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": 3,
  35    "metadata": {
  36     "collapsed": true
  37    },
  38    "outputs": [],
  39    "source": [
  40     "s1 = \"aabcc\"\n",
  41     "s2 = \"dbbca\"\n",
  42     "\n",
  43     "s3t = \"aadbbcbcac\"\n",
  44     "s3f = \"aadbbbaccc\""
  45    ]
  46   },
  47   {
  48    "cell_type": "code",
  49    "execution_count": 4,
  50    "metadata": {},
  51    "outputs": [
  52     {
  53      "data": {
  54       "text/plain": [
  55        "[(0, ''), (1, 'a'), (2, 'aa'), (3, 'aab'), (4, 'aabc'), (5, 'aabcc')]"
  56       ]
  57      },
  58      "execution_count": 4,
  59      "metadata": {},
  60      "output_type": "execute_result"
  61     }
  62    ],
  63    "source": [
  64     "[(i, s1[:i]) for i in range(len(s1)+1)]"
  65    ]
  66   },
  67   {
  68    "cell_type": "markdown",
  69    "metadata": {},
  70    "source": [
  71     "`dp_table[i, j]` is True if first `i` + `j` characters of `s3` can be formed from interleaving of first `i` characters of `s1` and first `j` characters of `s2`."
  72    ]
  73   },
  74   {
  75    "cell_type": "code",
  76    "execution_count": 5,
  77    "metadata": {},
  78    "outputs": [
  79     {
  80      "data": {
  81       "text/plain": [
  82        "[[True, False, False, False, False, False],\n",
  83        " [False, False, False, False, False, False],\n",
  84        " [False, False, False, False, False, False],\n",
  85        " [False, False, False, False, False, False],\n",
  86        " [False, False, False, False, False, False],\n",
  87        " [False, False, False, False, False, False]]"
  88       ]
  89      },
  90      "execution_count": 5,
  91      "metadata": {},
  92      "output_type": "execute_result"
  93     }
  94    ],
  95    "source": [
  96     "dp_table = [[False] * (len(s1) + 1) for _ in range(len(s2) + 1)]\n",
  97     "dp_table[0][0] = True\n",
  98     "dp_table"
  99    ]
 100   },
 101   {
 102    "cell_type": "code",
 103    "execution_count": 6,
 104    "metadata": {
 105     "scrolled": true
 106    },
 107    "outputs": [
 108     {
 109      "data": {
 110       "text/plain": [
 111        "{(0, 0): False,\n",
 112        " (0, 1): False,\n",
 113        " (0, 2): False,\n",
 114        " (0, 3): False,\n",
 115        " (0, 4): False,\n",
 116        " (0, 5): False,\n",
 117        " (1, 0): False,\n",
 118        " (1, 1): False,\n",
 119        " (1, 2): False,\n",
 120        " (1, 3): False,\n",
 121        " (1, 4): False,\n",
 122        " (1, 5): False,\n",
 123        " (2, 0): False,\n",
 124        " (2, 1): False,\n",
 125        " (2, 2): False,\n",
 126        " (2, 3): False,\n",
 127        " (2, 4): False,\n",
 128        " (2, 5): False,\n",
 129        " (3, 0): False,\n",
 130        " (3, 1): False,\n",
 131        " (3, 2): False,\n",
 132        " (3, 3): False,\n",
 133        " (3, 4): False,\n",
 134        " (3, 5): False,\n",
 135        " (4, 0): False,\n",
 136        " (4, 1): False,\n",
 137        " (4, 2): False,\n",
 138        " (4, 3): False,\n",
 139        " (4, 4): False,\n",
 140        " (4, 5): False,\n",
 141        " (5, 0): False,\n",
 142        " (5, 1): False,\n",
 143        " (5, 2): False,\n",
 144        " (5, 3): False,\n",
 145        " (5, 4): False,\n",
 146        " (5, 5): False}"
 147       ]
 148      },
 149      "execution_count": 6,
 150      "metadata": {},
 151      "output_type": "execute_result"
 152     }
 153    ],
 154    "source": [
 155     "dp_table = {(i, j): False\n",
 156     "           for i in range(len(s1)+1)\n",
 157     "           for j in range(len(s2)+1)}\n",
 158     "dp_table"
 159    ]
 160   },
 161   {
 162    "cell_type": "code",
 163    "execution_count": 7,
 164    "metadata": {
 165     "collapsed": true
 166    },
 167    "outputs": [],
 168    "source": [
 169     "def show_table(table):\n",
 170     "    return '\\n'.join(\n",
 171     "        ' '.join(str(table[i, j])[0] for j in sorted(set([k[1] for k in table])))\n",
 172     "        for i in sorted(set([k[0] for k in table])))        "
 173    ]
 174   },
 175   {
 176    "cell_type": "code",
 177    "execution_count": 8,
 178    "metadata": {
 179     "collapsed": true
 180    },
 181    "outputs": [],
 182    "source": [
 183     "def show_table(table):\n",
 184     "    return '\\n'.join(\n",
 185     "        ' '.join('T' if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n",
 186     "        for i in sorted(set([k[0] for k in table])))        "
 187    ]
 188   },
 189   {
 190    "cell_type": "code",
 191    "execution_count": 9,
 192    "metadata": {},
 193    "outputs": [
 194     {
 195      "name": "stdout",
 196      "output_type": "stream",
 197      "text": [
 198       ". . . . . .\n",
 199       ". . . . . .\n",
 200       ". . . . . .\n",
 201       ". . . . . .\n",
 202       ". . . . . .\n",
 203       ". . . . . .\n"
 204      ]
 205     }
 206    ],
 207    "source": [
 208     "print(show_table(dp_table))"
 209    ]
 210   },
 211   {
 212    "cell_type": "code",
 213    "execution_count": 10,
 214    "metadata": {},
 215    "outputs": [
 216     {
 217      "name": "stdout",
 218      "output_type": "stream",
 219      "text": [
 220       "aabcc dbbca aadbbcbcac\n",
 221       "aa 0 0 ! ! ! True\n",
 222       "s2 0 1 ! d a False\n",
 223       "s2 0 2 ! b a False\n",
 224       "s2 0 3 ! b d False\n",
 225       "s2 0 4 ! c b False\n",
 226       "s2 0 5 ! a b False\n",
 227       "s1 1 0 a ! a True\n",
 228       "xx 1 1 a d a False\n",
 229       "xx 1 2 a b d False\n",
 230       "xx 1 3 a b b False\n",
 231       "xx 1 4 a c b False\n",
 232       "xx 1 5 a a c False\n",
 233       "s1 2 0 a ! a True\n",
 234       "s2 2 1 a d d True\n",
 235       "s2 2 2 a b b True\n",
 236       "s2 2 3 a b b True\n",
 237       "s2 2 4 a c c True\n",
 238       "xx 2 5 a a b False\n",
 239       "s1 3 0 b ! d False\n",
 240       "s1 3 1 b d b True\n",
 241       "s2 3 2 b b b True\n",
 242       "s1 3 2 b b b True\n",
 243       "xx 3 3 b b c False\n",
 244       "s1 3 4 b c b True\n",
 245       "xx 3 5 b a c False\n",
 246       "s1 4 0 c ! b False\n",
 247       "xx 4 1 c d b False\n",
 248       "s1 4 2 c b c True\n",
 249       "s2 4 3 c b b True\n",
 250       "s2 4 4 c c c True\n",
 251       "s1 4 4 c c c True\n",
 252       "s2 4 5 c a a True\n",
 253       "s1 5 0 c ! b False\n",
 254       "xx 5 1 c d c False\n",
 255       "xx 5 2 c b b False\n",
 256       "s1 5 3 c b c True\n",
 257       "xx 5 4 c c a False\n",
 258       "s1 5 5 c a c True\n",
 259       "T . . . . .\n",
 260       "T . . . . .\n",
 261       "T T T T T .\n",
 262       ". T T . T .\n",
 263       ". . T T T T\n",
 264       ". . . T . T\n"
 265      ]
 266     },
 267     {
 268      "data": {
 269       "text/plain": [
 270        "{(1, 0): (0, 0, 'a', 's1'),\n",
 271        " (2, 0): (1, 0, 'a', 's1'),\n",
 272        " (2, 1): (2, 0, 'd', 's2'),\n",
 273        " (2, 2): (2, 1, 'b', 's2'),\n",
 274        " (2, 3): (2, 2, 'b', 's2'),\n",
 275        " (2, 4): (2, 3, 'c', 's2'),\n",
 276        " (3, 1): (2, 1, 'b', 's1'),\n",
 277        " (3, 2): (2, 2, 'b', 's1'),\n",
 278        " (3, 4): (2, 4, 'b', 's1'),\n",
 279        " (4, 2): (3, 2, 'c', 's1'),\n",
 280        " (4, 3): (4, 2, 'b', 's2'),\n",
 281        " (4, 4): (3, 4, 'c', 's1'),\n",
 282        " (4, 5): (4, 4, 'a', 's2'),\n",
 283        " (5, 3): (4, 3, 'c', 's1'),\n",
 284        " (5, 5): (4, 5, 'c', 's1')}"
 285       ]
 286      },
 287      "execution_count": 10,
 288      "metadata": {},
 289      "output_type": "execute_result"
 290     }
 291    ],
 292    "source": [
 293     "s3 = s3t\n",
 294     "\n",
 295     "print(s1, s2, s3)\n",
 296     "\n",
 297     "dp_table = {(i, j): False\n",
 298     "           for i in range(len(s1)+1)\n",
 299     "           for j in range(len(s2)+1)}\n",
 300     "\n",
 301     "backpointers = {}\n",
 302     "\n",
 303     "for i in range(len(s1)+1):\n",
 304     "    for j in range(len(s2)+1):\n",
 305     "        if i == 0 and j == 0:\n",
 306     "            dp_table[i, j] = True\n",
 307     "            print('aa', i, j, '!', '!', '!', dp_table[i, j])\n",
 308     "        elif i == 0:\n",
 309     "            # extend by character from s2\n",
 310     "            if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
 311     "                dp_table[i, j] = True\n",
 312     "                backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
 313     "            print('s2', i, j, '!', s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 314     "        elif j == 0:\n",
 315     "            # extend by character from s1\n",
 316     "            if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
 317     "                dp_table[i, j] = True\n",
 318     "                backpointers[i, j] = (i-1, j, s1[i-1], 's1')\n",
 319     "            print('s1', i, j, s1[i-1], '!', s3[i+j-1], dp_table[i, j])\n",
 320     "        else:\n",
 321     "            # extend by character from s2\n",
 322     "            if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
 323     "                dp_table[i, j] = True\n",
 324     "                backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
 325     "                print('s2', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])                \n",
 326     "            # extend by character from s1\n",
 327     "            if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
 328     "                dp_table[i, j] = True\n",
 329     "                backpointers[i, j] = (i-1, j, s1[i-1], 's1')                \n",
 330     "                print('s1', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 331     "            if not dp_table[i, j]:\n",
 332     "                print('xx', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 333     "\n",
 334     "print(show_table(dp_table))\n",
 335     "backpointers"
 336    ]
 337   },
 338   {
 339    "cell_type": "code",
 340    "execution_count": 11,
 341    "metadata": {
 342     "collapsed": true
 343    },
 344    "outputs": [],
 345    "source": [
 346     "def is_interleave(seq1, seq2, seq3, return_backpointers=False, return_table=False, debug=False):\n",
 347     "    \"\"\"Return true if seq3 is some interleaved merge of seq1 and seq2.\n",
 348     "    If return_backpointers, also return the set of backpointers to\n",
 349     "    reconstruct the interleaving\"\"\"\n",
 350     "    \n",
 351     "    # dp_table[i, j] is True if first i+j characters of seq is made up of \n",
 352     "    # an interleaving of the first i characters of seq1 and the \n",
 353     "    # first j characters of seq2\n",
 354     "    \n",
 355     "    if len(seq1) + len(seq2) != len(seq3):\n",
 356     "        if return_backpointers or return_table:\n",
 357     "            retval = [False]\n",
 358     "            if return_backpointers:\n",
 359     "                retval += [{}]\n",
 360     "            if return_table:\n",
 361     "                retval += [{}]\n",
 362     "            return tuple(retval)\n",
 363     "        else:\n",
 364     "            return False\n",
 365     "    \n",
 366     "    dp_table = {(i, j): False\n",
 367     "               for i in range(len(seq1)+1)\n",
 368     "               for j in range(len(seq2)+1)}\n",
 369     "\n",
 370     "    backpointers = {}\n",
 371     "\n",
 372     "    for i in range(len(seq1)+1):\n",
 373     "        for j in range(len(seq2)+1):\n",
 374     "            if i == 0 and j == 0:\n",
 375     "                dp_table[i, j] = True\n",
 376     "                if debug: print('xxxx', i, j, '!', '!', '!', dp_table[i, j])\n",
 377     "            elif i == 0:\n",
 378     "                # extend by character from seq2\n",
 379     "                if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
 380     "                    dp_table[i, j] = True\n",
 381     "                    backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
 382     "                if debug: print('seq2', i, j, '!', seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 383     "            elif j == 0:\n",
 384     "                # extend by character from seq1\n",
 385     "                if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
 386     "                    dp_table[i, j] = True\n",
 387     "                    backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')\n",
 388     "                if debug: print('seq1', i, j, seq1[i-1], '!', seq3[i+j-1], dp_table[i, j])\n",
 389     "            else:\n",
 390     "                # extend by character from seq2\n",
 391     "                if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
 392     "                    dp_table[i, j] = True\n",
 393     "                    backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
 394     "                    if debug: print('seq2', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])                \n",
 395     "                # extend by character from seq1\n",
 396     "                if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
 397     "                    dp_table[i, j] = True\n",
 398     "                    backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')                \n",
 399     "                    if debug: print('seq1', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 400     "                if not dp_table[i, j]:\n",
 401     "                    if debug: print('xxxx', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 402     "\n",
 403     "    if return_backpointers or return_table:\n",
 404     "        retval = [dp_table[len(seq1), len(seq2)]]\n",
 405     "        if return_backpointers:\n",
 406     "            retval += [backpointers]\n",
 407     "        if return_table:\n",
 408     "            retval += [dp_table]\n",
 409     "        return tuple(retval)\n",
 410     "    else:\n",
 411     "        return dp_table[len(seq1), len(seq2)]"
 412    ]
 413   },
 414   {
 415    "cell_type": "code",
 416    "execution_count": 12,
 417    "metadata": {},
 418    "outputs": [
 419     {
 420      "data": {
 421       "text/plain": [
 422        "True"
 423       ]
 424      },
 425      "execution_count": 12,
 426      "metadata": {},
 427      "output_type": "execute_result"
 428     }
 429    ],
 430    "source": [
 431     "is_interleave(s1, s2, s3t)"
 432    ]
 433   },
 434   {
 435    "cell_type": "code",
 436    "execution_count": 13,
 437    "metadata": {},
 438    "outputs": [
 439     {
 440      "data": {
 441       "text/plain": [
 442        "(True,\n",
 443        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 444        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 445        "  (2, 1): (2, 0, 'd', 'seq2'),\n",
 446        "  (2, 2): (2, 1, 'b', 'seq2'),\n",
 447        "  (2, 3): (2, 2, 'b', 'seq2'),\n",
 448        "  (2, 4): (2, 3, 'c', 'seq2'),\n",
 449        "  (3, 1): (2, 1, 'b', 'seq1'),\n",
 450        "  (3, 2): (2, 2, 'b', 'seq1'),\n",
 451        "  (3, 4): (2, 4, 'b', 'seq1'),\n",
 452        "  (4, 2): (3, 2, 'c', 'seq1'),\n",
 453        "  (4, 3): (4, 2, 'b', 'seq2'),\n",
 454        "  (4, 4): (3, 4, 'c', 'seq1'),\n",
 455        "  (4, 5): (4, 4, 'a', 'seq2'),\n",
 456        "  (5, 3): (4, 3, 'c', 'seq1'),\n",
 457        "  (5, 5): (4, 5, 'c', 'seq1')})"
 458       ]
 459      },
 460      "execution_count": 13,
 461      "metadata": {},
 462      "output_type": "execute_result"
 463     }
 464    ],
 465    "source": [
 466     "is_interleave(s1, s2, s3t, return_backpointers=True)"
 467    ]
 468   },
 469   {
 470    "cell_type": "code",
 471    "execution_count": 14,
 472    "metadata": {
 473     "scrolled": true
 474    },
 475    "outputs": [
 476     {
 477      "data": {
 478       "text/plain": [
 479        "(True,\n",
 480        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 481        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 482        "  (2, 1): (2, 0, 'd', 'seq2'),\n",
 483        "  (2, 2): (2, 1, 'b', 'seq2'),\n",
 484        "  (2, 3): (2, 2, 'b', 'seq2'),\n",
 485        "  (2, 4): (2, 3, 'c', 'seq2'),\n",
 486        "  (3, 1): (2, 1, 'b', 'seq1'),\n",
 487        "  (3, 2): (2, 2, 'b', 'seq1'),\n",
 488        "  (3, 4): (2, 4, 'b', 'seq1'),\n",
 489        "  (4, 2): (3, 2, 'c', 'seq1'),\n",
 490        "  (4, 3): (4, 2, 'b', 'seq2'),\n",
 491        "  (4, 4): (3, 4, 'c', 'seq1'),\n",
 492        "  (4, 5): (4, 4, 'a', 'seq2'),\n",
 493        "  (5, 3): (4, 3, 'c', 'seq1'),\n",
 494        "  (5, 5): (4, 5, 'c', 'seq1')},\n",
 495        " {(0, 0): True,\n",
 496        "  (0, 1): False,\n",
 497        "  (0, 2): False,\n",
 498        "  (0, 3): False,\n",
 499        "  (0, 4): False,\n",
 500        "  (0, 5): False,\n",
 501        "  (1, 0): True,\n",
 502        "  (1, 1): False,\n",
 503        "  (1, 2): False,\n",
 504        "  (1, 3): False,\n",
 505        "  (1, 4): False,\n",
 506        "  (1, 5): False,\n",
 507        "  (2, 0): True,\n",
 508        "  (2, 1): True,\n",
 509        "  (2, 2): True,\n",
 510        "  (2, 3): True,\n",
 511        "  (2, 4): True,\n",
 512        "  (2, 5): False,\n",
 513        "  (3, 0): False,\n",
 514        "  (3, 1): True,\n",
 515        "  (3, 2): True,\n",
 516        "  (3, 3): False,\n",
 517        "  (3, 4): True,\n",
 518        "  (3, 5): False,\n",
 519        "  (4, 0): False,\n",
 520        "  (4, 1): False,\n",
 521        "  (4, 2): True,\n",
 522        "  (4, 3): True,\n",
 523        "  (4, 4): True,\n",
 524        "  (4, 5): True,\n",
 525        "  (5, 0): False,\n",
 526        "  (5, 1): False,\n",
 527        "  (5, 2): False,\n",
 528        "  (5, 3): True,\n",
 529        "  (5, 4): False,\n",
 530        "  (5, 5): True})"
 531       ]
 532      },
 533      "execution_count": 14,
 534      "metadata": {},
 535      "output_type": "execute_result"
 536     }
 537    ],
 538    "source": [
 539     "is_interleave(s1, s2, s3t, return_backpointers=True, return_table=True)"
 540    ]
 541   },
 542   {
 543    "cell_type": "code",
 544    "execution_count": 15,
 545    "metadata": {},
 546    "outputs": [
 547     {
 548      "data": {
 549       "text/plain": [
 550        "False"
 551       ]
 552      },
 553      "execution_count": 15,
 554      "metadata": {},
 555      "output_type": "execute_result"
 556     }
 557    ],
 558    "source": [
 559     "is_interleave(s1, s2, s3f)"
 560    ]
 561   },
 562   {
 563    "cell_type": "code",
 564    "execution_count": 16,
 565    "metadata": {},
 566    "outputs": [
 567     {
 568      "name": "stdout",
 569      "output_type": "stream",
 570      "text": [
 571       "xxxx 0 0 ! ! ! True\n",
 572       "seq2 0 1 ! b a False\n",
 573       "seq2 0 2 ! b a False\n",
 574       "seq2 0 3 ! b a False\n",
 575       "seq1 1 0 a ! a True\n",
 576       "xxxx 1 1 a b a False\n",
 577       "xxxx 1 2 a b a False\n",
 578       "xxxx 1 3 a b b False\n",
 579       "seq1 2 0 a ! a True\n",
 580       "xxxx 2 1 a b a False\n",
 581       "xxxx 2 2 a b b False\n",
 582       "xxxx 2 3 a b a False\n",
 583       "seq1 3 0 a ! a True\n",
 584       "seq2 3 1 a b b True\n",
 585       "xxxx 3 2 a b a False\n",
 586       "xxxx 3 3 a b b False\n",
 587       "seq1 4 0 a ! b False\n",
 588       "seq1 4 1 a b a True\n",
 589       "seq2 4 2 a b b True\n",
 590       "seq2 4 3 a b b True\n"
 591      ]
 592     },
 593     {
 594      "data": {
 595       "text/plain": [
 596        "(True,\n",
 597        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 598        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 599        "  (3, 0): (2, 0, 'a', 'seq1'),\n",
 600        "  (3, 1): (3, 0, 'b', 'seq2'),\n",
 601        "  (4, 1): (3, 1, 'a', 'seq1'),\n",
 602        "  (4, 2): (4, 1, 'b', 'seq2'),\n",
 603        "  (4, 3): (4, 2, 'b', 'seq2')})"
 604       ]
 605      },
 606      "execution_count": 16,
 607      "metadata": {},
 608      "output_type": "execute_result"
 609     }
 610    ],
 611    "source": [
 612     "is_interleave('aaaa', 'bbb', 'aaababb', return_backpointers=True, debug=True)"
 613    ]
 614   },
 615   {
 616    "cell_type": "code",
 617    "execution_count": 17,
 618    "metadata": {
 619     "collapsed": true
 620    },
 621    "outputs": [],
 622    "source": [
 623     "def show_backtrace(bps):\n",
 624     "    i = max([0] + [k[0] for k in bps])\n",
 625     "    j = max([0] + [k[1] for k in bps])\n",
 626     "    chars = ''\n",
 627     "    if (i, j) in bps:\n",
 628     "        while i != 0 or j != 0:\n",
 629     "            if bps[i, j][3] == 'seq1':\n",
 630     "                chars += bps[i, j][2].upper()\n",
 631     "            else:\n",
 632     "                chars += bps[i, j][2]\n",
 633     "            i, j = bps[i, j][0], bps[i, j][1] \n",
 634     "        return ''.join(list(reversed(chars)))\n",
 635     "    else:\n",
 636     "        return ''"
 637    ]
 638   },
 639   {
 640    "cell_type": "code",
 641    "execution_count": 18,
 642    "metadata": {
 643     "collapsed": true
 644    },
 645    "outputs": [],
 646    "source": [
 647     "def make_string(length, alphabet=None):\n",
 648     "    if not alphabet:\n",
 649     "        alphabet = 'abcdefgh'\n",
 650     "    return ''.join(random.choice(alphabet) for _ in range(length))    "
 651    ]
 652   },
 653   {
 654    "cell_type": "code",
 655    "execution_count": 19,
 656    "metadata": {},
 657    "outputs": [
 658     {
 659      "data": {
 660       "text/plain": [
 661        "'ddbcceaffddbbddddehffcdffbffdfdfdddcehhgaddfddbgda'"
 662       ]
 663      },
 664      "execution_count": 19,
 665      "metadata": {},
 666      "output_type": "execute_result"
 667     }
 668    ],
 669    "source": [
 670     "make_string(50)"
 671    ]
 672   },
 673   {
 674    "cell_type": "code",
 675    "execution_count": 20,
 676    "metadata": {
 677     "collapsed": true
 678    },
 679    "outputs": [],
 680    "source": [
 681     "def interleave(s1, s2, wander_limit=10, debug=False):\n",
 682     "    i1 = i2 = wander = 0\n",
 683     "    interleaved = []\n",
 684     "    while i1 <= len(s1) and i2 <= len(s2):\n",
 685     "        if i1 == len(s1):\n",
 686     "            if debug: print(i1, i2, wander, 'remaining s2', s2[i2:])\n",
 687     "            interleaved += s2[i2:]\n",
 688     "            i2 = len(s2) + 1\n",
 689     "        elif i2 == len(s2):\n",
 690     "            if debug: print(i1, i2, wander, 'remaining s1', s1[i1:])\n",
 691     "            interleaved += s1[i1:]\n",
 692     "            i1 = len(s1) + 1\n",
 693     "        else:\n",
 694     "            if wander == wander_limit:\n",
 695     "                step = -1\n",
 696     "            elif wander == -wander_limit:\n",
 697     "                step = +1\n",
 698     "            else:\n",
 699     "                step = random.choice([+1, -1])\n",
 700     "            if step == +1:\n",
 701     "                if debug: print(i1, i2, wander, 'adding', s1[i1])\n",
 702     "                interleaved += s1[i1]\n",
 703     "                i1 += 1\n",
 704     "                wander += 1\n",
 705     "            else:\n",
 706     "                if debug: print(i1, i2, wander, 'adding', s2[i2])\n",
 707     "                interleaved += s2[i2]\n",
 708     "                i2 += 1\n",
 709     "                wander -= 1\n",
 710     "    return ''.join(interleaved)\n",
 711     "            "
 712    ]
 713   },
 714   {
 715    "cell_type": "code",
 716    "execution_count": 21,
 717    "metadata": {},
 718    "outputs": [
 719     {
 720      "name": "stdout",
 721      "output_type": "stream",
 722      "text": [
 723       "0 0 0 adding f\n",
 724       "1 0 1 adding f\n",
 725       "2 0 2 adding d\n",
 726       "3 0 3 adding v\n",
 727       "3 1 2 adding d\n",
 728       "4 1 3 adding g\n",
 729       "5 1 4 adding g\n",
 730       "6 1 5 adding v\n",
 731       "6 2 4 adding d\n",
 732       "7 2 5 adding z\n",
 733       "7 3 4 adding h\n",
 734       "8 3 5 adding w\n",
 735       "8 4 4 adding z\n",
 736       "8 5 3 adding y\n",
 737       "8 6 2 adding b\n",
 738       "9 6 3 adding u\n",
 739       "9 7 2 adding d\n",
 740       "10 7 3 adding w\n",
 741       "10 8 2 adding u\n",
 742       "10 9 1 adding w\n",
 743       "10 10 0 adding u\n",
 744       "10 11 -1 adding g\n",
 745       "11 11 0 adding c\n",
 746       "12 11 1 adding x\n",
 747       "12 12 0 adding z\n",
 748       "12 13 -1 adding b\n",
 749       "13 13 0 adding a\n",
 750       "14 13 1 adding v\n",
 751       "14 14 0 adding a\n",
 752       "15 14 1 adding x\n",
 753       "15 15 0 adding f\n",
 754       "16 15 1 adding f\n",
 755       "17 15 2 adding v\n",
 756       "17 16 1 adding c\n",
 757       "18 16 2 adding a\n",
 758       "19 16 3 adding h\n",
 759       "20 16 4 remaining s2 vzxy\n"
 760      ]
 761     },
 762     {
 763      "data": {
 764       "text/plain": [
 765        "('ffddggdhbdgcbaaffcah',\n",
 766        " 'vvzwzyuwuwuxzvxvvzxy',\n",
 767        " 'ffdvdggvdzhwzybudwuwugcxzbavaxffvcahvzxy',\n",
 768        " 40)"
 769       ]
 770      },
 771      "execution_count": 21,
 772      "metadata": {},
 773      "output_type": "execute_result"
 774     }
 775    ],
 776    "source": [
 777     "s1 = make_string(20)\n",
 778     "s2 = make_string(20, alphabet='uvwxyz')\n",
 779     "il = interleave(s1, s2, wander_limit=5, debug=True)\n",
 780     "s1, s2, il, len(il)"
 781    ]
 782   },
 783   {
 784    "cell_type": "code",
 785    "execution_count": 22,
 786    "metadata": {},
 787    "outputs": [
 788     {
 789      "name": "stdout",
 790      "output_type": "stream",
 791      "text": [
 792       "xxxx 0 0 ! ! ! True\n",
 793       "seq2 0 1 ! f f True\n",
 794       "seq2 0 2 ! f f True\n",
 795       "seq2 0 3 ! d d True\n",
 796       "seq2 0 4 ! d v False\n",
 797       "seq2 0 5 ! g d False\n",
 798       "seq2 0 6 ! g g False\n",
 799       "seq2 0 7 ! d g False\n",
 800       "seq2 0 8 ! h v False\n",
 801       "seq2 0 9 ! b d False\n",
 802       "seq2 0 10 ! d z False\n",
 803       "seq2 0 11 ! g h False\n",
 804       "seq2 0 12 ! c w False\n",
 805       "seq2 0 13 ! b z False\n",
 806       "seq2 0 14 ! a y False\n",
 807       "seq2 0 15 ! a b False\n",
 808       "seq2 0 16 ! f u False\n",
 809       "seq2 0 17 ! f d False\n",
 810       "seq2 0 18 ! c w False\n",
 811       "seq2 0 19 ! a u False\n",
 812       "seq2 0 20 ! h w False\n",
 813       "seq1 1 0 v ! f False\n",
 814       "xxxx 1 1 v f f False\n",
 815       "xxxx 1 2 v f d False\n",
 816       "seq1 1 3 v d v True\n",
 817       "seq2 1 4 v d d True\n",
 818       "seq2 1 5 v g g True\n",
 819       "seq2 1 6 v g g True\n",
 820       "xxxx 1 7 v d v False\n",
 821       "xxxx 1 8 v h d False\n",
 822       "xxxx 1 9 v b z False\n",
 823       "xxxx 1 10 v d h False\n",
 824       "xxxx 1 11 v g w False\n",
 825       "xxxx 1 12 v c z False\n",
 826       "xxxx 1 13 v b y False\n",
 827       "xxxx 1 14 v a b False\n",
 828       "xxxx 1 15 v a u False\n",
 829       "xxxx 1 16 v f d False\n",
 830       "xxxx 1 17 v f w False\n",
 831       "xxxx 1 18 v c u False\n",
 832       "xxxx 1 19 v a w False\n",
 833       "xxxx 1 20 v h u False\n",
 834       "seq1 2 0 v ! f False\n",
 835       "xxxx 2 1 v f d False\n",
 836       "xxxx 2 2 v f v False\n",
 837       "xxxx 2 3 v d d False\n",
 838       "xxxx 2 4 v d g False\n",
 839       "xxxx 2 5 v g g False\n",
 840       "seq1 2 6 v g v True\n",
 841       "seq2 2 7 v d d True\n",
 842       "xxxx 2 8 v h z False\n",
 843       "xxxx 2 9 v b h False\n",
 844       "xxxx 2 10 v d w False\n",
 845       "xxxx 2 11 v g z False\n",
 846       "xxxx 2 12 v c y False\n",
 847       "xxxx 2 13 v b b False\n",
 848       "xxxx 2 14 v a u False\n",
 849       "xxxx 2 15 v a d False\n",
 850       "xxxx 2 16 v f w False\n",
 851       "xxxx 2 17 v f u False\n",
 852       "xxxx 2 18 v c w False\n",
 853       "xxxx 2 19 v a u False\n",
 854       "xxxx 2 20 v h g False\n",
 855       "seq1 3 0 z ! d False\n",
 856       "xxxx 3 1 z f v False\n",
 857       "xxxx 3 2 z f d False\n",
 858       "xxxx 3 3 z d g False\n",
 859       "xxxx 3 4 z d g False\n",
 860       "xxxx 3 5 z g v False\n",
 861       "xxxx 3 6 z g d False\n",
 862       "seq1 3 7 z d z True\n",
 863       "seq2 3 8 z h h True\n",
 864       "xxxx 3 9 z b w False\n",
 865       "xxxx 3 10 z d z False\n",
 866       "xxxx 3 11 z g y False\n",
 867       "xxxx 3 12 z c b False\n",
 868       "xxxx 3 13 z b u False\n",
 869       "xxxx 3 14 z a d False\n",
 870       "xxxx 3 15 z a w False\n",
 871       "xxxx 3 16 z f u False\n",
 872       "xxxx 3 17 z f w False\n",
 873       "xxxx 3 18 z c u False\n",
 874       "xxxx 3 19 z a g False\n",
 875       "xxxx 3 20 z h c False\n",
 876       "seq1 4 0 w ! v False\n",
 877       "xxxx 4 1 w f d False\n",
 878       "xxxx 4 2 w f g False\n",
 879       "xxxx 4 3 w d g False\n",
 880       "xxxx 4 4 w d v False\n",
 881       "xxxx 4 5 w g d False\n",
 882       "xxxx 4 6 w g z False\n",
 883       "xxxx 4 7 w d h False\n",
 884       "seq1 4 8 w h w True\n",
 885       "xxxx 4 9 w b z False\n",
 886       "xxxx 4 10 w d y False\n",
 887       "xxxx 4 11 w g b False\n",
 888       "xxxx 4 12 w c u False\n",
 889       "xxxx 4 13 w b d False\n",
 890       "xxxx 4 14 w a w False\n",
 891       "xxxx 4 15 w a u False\n",
 892       "xxxx 4 16 w f w False\n",
 893       "xxxx 4 17 w f u False\n",
 894       "xxxx 4 18 w c g False\n",
 895       "xxxx 4 19 w a c False\n",
 896       "xxxx 4 20 w h x False\n",
 897       "seq1 5 0 z ! d False\n",
 898       "xxxx 5 1 z f g False\n",
 899       "xxxx 5 2 z f g False\n",
 900       "xxxx 5 3 z d v False\n",
 901       "xxxx 5 4 z d d False\n",
 902       "xxxx 5 5 z g z False\n",
 903       "xxxx 5 6 z g h False\n",
 904       "xxxx 5 7 z d w False\n",
 905       "seq1 5 8 z h z True\n",
 906       "xxxx 5 9 z b y False\n",
 907       "xxxx 5 10 z d b False\n",
 908       "xxxx 5 11 z g u False\n",
 909       "xxxx 5 12 z c d False\n",
 910       "xxxx 5 13 z b w False\n",
 911       "xxxx 5 14 z a u False\n",
 912       "xxxx 5 15 z a w False\n",
 913       "xxxx 5 16 z f u False\n",
 914       "xxxx 5 17 z f g False\n",
 915       "xxxx 5 18 z c c False\n",
 916       "xxxx 5 19 z a x False\n",
 917       "xxxx 5 20 z h z False\n",
 918       "seq1 6 0 y ! g False\n",
 919       "xxxx 6 1 y f g False\n",
 920       "xxxx 6 2 y f v False\n",
 921       "xxxx 6 3 y d d False\n",
 922       "xxxx 6 4 y d z False\n",
 923       "xxxx 6 5 y g h False\n",
 924       "xxxx 6 6 y g w False\n",
 925       "xxxx 6 7 y d z False\n",
 926       "seq1 6 8 y h y True\n",
 927       "seq2 6 9 y b b True\n",
 928       "xxxx 6 10 y d u False\n",
 929       "xxxx 6 11 y g d False\n",
 930       "xxxx 6 12 y c w False\n",
 931       "xxxx 6 13 y b u False\n",
 932       "xxxx 6 14 y a w False\n",
 933       "xxxx 6 15 y a u False\n",
 934       "xxxx 6 16 y f g False\n",
 935       "xxxx 6 17 y f c False\n",
 936       "xxxx 6 18 y c x False\n",
 937       "xxxx 6 19 y a z False\n",
 938       "xxxx 6 20 y h b False\n",
 939       "seq1 7 0 u ! g False\n",
 940       "xxxx 7 1 u f v False\n",
 941       "xxxx 7 2 u f d False\n",
 942       "xxxx 7 3 u d z False\n",
 943       "xxxx 7 4 u d h False\n",
 944       "xxxx 7 5 u g w False\n",
 945       "xxxx 7 6 u g z False\n",
 946       "xxxx 7 7 u d y False\n",
 947       "xxxx 7 8 u h b False\n",
 948       "seq1 7 9 u b u True\n",
 949       "seq2 7 10 u d d True\n",
 950       "xxxx 7 11 u g w False\n",
 951       "xxxx 7 12 u c u False\n",
 952       "xxxx 7 13 u b w False\n",
 953       "xxxx 7 14 u a u False\n",
 954       "xxxx 7 15 u a g False\n",
 955       "xxxx 7 16 u f c False\n",
 956       "xxxx 7 17 u f x False\n",
 957       "xxxx 7 18 u c z False\n",
 958       "xxxx 7 19 u a b False\n",
 959       "xxxx 7 20 u h a False\n",
 960       "seq1 8 0 w ! v False\n",
 961       "xxxx 8 1 w f d False\n",
 962       "xxxx 8 2 w f z False\n",
 963       "xxxx 8 3 w d h False\n",
 964       "xxxx 8 4 w d w False\n",
 965       "xxxx 8 5 w g z False\n",
 966       "xxxx 8 6 w g y False\n",
 967       "xxxx 8 7 w d b False\n",
 968       "xxxx 8 8 w h u False\n",
 969       "xxxx 8 9 w b d False\n",
 970       "seq1 8 10 w d w True\n",
 971       "xxxx 8 11 w g u False\n",
 972       "xxxx 8 12 w c w False\n",
 973       "xxxx 8 13 w b u False\n",
 974       "xxxx 8 14 w a g False\n",
 975       "xxxx 8 15 w a c False\n",
 976       "xxxx 8 16 w f x False\n",
 977       "xxxx 8 17 w f z False\n",
 978       "xxxx 8 18 w c b False\n",
 979       "xxxx 8 19 w a a False\n",
 980       "xxxx 8 20 w h v False\n",
 981       "seq1 9 0 u ! d False\n",
 982       "xxxx 9 1 u f z False\n",
 983       "xxxx 9 2 u f h False\n",
 984       "xxxx 9 3 u d w False\n",
 985       "xxxx 9 4 u d z False\n",
 986       "xxxx 9 5 u g y False\n",
 987       "xxxx 9 6 u g b False\n",
 988       "xxxx 9 7 u d u False\n",
 989       "xxxx 9 8 u h d False\n",
 990       "xxxx 9 9 u b w False\n",
 991       "seq1 9 10 u d u True\n",
 992       "xxxx 9 11 u g w False\n",
 993       "xxxx 9 12 u c u False\n",
 994       "xxxx 9 13 u b g False\n",
 995       "xxxx 9 14 u a c False\n",
 996       "xxxx 9 15 u a x False\n",
 997       "xxxx 9 16 u f z False\n",
 998       "xxxx 9 17 u f b False\n",
 999       "xxxx 9 18 u c a False\n",
1000       "xxxx 9 19 u a v False\n",
1001       "xxxx 9 20 u h a False\n",
1002       "seq1 10 0 w ! z False\n",
1003       "xxxx 10 1 w f h False\n",
1004       "xxxx 10 2 w f w False\n",
1005       "xxxx 10 3 w d z False\n",
1006       "xxxx 10 4 w d y False\n",
1007       "xxxx 10 5 w g b False\n",
1008       "xxxx 10 6 w g u False\n",
1009       "xxxx 10 7 w d d False\n",
1010       "xxxx 10 8 w h w False\n",
1011       "xxxx 10 9 w b u False\n",
1012       "seq1 10 10 w d w True\n",
1013       "xxxx 10 11 w g u False\n",
1014       "xxxx 10 12 w c g False\n",
1015       "xxxx 10 13 w b c False\n",
1016       "xxxx 10 14 w a x False\n",
1017       "xxxx 10 15 w a z False\n",
1018       "xxxx 10 16 w f b False\n",
1019       "xxxx 10 17 w f a False\n",
1020       "xxxx 10 18 w c v False\n",
1021       "xxxx 10 19 w a a False\n",
1022       "xxxx 10 20 w h x False\n",
1023       "seq1 11 0 u ! h False\n",
1024       "xxxx 11 1 u f w False\n",
1025       "xxxx 11 2 u f z False\n",
1026       "xxxx 11 3 u d y False\n",
1027       "xxxx 11 4 u d b False\n",
1028       "xxxx 11 5 u g u False\n",
1029       "xxxx 11 6 u g d False\n",
1030       "xxxx 11 7 u d w False\n",
1031       "xxxx 11 8 u h u False\n",
1032       "xxxx 11 9 u b w False\n",
1033       "seq1 11 10 u d u True\n",
1034       "seq2 11 11 u g g True\n",
1035       "seq2 11 12 u c c True\n",
1036       "xxxx 11 13 u b x False\n",
1037       "xxxx 11 14 u a z False\n",
1038       "xxxx 11 15 u a b False\n",
1039       "xxxx 11 16 u f a False\n",
1040       "xxxx 11 17 u f v False\n",
1041       "xxxx 11 18 u c a False\n",
1042       "xxxx 11 19 u a x False\n",
1043       "xxxx 11 20 u h f False\n",
1044       "seq1 12 0 x ! w False\n",
1045       "xxxx 12 1 x f z False\n",
1046       "xxxx 12 2 x f y False\n",
1047       "xxxx 12 3 x d b False\n",
1048       "xxxx 12 4 x d u False\n",
1049       "xxxx 12 5 x g d False\n",
1050       "xxxx 12 6 x g w False\n",
1051       "xxxx 12 7 x d u False\n",
1052       "xxxx 12 8 x h w False\n",
1053       "xxxx 12 9 x b u False\n",
1054       "xxxx 12 10 x d g False\n",
1055       "xxxx 12 11 x g c False\n",
1056       "seq1 12 12 x c x True\n",
1057       "xxxx 12 13 x b z False\n",
1058       "xxxx 12 14 x a b False\n",
1059       "xxxx 12 15 x a a False\n",
1060       "xxxx 12 16 x f v False\n",
1061       "xxxx 12 17 x f a False\n",
1062       "xxxx 12 18 x c x False\n",
1063       "xxxx 12 19 x a f False\n",
1064       "xxxx 12 20 x h f False\n",
1065       "seq1 13 0 z ! z False\n",
1066       "xxxx 13 1 z f y False\n",
1067       "xxxx 13 2 z f b False\n",
1068       "xxxx 13 3 z d u False\n",
1069       "xxxx 13 4 z d d False\n",
1070       "xxxx 13 5 z g w False\n",
1071       "xxxx 13 6 z g u False\n",
1072       "xxxx 13 7 z d w False\n",
1073       "xxxx 13 8 z h u False\n",
1074       "xxxx 13 9 z b g False\n",
1075       "xxxx 13 10 z d c False\n",
1076       "xxxx 13 11 z g x False\n",
1077       "seq1 13 12 z c z True\n",
1078       "seq2 13 13 z b b True\n",
1079       "seq2 13 14 z a a True\n",
1080       "xxxx 13 15 z a v False\n",
1081       "xxxx 13 16 z f a False\n",
1082       "xxxx 13 17 z f x False\n",
1083       "xxxx 13 18 z c f False\n",
1084       "xxxx 13 19 z a f False\n",
1085       "xxxx 13 20 z h v False\n",
1086       "seq1 14 0 v ! y False\n",
1087       "xxxx 14 1 v f b False\n",
1088       "xxxx 14 2 v f u False\n",
1089       "xxxx 14 3 v d d False\n",
1090       "xxxx 14 4 v d w False\n",
1091       "xxxx 14 5 v g u False\n",
1092       "xxxx 14 6 v g w False\n",
1093       "xxxx 14 7 v d u False\n",
1094       "xxxx 14 8 v h g False\n",
1095       "xxxx 14 9 v b c False\n",
1096       "xxxx 14 10 v d x False\n",
1097       "xxxx 14 11 v g z False\n",
1098       "xxxx 14 12 v c b False\n",
1099       "xxxx 14 13 v b a False\n",
1100       "seq1 14 14 v a v True\n",
1101       "seq2 14 15 v a a True\n",
1102       "xxxx 14 16 v f x False\n",
1103       "xxxx 14 17 v f f False\n",
1104       "xxxx 14 18 v c f False\n",
1105       "xxxx 14 19 v a v False\n",
1106       "xxxx 14 20 v h c False\n",
1107       "seq1 15 0 x ! b False\n",
1108       "xxxx 15 1 x f u False\n",
1109       "xxxx 15 2 x f d False\n",
1110       "xxxx 15 3 x d w False\n",
1111       "xxxx 15 4 x d u False\n",
1112       "xxxx 15 5 x g w False\n",
1113       "xxxx 15 6 x g u False\n",
1114       "xxxx 15 7 x d g False\n",
1115       "xxxx 15 8 x h c False\n",
1116       "xxxx 15 9 x b x False\n",
1117       "xxxx 15 10 x d z False\n",
1118       "xxxx 15 11 x g b False\n",
1119       "xxxx 15 12 x c a False\n",
1120       "xxxx 15 13 x b v False\n",
1121       "xxxx 15 14 x a a False\n",
1122       "seq1 15 15 x a x True\n",
1123       "seq2 15 16 x f f True\n",
1124       "seq2 15 17 x f f True\n",
1125       "xxxx 15 18 x c v False\n",
1126       "xxxx 15 19 x a c False\n",
1127       "xxxx 15 20 x h a False\n",
1128       "seq1 16 0 v ! u False\n",
1129       "xxxx 16 1 v f d False\n",
1130       "xxxx 16 2 v f w False\n",
1131       "xxxx 16 3 v d u False\n",
1132       "xxxx 16 4 v d w False\n",
1133       "xxxx 16 5 v g u False\n",
1134       "xxxx 16 6 v g g False\n",
1135       "xxxx 16 7 v d c False\n",
1136       "xxxx 16 8 v h x False\n",
1137       "xxxx 16 9 v b z False\n",
1138       "xxxx 16 10 v d b False\n",
1139       "xxxx 16 11 v g a False\n",
1140       "xxxx 16 12 v c v False\n",
1141       "xxxx 16 13 v b a False\n",
1142       "xxxx 16 14 v a x False\n",
1143       "xxxx 16 15 v a f False\n",
1144       "xxxx 16 16 v f f False\n",
1145       "seq1 16 17 v f v True\n",
1146       "seq2 16 18 v c c True\n",
1147       "seq2 16 19 v a a True\n",
1148       "seq2 16 20 v h h True\n",
1149       "seq1 17 0 v ! d False\n",
1150       "xxxx 17 1 v f w False\n",
1151       "xxxx 17 2 v f u False\n",
1152       "xxxx 17 3 v d w False\n",
1153       "xxxx 17 4 v d u False\n",
1154       "xxxx 17 5 v g g False\n",
1155       "xxxx 17 6 v g c False\n",
1156       "xxxx 17 7 v d x False\n",
1157       "xxxx 17 8 v h z False\n",
1158       "xxxx 17 9 v b b False\n",
1159       "xxxx 17 10 v d a False\n",
1160       "xxxx 17 11 v g v False\n",
1161       "xxxx 17 12 v c a False\n",
1162       "xxxx 17 13 v b x False\n",
1163       "xxxx 17 14 v a f False\n",
1164       "xxxx 17 15 v a f False\n",
1165       "xxxx 17 16 v f v False\n",
1166       "xxxx 17 17 v f c False\n",
1167       "xxxx 17 18 v c a False\n",
1168       "xxxx 17 19 v a h False\n",
1169       "seq1 17 20 v h v True\n",
1170       "seq1 18 0 z ! w False\n",
1171       "xxxx 18 1 z f u False\n",
1172       "xxxx 18 2 z f w False\n",
1173       "xxxx 18 3 z d u False\n",
1174       "xxxx 18 4 z d g False\n",
1175       "xxxx 18 5 z g c False\n",
1176       "xxxx 18 6 z g x False\n",
1177       "xxxx 18 7 z d z False\n",
1178       "xxxx 18 8 z h b False\n",
1179       "xxxx 18 9 z b a False\n",
1180       "xxxx 18 10 z d v False\n",
1181       "xxxx 18 11 z g a False\n",
1182       "xxxx 18 12 z c x False\n",
1183       "xxxx 18 13 z b f False\n",
1184       "xxxx 18 14 z a f False\n",
1185       "xxxx 18 15 z a v False\n",
1186       "xxxx 18 16 z f c False\n",
1187       "xxxx 18 17 z f a False\n",
1188       "xxxx 18 18 z c h False\n",
1189       "xxxx 18 19 z a v False\n",
1190       "seq1 18 20 z h z True\n",
1191       "seq1 19 0 x ! u False\n",
1192       "xxxx 19 1 x f w False\n",
1193       "xxxx 19 2 x f u False\n",
1194       "xxxx 19 3 x d g False\n",
1195       "xxxx 19 4 x d c False\n",
1196       "xxxx 19 5 x g x False\n",
1197       "xxxx 19 6 x g z False\n",
1198       "xxxx 19 7 x d b False\n",
1199       "xxxx 19 8 x h a False\n",
1200       "xxxx 19 9 x b v False\n",
1201       "xxxx 19 10 x d a False\n",
1202       "xxxx 19 11 x g x False\n",
1203       "xxxx 19 12 x c f False\n",
1204       "xxxx 19 13 x b f False\n",
1205       "xxxx 19 14 x a v False\n",
1206       "xxxx 19 15 x a c False\n",
1207       "xxxx 19 16 x f a False\n",
1208       "xxxx 19 17 x f h False\n",
1209       "xxxx 19 18 x c v False\n",
1210       "xxxx 19 19 x a z False\n",
1211       "seq1 19 20 x h x True\n",
1212       "seq1 20 0 y ! w False\n",
1213       "xxxx 20 1 y f u False\n",
1214       "xxxx 20 2 y f g False\n",
1215       "xxxx 20 3 y d c False\n",
1216       "xxxx 20 4 y d x False\n",
1217       "xxxx 20 5 y g z False\n",
1218       "xxxx 20 6 y g b False\n",
1219       "xxxx 20 7 y d a False\n",
1220       "xxxx 20 8 y h v False\n",
1221       "xxxx 20 9 y b a False\n",
1222       "xxxx 20 10 y d x False\n",
1223       "xxxx 20 11 y g f False\n",
1224       "xxxx 20 12 y c f False\n",
1225       "xxxx 20 13 y b v False\n",
1226       "xxxx 20 14 y a c False\n",
1227       "xxxx 20 15 y a a False\n",
1228       "xxxx 20 16 y f h False\n",
1229       "xxxx 20 17 y f v False\n",
1230       "xxxx 20 18 y c z False\n",
1231       "xxxx 20 19 y a x False\n",
1232       "seq1 20 20 y h y True\n",
1233       "T T T T . . . . . . . . . . . . . . . . .\n",
1234       ". . . T T T T . . . . . . . . . . . . . .\n",
1235       ". . . . . . T T . . . . . . . . . . . . .\n",
1236       ". . . . . . . T T . . . . . . . . . . . .\n",
1237       ". . . . . . . . T . . . . . . . . . . . .\n",
1238       ". . . . . . . . T . . . . . . . . . . . .\n",
1239       ". . . . . . . . T T . . . . . . . . . . .\n",
1240       ". . . . . . . . . T T . . . . . . . . . .\n",
1241       ". . . . . . . . . . T . . . . . . . . . .\n",
1242       ". . . . . . . . . . T . . . . . . . . . .\n",
1243       ". . . . . . . . . . T . . . . . . . . . .\n",
1244       ". . . . . . . . . . T T T . . . . . . . .\n",
1245       ". . . . . . . . . . . . T . . . . . . . .\n",
1246       ". . . . . . . . . . . . T T T . . . . . .\n",
1247       ". . . . . . . . . . . . . . T T . . . . .\n",
1248       ". . . . . . . . . . . . . . . T T T . . .\n",
1249       ". . . . . . . . . . . . . . . . . T T T T\n",
1250       ". . . . . . . . . . . . . . . . . . . . T\n",
1251       ". . . . . . . . . . . . . . . . . . . . T\n",
1252       ". . . . . . . . . . . . . . . . . . . . T\n",
1253       ". . . . . . . . . . . . . . . . . . . . T\n"
1254      ]
1255     }
1256    ],
1257    "source": [
1258     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True, debug=True)\n",
1259     "print(show_table(t))"
1260    ]
1261   },
1262   {
1263    "cell_type": "code",
1264    "execution_count": 23,
1265    "metadata": {},
1266    "outputs": [
1267     {
1268      "data": {
1269       "text/plain": [
1270        "'ffdVdggVdZhWZYbUdWUWUgcXZbaVaXffVcahVZXY'"
1271       ]
1272      },
1273      "execution_count": 23,
1274      "metadata": {},
1275      "output_type": "execute_result"
1276     }
1277    ],
1278    "source": [
1279     "show_backtrace(bp)"
1280    ]
1281   },
1282   {
1283    "cell_type": "code",
1284    "execution_count": 24,
1285    "metadata": {},
1286    "outputs": [
1287     {
1288      "name": "stdout",
1289      "output_type": "stream",
1290      "text": [
1291       "T T T T . . . . . . . . . . . . . . . . .\n",
1292       ". . . T T T T . . . . . . . . . . . . . .\n",
1293       ". . . . . . T T . . . . . . . . . . . . .\n",
1294       ". . . . . . . T T . . . . . . . . . . . .\n",
1295       ". . . . . . . . T . . . . . . . . . . . .\n",
1296       ". . . . . . . . T . . . . . . . . . . . .\n",
1297       ". . . . . . . . T T . . . . . . . . . . .\n",
1298       ". . . . . . . . . T T . . . . . . . . . .\n",
1299       ". . . . . . . . . . T . . . . . . . . . .\n",
1300       ". . . . . . . . . . T . . . . . . . . . .\n",
1301       ". . . . . . . . . . T . . . . . . . . . .\n",
1302       ". . . . . . . . . . T T T . . . . . . . .\n",
1303       ". . . . . . . . . . . . T . . . . . . . .\n",
1304       ". . . . . . . . . . . . T T T . . . . . .\n",
1305       ". . . . . . . . . . . . . . T T . . . . .\n",
1306       ". . . . . . . . . . . . . . . T T T . . .\n",
1307       ". . . . . . . . . . . . . . . . . T T T T\n",
1308       ". . . . . . . . . . . . . . . . . . . . T\n",
1309       ". . . . . . . . . . . . . . . . . . . . T\n",
1310       ". . . . . . . . . . . . . . . . . . . . T\n",
1311       ". . . . . . . . . . . . . . . . . . . . T\n",
1312       "ffdVdggVdZhWZYbUdWUWUgcXZbaVaXffVcahVZXY\n"
1313      ]
1314     },
1315     {
1316      "data": {
1317       "text/plain": [
1318        "True"
1319       ]
1320      },
1321      "execution_count": 24,
1322      "metadata": {},
1323      "output_type": "execute_result"
1324     }
1325    ],
1326    "source": [
1327     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1328     "print(show_table(t))\n",
1329     "print(show_backtrace(bp))\n",
1330     "v"
1331    ]
1332   },
1333   {
1334    "cell_type": "code",
1335    "execution_count": 25,
1336    "metadata": {},
1337    "outputs": [
1338     {
1339      "data": {
1340       "text/plain": [
1341        "('fcbhdfdbgebhgbgbcbhceagfbfhedffbbbehbfbbgedbacecdg',\n",
1342        " 'dfbgbebeggbcdahfbddbfcgcehhffhgfhdfffbeedgcghhhaga',\n",
1343        " 'dfbfcbghbedbfedbggbcdgeahfbhbdgbgbcdbbfcghcehceahgfbffhgfhfedhdfffffbebbbedehgbfcbghbghehdbaacgecadg',\n",
1344        " 100)"
1345       ]
1346      },
1347      "execution_count": 25,
1348      "metadata": {},
1349      "output_type": "execute_result"
1350     }
1351    ],
1352    "source": [
1353     "s1 = make_string(50)\n",
1354     "s2 = make_string(50)\n",
1355     "il = interleave(s1, s2)\n",
1356     "s1, s2, il, len(il)"
1357    ]
1358   },
1359   {
1360    "cell_type": "code",
1361    "execution_count": 26,
1362    "metadata": {},
1363    "outputs": [
1364     {
1365      "name": "stdout",
1366      "output_type": "stream",
1367      "text": [
1368       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1369       "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1370       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1371       "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1372       ". . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1373       ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1374       ". . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1375       ". . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1376       ". . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1377       ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1378       ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1379       ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1380       ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1381       ". . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1382       ". . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1383       ". . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1384       ". . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1385       ". . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1386       ". . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1387       ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1388       ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1389       ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1390       ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1391       ". . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1392       ". . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1393       ". . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1394       ". . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1395       ". . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1396       ". . . . . . . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1397       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1398       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1399       ". . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1400       ". . . . . . . . . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . .\n",
1401       ". . . . . . . . . . . . . . . . . . . . . . . . . T T . . T . . . . . . . . . . . . . . . . . . . . .\n",
1402       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . .\n",
1403       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . .\n",
1404       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . .\n",
1405       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n",
1406       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
1407       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . .\n",
1408       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1409       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . .\n",
1410       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . .\n",
1411       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . .\n",
1412       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
1413       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . .\n",
1414       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . .\n",
1415       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . .\n",
1416       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . .\n",
1417       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . .\n",
1418       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T\n",
1419       "DFBfcbGhBEdBfEdbGGBCDgeAHFbhBDgbgbcDbBFCGhCEHceaHgfbFFHGfhFedHDffFFFBEbbbEDehGbfCbGHbgHeHdbaAcGecAdg\n"
1420      ]
1421     },
1422     {
1423      "data": {
1424       "text/plain": [
1425        "True"
1426       ]
1427      },
1428      "execution_count": 26,
1429      "metadata": {},
1430      "output_type": "execute_result"
1431     }
1432    ],
1433    "source": [
1434     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1435     "print(show_table(t))\n",
1436     "print(show_backtrace(bp))\n",
1437     "v"
1438    ]
1439   },
1440   {
1441    "cell_type": "code",
1442    "execution_count": 27,
1443    "metadata": {},
1444    "outputs": [
1445     {
1446      "name": "stdout",
1447      "output_type": "stream",
1448      "text": [
1449       "1000 loops, best of 3: 1.29 ms per loop\n"
1450      ]
1451     }
1452    ],
1453    "source": [
1454     "%%timeit\n",
1455     "is_interleave(s2, s1, il)"
1456    ]
1457   },
1458   {
1459    "cell_type": "code",
1460    "execution_count": 28,
1461    "metadata": {},
1462    "outputs": [
1463     {
1464      "name": "stdout",
1465      "output_type": "stream",
1466      "text": [
1467       "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1468       ". T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1469       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1470       ". . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1471       ". . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1472       ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1473       ". . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1474       ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1475       ". . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1476       ". . . . . . . . T T . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1477       ". . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1478       ". . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1479       ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1480       ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1481       ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1482       ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1483       ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1484       ". . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1485       ". . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1486       ". . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1487       ". . . . . . . . . . . . . . . . . . . . . . . T . . T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1488       ". . . . . . . . . . . . . . . . . . . . . . . T . . T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1489       ". . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1490       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . .\n",
1491       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1492       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T . . . . . . . . . . . . . . . . .\n",
1493       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . T . T . . . . . . . . . . . . . . . . .\n",
1494       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . T T . . . . . . . . . . . . . . . . . .\n",
1495       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . .\n",
1496       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . .\n",
1497       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . .\n",
1498       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . .\n",
1499       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . .\n",
1500       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
1501       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . .\n",
1502       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . .\n",
1503       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . .\n",
1504       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
1505       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
1506       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . .\n",
1507       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . .\n",
1508       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . .\n",
1509       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . .\n",
1510       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . .\n",
1511       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . .\n",
1512       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . .\n",
1513       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T .\n",
1514       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T .\n",
1515       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T\n",
1516       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1517       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1518       "dfbFCBgHbeDbFeDBggbcdGEahfBHbdGBGBCdbBfcgHcehCEAhGFBffhgFHfEDhdfffFFbeBBBedEHgBFcBghBGhEhDBaACgECaDG\n"
1519      ]
1520     },
1521     {
1522      "data": {
1523       "text/plain": [
1524        "True"
1525       ]
1526      },
1527      "execution_count": 28,
1528      "metadata": {},
1529      "output_type": "execute_result"
1530     }
1531    ],
1532    "source": [
1533     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1534     "print(show_table(t))\n",
1535     "print(show_backtrace(bp))\n",
1536     "v"
1537    ]
1538   },
1539   {
1540    "cell_type": "code",
1541    "execution_count": 29,
1542    "metadata": {},
1543    "outputs": [
1544     {
1545      "data": {
1546       "text/plain": [
1547        "True"
1548       ]
1549      },
1550      "execution_count": 29,
1551      "metadata": {},
1552      "output_type": "execute_result"
1553     }
1554    ],
1555    "source": [
1556     "show_backtrace(bp).lower() == il"
1557    ]
1558   },
1559   {
1560    "cell_type": "code",
1561    "execution_count": 30,
1562    "metadata": {},
1563    "outputs": [
1564     {
1565      "data": {
1566       "text/plain": [
1567        "('dbgdadhhhhacehhbdfdcffdghcahbbceegebbfhabafecadhhe', False, False)"
1568       ]
1569      },
1570      "execution_count": 30,
1571      "metadata": {},
1572      "output_type": "execute_result"
1573     }
1574    ],
1575    "source": [
1576     "s3 = make_string(50)\n",
1577     "s3, is_interleave(s1, s3, il), is_interleave(s2, s3, il)"
1578    ]
1579   },
1580   {
1581    "cell_type": "code",
1582    "execution_count": 31,
1583    "metadata": {},
1584    "outputs": [
1585     {
1586      "name": "stdout",
1587      "output_type": "stream",
1588      "text": [
1589       "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1590       ". T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1591       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1592       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1593       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1594       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1595       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1596       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1597       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1598       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1599       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1600       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1601       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1602       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1603       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1604       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1605       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1606       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1607       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1608       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1609       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1610       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1611       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1612       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1613       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1614       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1615       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1616       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1617       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1618       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1619       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1620       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1621       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1622       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1623       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1624       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1625       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1626       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1627       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1628       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1629       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1630       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1631       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1632       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1633       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1634       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1635       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1636       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1637       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1638       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1639       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1640       "dFb\n"
1641      ]
1642     },
1643     {
1644      "data": {
1645       "text/plain": [
1646        "False"
1647       ]
1648      },
1649      "execution_count": 31,
1650      "metadata": {},
1651      "output_type": "execute_result"
1652     }
1653    ],
1654    "source": [
1655     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1656     "print(show_table(t))\n",
1657     "print(show_backtrace(bp))\n",
1658     "v"
1659    ]
1660   },
1661   {
1662    "cell_type": "code",
1663    "execution_count": 32,
1664    "metadata": {
1665     "collapsed": true
1666    },
1667    "outputs": [],
1668    "source": [
1669     "def is_interleave_recursive(s1, s2, s3):\n",
1670     "    if not s1:\n",
1671     "        return s2 == s3\n",
1672     "    elif not s2:\n",
1673     "        return s1 == s3\n",
1674     "    else:\n",
1675     "        if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
1676     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n",
1677     "        elif s1[-1] == s3[-1]:\n",
1678     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
1679     "        elif s2[-1] == s3[-1]:\n",
1680     "            return is_interleave(s1, s2[:-1], s3[:-1])\n",
1681     "        else:\n",
1682     "            return False"
1683    ]
1684   },
1685   {
1686    "cell_type": "code",
1687    "execution_count": 33,
1688    "metadata": {
1689     "collapsed": true
1690    },
1691    "outputs": [],
1692    "source": [
1693     "import uuid"
1694    ]
1695   },
1696   {
1697    "cell_type": "code",
1698    "execution_count": null,
1699    "metadata": {
1700     "collapsed": true
1701    },
1702    "outputs": [],
1703    "source": [
1704     "def is_subseq_recursive_dot(s1, s2):\n",
1705     "    node_id = uuid.uuid4().hex\n",
1706     "    node_string = 'n{} [label=\"{}\\\\n{}\"];'.format(node_id, s1, s2)\n",
1707     "#     print(s1, s2, node_string)\n",
1708     "    if not s1:\n",
1709     "        return node_id, ['n{} [label=\"-\\\\n{}\\\\nTrue\"];'.format(node_id, s2)]\n",
1710     "    elif len(s1) > len(s2):\n",
1711     "        return node_id, ['n{} [label=\"{}\\\\n{}\\\\nFalse\"];'.format(node_id, s1, s2)]\n",
1712     "    else:\n",
1713     "        if s1[-1] == s2[-1]:\n",
1714     "            node1_id, node1_graph = is_subseq_recursive_dot(s1[:-1], s2[:-1])\n",
1715     "            node2_id, node2_graph = is_subseq_recursive_dot(s1, s2[:-1])\n",
1716     "            return node_id, ([node_string, \n",
1717     "                    'n{} -> n{};'.format(node_id, node1_id), \n",
1718     "                    'n{} -> n{};'.format(node_id, node2_id)] + \n",
1719     "                    node1_graph + node2_graph)\n",
1720     "        else:\n",
1721     "            node1_id, node1_graph = is_subseq_recursive_dot(s1, s2[:-1])\n",
1722     "            return node_id, ([node_string, \n",
1723     "                    'n{} -> n{};'.format(node_id, node1_id)] + \n",
1724     "                    node1_graph)"
1725    ]
1726   },
1727   {
1728    "cell_type": "code",
1729    "execution_count": 69,
1730    "metadata": {
1731     "collapsed": true
1732    },
1733    "outputs": [],
1734    "source": [
1735     "def is_interleave_recursive_dot(s1, s2, s3):\n",
1736     "    \n",
1737     "#     print(s1, s2, s3)\n",
1738     "    node_id = uuid.uuid4().hex\n",
1739     "    node_string = 'n{} [label=\"{}\\\\n{}\\\\n{}\"];'.format(node_id, s1, s2, s3)\n",
1740     "\n",
1741     "    if not s1:\n",
1742     "        if s2 == s3:\n",
1743     "            return node_id, ['n{} [label=\"-\\\\n{}\\\\n{}\\\\nTrue\"];'.format(node_id, s2, s3)]\n",
1744     "        else:\n",
1745     "            return node_id, ['n{} [label=\"-\\\\n{}\\\\n{}\\\\nFalse\"];'.format(node_id, s2, s3)]\n",
1746     "    elif not s2:\n",
1747     "        if s1 == s3:\n",
1748     "            return node_id, ['n{} [label=\"{}\\\\n-\\\\n{}\\\\nTrue\"];'.format(node_id, s1, s3)]\n",
1749     "        else:\n",
1750     "            return node_id, ['n{} [label=\"{}\\\\n-\\\\n{}\\\\nFalse\"];'.format(node_id, s1, s3)]\n",
1751     "    else:\n",
1752     "        if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
1753     "            node1_id, node1_graph = is_interleave_recursive_dot(s1[:-1], s2, s3[:-1])\n",
1754     "            node2_id, node2_graph = is_interleave_recursive_dot(s1, s2[:-1], s3[:-1])\n",
1755     "            return node_id, ([node_string, \n",
1756     "                    'n{} -> n{};'.format(node_id, node1_id), \n",
1757     "                    'n{} -> n{};'.format(node_id, node2_id)] + \n",
1758     "                    node1_graph + node2_graph)\n",
1759     "        elif s1[-1] == s3[-1]:\n",
1760     "            node1_id, node1_graph = is_interleave_recursive_dot(s1[:-1], s2, s3[:-1])\n",
1761     "            return node_id, ([node_string, \n",
1762     "                    'n{} -> n{};'.format(node_id, node1_id)] + \n",
1763     "                    node1_graph)\n",
1764     "        elif s2[-1] == s3[-1]:\n",
1765     "            node1_id, node1_graph = is_interleave_recursive_dot(s1, s2[:-1], s3[:-1])\n",
1766     "            return node_id, ([node_string, \n",
1767     "                    'n{} -> n{};'.format(node_id, node1_id)] + \n",
1768     "                    node1_graph)\n",
1769     "        else:\n",
1770     "            return node_id, ['n{} [label=\"{}\\\\n{}\\\\n{}\\\\nFalse\"];'.format(node_id, s1, s2, s3)]"
1771    ]
1772   },
1773   {
1774    "cell_type": "code",
1775    "execution_count": 61,
1776    "metadata": {
1777     "collapsed": true
1778    },
1779    "outputs": [],
1780    "source": [
1781     "s1 = \"aabcc\"\n",
1782     "s2 = \"dbbca\"\n",
1783     "\n",
1784     "s3t = \"aadbbcbcac\"\n",
1785     "s3f = \"aadbbbaccc\""
1786    ]
1787   },
1788   {
1789    "cell_type": "code",
1790    "execution_count": 70,
1791    "metadata": {},
1792    "outputs": [
1793     {
1794      "name": "stdout",
1795      "output_type": "stream",
1796      "text": [
1797       "n825af3fb1bf441a3b97d8fbfcdce6f3d [label=\"aabcc\\ndbbca\\naadbbcbcac\"];\n",
1798       "n825af3fb1bf441a3b97d8fbfcdce6f3d -> n944a00ca9b134f3c98aeef34526ff17d;\n",
1799       "n944a00ca9b134f3c98aeef34526ff17d [label=\"aabc\\ndbbca\\naadbbcbca\"];\n",
1800       "n944a00ca9b134f3c98aeef34526ff17d -> n1586862dcfb74b1a9e9f964b7de102ef;\n",
1801       "n1586862dcfb74b1a9e9f964b7de102ef [label=\"aabc\\ndbbc\\naadbbcbc\"];\n",
1802       "n1586862dcfb74b1a9e9f964b7de102ef -> nf59278631d8047e7b0cca670e412297b;\n",
1803       "n1586862dcfb74b1a9e9f964b7de102ef -> nd83e9c32d1fa43bab45dc21d46830924;\n",
1804       "nf59278631d8047e7b0cca670e412297b [label=\"aab\\ndbbc\\naadbbcb\"];\n",
1805       "nf59278631d8047e7b0cca670e412297b -> nb0424588e9354d2aa61b587a7edfb7f6;\n",
1806       "nb0424588e9354d2aa61b587a7edfb7f6 [label=\"aa\\ndbbc\\naadbbc\"];\n",
1807       "nb0424588e9354d2aa61b587a7edfb7f6 -> nb73d85cfb09e43d692de22a49de48b35;\n",
1808       "nb73d85cfb09e43d692de22a49de48b35 [label=\"aa\\ndbb\\naadbb\"];\n",
1809       "nb73d85cfb09e43d692de22a49de48b35 -> n9e34f866ae1746d797cebd4e1fc73af9;\n",
1810       "n9e34f866ae1746d797cebd4e1fc73af9 [label=\"aa\\ndb\\naadb\"];\n",
1811       "n9e34f866ae1746d797cebd4e1fc73af9 -> n5c7027bfea9f494894cea01fd5e25387;\n",
1812       "n5c7027bfea9f494894cea01fd5e25387 [label=\"aa\\nd\\naad\"];\n",
1813       "n5c7027bfea9f494894cea01fd5e25387 -> n650da0feb2624011a20e209bada2445c;\n",
1814       "n650da0feb2624011a20e209bada2445c [label=\"aa\\n-\\naa\\nTrue\"];\n",
1815       "nd83e9c32d1fa43bab45dc21d46830924 [label=\"aabc\\ndbb\\naadbbcb\"];\n",
1816       "nd83e9c32d1fa43bab45dc21d46830924 -> n1c4772b660f24d6da9194d16be602b3a;\n",
1817       "n1c4772b660f24d6da9194d16be602b3a [label=\"aabc\\ndb\\naadbbc\"];\n",
1818       "n1c4772b660f24d6da9194d16be602b3a -> n0393745322e447c79515cffb4afc4d5b;\n",
1819       "n0393745322e447c79515cffb4afc4d5b [label=\"aab\\ndb\\naadbb\"];\n",
1820       "n0393745322e447c79515cffb4afc4d5b -> na9ae42f3b7dd415886e78bb960b94184;\n",
1821       "n0393745322e447c79515cffb4afc4d5b -> nccaf23a4e311415cbe42bedd8a3727c2;\n",
1822       "na9ae42f3b7dd415886e78bb960b94184 [label=\"aa\\ndb\\naadb\"];\n",
1823       "na9ae42f3b7dd415886e78bb960b94184 -> nab2d4f76a75c4c6686166212cad4b4a3;\n",
1824       "nab2d4f76a75c4c6686166212cad4b4a3 [label=\"aa\\nd\\naad\"];\n",
1825       "nab2d4f76a75c4c6686166212cad4b4a3 -> nee8a56cc920943e0a2593a8ee863c53c;\n",
1826       "nee8a56cc920943e0a2593a8ee863c53c [label=\"aa\\n-\\naa\\nTrue\"];\n",
1827       "nccaf23a4e311415cbe42bedd8a3727c2 [label=\"aab\\nd\\naadb\"];\n",
1828       "nccaf23a4e311415cbe42bedd8a3727c2 -> ne1d3cf2b04074c10986fdefb464e5da8;\n",
1829       "ne1d3cf2b04074c10986fdefb464e5da8 [label=\"aa\\nd\\naad\"];\n",
1830       "ne1d3cf2b04074c10986fdefb464e5da8 -> n9091b74bc8a64b91a9e75aef6b016a64;\n",
1831       "n9091b74bc8a64b91a9e75aef6b016a64 [label=\"aa\\n-\\naa\\nTrue\"];\n"
1832      ]
1833     }
1834    ],
1835    "source": [
1836     "root, graph = is_interleave_recursive_dot(s1, s2, s3t)\n",
1837     "print('\\n'.join(graph))"
1838    ]
1839   },
1840   {
1841    "cell_type": "code",
1842    "execution_count": 71,
1843    "metadata": {},
1844    "outputs": [
1845     {
1846      "name": "stdout",
1847      "output_type": "stream",
1848      "text": [
1849       "n894a2781e978478699af2875308ec4ad [label=\"aaa\\naaa\\naaaaaa\"];\n",
1850       "n894a2781e978478699af2875308ec4ad -> n863e03f8030547bf9f4e7a4815c4e027;\n",
1851       "n894a2781e978478699af2875308ec4ad -> n4c492e6eb94741d2b11567b1b4c729fa;\n",
1852       "n863e03f8030547bf9f4e7a4815c4e027 [label=\"aa\\naaa\\naaaaa\"];\n",
1853       "n863e03f8030547bf9f4e7a4815c4e027 -> n8f044087a7324ef69d5cf2ae120c0902;\n",
1854       "n863e03f8030547bf9f4e7a4815c4e027 -> n5510c6a96018480ba0fc2315d34a69e6;\n",
1855       "n8f044087a7324ef69d5cf2ae120c0902 [label=\"a\\naaa\\naaaa\"];\n",
1856       "n8f044087a7324ef69d5cf2ae120c0902 -> n6f3153ef68384ebbbe5860a48c774d55;\n",
1857       "n8f044087a7324ef69d5cf2ae120c0902 -> n4d068ce52cf248adb3b537805a233dda;\n",
1858       "n6f3153ef68384ebbbe5860a48c774d55 [label=\"-\\naaa\\naaa\\nTrue\"];\n",
1859       "n4d068ce52cf248adb3b537805a233dda [label=\"a\\naa\\naaa\"];\n",
1860       "n4d068ce52cf248adb3b537805a233dda -> nb85aee31625f4998b596d9b6ea3b77fd;\n",
1861       "n4d068ce52cf248adb3b537805a233dda -> nec2837ce384246ffb06e3d4090adfb37;\n",
1862       "nb85aee31625f4998b596d9b6ea3b77fd [label=\"-\\naa\\naa\\nTrue\"];\n",
1863       "nec2837ce384246ffb06e3d4090adfb37 [label=\"a\\na\\naa\"];\n",
1864       "nec2837ce384246ffb06e3d4090adfb37 -> n9c395901af2d4e67a7e5a370f759bce6;\n",
1865       "nec2837ce384246ffb06e3d4090adfb37 -> nff84b0c784744901afb3ac8a5aef3c23;\n",
1866       "n9c395901af2d4e67a7e5a370f759bce6 [label=\"-\\na\\na\\nTrue\"];\n",
1867       "nff84b0c784744901afb3ac8a5aef3c23 [label=\"a\\n-\\na\\nTrue\"];\n",
1868       "n5510c6a96018480ba0fc2315d34a69e6 [label=\"aa\\naa\\naaaa\"];\n",
1869       "n5510c6a96018480ba0fc2315d34a69e6 -> n5eaaabd1caef4c3f8f6607a8bb254906;\n",
1870       "n5510c6a96018480ba0fc2315d34a69e6 -> n6041081af67d4f57968572aa2051d1bc;\n",
1871       "n5eaaabd1caef4c3f8f6607a8bb254906 [label=\"a\\naa\\naaa\"];\n",
1872       "n5eaaabd1caef4c3f8f6607a8bb254906 -> n6dd23a9ed026429fb57cbf94e6283364;\n",
1873       "n5eaaabd1caef4c3f8f6607a8bb254906 -> n3042bda75e7c4d8f8a9ccc464f0ba724;\n",
1874       "n6dd23a9ed026429fb57cbf94e6283364 [label=\"-\\naa\\naa\\nTrue\"];\n",
1875       "n3042bda75e7c4d8f8a9ccc464f0ba724 [label=\"a\\na\\naa\"];\n",
1876       "n3042bda75e7c4d8f8a9ccc464f0ba724 -> n5e702eeee87042deb3157b6663b1f07a;\n",
1877       "n3042bda75e7c4d8f8a9ccc464f0ba724 -> n37928d6516f942008c5e89b5c37098ee;\n",
1878       "n5e702eeee87042deb3157b6663b1f07a [label=\"-\\na\\na\\nTrue\"];\n",
1879       "n37928d6516f942008c5e89b5c37098ee [label=\"a\\n-\\na\\nTrue\"];\n",
1880       "n6041081af67d4f57968572aa2051d1bc [label=\"aa\\na\\naaa\"];\n",
1881       "n6041081af67d4f57968572aa2051d1bc -> nbb96e07d3c89450cb92ad725f6fc4845;\n",
1882       "n6041081af67d4f57968572aa2051d1bc -> n0dbe764d7e4a429298f2d3583e8c84b1;\n",
1883       "nbb96e07d3c89450cb92ad725f6fc4845 [label=\"a\\na\\naa\"];\n",
1884       "nbb96e07d3c89450cb92ad725f6fc4845 -> nbe5a7be2ec824370a293e7aa8f3a5467;\n",
1885       "nbb96e07d3c89450cb92ad725f6fc4845 -> ndc15a7d84b734bb793055e4712a82d5c;\n",
1886       "nbe5a7be2ec824370a293e7aa8f3a5467 [label=\"-\\na\\na\\nTrue\"];\n",
1887       "ndc15a7d84b734bb793055e4712a82d5c [label=\"a\\n-\\na\\nTrue\"];\n",
1888       "n0dbe764d7e4a429298f2d3583e8c84b1 [label=\"aa\\n-\\naa\\nTrue\"];\n",
1889       "n4c492e6eb94741d2b11567b1b4c729fa [label=\"aaa\\naa\\naaaaa\"];\n",
1890       "n4c492e6eb94741d2b11567b1b4c729fa -> n0e78dd2900a34a7297cc0ea2bb27e30c;\n",
1891       "n4c492e6eb94741d2b11567b1b4c729fa -> nc18fe2c53e9e4209a9af9c0678465b1f;\n",
1892       "n0e78dd2900a34a7297cc0ea2bb27e30c [label=\"aa\\naa\\naaaa\"];\n",
1893       "n0e78dd2900a34a7297cc0ea2bb27e30c -> n1b98c16a65994faaa980d9c530383c77;\n",
1894       "n0e78dd2900a34a7297cc0ea2bb27e30c -> n33dbe313802045f8895d0e904d588881;\n",
1895       "n1b98c16a65994faaa980d9c530383c77 [label=\"a\\naa\\naaa\"];\n",
1896       "n1b98c16a65994faaa980d9c530383c77 -> n5e7c6dff46ff49f7903eb543c02fa22b;\n",
1897       "n1b98c16a65994faaa980d9c530383c77 -> n33391a1fab3849cf9823ccc7396aa7d4;\n",
1898       "n5e7c6dff46ff49f7903eb543c02fa22b [label=\"-\\naa\\naa\\nTrue\"];\n",
1899       "n33391a1fab3849cf9823ccc7396aa7d4 [label=\"a\\na\\naa\"];\n",
1900       "n33391a1fab3849cf9823ccc7396aa7d4 -> n13b4732016804c3986853f6d2fe4a28b;\n",
1901       "n33391a1fab3849cf9823ccc7396aa7d4 -> n767be985e5a5469da7cfeea0272705b3;\n",
1902       "n13b4732016804c3986853f6d2fe4a28b [label=\"-\\na\\na\\nTrue\"];\n",
1903       "n767be985e5a5469da7cfeea0272705b3 [label=\"a\\n-\\na\\nTrue\"];\n",
1904       "n33dbe313802045f8895d0e904d588881 [label=\"aa\\na\\naaa\"];\n",
1905       "n33dbe313802045f8895d0e904d588881 -> nf59143762fc643f0bd58507b5097b837;\n",
1906       "n33dbe313802045f8895d0e904d588881 -> n30d968450bf147b68a8d7df49177722c;\n",
1907       "nf59143762fc643f0bd58507b5097b837 [label=\"a\\na\\naa\"];\n",
1908       "nf59143762fc643f0bd58507b5097b837 -> ncd2168bdc52c459d821427219fb885d1;\n",
1909       "nf59143762fc643f0bd58507b5097b837 -> nc6011f3f746f425ab01fd89e1f17cbb4;\n",
1910       "ncd2168bdc52c459d821427219fb885d1 [label=\"-\\na\\na\\nTrue\"];\n",
1911       "nc6011f3f746f425ab01fd89e1f17cbb4 [label=\"a\\n-\\na\\nTrue\"];\n",
1912       "n30d968450bf147b68a8d7df49177722c [label=\"aa\\n-\\naa\\nTrue\"];\n",
1913       "nc18fe2c53e9e4209a9af9c0678465b1f [label=\"aaa\\na\\naaaa\"];\n",
1914       "nc18fe2c53e9e4209a9af9c0678465b1f -> n38a7aa8aab21444d8b9d50ca71871b7e;\n",
1915       "nc18fe2c53e9e4209a9af9c0678465b1f -> n1ec1cf69ce3c4798b305338648a6e46b;\n",
1916       "n38a7aa8aab21444d8b9d50ca71871b7e [label=\"aa\\na\\naaa\"];\n",
1917       "n38a7aa8aab21444d8b9d50ca71871b7e -> nad5433a86522484e85d560ac7d202b3d;\n",
1918       "n38a7aa8aab21444d8b9d50ca71871b7e -> n6bfb83c32f9e46a19e9408fc087e74ae;\n",
1919       "nad5433a86522484e85d560ac7d202b3d [label=\"a\\na\\naa\"];\n",
1920       "nad5433a86522484e85d560ac7d202b3d -> n292f0206736a40ac8f6045ac0d8a0a07;\n",
1921       "nad5433a86522484e85d560ac7d202b3d -> n07c65e03d3bd473f97579a2c63f922c7;\n",
1922       "n292f0206736a40ac8f6045ac0d8a0a07 [label=\"-\\na\\na\\nTrue\"];\n",
1923       "n07c65e03d3bd473f97579a2c63f922c7 [label=\"a\\n-\\na\\nTrue\"];\n",
1924       "n6bfb83c32f9e46a19e9408fc087e74ae [label=\"aa\\n-\\naa\\nTrue\"];\n",
1925       "n1ec1cf69ce3c4798b305338648a6e46b [label=\"aaa\\n-\\naaa\\nTrue\"];\n"
1926      ]
1927     }
1928    ],
1929    "source": [
1930     "root, graph = is_interleave_recursive_dot('aaa', 'aaa', 'aaaaaa')\n",
1931     "print('\\n'.join(graph))"
1932    ]
1933   },
1934   {
1935    "cell_type": "code",
1936    "execution_count": 35,
1937    "metadata": {
1938     "collapsed": true
1939    },
1940    "outputs": [],
1941    "source": [
1942     "s1 = make_string(500)\n",
1943     "s2 = make_string(500)\n",
1944     "s3 = make_string(500)\n",
1945     "s12 = interleave(s1, s2)\n",
1946     "s23 = interleave(s2, s3)"
1947    ]
1948   },
1949   {
1950    "cell_type": "code",
1951    "execution_count": 36,
1952    "metadata": {},
1953    "outputs": [
1954     {
1955      "data": {
1956       "text/plain": [
1957        "True"
1958       ]
1959      },
1960      "execution_count": 36,
1961      "metadata": {},
1962      "output_type": "execute_result"
1963     }
1964    ],
1965    "source": [
1966     "is_interleave_recursive(s1, s2, s12)"
1967    ]
1968   },
1969   {
1970    "cell_type": "code",
1971    "execution_count": 37,
1972    "metadata": {},
1973    "outputs": [
1974     {
1975      "data": {
1976       "text/plain": [
1977        "False"
1978       ]
1979      },
1980      "execution_count": 37,
1981      "metadata": {},
1982      "output_type": "execute_result"
1983     }
1984    ],
1985    "source": [
1986     "is_interleave_recursive(s1, s2, s23)"
1987    ]
1988   },
1989   {
1990    "cell_type": "markdown",
1991    "metadata": {},
1992    "source": [
1993     "## Example"
1994    ]
1995   },
1996   {
1997    "cell_type": "code",
1998    "execution_count": 38,
1999    "metadata": {
2000     "collapsed": true
2001    },
2002    "outputs": [],
2003    "source": [
2004     "def show_annotated_table(table, bps):\n",
2005     "    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",
2006     "        for i in sorted(set([k[0] for k in table])))"
2007    ]
2008   },
2009   {
2010    "cell_type": "code",
2011    "execution_count": 39,
2012    "metadata": {
2013     "collapsed": true
2014    },
2015    "outputs": [],
2016    "source": [
2017     "def show_backtrace_star(bps):\n",
2018     "    i = max([0] + [k[0] for k in bps])\n",
2019     "    j = max([0] + [k[1] for k in bps])\n",
2020     "    chars = ''\n",
2021     "    stars = ''\n",
2022     "    if (i, j) in bps:\n",
2023     "        while i != 0 or j != 0:\n",
2024     "            chars += bps[i, j][2]\n",
2025     "            if bps[i, j][3] == 'seq1':\n",
2026     "                stars += '*'\n",
2027     "            else:\n",
2028     "                stars += ' '\n",
2029     "            i, j = bps[i, j][0], bps[i, j][1] \n",
2030     "        return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n",
2031     "    else:\n",
2032     "        return ''"
2033    ]
2034   },
2035   {
2036    "cell_type": "code",
2037    "execution_count": 40,
2038    "metadata": {},
2039    "outputs": [
2040     {
2041      "name": "stdout",
2042      "output_type": "stream",
2043      "text": [
2044       "0: baddacaddb\n",
2045       "1: bcccacbacb\n",
2046       "2: cdcddbcccacbacbaabcc\n",
2047       "3: cdccdbadcaacbbcccaac\n",
2048       "4: bbacccdacdacadbdbacb\n",
2049       "5: cbaccbbcadadaaccaddb\n",
2050       "6: cbaccbcaac\n"
2051      ]
2052     },
2053     {
2054      "data": {
2055       "text/plain": [
2056        "['bbacccdacdacadbdbacb']"
2057       ]
2058      },
2059      "execution_count": 40,
2060      "metadata": {},
2061      "output_type": "execute_result"
2062     }
2063    ],
2064    "source": [
2065     "s1 = make_string(10, alphabet='abcd')\n",
2066     "s2 = make_string(10, alphabet='abcd')\n",
2067     "s3 = make_string(10, alphabet='abcd')\n",
2068     "s4 = make_string(10, alphabet='abcd')\n",
2069     "il = interleave(s1, s2)\n",
2070     "bs = [s3, il, interleave(s3, s4), interleave(s2, s4), interleave(s1, s3)]\n",
2071     "random.shuffle(bs)\n",
2072     "bs = [s1, s2] + bs\n",
2073     "tg = [l for l in bs if is_interleave(s1, s2, l)]\n",
2074     "print('\\n'.join(['{}: {}'.format(i, s) for i, s in enumerate(bs)]))\n",
2075     "tg"
2076    ]
2077   },
2078   {
2079    "cell_type": "code",
2080    "execution_count": 41,
2081    "metadata": {},
2082    "outputs": [
2083     {
2084      "name": "stdout",
2085      "output_type": "stream",
2086      "text": [
2087       "* b . . . . . . . . .\n",
2088       "b b . . . . . . . . .\n",
2089       ". a c c c . . . . . .\n",
2090       ". . . . d a c . . . .\n",
2091       ". . . . . . d . . . .\n",
2092       ". . . . . . a . . . .\n",
2093       ". . . . . . c . . . .\n",
2094       ". . . . . . a . . . .\n",
2095       ". . . . . . d b . . .\n",
2096       ". . . . . . . d . . .\n",
2097       ". . . . . . . b a c b\n",
2098       "bBAcccDacDACADbDBacb\n",
2099       "bbacccdacdacadbdbacb\n",
2100       " **   *  ***** **   \n"
2101      ]
2102     },
2103     {
2104      "data": {
2105       "text/plain": [
2106        "True"
2107       ]
2108      },
2109      "execution_count": 41,
2110      "metadata": {},
2111      "output_type": "execute_result"
2112     }
2113    ],
2114    "source": [
2115     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
2116     "print(show_annotated_table(t, bp))\n",
2117     "print(show_backtrace(bp))\n",
2118     "print(show_backtrace_star(bp))\n",
2119     "v"
2120    ]
2121   },
2122   {
2123    "cell_type": "code",
2124    "execution_count": 42,
2125    "metadata": {},
2126    "outputs": [
2127     {
2128      "name": "stdout",
2129      "output_type": "stream",
2130      "text": [
2131       "cbaccbbcadadaaccaddb\n",
2132       "      * ** * * *****\n"
2133      ]
2134     },
2135     {
2136      "data": {
2137       "text/plain": [
2138        "5"
2139       ]
2140      },
2141      "execution_count": 42,
2142      "metadata": {},
2143      "output_type": "execute_result"
2144     }
2145    ],
2146    "source": [
2147     "ind = [i for i, b in enumerate(bs) if is_interleave(s1, s3, b)][0]\n",
2148     "v, bp = is_interleave(s1, s3, bs[ind], return_backpointers=True)\n",
2149     "print(show_backtrace_star(bp))\n",
2150     "ind"
2151    ]
2152   },
2153   {
2154    "cell_type": "code",
2155    "execution_count": 43,
2156    "metadata": {},
2157    "outputs": [
2158     {
2159      "name": "stdout",
2160      "output_type": "stream",
2161      "text": [
2162       "* b . . . . . . . . .\n",
2163       "b b a . . . . . . . .\n",
2164       ". . c . . . . . . . .\n",
2165       ". . c . . . . . . . .\n",
2166       ". . c d . . . . . . .\n",
2167       ". . . a . . . . . . .\n",
2168       ". . . c d a c a d . .\n",
2169       ". . . . . . . . b d b\n",
2170       ". . . . . . . . . . a\n",
2171       ". . . . . . . . . . c\n",
2172       ". . . . . . . . . . b\n",
2173       "bBaCCCdACdacadBdbACB\n",
2174       "bbacccdacdacadbdbacb\n",
2175       " * *** **     *  ***\n"
2176      ]
2177     },
2178     {
2179      "data": {
2180       "text/plain": [
2181        "True"
2182       ]
2183      },
2184      "execution_count": 43,
2185      "metadata": {},
2186      "output_type": "execute_result"
2187     }
2188    ],
2189    "source": [
2190     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
2191     "print(show_annotated_table(t, bp))\n",
2192     "print(show_backtrace(bp))\n",
2193     "print(show_backtrace_star(bp))\n",
2194     "v"
2195    ]
2196   },
2197   {
2198    "cell_type": "code",
2199    "execution_count": 44,
2200    "metadata": {},
2201    "outputs": [
2202     {
2203      "name": "stdout",
2204      "output_type": "stream",
2205      "text": [
2206       "* . . . . . . . . . .\n",
2207       "b . . . . . . . . . .\n",
2208       ". . . . . . . . . . .\n",
2209       ". . . . . . . . . . .\n",
2210       ". . . . . . . . . . .\n",
2211       ". . . . . . . . . . .\n",
2212       ". . . . . . . . . . .\n",
2213       ". . . . . . . . . . .\n",
2214       ". . . . . . . . . . .\n",
2215       ". . . . . . . . . . .\n",
2216       ". . . . . . . . . . .\n",
2217       "B\n",
2218       "b\n",
2219       "*\n"
2220      ]
2221     },
2222     {
2223      "data": {
2224       "text/plain": [
2225        "False"
2226       ]
2227      },
2228      "execution_count": 44,
2229      "metadata": {},
2230      "output_type": "execute_result"
2231     }
2232    ],
2233    "source": [
2234     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
2235     "print(show_annotated_table(t, bp))\n",
2236     "print(show_backtrace(bp))\n",
2237     "print(show_backtrace_star(bp))\n",
2238     "v"
2239    ]
2240   },
2241   {
2242    "cell_type": "code",
2243    "execution_count": 45,
2244    "metadata": {},
2245    "outputs": [
2246     {
2247      "name": "stdout",
2248      "output_type": "stream",
2249      "text": [
2250       "* . . . . . . . . . .\n",
2251       "b . . . . . . . . . .\n",
2252       ". . . . . . . . . . .\n",
2253       ". . . . . . . . . . .\n",
2254       ". . . . . . . . . . .\n",
2255       ". . . . . . . . . . .\n",
2256       ". . . . . . . . . . .\n",
2257       ". . . . . . . . . . .\n",
2258       ". . . . . . . . . . .\n",
2259       ". . . . . . . . . . .\n",
2260       ". . . . . . . . . . .\n",
2261       "B\n",
2262       "b\n",
2263       "*\n"
2264      ]
2265     },
2266     {
2267      "data": {
2268       "text/plain": [
2269        "False"
2270       ]
2271      },
2272      "execution_count": 45,
2273      "metadata": {},
2274      "output_type": "execute_result"
2275     }
2276    ],
2277    "source": [
2278     "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n",
2279     "print(show_annotated_table(t, bp))\n",
2280     "print(show_backtrace(bp))\n",
2281     "print(show_backtrace_star(bp))\n",
2282     "v"
2283    ]
2284   },
2285   {
2286    "cell_type": "markdown",
2287    "metadata": {
2288     "collapsed": true
2289    },
2290    "source": [
2291     "# Make puzzle data\n",
2292     "\n",
2293     "## Note to self\n",
2294     "Include some distractors in the test set, such that:\n",
2295     "* subsequence(my_bill, distractor) is true\n",
2296     "* subsequence(friend_bill, distractor) is true\n",
2297     "* interleave(my_bill, friend_bill, distractor) is false\n",
2298     "\n",
2299     "(i.e. characters are shared between my_bill and friend_bill)\n",
2300     "\n",
2301     "Students are taking a greedy approach to subsequence, and saying the interleave is true if both bills are subsequences of the distractor.\n",
2302     "\n",
2303     "i.e. \"aaa\" and \"aab\" are both subsequences of \"aaabbb\", but cannot be interleaved to form \"aaabbb\".\n"
2304    ]
2305   },
2306   {
2307    "cell_type": "code",
2308    "execution_count": 46,
2309    "metadata": {
2310     "collapsed": true
2311    },
2312    "outputs": [],
2313    "source": [
2314     "my_bill = make_string(200)\n",
2315     "friend_bill = make_string(200)\n",
2316     "other_bills = [make_string(200) for _ in range(98)]\n",
2317     "\n",
2318     "target_interleaved = interleave(my_bill, friend_bill)\n",
2319     "mine_interleaved = [interleave(my_bill, o) for o in random.sample(other_bills, 21)]\n",
2320     "friend_interleaved = [interleave(friend_bill, o) for o in random.sample(other_bills, 13)]\n",
2321     "other_interleaved = []\n",
2322     "for _ in range(103):\n",
2323     "    s1, s2 = random.sample(other_bills, 2)\n",
2324     "    other_interleaved += [interleave(s1, s2)]"
2325    ]
2326   },
2327   {
2328    "cell_type": "code",
2329    "execution_count": 47,
2330    "metadata": {
2331     "collapsed": true
2332    },
2333    "outputs": [],
2334    "source": [
2335     "all_targets = [target_interleaved] + mine_interleaved + friend_interleaved + other_interleaved"
2336    ]
2337   },
2338   {
2339    "cell_type": "code",
2340    "execution_count": 48,
2341    "metadata": {},
2342    "outputs": [
2343     {
2344      "name": "stdout",
2345      "output_type": "stream",
2346      "text": [
2347       "CPU times: user 2.96 s, sys: 4 ms, total: 2.97 s\n",
2348       "Wall time: 2.97 s\n"
2349      ]
2350     },
2351     {
2352      "data": {
2353       "text/plain": [
2354        "[0]"
2355       ]
2356      },
2357      "execution_count": 48,
2358      "metadata": {},
2359      "output_type": "execute_result"
2360     }
2361    ],
2362    "source": [
2363     "%time [i for i, s12 in enumerate(all_targets) if is_interleave(my_bill, friend_bill, s12)]"
2364    ]
2365   },
2366   {
2367    "cell_type": "code",
2368    "execution_count": 49,
2369    "metadata": {},
2370    "outputs": [
2371     {
2372      "name": "stdout",
2373      "output_type": "stream",
2374      "text": [
2375       "CPU times: user 660 ms, sys: 0 ns, total: 660 ms\n",
2376       "Wall time: 658 ms\n"
2377      ]
2378     },
2379     {
2380      "data": {
2381       "text/plain": [
2382        "[0]"
2383       ]
2384      },
2385      "execution_count": 49,
2386      "metadata": {},
2387      "output_type": "execute_result"
2388     }
2389    ],
2390    "source": [
2391     "%time [i for i, s12 in enumerate(all_targets) if is_interleave_recursive(my_bill, friend_bill, s12)]"
2392    ]
2393   },
2394   {
2395    "cell_type": "code",
2396    "execution_count": 50,
2397    "metadata": {
2398     "collapsed": true
2399    },
2400    "outputs": [],
2401    "source": [
2402     "bill_set = all_targets + random.sample(other_bills, 8)\n",
2403     "random.shuffle(bill_set)\n",
2404     "bill_set = [my_bill, friend_bill] + bill_set\n",
2405     "\n",
2406     "# with open('09-bills.txt', 'w') as f:\n",
2407     "#     for i, b in enumerate(bill_set):\n",
2408     "#         f.write('{}: {}\\n'.format(i, b))"
2409    ]
2410   },
2411   {
2412    "cell_type": "code",
2413    "execution_count": 51,
2414    "metadata": {
2415     "collapsed": true
2416    },
2417    "outputs": [],
2418    "source": [
2419     "def is_subseq_greedy(s1, s2):\n",
2420     "    i = j = 0\n",
2421     "    while i < len(s1) and j < len(s2):\n",
2422     "        if s1[i] == s2[j]:\n",
2423     "            i += 1\n",
2424     "        j += 1\n",
2425     "    return i == len(s1)"
2426    ]
2427   },
2428   {
2429    "cell_type": "code",
2430    "execution_count": 52,
2431    "metadata": {
2432     "collapsed": true
2433    },
2434    "outputs": [],
2435    "source": [
2436     "def subseq_partition(s1, s2):\n",
2437     "    i = j = 0\n",
2438     "    remainder = ''\n",
2439     "    while i < len(s1) and j < len(s2):\n",
2440     "        if s1[i] == s2[j]:\n",
2441     "            i += 1\n",
2442     "        else:\n",
2443     "            remainder += s2[j]\n",
2444     "        j += 1\n",
2445     "    return i == len(s1), remainder"
2446    ]
2447   },
2448   {
2449    "cell_type": "code",
2450    "execution_count": 53,
2451    "metadata": {},
2452    "outputs": [
2453     {
2454      "data": {
2455       "text/plain": [
2456        "(40, 40, 20, 20)"
2457       ]
2458      },
2459      "execution_count": 53,
2460      "metadata": {},
2461      "output_type": "execute_result"
2462     }
2463    ],
2464    "source": [
2465     "common = make_string(10)\n",
2466     "padding = make_string(10)\n",
2467     "middle = interleave(common, padding)\n",
2468     "\n",
2469     "pre1 = make_string(5)\n",
2470     "suf1 = make_string(5)\n",
2471     "\n",
2472     "pre2 = make_string(5)\n",
2473     "suf2 = make_string(5)\n",
2474     "\n",
2475     "pre = interleave(pre1, pre2)\n",
2476     "suf = interleave(suf1, suf2)\n",
2477     "\n",
2478     "distractor = pre + middle + suf\n",
2479     "\n",
2480     "sub1 = pre1 + common + suf1\n",
2481     "sub2 = pre2 + common + suf2\n",
2482     "\n",
2483     "valid = interleave(sub1, sub2)\n",
2484     "\n",
2485     "len(distractor), len(valid), len(sub1), len(sub2)"
2486    ]
2487   },
2488   {
2489    "cell_type": "code",
2490    "execution_count": 54,
2491    "metadata": {},
2492    "outputs": [
2493     {
2494      "data": {
2495       "text/plain": [
2496        "(True, True)"
2497       ]
2498      },
2499      "execution_count": 54,
2500      "metadata": {},
2501      "output_type": "execute_result"
2502     }
2503    ],
2504    "source": [
2505     "is_subseq_greedy(sub1, distractor), is_subseq_greedy(sub2, distractor)"
2506    ]
2507   },
2508   {
2509    "cell_type": "code",
2510    "execution_count": 55,
2511    "metadata": {},
2512    "outputs": [
2513     {
2514      "data": {
2515       "text/plain": [
2516        "(True, True)"
2517       ]
2518      },
2519      "execution_count": 55,
2520      "metadata": {},
2521      "output_type": "execute_result"
2522     }
2523    ],
2524    "source": [
2525     "is_subseq_greedy(sub1, valid), is_subseq_greedy(sub2, valid)"
2526    ]
2527   },
2528   {
2529    "cell_type": "code",
2530    "execution_count": 56,
2531    "metadata": {},
2532    "outputs": [
2533     {
2534      "data": {
2535       "text/plain": [
2536        "(False, True)"
2537       ]
2538      },
2539      "execution_count": 56,
2540      "metadata": {},
2541      "output_type": "execute_result"
2542     }
2543    ],
2544    "source": [
2545     "is_interleave(sub1, sub2, distractor), is_interleave(sub1, sub2, valid)"
2546    ]
2547   },
2548   {
2549    "cell_type": "code",
2550    "execution_count": 57,
2551    "metadata": {},
2552    "outputs": [
2553     {
2554      "data": {
2555       "text/plain": [
2556        "('echgeaeeefdcebeaahaf',\n",
2557        " 'eeahaaeeefdcebedghbg',\n",
2558        " 'eeecahahgeaaeeebafaadgceadabefdaghbgahaf',\n",
2559        " 'eecheagehaaaeeeeeefdcebefadahcaebfedghbg')"
2560       ]
2561      },
2562      "execution_count": 57,
2563      "metadata": {},
2564      "output_type": "execute_result"
2565     }
2566    ],
2567    "source": [
2568     "sub1, sub2, distractor, valid"
2569    ]
2570   },
2571   {
2572    "cell_type": "code",
2573    "execution_count": 58,
2574    "metadata": {},
2575    "outputs": [
2576     {
2577      "data": {
2578       "text/plain": [
2579        "False"
2580       ]
2581      },
2582      "execution_count": 58,
2583      "metadata": {},
2584      "output_type": "execute_result"
2585     }
2586    ],
2587    "source": [
2588     "a, b = subseq_partition(sub1, distractor)\n",
2589     "b == sub2"
2590    ]
2591   },
2592   {
2593    "cell_type": "code",
2594    "execution_count": 59,
2595    "metadata": {},
2596    "outputs": [
2597     {
2598      "data": {
2599       "text/plain": [
2600        "('eeahaaeeefdceb', 'eeahaaeeefdcebedghbg')"
2601       ]
2602      },
2603      "execution_count": 59,
2604      "metadata": {},
2605      "output_type": "execute_result"
2606     }
2607    ],
2608    "source": [
2609     "a, b = subseq_partition(sub1, valid)\n",
2610     "b, sub2"
2611    ]
2612   },
2613   {
2614    "cell_type": "code",
2615    "execution_count": null,
2616    "metadata": {
2617     "collapsed": true
2618    },
2619    "outputs": [],
2620    "source": []
2621   }
2622  ],
2623  "metadata": {
2624   "kernelspec": {
2625    "display_name": "Python 3",
2626    "language": "python",
2627    "name": "python3"
2628   },
2629   "language_info": {
2630    "codemirror_mode": {
2631     "name": "ipython",
2632     "version": 3
2633    },
2634    "file_extension": ".py",
2635    "mimetype": "text/x-python",
2636    "name": "python",
2637    "nbconvert_exporter": "python",
2638    "pygments_lexer": "ipython3",
2639    "version": "3.5.2+"
2640   }
2641  },
2642  "nbformat": 4,
2643  "nbformat_minor": 1
2644 }