\ndb\\naadbb\"];\n",
1985       "n0571e43544db4baea762dd9382a90eab -> nd24f1944051440d6b94710a3b971c134;\n",
1986       "n0571e43544db4baea762dd9382a90eab -> n671eff7dd1f945a28e7bcd0647d7d40d;\n",
1987       "nd24f1944051440d6b94710a3b971c134 [label=\"aa\\ndb\\naadb\"];\n",
1988       "nd24f1944051440d6b94710a3b971c134 -> n26480b1bcee847adaeb205f2e844a4e5;\n",
1989       "n26480b1bcee847adaeb205f2e844a4e5 [label=\"aa\\nd\\naad\"];\n",
1990       "n26480b1bcee847adaeb205f2e844a4e5 -> n162a36ef08174bafa51dbf89a58965df;\n",
1991       "n162a36ef08174bafa51dbf89a58965df [label=\"aa\\n-\\naa\\nTrue\"];\n",
1992       "n671eff7dd1f945a28e7bcd0647d7d40d [label=\"aab\\nd\\naadb\"];\n",
1993       "n671eff7dd1f945a28e7bcd0647d7d40d -> n8d9c2dc78a9047d4a243d316e87dd782;\n",
1994       "n8d9c2dc78a9047d4a243d316e87dd782 [label=\"aa\\nd\\naad\"];\n",
1995       "n8d9c2dc78a9047d4a243d316e87dd782 -> n6d893e899f6f4f77a30c3be1eeef25d0;\n",
1996       "n6d893e899f6f4f77a30c3be1eeef25d0 [label=\"aa\\n-\\naa\\nTrue\"];\n"
1997      ]
1998     }
1999    ],
2000    "source": [
2001     "root, graph = is_interleave_recursive_dot(s1, s2, s3t)\n",
2002     "print('\\n'.join(graph))"
2003    ]
2004   },
2005   {
2006    "cell_type": "code",
2007    "execution_count": 43,
2008    "metadata": {
2009     "scrolled": true
2010    },
2011    "outputs": [
2012     {
2013      "name": "stdout",
2014      "output_type": "stream",
2015      "text": [
2016       "n8ab105a57ff44daa8fa8c0bd8275721c [label=\"aaa\\naaa\\naaaaaa\"];\n",
2017       "n8ab105a57ff44daa8fa8c0bd8275721c -> ndd3ec050e4d441ba9f5eca4140804aa2;\n",
2018       "n8ab105a57ff44daa8fa8c0bd8275721c -> n5fe9af06410d4e3796f3e5b09724befb;\n",
2019       "ndd3ec050e4d441ba9f5eca4140804aa2 [label=\"aa\\naaa\\naaaaa\"];\n",
2020       "ndd3ec050e4d441ba9f5eca4140804aa2 -> n4da003b54dd94728a1aa1890f1a9250a;\n",
2021       "ndd3ec050e4d441ba9f5eca4140804aa2 -> ncb2a3fd92dc6414a99dc115990760e7c;\n",
2022       "n4da003b54dd94728a1aa1890f1a9250a [label=\"a\\naaa\\naaaa\"];\n",
2023       "n4da003b54dd94728a1aa1890f1a9250a -> n699e6ec8bba74ec394a68d5c2d306c30;\n",
2024       "n4da003b54dd94728a1aa1890f1a9250a -> n71376b3b5e614617ba68dccf8d9677cc;\n",
2025       "n699e6ec8bba74ec394a68d5c2d306c30 [label=\"-\\naaa\\naaa\\nTrue\"];\n",
2026       "n71376b3b5e614617ba68dccf8d9677cc [label=\"a\\naa\\naaa\"];\n",
2027       "n71376b3b5e614617ba68dccf8d9677cc -> nb876b970b38f4ba2937a69ba491f308c;\n",
2028       "n71376b3b5e614617ba68dccf8d9677cc -> nfb2ebec95c5c46c6b160c511031f5417;\n",
2029       "nb876b970b38f4ba2937a69ba491f308c [label=\"-\\naa\\naa\\nTrue\"];\n",
2030       "nfb2ebec95c5c46c6b160c511031f5417 [label=\"a\\na\\naa\"];\n",
2031       "nfb2ebec95c5c46c6b160c511031f5417 -> ndcf30cbbd8f646adb30c01e8fbc8aaaf;\n",
2032       "nfb2ebec95c5c46c6b160c511031f5417 -> n9bb6593bab3c47e59f83df2767b67a3a;\n",
2033       "ndcf30cbbd8f646adb30c01e8fbc8aaaf [label=\"-\\na\\na\\nTrue\"];\n",
2034       "n9bb6593bab3c47e59f83df2767b67a3a [label=\"a\\n-\\na\\nTrue\"];\n",
2035       "ncb2a3fd92dc6414a99dc115990760e7c [label=\"aa\\naa\\naaaa\"];\n",
2036       "ncb2a3fd92dc6414a99dc115990760e7c -> n937d754714994223bc97015534e1806e;\n",
2037       "ncb2a3fd92dc6414a99dc115990760e7c -> n553eac2d6c4542448a5c82b781e963b1;\n",
2038       "n937d754714994223bc97015534e1806e [label=\"a\\naa\\naaa\"];\n",
2039       "n937d754714994223bc97015534e1806e -> n08a6688eb7df48f8834787728a0e36a2;\n",
2040       "n937d754714994223bc97015534e1806e -> n063d395576474c5b82d810b2b70e7e3c;\n",
2041       "n08a6688eb7df48f8834787728a0e36a2 [label=\"-\\naa\\naa\\nTrue\"];\n",
2042       "n063d395576474c5b82d810b2b70e7e3c [label=\"a\\na\\naa\"];\n",
2043       "n063d395576474c5b82d810b2b70e7e3c -> n04b9f6aea46c458da227558ab02a0b4c;\n",
2044       "n063d395576474c5b82d810b2b70e7e3c -> nc067208a5ab64f8c9904d58b738b81e4;\n",
2045       "n04b9f6aea46c458da227558ab02a0b4c [label=\"-\\na\\na\\nTrue\"];\n",
2046       "nc067208a5ab64f8c9904d58b738b81e4 [label=\"a\\n-\\na\\nTrue\"];\n",
2047       "n553eac2d6c4542448a5c82b781e963b1 [label=\"aa\\na\\naaa\"];\n",
2048       "n553eac2d6c4542448a5c82b781e963b1 -> n5d50905c46ce4dc8bcb59fb62984fa54;\n",
2049       "n553eac2d6c4542448a5c82b781e963b1 -> n6768e9ad78804e65b1bde9cb655f2a60;\n",
2050       "n5d50905c46ce4dc8bcb59fb62984fa54 [label=\"a\\na\\naa\"];\n",
2051       "n5d50905c46ce4dc8bcb59fb62984fa54 -> n22bc48dd2aa84e79a387252cc28f3a92;\n",
2052       "n5d50905c46ce4dc8bcb59fb62984fa54 -> n853ef88a20ee48a4bccf390498c96f5d;\n",
2053       "n22bc48dd2aa84e79a387252cc28f3a92 [label=\"-\\na\\na\\nTrue\"];\n",
2054       "n853ef88a20ee48a4bccf390498c96f5d [label=\"a\\n-\\na\\nTrue\"];\n",
2055       "n6768e9ad78804e65b1bde9cb655f2a60 [label=\"aa\\n-\\naa\\nTrue\"];\n",
2056       "n5fe9af06410d4e3796f3e5b09724befb [label=\"aaa\\naa\\naaaaa\"];\n",
2057       "n5fe9af06410d4e3796f3e5b09724befb -> ne6b19fc7e02b4981a1edc20c7fe0cce0;\n",
2058       "n5fe9af06410d4e3796f3e5b09724befb -> ne0c07d6d54f045a5b4bf9eb10bd8d810;\n",
2059       "ne6b19fc7e02b4981a1edc20c7fe0cce0 [label=\"aa\\naa\\naaaa\"];\n",
2060       "ne6b19fc7e02b4981a1edc20c7fe0cce0 -> n9d2cfd4e9cf2473bbd05a8a7e2a96714;\n",
2061       "ne6b19fc7e02b4981a1edc20c7fe0cce0 -> n3d4e61bc032c4f8387c269d8ac49cc3f;\n",
2062       "n9d2cfd4e9cf2473bbd05a8a7e2a96714 [label=\"a\\naa\\naaa\"];\n",
2063       "n9d2cfd4e9cf2473bbd05a8a7e2a96714 -> n214f88e71d504eaba78b46c5a5bbe31d;\n",
2064       "n9d2cfd4e9cf2473bbd05a8a7e2a96714 -> n2890559b11cb49c9aa083a76a7b68ce4;\n",
2065       "n214f88e71d504eaba78b46c5a5bbe31d [label=\"-\\naa\\naa\\nTrue\"];\n",
2066       "n2890559b11cb49c9aa083a76a7b68ce4 [label=\"a\\na\\naa\"];\n",
2067       "n2890559b11cb49c9aa083a76a7b68ce4 -> n5d37f312b10341d09e2faa4fb4f40e3c;\n",
2068       "n2890559b11cb49c9aa083a76a7b68ce4 -> nd73fc499c4214ddbbe7155f97c9ff394;\n",
2069       "n5d37f312b10341d09e2faa4fb4f40e3c [label=\"-\\na\\na\\nTrue\"];\n",
2070       "nd73fc499c4214ddbbe7155f97c9ff394 [label=\"a\\n-\\na\\nTrue\"];\n",
2071       "n3d4e61bc032c4f8387c269d8ac49cc3f [label=\"aa\\na\\naaa\"];\n",
2072       "n3d4e61bc032c4f8387c269d8ac49cc3f -> nfac20fc8bb7441f891ac0380259f3b76;\n",
2073       "n3d4e61bc032c4f8387c269d8ac49cc3f -> n9d9c86dc313f48b69d9c2693ee32e7ab;\n",
2074       "nfac20fc8bb7441f891ac0380259f3b76 [label=\"a\\na\\naa\"];\n",
2075       "nfac20fc8bb7441f891ac0380259f3b76 -> n14489559bae24e99b2d816716ceef683;\n",
2076       "nfac20fc8bb7441f891ac0380259f3b76 -> n44c425cd261c4c19971a47901723f942;\n",
2077       "n14489559bae24e99b2d816716ceef683 [label=\"-\\na\\na\\nTrue\"];\n",
2078       "n44c425cd261c4c19971a47901723f942 [label=\"a\\n-\\na\\nTrue\"];\n",
2079       "n9d9c86dc313f48b69d9c2693ee32e7ab [label=\"aa\\n-\\naa\\nTrue\"];\n",
2080       "ne0c07d6d54f045a5b4bf9eb10bd8d810 [label=\"aaa\\na\\naaaa\"];\n",
2081       "ne0c07d6d54f045a5b4bf9eb10bd8d810 -> n8d8289489db44271b99f22c572668eaa;\n",
2082       "ne0c07d6d54f045a5b4bf9eb10bd8d810 -> n4eda0dd1e0e34c8c9a81beba5c70fe5f;\n",
2083       "n8d8289489db44271b99f22c572668eaa [label=\"aa\\na\\naaa\"];\n",
2084       "n8d8289489db44271b99f22c572668eaa -> n156514e9dbcb44a8a6b4d96f1ec3e48f;\n",
2085       "n8d8289489db44271b99f22c572668eaa -> n3ba7c5a0cc3b405aa6ca7899ee85a518;\n",
2086       "n156514e9dbcb44a8a6b4d96f1ec3e48f [label=\"a\\na\\naa\"];\n",
2087       "n156514e9dbcb44a8a6b4d96f1ec3e48f -> n3b99ff94eb914661bafe9ba4c0c997e2;\n",
2088       "n156514e9dbcb44a8a6b4d96f1ec3e48f -> n91eac98d4ed74a1f99fd48ca60111d2c;\n",
2089       "n3b99ff94eb914661bafe9ba4c0c997e2 [label=\"-\\na\\na\\nTrue\"];\n",
2090       "n91eac98d4ed74a1f99fd48ca60111d2c [label=\"a\\n-\\na\\nTrue\"];\n",
2091       "n3ba7c5a0cc3b405aa6ca7899ee85a518 [label=\"aa\\n-\\naa\\nTrue\"];\n",
2092       "n4eda0dd1e0e34c8c9a81beba5c70fe5f [label=\"aaa\\n-\\naaa\\nTrue\"];\n"
2093      ]
2094     }
2095    ],
2096    "source": [
2097     "root, graph = is_interleave_recursive_dot('aaa', 'aaa', 'aaaaaa')\n",
2098     "print('\\n'.join(graph))"
2099    ]
2100   },
2101   {
2102    "cell_type": "code",
2103    "execution_count": 44,
2104    "metadata": {
2105     "scrolled": true
2106    },
2107    "outputs": [
2108     {
2109      "name": "stdout",
2110      "output_type": "stream",
2111      "text": [
2112       "n5d63e71661ed4a8ead31b5c5f9c1949b [label=\"acb\\naba\\nabacab\"];\n",
2113       "n5d63e71661ed4a8ead31b5c5f9c1949b -> n11bd1802979b4332bdf9cf6cc3b2a51c;\n",
2114       "n11bd1802979b4332bdf9cf6cc3b2a51c [label=\"ac\\naba\\nabaca\"];\n",
2115       "n11bd1802979b4332bdf9cf6cc3b2a51c -> n8a082af1ba074b84b7410b97554be94f;\n",
2116       "n8a082af1ba074b84b7410b97554be94f [label=\"ac\\nab\\nabac\"];\n",
2117       "n8a082af1ba074b84b7410b97554be94f -> n6ec78858d88046c8b8531a63f38825b3;\n",
2118       "n6ec78858d88046c8b8531a63f38825b3 [label=\"a\\nab\\naba\"];\n",
2119       "n6ec78858d88046c8b8531a63f38825b3 -> na563514a3f194725be7160850c3c8369;\n",
2120       "na563514a3f194725be7160850c3c8369 [label=\"-\\nab\\nab\\nTrue\"];\n"
2121      ]
2122     }
2123    ],
2124    "source": [
2125     "root, graph = is_interleave_recursive_dot(e1, e2, e3)\n",
2126     "print('\\n'.join(graph))"
2127    ]
2128   },
2129   {
2130    "cell_type": "code",
2131    "execution_count": 45,
2132    "metadata": {
2133     "collapsed": true
2134    },
2135    "outputs": [],
2136    "source": [
2137     "s1 = make_string(500)\n",
2138     "s2 = make_string(500)\n",
2139     "s3 = make_string(500)\n",
2140     "s12 = interleave(s1, s2)\n",
2141     "s23 = interleave(s2, s3)"
2142    ]
2143   },
2144   {
2145    "cell_type": "code",
2146    "execution_count": 48,
2147    "metadata": {},
2148    "outputs": [
2149     {
2150      "data": {
2151       "text/plain": [
2152        "True"
2153       ]
2154      },
2155      "execution_count": 48,
2156      "metadata": {},
2157      "output_type": "execute_result"
2158     }
2159    ],
2160    "source": [
2161     "is_interleave_recursive(s1, s2, s12)"
2162    ]
2163   },
2164   {
2165    "cell_type": "code",
2166    "execution_count": 49,
2167    "metadata": {},
2168    "outputs": [
2169     {
2170      "data": {
2171       "text/plain": [
2172        "False"
2173       ]
2174      },
2175      "execution_count": 49,
2176      "metadata": {},
2177      "output_type": "execute_result"
2178     }
2179    ],
2180    "source": [
2181     "is_interleave_recursive(s1, s2, s23)"
2182    ]
2183   },
2184   {
2185    "cell_type": "markdown",
2186    "metadata": {},
2187    "source": [
2188     "## Example"
2189    ]
2190   },
2191   {
2192    "cell_type": "code",
2193    "execution_count": 50,
2194    "metadata": {
2195     "collapsed": true
2196    },
2197    "outputs": [],
2198    "source": [
2199     "def show_annotated_table(table, bps):\n",
2200     "    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",
2201     "        for i in sorted(set([k[0] for k in table])))"
2202    ]
2203   },
2204   {
2205    "cell_type": "code",
2206    "execution_count": 51,
2207    "metadata": {
2208     "collapsed": true
2209    },
2210    "outputs": [],
2211    "source": [
2212     "def show_backtrace_star(bps):\n",
2213     "    i = max([0] + [k[0] for k in bps])\n",
2214     "    j = max([0] + [k[1] for k in bps])\n",
2215     "    chars = ''\n",
2216     "    stars = ''\n",
2217     "    if (i, j) in bps:\n",
2218     "        while i != 0 or j != 0:\n",
2219     "            chars += bps[i, j][2]\n",
2220     "            if bps[i, j][3] == 'seq1':\n",
2221     "                stars += '*'\n",
2222     "            else:\n",
2223     "                stars += ' '\n",
2224     "            i, j = bps[i, j][0], bps[i, j][1] \n",
2225     "        return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n",
2226     "    else:\n",
2227     "        return ''"
2228    ]
2229   },
2230   {
2231    "cell_type": "code",
2232    "execution_count": 52,
2233    "metadata": {},
2234    "outputs": [
2235     {
2236      "name": "stdout",
2237      "output_type": "stream",
2238      "text": [
2239       "0: ddadbdcbdc\n",
2240       "1: bbcbbabdab\n",
2241       "2: dcddddbbdb\n",
2242       "3: cccbbbcbabadbddcabda\n",
2243       "4: ddcdddadddbbbddbcbdc\n",
2244       "5: dcccdddcbdbadbdbdcda\n",
2245       "6: ddadbbcbbbdacbbdcdab\n"
2246      ]
2247     },
2248     {
2249      "data": {
2250       "text/plain": [
2251        "['ddadbbcbbbdacbbdcdab']"
2252       ]
2253      },
2254      "execution_count": 52,
2255      "metadata": {},
2256      "output_type": "execute_result"
2257     }
2258    ],
2259    "source": [
2260     "s1 = make_string(10, alphabet='abcd')\n",
2261     "s2 = make_string(10, alphabet='abcd')\n",
2262     "s3 = make_string(10, alphabet='abcd')\n",
2263     "s4 = make_string(10, alphabet='abcd')\n",
2264     "il = interleave(s1, s2)\n",
2265     "bs = [s3, il, interleave(s3, s4), interleave(s2, s4), interleave(s1, s3)]\n",
2266     "random.shuffle(bs)\n",
2267     "bs = [s1, s2] + bs\n",
2268     "tg = [l for l in bs if is_interleave(s1, s2, l)]\n",
2269     "print('\\n'.join(['{}: {}'.format(i, s) for i, s in enumerate(bs)]))\n",
2270     "tg"
2271    ]
2272   },
2273   {
2274    "cell_type": "code",
2275    "execution_count": 53,
2276    "metadata": {},
2277    "outputs": [
2278     {
2279      "name": "stdout",
2280      "output_type": "stream",
2281      "text": [
2282       "* . . . . . . . . . .\n",
2283       "d . . . . . . . . . .\n",
2284       "d . . . . . . . . . .\n",
2285       "a . . . . . . . . . .\n",
2286       "d b b c b b . . . . .\n",
2287       "b b . b b b . . . . .\n",
2288       ". . . . . d a . . . .\n",
2289       ". . . . . . c b . . .\n",
2290       ". . . . . . b b d . .\n",
2291       ". . . . . . . d . . .\n",
2292       ". . . . . . . c d a b\n",
2293       "DDADbbcbbBDaCbBDCdab\n",
2294       "ddadbbcbbbdacbbdcdab\n",
2295       "****     ** * ***   \n"
2296      ]
2297     },
2298     {
2299      "data": {
2300       "text/plain": [
2301        "True"
2302       ]
2303      },
2304      "execution_count": 53,
2305      "metadata": {},
2306      "output_type": "execute_result"
2307     }
2308    ],
2309    "source": [
2310     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
2311     "print(show_annotated_table(t, bp))\n",
2312     "print(show_backtrace(bp))\n",
2313     "print(show_backtrace_star(bp))\n",
2314     "v"
2315    ]
2316   },
2317   {
2318    "cell_type": "code",
2319    "execution_count": 54,
2320    "metadata": {},
2321    "outputs": [
2322     {
2323      "name": "stdout",
2324      "output_type": "stream",
2325      "text": [
2326       "ddcdddadddbbbddbcbdc\n",
2327       " *   **  *  * * ****\n"
2328      ]
2329     },
2330     {
2331      "data": {
2332       "text/plain": [
2333        "4"
2334       ]
2335      },
2336      "execution_count": 54,
2337      "metadata": {},
2338      "output_type": "execute_result"
2339     }
2340    ],
2341    "source": [
2342     "ind = [i for i, b in enumerate(bs) if is_interleave(s1, s3, b)][0]\n",
2343     "v, bp = is_interleave(s1, s3, bs[ind], return_backpointers=True)\n",
2344     "print(show_backtrace_star(bp))\n",
2345     "ind"
2346    ]
2347   },
2348   {
2349    "cell_type": "code",
2350    "execution_count": 55,
2351    "metadata": {},
2352    "outputs": [
2353     {
2354      "name": "stdout",
2355      "output_type": "stream",
2356      "text": [
2357       "* d d a d b . . . . .\n",
2358       ". . . . b b . . . . .\n",
2359       ". . . . b . . . . . .\n",
2360       ". . . . c b . . . . .\n",
2361       ". . . . b b . . . . .\n",
2362       ". . . . b b d . . . .\n",
2363       ". . . . . . a c b . .\n",
2364       ". . . . . . . b b d c\n",
2365       ". . . . . . . . d . d\n",
2366       ". . . . . . . . . . a\n",
2367       ". . . . . . . . . . b\n",
2368       "ddadBBCbBBdAcbBdcDAB\n",
2369       "ddadbbcbbbdacbbdcdab\n",
2370       "    *** ** *  *  ***\n"
2371      ]
2372     },
2373     {
2374      "data": {
2375       "text/plain": [
2376        "True"
2377       ]
2378      },
2379      "execution_count": 55,
2380      "metadata": {},
2381      "output_type": "execute_result"
2382     }
2383    ],
2384    "source": [
2385     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
2386     "print(show_annotated_table(t, bp))\n",
2387     "print(show_backtrace(bp))\n",
2388     "print(show_backtrace_star(bp))\n",
2389     "v"
2390    ]
2391   },
2392   {
2393    "cell_type": "code",
2394    "execution_count": 56,
2395    "metadata": {},
2396    "outputs": [
2397     {
2398      "name": "stdout",
2399      "output_type": "stream",
2400      "text": [
2401       "* d . . . . . . . . .\n",
2402       "d d . . . . . . . . .\n",
2403       "d . . . . . . . . . .\n",
2404       "a d . . . . . . . . .\n",
2405       "d . . . . . . . . . .\n",
2406       "b . . . . . . . . . .\n",
2407       ". . . . . . . . . . .\n",
2408       ". . . . . . . . . . .\n",
2409       ". . . . . . . . . . .\n",
2410       ". . . . . . . . . . .\n",
2411       ". . . . . . . . . . .\n",
2412       "\n",
2413       "\n"
2414      ]
2415     },
2416     {
2417      "data": {
2418       "text/plain": [
2419        "False"
2420       ]
2421      },
2422      "execution_count": 56,
2423      "metadata": {},
2424      "output_type": "execute_result"
2425     }
2426    ],
2427    "source": [
2428     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
2429     "print(show_annotated_table(t, bp))\n",
2430     "print(show_backtrace(bp))\n",
2431     "print(show_backtrace_star(bp))\n",
2432     "v"
2433    ]
2434   },
2435   {
2436    "cell_type": "code",
2437    "execution_count": 57,
2438    "metadata": {},
2439    "outputs": [
2440     {
2441      "name": "stdout",
2442      "output_type": "stream",
2443      "text": [
2444       "* d . . . . . . . . .\n",
2445       ". . . . . . . . . . .\n",
2446       ". . . . . . . . . . .\n",
2447       ". . . . . . . . . . .\n",
2448       ". . . . . . . . . . .\n",
2449       ". . . . . . . . . . .\n",
2450       ". . . . . . . . . . .\n",
2451       ". . . . . . . . . . .\n",
2452       ". . . . . . . . . . .\n",
2453       ". . . . . . . . . . .\n",
2454       ". . . . . . . . . . .\n",
2455       "d\n",
2456       "d\n",
2457       " \n"
2458      ]
2459     },
2460     {
2461      "data": {
2462       "text/plain": [
2463        "False"
2464       ]
2465      },
2466      "execution_count": 57,
2467      "metadata": {},
2468      "output_type": "execute_result"
2469     }
2470    ],
2471    "source": [
2472     "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n",
2473     "print(show_annotated_table(t, bp))\n",
2474     "print(show_backtrace(bp))\n",
2475     "print(show_backtrace_star(bp))\n",
2476     "v"
2477    ]
2478   },
2479   {
2480    "cell_type": "markdown",
2481    "metadata": {
2482     "collapsed": true
2483    },
2484    "source": [
2485     "# Make puzzle data\n",
2486     "\n",
2487     "## Note to self\n",
2488     "Include some distractors in the test set, such that:\n",
2489     "* subsequence(my_bill, distractor) is true\n",
2490     "* subsequence(friend_bill, distractor) is true\n",
2491     "* interleave(my_bill, friend_bill, distractor) is false\n",
2492     "\n",
2493     "(i.e. characters are shared between my_bill and friend_bill)\n",
2494     "\n",
2495     "Students are taking a greedy approach to subsequence, and saying the interleave is true if both bills are subsequences of the distractor.\n",
2496     "\n",
2497     "i.e. \"aaa\" and \"aab\" are both subsequences of \"aaabbb\", but cannot be interleaved to form \"aaabbb\".\n"
2498    ]
2499   },
2500   {
2501    "cell_type": "code",
2502    "execution_count": 58,
2503    "metadata": {
2504     "collapsed": true
2505    },
2506    "outputs": [],
2507    "source": [
2508     "my_bill = make_string(200)\n",
2509     "friend_bill = make_string(200)\n",
2510     "other_bills = [make_string(200) for _ in range(98)]\n",
2511     "\n",
2512     "target_interleaved = interleave(my_bill, friend_bill)\n",
2513     "mine_interleaved = [interleave(my_bill, o) for o in random.sample(other_bills, 21)]\n",
2514     "friend_interleaved = [interleave(friend_bill, o) for o in random.sample(other_bills, 13)]\n",
2515     "other_interleaved = []\n",
2516     "for _ in range(103):\n",
2517     "    s1, s2 = random.sample(other_bills, 2)\n",
2518     "    other_interleaved += [interleave(s1, s2)]"
2519    ]
2520   },
2521   {
2522    "cell_type": "code",
2523    "execution_count": 59,
2524    "metadata": {
2525     "collapsed": true
2526    },
2527    "outputs": [],
2528    "source": [
2529     "all_targets = [target_interleaved] + mine_interleaved + friend_interleaved + other_interleaved"
2530    ]
2531   },
2532   {
2533    "cell_type": "code",
2534    "execution_count": 60,
2535    "metadata": {},
2536    "outputs": [
2537     {
2538      "name": "stdout",
2539      "output_type": "stream",
2540      "text": [
2541       "CPU times: user 3.2 s, sys: 96 ms, total: 3.3 s\n",
2542       "Wall time: 3.3 s\n"
2543      ]
2544     },
2545     {
2546      "data": {
2547       "text/plain": [
2548        "[0]"
2549       ]
2550      },
2551      "execution_count": 60,
2552      "metadata": {},
2553      "output_type": "execute_result"
2554     }
2555    ],
2556    "source": [
2557     "%time [i for i, s12 in enumerate(all_targets) if is_interleave(my_bill, friend_bill, s12)]"
2558    ]
2559   },
2560   {
2561    "cell_type": "code",
2562    "execution_count": 61,
2563    "metadata": {},
2564    "outputs": [
2565     {
2566      "name": "stdout",
2567      "output_type": "stream",
2568      "text": [
2569       "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
2570       "Wall time: 570 µs\n"
2571      ]
2572     },
2573     {
2574      "data": {
2575       "text/plain": [
2576        "[0]"
2577       ]
2578      },
2579      "execution_count": 61,
2580      "metadata": {},
2581      "output_type": "execute_result"
2582     }
2583    ],
2584    "source": [
2585     "%time [i for i, s12 in enumerate(all_targets) if is_interleave_recursive(my_bill, friend_bill, s12)]"
2586    ]
2587   },
2588   {
2589    "cell_type": "code",
2590    "execution_count": 62,
2591    "metadata": {
2592     "collapsed": true
2593    },
2594    "outputs": [],
2595    "source": [
2596     "bill_set = all_targets + random.sample(other_bills, 8)\n",
2597     "random.shuffle(bill_set)\n",
2598     "bill_set = [my_bill, friend_bill] + bill_set\n",
2599     "\n",
2600     "# with open('09-bills.txt', 'w') as f:\n",
2601     "#     for i, b in enumerate(bill_set):\n",
2602     "#         f.write('{}: {}\\n'.format(i, b))"
2603    ]
2604   },
2605   {
2606    "cell_type": "code",
2607    "execution_count": 63,
2608    "metadata": {
2609     "collapsed": true
2610    },
2611    "outputs": [],
2612    "source": [
2613     "def is_subseq_greedy(s1, s2):\n",
2614     "    i = j = 0\n",
2615     "    while i < len(s1) and j < len(s2):\n",
2616     "        if s1[i] == s2[j]:\n",
2617     "            i += 1\n",
2618     "        j += 1\n",
2619     "    return i == len(s1)"
2620    ]
2621   },
2622   {
2623    "cell_type": "code",
2624    "execution_count": 64,
2625    "metadata": {
2626     "collapsed": true
2627    },
2628    "outputs": [],
2629    "source": [
2630     "def subseq_partition(s1, s2):\n",
2631     "    i = j = 0\n",
2632     "    remainder = ''\n",
2633     "    while i < len(s1) and j < len(s2):\n",
2634     "        if s1[i] == s2[j]:\n",
2635     "            i += 1\n",
2636     "        else:\n",
2637     "            remainder += s2[j]\n",
2638     "        j += 1\n",
2639     "    return i == len(s1), remainder"
2640    ]
2641   },
2642   {
2643    "cell_type": "code",
2644    "execution_count": 65,
2645    "metadata": {},
2646    "outputs": [
2647     {
2648      "data": {
2649       "text/plain": [
2650        "(40, 40, 20, 20)"
2651       ]
2652      },
2653      "execution_count": 65,
2654      "metadata": {},
2655      "output_type": "execute_result"
2656     }
2657    ],
2658    "source": [
2659     "common = make_string(10)\n",
2660     "padding = make_string(10)\n",
2661     "middle = interleave(common, padding)\n",
2662     "\n",
2663     "pre1 = make_string(5)\n",
2664     "suf1 = make_string(5)\n",
2665     "\n",
2666     "pre2 = make_string(5)\n",
2667     "suf2 = make_string(5)\n",
2668     "\n",
2669     "pre = interleave(pre1, pre2)\n",
2670     "suf = interleave(suf1, suf2)\n",
2671     "\n",
2672     "distractor = pre + middle + suf\n",
2673     "\n",
2674     "sub1 = pre1 + common + suf1\n",
2675     "sub2 = pre2 + common + suf2\n",
2676     "\n",
2677     "valid = interleave(sub1, sub2)\n",
2678     "\n",
2679     "len(distractor), len(valid), len(sub1), len(sub2)"
2680    ]
2681   },
2682   {
2683    "cell_type": "code",
2684    "execution_count": 66,
2685    "metadata": {},
2686    "outputs": [
2687     {
2688      "data": {
2689       "text/plain": [
2690        "(True, True)"
2691       ]
2692      },
2693      "execution_count": 66,
2694      "metadata": {},
2695      "output_type": "execute_result"
2696     }
2697    ],
2698    "source": [
2699     "is_subseq_greedy(sub1, distractor), is_subseq_greedy(sub2, distractor)"
2700    ]
2701   },
2702   {
2703    "cell_type": "code",
2704    "execution_count": 67,
2705    "metadata": {},
2706    "outputs": [
2707     {
2708      "data": {
2709       "text/plain": [
2710        "(True, True)"
2711       ]
2712      },
2713      "execution_count": 67,
2714      "metadata": {},
2715      "output_type": "execute_result"
2716     }
2717    ],
2718    "source": [
2719     "is_subseq_greedy(sub1, valid), is_subseq_greedy(sub2, valid)"
2720    ]
2721   },
2722   {
2723    "cell_type": "code",
2724    "execution_count": 68,
2725    "metadata": {},
2726    "outputs": [
2727     {
2728      "data": {
2729       "text/plain": [
2730        "(False, True)"
2731       ]
2732      },
2733      "execution_count": 68,
2734      "metadata": {},
2735      "output_type": "execute_result"
2736     }
2737    ],
2738    "source": [
2739     "is_interleave(sub1, sub2, distractor), is_interleave(sub1, sub2, valid)"
2740    ]
2741   },
2742   {
2743    "cell_type": "code",
2744    "execution_count": 69,
2745    "metadata": {},
2746    "outputs": [
2747     {
2748      "data": {
2749       "text/plain": [
2750        "('hbgbfhdaghfbcagbhhgh',\n",
2751        " 'eccfdhdaghfbcaggbaae',\n",
2752        " 'ehccbfgbdfhfefdbagefagehfgbcaggbbhahgaeh',\n",
2753        " 'hecbgbfhdagchffbdhcagdbhaghhfgbchaggbaae')"
2754       ]
2755      },
2756      "execution_count": 69,
2757      "metadata": {},
2758      "output_type": "execute_result"
2759     }
2760    ],
2761    "source": [
2762     "sub1, sub2, distractor, valid"
2763    ]
2764   },
2765   {
2766    "cell_type": "code",
2767    "execution_count": 70,
2768    "metadata": {},
2769    "outputs": [
2770     {
2771      "data": {
2772       "text/plain": [
2773        "False"
2774       ]
2775      },
2776      "execution_count": 70,
2777      "metadata": {},
2778      "output_type": "execute_result"
2779     }
2780    ],
2781    "source": [
2782     "a, b = subseq_partition(sub1, distractor)\n",
2783     "b == sub2"
2784    ]
2785   },
2786   {
2787    "cell_type": "code",
2788    "execution_count": 71,
2789    "metadata": {},
2790    "outputs": [
2791     {
2792      "data": {
2793       "text/plain": [
2794        "('eccfdhdaghfbc', 'eccfdhdaghfbcaggbaae')"
2795       ]
2796      },
2797      "execution_count": 71,
2798      "metadata": {},
2799      "output_type": "execute_result"
2800     }
2801    ],
2802    "source": [
2803     "a, b = subseq_partition(sub1, valid)\n",
2804     "b, sub2"
2805    ]
2806   },
2807   {
2808    "cell_type": "code",
2809    "execution_count": null,
2810    "metadata": {
2811     "collapsed": true
2812    },
2813    "outputs": [],
2814    "source": []
2815   }
2816  ],
2817  "metadata": {
2818   "kernelspec": {
2819    "display_name": "Python 3",
2820    "language": "python",
2821    "name": "python3"
2822   },
2823   "language_info": {
2824    "codemirror_mode": {
2825     "name": "ipython",
2826     "version": 3
2827    },
2828    "file_extension": ".py",
2829    "mimetype": "text/x-python",
2830    "name": "python",
2831    "nbconvert_exporter": "python",
2832    "pygments_lexer": "ipython3",
2833    "version": "3.5.2+"
2834   }
2835  },
2836  "nbformat": 4,
2837  "nbformat_minor": 1
2838 }