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": 1,
  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": 2,
  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": 3,
  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": 3,
  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": 4,
  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": 4,
  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": 5,
 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": 5,
 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": 6,
 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": 7,
 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": 8,
 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": 9,
 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": 9,
 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": 10,
 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": 11,
 417    "metadata": {},
 418    "outputs": [
 419     {
 420      "data": {
 421       "text/plain": [
 422        "True"
 423       ]
 424      },
 425      "execution_count": 11,
 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": 12,
 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": 12,
 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": 13,
 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": 13,
 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": 14,
 545    "metadata": {},
 546    "outputs": [
 547     {
 548      "data": {
 549       "text/plain": [
 550        "False"
 551       ]
 552      },
 553      "execution_count": 14,
 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": 15,
 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": 15,
 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": 16,
 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": 17,
 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": 18,
 656    "metadata": {},
 657    "outputs": [
 658     {
 659      "data": {
 660       "text/plain": [
 661        "'cccbggadggfbghfbeeeecgabbcdehcgfdhegefddahcdcabbch'"
 662       ]
 663      },
 664      "execution_count": 18,
 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": 19,
 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": 20,
 717    "metadata": {},
 718    "outputs": [
 719     {
 720      "name": "stdout",
 721      "output_type": "stream",
 722      "text": [
 723       "0 0 0 adding x\n",
 724       "0 1 -1 adding c\n",
 725       "1 1 0 adding v\n",
 726       "1 2 -1 adding a\n",
 727       "2 2 0 adding f\n",
 728       "3 2 1 adding u\n",
 729       "3 3 0 adding z\n",
 730       "3 4 -1 adding y\n",
 731       "3 5 -2 adding w\n",
 732       "3 6 -3 adding e\n",
 733       "4 6 -2 adding u\n",
 734       "4 7 -3 adding h\n",
 735       "5 7 -2 adding x\n",
 736       "5 8 -3 adding b\n",
 737       "6 8 -2 adding h\n",
 738       "7 8 -1 adding z\n",
 739       "7 9 -2 adding f\n",
 740       "8 9 -1 adding d\n",
 741       "9 9 0 adding c\n",
 742       "10 9 1 adding u\n",
 743       "10 10 0 adding v\n",
 744       "10 11 -1 adding c\n",
 745       "11 11 0 adding f\n",
 746       "12 11 1 adding a\n",
 747       "13 11 2 adding y\n",
 748       "13 12 1 adding y\n",
 749       "13 13 0 adding y\n",
 750       "13 14 -1 adding u\n",
 751       "13 15 -2 adding e\n",
 752       "14 15 -1 adding z\n",
 753       "14 16 -2 adding e\n",
 754       "15 16 -1 adding b\n",
 755       "16 16 0 adding c\n",
 756       "17 16 1 adding g\n",
 757       "18 16 2 adding w\n",
 758       "18 17 1 adding u\n",
 759       "18 18 0 adding e\n",
 760       "19 18 1 adding w\n",
 761       "19 19 0 adding b\n",
 762       "20 19 1 remaining s2 y\n"
 763      ]
 764     },
 765     {
 766      "data": {
 767       "text/plain": [
 768        "('cafehbhfdccfaeebcgeb',\n",
 769        " 'xvuzywuxzuvyyyuzwuwy',\n",
 770        " 'xcvafuzyweuhxbhzfdcuvcfayyyuezebcgwuewby',\n",
 771        " 40)"
 772       ]
 773      },
 774      "execution_count": 20,
 775      "metadata": {},
 776      "output_type": "execute_result"
 777     }
 778    ],
 779    "source": [
 780     "s1 = make_string(20)\n",
 781     "s2 = make_string(20, alphabet='uvwxyz')\n",
 782     "il = interleave(s1, s2, wander_limit=5, debug=True)\n",
 783     "s1, s2, il, len(il)"
 784    ]
 785   },
 786   {
 787    "cell_type": "code",
 788    "execution_count": 21,
 789    "metadata": {},
 790    "outputs": [
 791     {
 792      "name": "stdout",
 793      "output_type": "stream",
 794      "text": [
 795       "xxxx 0 0 ! ! ! True\n",
 796       "seq2 0 1 ! c x False\n",
 797       "seq2 0 2 ! a c False\n",
 798       "seq2 0 3 ! f v False\n",
 799       "seq2 0 4 ! e a False\n",
 800       "seq2 0 5 ! h f False\n",
 801       "seq2 0 6 ! b u False\n",
 802       "seq2 0 7 ! h z False\n",
 803       "seq2 0 8 ! f y False\n",
 804       "seq2 0 9 ! d w False\n",
 805       "seq2 0 10 ! c e False\n",
 806       "seq2 0 11 ! c u False\n",
 807       "seq2 0 12 ! f h False\n",
 808       "seq2 0 13 ! a x False\n",
 809       "seq2 0 14 ! e b False\n",
 810       "seq2 0 15 ! e h False\n",
 811       "seq2 0 16 ! b z False\n",
 812       "seq2 0 17 ! c f False\n",
 813       "seq2 0 18 ! g d False\n",
 814       "seq2 0 19 ! e c False\n",
 815       "seq2 0 20 ! b u False\n",
 816       "seq1 1 0 x ! x True\n",
 817       "seq2 1 1 x c c True\n",
 818       "xxxx 1 2 x a v False\n",
 819       "xxxx 1 3 x f a False\n",
 820       "xxxx 1 4 x e f False\n",
 821       "xxxx 1 5 x h u False\n",
 822       "xxxx 1 6 x b z False\n",
 823       "xxxx 1 7 x h y False\n",
 824       "xxxx 1 8 x f w False\n",
 825       "xxxx 1 9 x d e False\n",
 826       "xxxx 1 10 x c u False\n",
 827       "xxxx 1 11 x c h False\n",
 828       "xxxx 1 12 x f x False\n",
 829       "xxxx 1 13 x a b False\n",
 830       "xxxx 1 14 x e h False\n",
 831       "xxxx 1 15 x e z False\n",
 832       "xxxx 1 16 x b f False\n",
 833       "xxxx 1 17 x c d False\n",
 834       "xxxx 1 18 x g c False\n",
 835       "xxxx 1 19 x e u False\n",
 836       "xxxx 1 20 x b v False\n",
 837       "seq1 2 0 v ! c False\n",
 838       "seq1 2 1 v c v True\n",
 839       "seq2 2 2 v a a True\n",
 840       "seq2 2 3 v f f True\n",
 841       "xxxx 2 4 v e u False\n",
 842       "xxxx 2 5 v h z False\n",
 843       "xxxx 2 6 v b y False\n",
 844       "xxxx 2 7 v h w False\n",
 845       "xxxx 2 8 v f e False\n",
 846       "xxxx 2 9 v d u False\n",
 847       "xxxx 2 10 v c h False\n",
 848       "xxxx 2 11 v c x False\n",
 849       "xxxx 2 12 v f b False\n",
 850       "xxxx 2 13 v a h False\n",
 851       "xxxx 2 14 v e z False\n",
 852       "xxxx 2 15 v e f False\n",
 853       "xxxx 2 16 v b d False\n",
 854       "xxxx 2 17 v c c False\n",
 855       "xxxx 2 18 v g u False\n",
 856       "xxxx 2 19 v e v False\n",
 857       "xxxx 2 20 v b c False\n",
 858       "seq1 3 0 u ! v False\n",
 859       "xxxx 3 1 u c a False\n",
 860       "xxxx 3 2 u a f False\n",
 861       "seq1 3 3 u f u True\n",
 862       "xxxx 3 4 u e z False\n",
 863       "xxxx 3 5 u h y False\n",
 864       "xxxx 3 6 u b w False\n",
 865       "xxxx 3 7 u h e False\n",
 866       "xxxx 3 8 u f u False\n",
 867       "xxxx 3 9 u d h False\n",
 868       "xxxx 3 10 u c x False\n",
 869       "xxxx 3 11 u c b False\n",
 870       "xxxx 3 12 u f h False\n",
 871       "xxxx 3 13 u a z False\n",
 872       "xxxx 3 14 u e f False\n",
 873       "xxxx 3 15 u e d False\n",
 874       "xxxx 3 16 u b c False\n",
 875       "xxxx 3 17 u c u False\n",
 876       "xxxx 3 18 u g v False\n",
 877       "xxxx 3 19 u e c False\n",
 878       "xxxx 3 20 u b f False\n",
 879       "seq1 4 0 z ! a False\n",
 880       "xxxx 4 1 z c f False\n",
 881       "xxxx 4 2 z a u False\n",
 882       "seq1 4 3 z f z True\n",
 883       "xxxx 4 4 z e y False\n",
 884       "xxxx 4 5 z h w False\n",
 885       "xxxx 4 6 z b e False\n",
 886       "xxxx 4 7 z h u False\n",
 887       "xxxx 4 8 z f h False\n",
 888       "xxxx 4 9 z d x False\n",
 889       "xxxx 4 10 z c b False\n",
 890       "xxxx 4 11 z c h False\n",
 891       "xxxx 4 12 z f z False\n",
 892       "xxxx 4 13 z a f False\n",
 893       "xxxx 4 14 z e d False\n",
 894       "xxxx 4 15 z e c False\n",
 895       "xxxx 4 16 z b u False\n",
 896       "xxxx 4 17 z c v False\n",
 897       "xxxx 4 18 z g c False\n",
 898       "xxxx 4 19 z e f False\n",
 899       "xxxx 4 20 z b a False\n",
 900       "seq1 5 0 y ! f False\n",
 901       "xxxx 5 1 y c u False\n",
 902       "xxxx 5 2 y a z False\n",
 903       "seq1 5 3 y f y True\n",
 904       "xxxx 5 4 y e w False\n",
 905       "xxxx 5 5 y h e False\n",
 906       "xxxx 5 6 y b u False\n",
 907       "xxxx 5 7 y h h False\n",
 908       "xxxx 5 8 y f x False\n",
 909       "xxxx 5 9 y d b False\n",
 910       "xxxx 5 10 y c h False\n",
 911       "xxxx 5 11 y c z False\n",
 912       "xxxx 5 12 y f f False\n",
 913       "xxxx 5 13 y a d False\n",
 914       "xxxx 5 14 y e c False\n",
 915       "xxxx 5 15 y e u False\n",
 916       "xxxx 5 16 y b v False\n",
 917       "xxxx 5 17 y c c False\n",
 918       "xxxx 5 18 y g f False\n",
 919       "xxxx 5 19 y e a False\n",
 920       "xxxx 5 20 y b y False\n",
 921       "seq1 6 0 w ! u False\n",
 922       "xxxx 6 1 w c z False\n",
 923       "xxxx 6 2 w a y False\n",
 924       "seq1 6 3 w f w True\n",
 925       "seq2 6 4 w e e True\n",
 926       "xxxx 6 5 w h u False\n",
 927       "xxxx 6 6 w b h False\n",
 928       "xxxx 6 7 w h x False\n",
 929       "xxxx 6 8 w f b False\n",
 930       "xxxx 6 9 w d h False\n",
 931       "xxxx 6 10 w c z False\n",
 932       "xxxx 6 11 w c f False\n",
 933       "xxxx 6 12 w f d False\n",
 934       "xxxx 6 13 w a c False\n",
 935       "xxxx 6 14 w e u False\n",
 936       "xxxx 6 15 w e v False\n",
 937       "xxxx 6 16 w b c False\n",
 938       "xxxx 6 17 w c f False\n",
 939       "xxxx 6 18 w g a False\n",
 940       "xxxx 6 19 w e y False\n",
 941       "xxxx 6 20 w b y False\n",
 942       "seq1 7 0 u ! z False\n",
 943       "xxxx 7 1 u c y False\n",
 944       "xxxx 7 2 u a w False\n",
 945       "xxxx 7 3 u f e False\n",
 946       "seq1 7 4 u e u True\n",
 947       "seq2 7 5 u h h True\n",
 948       "xxxx 7 6 u b x False\n",
 949       "xxxx 7 7 u h b False\n",
 950       "xxxx 7 8 u f h False\n",
 951       "xxxx 7 9 u d z False\n",
 952       "xxxx 7 10 u c f False\n",
 953       "xxxx 7 11 u c d False\n",
 954       "xxxx 7 12 u f c False\n",
 955       "xxxx 7 13 u a u False\n",
 956       "xxxx 7 14 u e v False\n",
 957       "xxxx 7 15 u e c False\n",
 958       "xxxx 7 16 u b f False\n",
 959       "xxxx 7 17 u c a False\n",
 960       "xxxx 7 18 u g y False\n",
 961       "xxxx 7 19 u e y False\n",
 962       "xxxx 7 20 u b y False\n",
 963       "seq1 8 0 x ! y False\n",
 964       "xxxx 8 1 x c w False\n",
 965       "xxxx 8 2 x a e False\n",
 966       "xxxx 8 3 x f u False\n",
 967       "xxxx 8 4 x e h False\n",
 968       "seq1 8 5 x h x True\n",
 969       "seq2 8 6 x b b True\n",
 970       "seq2 8 7 x h h True\n",
 971       "xxxx 8 8 x f z False\n",
 972       "xxxx 8 9 x d f False\n",
 973       "xxxx 8 10 x c d False\n",
 974       "xxxx 8 11 x c c False\n",
 975       "xxxx 8 12 x f u False\n",
 976       "xxxx 8 13 x a v False\n",
 977       "xxxx 8 14 x e c False\n",
 978       "xxxx 8 15 x e f False\n",
 979       "xxxx 8 16 x b a False\n",
 980       "xxxx 8 17 x c y False\n",
 981       "xxxx 8 18 x g y False\n",
 982       "xxxx 8 19 x e y False\n",
 983       "xxxx 8 20 x b u False\n",
 984       "seq1 9 0 z ! w False\n",
 985       "xxxx 9 1 z c e False\n",
 986       "xxxx 9 2 z a u False\n",
 987       "xxxx 9 3 z f h False\n",
 988       "xxxx 9 4 z e x False\n",
 989       "xxxx 9 5 z h b False\n",
 990       "xxxx 9 6 z b h False\n",
 991       "seq1 9 7 z h z True\n",
 992       "seq2 9 8 z f f True\n",
 993       "seq2 9 9 z d d True\n",
 994       "seq2 9 10 z c c True\n",
 995       "xxxx 9 11 z c u False\n",
 996       "xxxx 9 12 z f v False\n",
 997       "xxxx 9 13 z a c False\n",
 998       "xxxx 9 14 z e f False\n",
 999       "xxxx 9 15 z e a False\n",
1000       "xxxx 9 16 z b y False\n",
1001       "xxxx 9 17 z c y False\n",
1002       "xxxx 9 18 z g y False\n",
1003       "xxxx 9 19 z e u False\n",
1004       "xxxx 9 20 z b e False\n",
1005       "seq1 10 0 u ! e False\n",
1006       "xxxx 10 1 u c u False\n",
1007       "xxxx 10 2 u a h False\n",
1008       "xxxx 10 3 u f x False\n",
1009       "xxxx 10 4 u e b False\n",
1010       "xxxx 10 5 u h h False\n",
1011       "xxxx 10 6 u b z False\n",
1012       "xxxx 10 7 u h f False\n",
1013       "xxxx 10 8 u f d False\n",
1014       "xxxx 10 9 u d c False\n",
1015       "seq1 10 10 u c u True\n",
1016       "xxxx 10 11 u c v False\n",
1017       "xxxx 10 12 u f c False\n",
1018       "xxxx 10 13 u a f False\n",
1019       "xxxx 10 14 u e a False\n",
1020       "xxxx 10 15 u e y False\n",
1021       "xxxx 10 16 u b y False\n",
1022       "xxxx 10 17 u c y False\n",
1023       "xxxx 10 18 u g u False\n",
1024       "xxxx 10 19 u e e False\n",
1025       "xxxx 10 20 u b z False\n",
1026       "seq1 11 0 v ! u False\n",
1027       "xxxx 11 1 v c h False\n",
1028       "xxxx 11 2 v a x False\n",
1029       "xxxx 11 3 v f b False\n",
1030       "xxxx 11 4 v e h False\n",
1031       "xxxx 11 5 v h z False\n",
1032       "xxxx 11 6 v b f False\n",
1033       "xxxx 11 7 v h d False\n",
1034       "xxxx 11 8 v f c False\n",
1035       "xxxx 11 9 v d u False\n",
1036       "seq1 11 10 v c v True\n",
1037       "seq2 11 11 v c c True\n",
1038       "seq2 11 12 v f f True\n",
1039       "seq2 11 13 v a a True\n",
1040       "xxxx 11 14 v e y False\n",
1041       "xxxx 11 15 v e y False\n",
1042       "xxxx 11 16 v b y False\n",
1043       "xxxx 11 17 v c u False\n",
1044       "xxxx 11 18 v g e False\n",
1045       "xxxx 11 19 v e z False\n",
1046       "xxxx 11 20 v b e False\n",
1047       "seq1 12 0 y ! h False\n",
1048       "xxxx 12 1 y c x False\n",
1049       "xxxx 12 2 y a b False\n",
1050       "xxxx 12 3 y f h False\n",
1051       "xxxx 12 4 y e z False\n",
1052       "xxxx 12 5 y h f False\n",
1053       "xxxx 12 6 y b d False\n",
1054       "xxxx 12 7 y h c False\n",
1055       "xxxx 12 8 y f u False\n",
1056       "xxxx 12 9 y d v False\n",
1057       "xxxx 12 10 y c c False\n",
1058       "xxxx 12 11 y c f False\n",
1059       "xxxx 12 12 y f a False\n",
1060       "seq1 12 13 y a y True\n",
1061       "xxxx 12 14 y e y False\n",
1062       "xxxx 12 15 y e y False\n",
1063       "xxxx 12 16 y b u False\n",
1064       "xxxx 12 17 y c e False\n",
1065       "xxxx 12 18 y g z False\n",
1066       "xxxx 12 19 y e e False\n",
1067       "xxxx 12 20 y b b False\n",
1068       "seq1 13 0 y ! x False\n",
1069       "xxxx 13 1 y c b False\n",
1070       "xxxx 13 2 y a h False\n",
1071       "xxxx 13 3 y f z False\n",
1072       "xxxx 13 4 y e f False\n",
1073       "xxxx 13 5 y h d False\n",
1074       "xxxx 13 6 y b c False\n",
1075       "xxxx 13 7 y h u False\n",
1076       "xxxx 13 8 y f v False\n",
1077       "xxxx 13 9 y d c False\n",
1078       "xxxx 13 10 y c f False\n",
1079       "xxxx 13 11 y c a False\n",
1080       "xxxx 13 12 y f y False\n",
1081       "seq1 13 13 y a y True\n",
1082       "xxxx 13 14 y e y False\n",
1083       "xxxx 13 15 y e u False\n",
1084       "xxxx 13 16 y b e False\n",
1085       "xxxx 13 17 y c z False\n",
1086       "xxxx 13 18 y g e False\n",
1087       "xxxx 13 19 y e b False\n",
1088       "xxxx 13 20 y b c False\n",
1089       "seq1 14 0 y ! b False\n",
1090       "xxxx 14 1 y c h False\n",
1091       "xxxx 14 2 y a z False\n",
1092       "xxxx 14 3 y f f False\n",
1093       "xxxx 14 4 y e d False\n",
1094       "xxxx 14 5 y h c False\n",
1095       "xxxx 14 6 y b u False\n",
1096       "xxxx 14 7 y h v False\n",
1097       "xxxx 14 8 y f c False\n",
1098       "xxxx 14 9 y d f False\n",
1099       "xxxx 14 10 y c a False\n",
1100       "xxxx 14 11 y c y False\n",
1101       "xxxx 14 12 y f y False\n",
1102       "seq1 14 13 y a y True\n",
1103       "xxxx 14 14 y e u False\n",
1104       "xxxx 14 15 y e e False\n",
1105       "xxxx 14 16 y b z False\n",
1106       "xxxx 14 17 y c e False\n",
1107       "xxxx 14 18 y g b False\n",
1108       "xxxx 14 19 y e c False\n",
1109       "xxxx 14 20 y b g False\n",
1110       "seq1 15 0 u ! h False\n",
1111       "xxxx 15 1 u c z False\n",
1112       "xxxx 15 2 u a f False\n",
1113       "xxxx 15 3 u f d False\n",
1114       "xxxx 15 4 u e c False\n",
1115       "xxxx 15 5 u h u False\n",
1116       "xxxx 15 6 u b v False\n",
1117       "xxxx 15 7 u h c False\n",
1118       "xxxx 15 8 u f f False\n",
1119       "xxxx 15 9 u d a False\n",
1120       "xxxx 15 10 u c y False\n",
1121       "xxxx 15 11 u c y False\n",
1122       "xxxx 15 12 u f y False\n",
1123       "seq1 15 13 u a u True\n",
1124       "seq2 15 14 u e e True\n",
1125       "xxxx 15 15 u e z False\n",
1126       "xxxx 15 16 u b e False\n",
1127       "xxxx 15 17 u c b False\n",
1128       "xxxx 15 18 u g c False\n",
1129       "xxxx 15 19 u e g False\n",
1130       "xxxx 15 20 u b w False\n",
1131       "seq1 16 0 z ! z False\n",
1132       "xxxx 16 1 z c f False\n",
1133       "xxxx 16 2 z a d False\n",
1134       "xxxx 16 3 z f c False\n",
1135       "xxxx 16 4 z e u False\n",
1136       "xxxx 16 5 z h v False\n",
1137       "xxxx 16 6 z b c False\n",
1138       "xxxx 16 7 z h f False\n",
1139       "xxxx 16 8 z f a False\n",
1140       "xxxx 16 9 z d y False\n",
1141       "xxxx 16 10 z c y False\n",
1142       "xxxx 16 11 z c y False\n",
1143       "xxxx 16 12 z f u False\n",
1144       "xxxx 16 13 z a e False\n",
1145       "seq1 16 14 z e z True\n",
1146       "seq2 16 15 z e e True\n",
1147       "seq2 16 16 z b b True\n",
1148       "seq2 16 17 z c c True\n",
1149       "seq2 16 18 z g g True\n",
1150       "xxxx 16 19 z e w False\n",
1151       "xxxx 16 20 z b u False\n",
1152       "seq1 17 0 w ! f False\n",
1153       "xxxx 17 1 w c d False\n",
1154       "xxxx 17 2 w a c False\n",
1155       "xxxx 17 3 w f u False\n",
1156       "xxxx 17 4 w e v False\n",
1157       "xxxx 17 5 w h c False\n",
1158       "xxxx 17 6 w b f False\n",
1159       "xxxx 17 7 w h a False\n",
1160       "xxxx 17 8 w f y False\n",
1161       "xxxx 17 9 w d y False\n",
1162       "xxxx 17 10 w c y False\n",
1163       "xxxx 17 11 w c u False\n",
1164       "xxxx 17 12 w f e False\n",
1165       "xxxx 17 13 w a z False\n",
1166       "xxxx 17 14 w e e False\n",
1167       "xxxx 17 15 w e b False\n",
1168       "xxxx 17 16 w b c False\n",
1169       "xxxx 17 17 w c g False\n",
1170       "seq1 17 18 w g w True\n",
1171       "xxxx 17 19 w e u False\n",
1172       "xxxx 17 20 w b e False\n",
1173       "seq1 18 0 u ! d False\n",
1174       "xxxx 18 1 u c c False\n",
1175       "xxxx 18 2 u a u False\n",
1176       "xxxx 18 3 u f v False\n",
1177       "xxxx 18 4 u e c False\n",
1178       "xxxx 18 5 u h f False\n",
1179       "xxxx 18 6 u b a False\n",
1180       "xxxx 18 7 u h y False\n",
1181       "xxxx 18 8 u f y False\n",
1182       "xxxx 18 9 u d y False\n",
1183       "xxxx 18 10 u c u False\n",
1184       "xxxx 18 11 u c e False\n",
1185       "xxxx 18 12 u f z False\n",
1186       "xxxx 18 13 u a e False\n",
1187       "xxxx 18 14 u e b False\n",
1188       "xxxx 18 15 u e c False\n",
1189       "xxxx 18 16 u b g False\n",
1190       "xxxx 18 17 u c w False\n",
1191       "seq1 18 18 u g u True\n",
1192       "seq2 18 19 u e e True\n",
1193       "xxxx 18 20 u b w False\n",
1194       "seq1 19 0 w ! c False\n",
1195       "xxxx 19 1 w c u False\n",
1196       "xxxx 19 2 w a v False\n",
1197       "xxxx 19 3 w f c False\n",
1198       "xxxx 19 4 w e f False\n",
1199       "xxxx 19 5 w h a False\n",
1200       "xxxx 19 6 w b y False\n",
1201       "xxxx 19 7 w h y False\n",
1202       "xxxx 19 8 w f y False\n",
1203       "xxxx 19 9 w d u False\n",
1204       "xxxx 19 10 w c e False\n",
1205       "xxxx 19 11 w c z False\n",
1206       "xxxx 19 12 w f e False\n",
1207       "xxxx 19 13 w a b False\n",
1208       "xxxx 19 14 w e c False\n",
1209       "xxxx 19 15 w e g False\n",
1210       "xxxx 19 16 w b w False\n",
1211       "xxxx 19 17 w c u False\n",
1212       "xxxx 19 18 w g e False\n",
1213       "seq1 19 19 w e w True\n",
1214       "seq2 19 20 w b b True\n",
1215       "seq1 20 0 y ! u False\n",
1216       "xxxx 20 1 y c v False\n",
1217       "xxxx 20 2 y a c False\n",
1218       "xxxx 20 3 y f f False\n",
1219       "xxxx 20 4 y e a False\n",
1220       "xxxx 20 5 y h y False\n",
1221       "xxxx 20 6 y b y False\n",
1222       "xxxx 20 7 y h y False\n",
1223       "xxxx 20 8 y f u False\n",
1224       "xxxx 20 9 y d e False\n",
1225       "xxxx 20 10 y c z False\n",
1226       "xxxx 20 11 y c e False\n",
1227       "xxxx 20 12 y f b False\n",
1228       "xxxx 20 13 y a c False\n",
1229       "xxxx 20 14 y e g False\n",
1230       "xxxx 20 15 y e w False\n",
1231       "xxxx 20 16 y b u False\n",
1232       "xxxx 20 17 y c e False\n",
1233       "xxxx 20 18 y g w False\n",
1234       "xxxx 20 19 y e b False\n",
1235       "seq1 20 20 y b y True\n",
1236       "T . . . . . . . . . . . . . . . . . . . .\n",
1237       "T T . . . . . . . . . . . . . . . . . . .\n",
1238       ". T T T . . . . . . . . . . . . . . . . .\n",
1239       ". . . T . . . . . . . . . . . . . . . . .\n",
1240       ". . . T . . . . . . . . . . . . . . . . .\n",
1241       ". . . T . . . . . . . . . . . . . . . . .\n",
1242       ". . . T T . . . . . . . . . . . . . . . .\n",
1243       ". . . . T T . . . . . . . . . . . . . . .\n",
1244       ". . . . . T T T . . . . . . . . . . . . .\n",
1245       ". . . . . . . T T T T . . . . . . . . . .\n",
1246       ". . . . . . . . . . T . . . . . . . . . .\n",
1247       ". . . . . . . . . . T T T T . . . . . . .\n",
1248       ". . . . . . . . . . . . . T . . . . . . .\n",
1249       ". . . . . . . . . . . . . T . . . . . . .\n",
1250       ". . . . . . . . . . . . . T . . . . . . .\n",
1251       ". . . . . . . . . . . . . T T . . . . . .\n",
1252       ". . . . . . . . . . . . . . T T T T T . .\n",
1253       ". . . . . . . . . . . . . . . . . . T . .\n",
1254       ". . . . . . . . . . . . . . . . . . T T .\n",
1255       ". . . . . . . . . . . . . . . . . . . T T\n",
1256       ". . . . . . . . . . . . . . . . . . . . T\n"
1257      ]
1258     }
1259    ],
1260    "source": [
1261     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True, debug=True)\n",
1262     "print(show_table(t))"
1263    ]
1264   },
1265   {
1266    "cell_type": "code",
1267    "execution_count": 22,
1268    "metadata": {},
1269    "outputs": [
1270     {
1271      "data": {
1272       "text/plain": [
1273        "'XcVafUZYWeUhXbhZfdcUVcfaYYYUeZebcgWUeWbY'"
1274       ]
1275      },
1276      "execution_count": 22,
1277      "metadata": {},
1278      "output_type": "execute_result"
1279     }
1280    ],
1281    "source": [
1282     "show_backtrace(bp)"
1283    ]
1284   },
1285   {
1286    "cell_type": "code",
1287    "execution_count": 23,
1288    "metadata": {},
1289    "outputs": [
1290     {
1291      "name": "stdout",
1292      "output_type": "stream",
1293      "text": [
1294       "T . . . . . . . . . . . . . . . . . . . .\n",
1295       "T T . . . . . . . . . . . . . . . . . . .\n",
1296       ". T T T . . . . . . . . . . . . . . . . .\n",
1297       ". . . T . . . . . . . . . . . . . . . . .\n",
1298       ". . . T . . . . . . . . . . . . . . . . .\n",
1299       ". . . T . . . . . . . . . . . . . . . . .\n",
1300       ". . . T T . . . . . . . . . . . . . . . .\n",
1301       ". . . . T T . . . . . . . . . . . . . . .\n",
1302       ". . . . . T T T . . . . . . . . . . . . .\n",
1303       ". . . . . . . T T T T . . . . . . . . . .\n",
1304       ". . . . . . . . . . T . . . . . . . . . .\n",
1305       ". . . . . . . . . . T T T T . . . . . . .\n",
1306       ". . . . . . . . . . . . . T . . . . . . .\n",
1307       ". . . . . . . . . . . . . T . . . . . . .\n",
1308       ". . . . . . . . . . . . . T . . . . . . .\n",
1309       ". . . . . . . . . . . . . T T . . . . . .\n",
1310       ". . . . . . . . . . . . . . T T T T T . .\n",
1311       ". . . . . . . . . . . . . . . . . . T . .\n",
1312       ". . . . . . . . . . . . . . . . . . T T .\n",
1313       ". . . . . . . . . . . . . . . . . . . T T\n",
1314       ". . . . . . . . . . . . . . . . . . . . T\n",
1315       "XcVafUZYWeUhXbhZfdcUVcfaYYYUeZebcgWUeWbY\n"
1316      ]
1317     },
1318     {
1319      "data": {
1320       "text/plain": [
1321        "True"
1322       ]
1323      },
1324      "execution_count": 23,
1325      "metadata": {},
1326      "output_type": "execute_result"
1327     }
1328    ],
1329    "source": [
1330     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1331     "print(show_table(t))\n",
1332     "print(show_backtrace(bp))\n",
1333     "v"
1334    ]
1335   },
1336   {
1337    "cell_type": "code",
1338    "execution_count": 24,
1339    "metadata": {},
1340    "outputs": [
1341     {
1342      "data": {
1343       "text/plain": [
1344        "('fdghaegbegehggbggcgcfecbgfacefhahahdhfafacchafacea',\n",
1345        " 'hdhadgebfeaehhhggbdghgcehabccgbddafeacagbgcahhfefe',\n",
1346        " 'fhdgdhahadgegebfbeegehaegghbhghggcggcfecbgbdgfhagcehabcccgbedfdhahaafeahcdhfaafaccghafbgacceahahfefe',\n",
1347        " 100)"
1348       ]
1349      },
1350      "execution_count": 24,
1351      "metadata": {},
1352      "output_type": "execute_result"
1353     }
1354    ],
1355    "source": [
1356     "s1 = make_string(50)\n",
1357     "s2 = make_string(50)\n",
1358     "il = interleave(s1, s2)\n",
1359     "s1, s2, il, len(il)"
1360    ]
1361   },
1362   {
1363    "cell_type": "code",
1364    "execution_count": 25,
1365    "metadata": {},
1366    "outputs": [
1367     {
1368      "name": "stdout",
1369      "output_type": "stream",
1370      "text": [
1371       "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1372       ". T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1373       ". T . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1374       ". . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1375       ". . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1376       ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1377       ". . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1378       ". . . . . T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1379       ". . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1380       ". . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1381       ". . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1382       ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1383       ". . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1384       ". . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1385       ". . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1386       ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1387       ". . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1388       ". . . . . . . . . . . . . . . . T . T T T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1389       ". . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1390       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1391       ". . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1392       ". . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1393       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . .\n",
1394       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1395       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1396       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1397       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1398       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . .\n",
1399       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . .\n",
1400       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . .\n",
1401       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . .\n",
1402       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
1403       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
1404       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . .\n",
1405       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T . . . . . . . . . . . . . . . .\n",
1406       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1407       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1408       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
1409       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . .\n",
1410       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . .\n",
1411       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . .\n",
1412       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . .\n",
1413       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . .\n",
1414       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T\n",
1415       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T .\n",
1416       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T\n",
1417       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1418       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1419       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1420       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1421       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1422       "fHdgDhaHADGegEBFbeEgehAEggHbHgHgGcgGcfecbgBDGfHaGCEHABcCCGBeDfDhahaAFEAhCdhfaAfaccGhafBGacCeAHaHFEFE\n"
1423      ]
1424     },
1425     {
1426      "data": {
1427       "text/plain": [
1428        "True"
1429       ]
1430      },
1431      "execution_count": 25,
1432      "metadata": {},
1433      "output_type": "execute_result"
1434     }
1435    ],
1436    "source": [
1437     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1438     "print(show_table(t))\n",
1439     "print(show_backtrace(bp))\n",
1440     "v"
1441    ]
1442   },
1443   {
1444    "cell_type": "code",
1445    "execution_count": 26,
1446    "metadata": {},
1447    "outputs": [
1448     {
1449      "name": "stdout",
1450      "output_type": "stream",
1451      "text": [
1452       "1000 loops, best of 3: 1.4 ms per loop\n"
1453      ]
1454     }
1455    ],
1456    "source": [
1457     "%%timeit\n",
1458     "is_interleave(s2, s1, il)"
1459    ]
1460   },
1461   {
1462    "cell_type": "code",
1463    "execution_count": 27,
1464    "metadata": {},
1465    "outputs": [
1466     {
1467      "name": "stdout",
1468      "output_type": "stream",
1469      "text": [
1470       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1471       "T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1472       ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1473       ". T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1474       ". . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1475       ". . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1476       ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1477       ". . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1478       ". . . . . . . T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1479       ". . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1480       ". . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1481       ". . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1482       ". . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1483       ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1484       ". . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1485       ". . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1486       ". . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1487       ". . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1488       ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1489       ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1490       ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1491       ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1492       ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1493       ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1494       ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1495       ". . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1496       ". . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1497       ". . . . . . . . . . . . . . . . . . . . . T T T T T T T T T . . . . . . . . . . . . . . . . . . . . .\n",
1498       ". . . . . . . . . . . . . . . . . . . . . . T . . . . T T T T T . . . . . . . . . . . . . . . . . . .\n",
1499       ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . T T . . . . . . . . . . . . . . . . . .\n",
1500       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . .\n",
1501       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . .\n",
1502       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . .\n",
1503       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . .\n",
1504       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . .\n",
1505       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
1506       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
1507       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
1508       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . .\n",
1509       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . .\n",
1510       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
1511       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
1512       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
1513       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . .\n",
1514       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . .\n",
1515       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . .\n",
1516       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . .\n",
1517       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
1518       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
1519       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . .\n",
1520       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T T T T T\n",
1521       "FhDGdhaHAdgEGebfBeEGEHaeGGhBhGhgGCgGCFECBGbdgFhAgcehabccCgbEdFdHAHaAfeaHcDHFaAFACCgHAFbgAcCEahAhfefe\n"
1522      ]
1523     },
1524     {
1525      "data": {
1526       "text/plain": [
1527        "True"
1528       ]
1529      },
1530      "execution_count": 27,
1531      "metadata": {},
1532      "output_type": "execute_result"
1533     }
1534    ],
1535    "source": [
1536     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1537     "print(show_table(t))\n",
1538     "print(show_backtrace(bp))\n",
1539     "v"
1540    ]
1541   },
1542   {
1543    "cell_type": "code",
1544    "execution_count": 28,
1545    "metadata": {},
1546    "outputs": [
1547     {
1548      "data": {
1549       "text/plain": [
1550        "True"
1551       ]
1552      },
1553      "execution_count": 28,
1554      "metadata": {},
1555      "output_type": "execute_result"
1556     }
1557    ],
1558    "source": [
1559     "show_backtrace(bp).lower() == il"
1560    ]
1561   },
1562   {
1563    "cell_type": "code",
1564    "execution_count": 29,
1565    "metadata": {},
1566    "outputs": [
1567     {
1568      "data": {
1569       "text/plain": [
1570        "('febffabcddaaaeffcdhcdaffgfafafcchfffdcbbbagbdfdbdd', False, False)"
1571       ]
1572      },
1573      "execution_count": 29,
1574      "metadata": {},
1575      "output_type": "execute_result"
1576     }
1577    ],
1578    "source": [
1579     "s3 = make_string(50)\n",
1580     "s3, is_interleave(s1, s3, il), is_interleave(s2, s3, il)"
1581    ]
1582   },
1583   {
1584    "cell_type": "code",
1585    "execution_count": 30,
1586    "metadata": {},
1587    "outputs": [
1588     {
1589      "name": "stdout",
1590      "output_type": "stream",
1591      "text": [
1592       "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1593       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\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       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1641       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1642       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1643       "\n"
1644      ]
1645     },
1646     {
1647      "data": {
1648       "text/plain": [
1649        "False"
1650       ]
1651      },
1652      "execution_count": 30,
1653      "metadata": {},
1654      "output_type": "execute_result"
1655     }
1656    ],
1657    "source": [
1658     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1659     "print(show_table(t))\n",
1660     "print(show_backtrace(bp))\n",
1661     "v"
1662    ]
1663   },
1664   {
1665    "cell_type": "code",
1666    "execution_count": 31,
1667    "metadata": {
1668     "collapsed": true
1669    },
1670    "outputs": [],
1671    "source": [
1672     "def is_interleave_recursive(s1, s2, s3):\n",
1673     "    if not s1:\n",
1674     "        return s2 == s3\n",
1675     "    elif not s2:\n",
1676     "        return s1 == s3\n",
1677     "    else:\n",
1678     "        if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
1679     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n",
1680     "        elif s1[-1] == s3[-1]:\n",
1681     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
1682     "        elif s2[-1] == s3[-1]:\n",
1683     "            return is_interleave(s1, s2[:-1], s3[:-1])\n",
1684     "        else:\n",
1685     "            return False"
1686    ]
1687   },
1688   {
1689    "cell_type": "code",
1690    "execution_count": 32,
1691    "metadata": {
1692     "collapsed": true
1693    },
1694    "outputs": [],
1695    "source": [
1696     "s1 = make_string(500)\n",
1697     "s2 = make_string(500)\n",
1698     "s3 = make_string(500)\n",
1699     "s12 = interleave(s1, s2)\n",
1700     "s23 = interleave(s2, s3)"
1701    ]
1702   },
1703   {
1704    "cell_type": "code",
1705    "execution_count": 33,
1706    "metadata": {},
1707    "outputs": [
1708     {
1709      "data": {
1710       "text/plain": [
1711        "True"
1712       ]
1713      },
1714      "execution_count": 33,
1715      "metadata": {},
1716      "output_type": "execute_result"
1717     }
1718    ],
1719    "source": [
1720     "is_interleave_recursive(s1, s2, s12)"
1721    ]
1722   },
1723   {
1724    "cell_type": "code",
1725    "execution_count": 34,
1726    "metadata": {},
1727    "outputs": [
1728     {
1729      "data": {
1730       "text/plain": [
1731        "False"
1732       ]
1733      },
1734      "execution_count": 34,
1735      "metadata": {},
1736      "output_type": "execute_result"
1737     }
1738    ],
1739    "source": [
1740     "is_interleave_recursive(s1, s2, s23)"
1741    ]
1742   },
1743   {
1744    "cell_type": "markdown",
1745    "metadata": {},
1746    "source": [
1747     "## Example"
1748    ]
1749   },
1750   {
1751    "cell_type": "code",
1752    "execution_count": 35,
1753    "metadata": {
1754     "collapsed": true
1755    },
1756    "outputs": [],
1757    "source": [
1758     "def show_annotated_table(table, bps):\n",
1759     "    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",
1760     "        for i in sorted(set([k[0] for k in table])))"
1761    ]
1762   },
1763   {
1764    "cell_type": "code",
1765    "execution_count": 36,
1766    "metadata": {
1767     "collapsed": true
1768    },
1769    "outputs": [],
1770    "source": [
1771     "def show_backtrace_star(bps):\n",
1772     "    i = max([0] + [k[0] for k in bps])\n",
1773     "    j = max([0] + [k[1] for k in bps])\n",
1774     "    chars = ''\n",
1775     "    stars = ''\n",
1776     "    if (i, j) in bps:\n",
1777     "        while i != 0 or j != 0:\n",
1778     "            chars += bps[i, j][2]\n",
1779     "            if bps[i, j][3] == 'seq1':\n",
1780     "                stars += '*'\n",
1781     "            else:\n",
1782     "                stars += ' '\n",
1783     "            i, j = bps[i, j][0], bps[i, j][1] \n",
1784     "        return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n",
1785     "    else:\n",
1786     "        return ''"
1787    ]
1788   },
1789   {
1790    "cell_type": "code",
1791    "execution_count": 37,
1792    "metadata": {},
1793    "outputs": [
1794     {
1795      "name": "stdout",
1796      "output_type": "stream",
1797      "text": [
1798       "0: cddcdbbdbc\n",
1799       "1: bdbacbdaaa\n",
1800       "2: bdccbaadcbdbdacacaac\n",
1801       "3: dccaadcdba\n",
1802       "4: dcccaadcdddcdbbbadbc\n",
1803       "5: bcdbddaccbddbbdaabca\n",
1804       "6: cdcccadbaadcddcbcaac\n"
1805      ]
1806     },
1807     {
1808      "data": {
1809       "text/plain": [
1810        "['bcdbddaccbddbbdaabca']"
1811       ]
1812      },
1813      "execution_count": 37,
1814      "metadata": {},
1815      "output_type": "execute_result"
1816     }
1817    ],
1818    "source": [
1819     "s1 = make_string(10, alphabet='abcd')\n",
1820     "s2 = make_string(10, alphabet='abcd')\n",
1821     "s3 = make_string(10, alphabet='abcd')\n",
1822     "s4 = make_string(10, alphabet='abcd')\n",
1823     "il = interleave(s1, s2)\n",
1824     "bs = [s3, il, interleave(s3, s4), interleave(s2, s4), interleave(s1, s3)]\n",
1825     "random.shuffle(bs)\n",
1826     "bs = [s1, s2] + bs\n",
1827     "tg = [l for l in bs if is_interleave(s1, s2, l)]\n",
1828     "print('\\n'.join(['{}: {}'.format(i, s) for i, s in enumerate(bs)]))\n",
1829     "tg"
1830    ]
1831   },
1832   {
1833    "cell_type": "code",
1834    "execution_count": 38,
1835    "metadata": {},
1836    "outputs": [
1837     {
1838      "name": "stdout",
1839      "output_type": "stream",
1840      "text": [
1841       "* b . . . . . . . . .\n",
1842       ". c d b . . . . . . .\n",
1843       ". d . d . . . . . . .\n",
1844       ". . . d a c . . . . .\n",
1845       ". . . . c c b d . . .\n",
1846       ". . . . . . d d . . .\n",
1847       ". . . . . . . b . . .\n",
1848       ". . . . . . . b . . .\n",
1849       ". . . . . . . d a a .\n",
1850       ". . . . . . . . . b .\n",
1851       ". . . . . . . . . c a\n",
1852       "bCdbDDacCbdDBBDaaBCa\n",
1853       "bcdbddaccbddbbdaabca\n",
1854       " *  **  *  ****  ** \n"
1855      ]
1856     },
1857     {
1858      "data": {
1859       "text/plain": [
1860        "True"
1861       ]
1862      },
1863      "execution_count": 38,
1864      "metadata": {},
1865      "output_type": "execute_result"
1866     }
1867    ],
1868    "source": [
1869     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1870     "print(show_annotated_table(t, bp))\n",
1871     "print(show_backtrace(bp))\n",
1872     "print(show_backtrace_star(bp))\n",
1873     "v"
1874    ]
1875   },
1876   {
1877    "cell_type": "code",
1878    "execution_count": 39,
1879    "metadata": {},
1880    "outputs": [
1881     {
1882      "name": "stdout",
1883      "output_type": "stream",
1884      "text": [
1885       "dcccaadcdddcdbbbadbc\n",
1886       "   *     **** ** ***\n"
1887      ]
1888     },
1889     {
1890      "data": {
1891       "text/plain": [
1892        "4"
1893       ]
1894      },
1895      "execution_count": 39,
1896      "metadata": {},
1897      "output_type": "execute_result"
1898     }
1899    ],
1900    "source": [
1901     "ind = [i for i, b in enumerate(bs) if is_interleave(s1, s3, b)][0]\n",
1902     "v, bp = is_interleave(s1, s3, bs[ind], return_backpointers=True)\n",
1903     "print(show_backtrace_star(bp))\n",
1904     "ind"
1905    ]
1906   },
1907   {
1908    "cell_type": "code",
1909    "execution_count": 40,
1910    "metadata": {},
1911    "outputs": [
1912     {
1913      "name": "stdout",
1914      "output_type": "stream",
1915      "text": [
1916       "* . . . . . . . . . .\n",
1917       "b c d . . . . . . . .\n",
1918       ". d . . . . . . . . .\n",
1919       ". b d d . . . . . . .\n",
1920       ". . . a c . . . . . .\n",
1921       ". . . c c . . . . . .\n",
1922       ". . . . b d . . . . .\n",
1923       ". . . . d d b b d . .\n",
1924       ". . . . . . . . a . .\n",
1925       ". . . . . . . . a b c\n",
1926       ". . . . . . . . . . a\n",
1927       "BcDBddAcCBdDbbdAAbcA\n",
1928       "bcdbddaccbddbbdaabca\n",
1929       "* **  * ** *   **  *\n"
1930      ]
1931     },
1932     {
1933      "data": {
1934       "text/plain": [
1935        "True"
1936       ]
1937      },
1938      "execution_count": 40,
1939      "metadata": {},
1940      "output_type": "execute_result"
1941     }
1942    ],
1943    "source": [
1944     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1945     "print(show_annotated_table(t, bp))\n",
1946     "print(show_backtrace(bp))\n",
1947     "print(show_backtrace_star(bp))\n",
1948     "v"
1949    ]
1950   },
1951   {
1952    "cell_type": "code",
1953    "execution_count": 41,
1954    "metadata": {},
1955    "outputs": [
1956     {
1957      "name": "stdout",
1958      "output_type": "stream",
1959      "text": [
1960       "* . . . . . . . . . .\n",
1961       ". . . . . . . . . . .\n",
1962       ". . . . . . . . . . .\n",
1963       ". . . . . . . . . . .\n",
1964       ". . . . . . . . . . .\n",
1965       ". . . . . . . . . . .\n",
1966       ". . . . . . . . . . .\n",
1967       ". . . . . . . . . . .\n",
1968       ". . . . . . . . . . .\n",
1969       ". . . . . . . . . . .\n",
1970       ". . . . . . . . . . .\n",
1971       "\n",
1972       "\n"
1973      ]
1974     },
1975     {
1976      "data": {
1977       "text/plain": [
1978        "False"
1979       ]
1980      },
1981      "execution_count": 41,
1982      "metadata": {},
1983      "output_type": "execute_result"
1984     }
1985    ],
1986    "source": [
1987     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1988     "print(show_annotated_table(t, bp))\n",
1989     "print(show_backtrace(bp))\n",
1990     "print(show_backtrace_star(bp))\n",
1991     "v"
1992    ]
1993   },
1994   {
1995    "cell_type": "code",
1996    "execution_count": 42,
1997    "metadata": {},
1998    "outputs": [
1999     {
2000      "name": "stdout",
2001      "output_type": "stream",
2002      "text": [
2003       "* . . . . . . . . . .\n",
2004       "b . . . . . . . . . .\n",
2005       ". . . . . . . . . . .\n",
2006       ". . . . . . . . . . .\n",
2007       ". . . . . . . . . . .\n",
2008       ". . . . . . . . . . .\n",
2009       ". . . . . . . . . . .\n",
2010       ". . . . . . . . . . .\n",
2011       ". . . . . . . . . . .\n",
2012       ". . . . . . . . . . .\n",
2013       ". . . . . . . . . . .\n",
2014       "B\n",
2015       "b\n",
2016       "*\n"
2017      ]
2018     },
2019     {
2020      "data": {
2021       "text/plain": [
2022        "False"
2023       ]
2024      },
2025      "execution_count": 42,
2026      "metadata": {},
2027      "output_type": "execute_result"
2028     }
2029    ],
2030    "source": [
2031     "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n",
2032     "print(show_annotated_table(t, bp))\n",
2033     "print(show_backtrace(bp))\n",
2034     "print(show_backtrace_star(bp))\n",
2035     "v"
2036    ]
2037   },
2038   {
2039    "cell_type": "markdown",
2040    "metadata": {
2041     "collapsed": true
2042    },
2043    "source": [
2044     "# Make puzzle data\n",
2045     "\n",
2046     "## Note to self\n",
2047     "Include some distractors in the test set, such that:\n",
2048     "* subsequence(my_bill, distractor) is true\n",
2049     "* subsequence(friend_bill, distractor) is true\n",
2050     "* interleave(my_bill, friend_bill, distractor) is false\n",
2051     "\n",
2052     "(i.e. characters are shared between my_bill and friend_bill)\n",
2053     "\n",
2054     "Students are taking a greedy approach to subsequence, and saying the interleave is true if both bills are subsequences of the distractor.\n",
2055     "\n",
2056     "i.e. \"aaa\" and \"aab\" are both subsequences of \"aaabbb\", but cannot be interleaved to form \"aaabbb\".\n"
2057    ]
2058   },
2059   {
2060    "cell_type": "code",
2061    "execution_count": 43,
2062    "metadata": {
2063     "collapsed": true
2064    },
2065    "outputs": [],
2066    "source": [
2067     "my_bill = make_string(200)\n",
2068     "friend_bill = make_string(200)\n",
2069     "other_bills = [make_string(200) for _ in range(98)]\n",
2070     "\n",
2071     "target_interleaved = interleave(my_bill, friend_bill)\n",
2072     "mine_interleaved = [interleave(my_bill, o) for o in random.sample(other_bills, 21)]\n",
2073     "friend_interleaved = [interleave(friend_bill, o) for o in random.sample(other_bills, 13)]\n",
2074     "other_interleaved = []\n",
2075     "for _ in range(103):\n",
2076     "    s1, s2 = random.sample(other_bills, 2)\n",
2077     "    other_interleaved += [interleave(s1, s2)]"
2078    ]
2079   },
2080   {
2081    "cell_type": "code",
2082    "execution_count": 44,
2083    "metadata": {
2084     "collapsed": true
2085    },
2086    "outputs": [],
2087    "source": [
2088     "all_targets = [target_interleaved] + mine_interleaved + friend_interleaved + other_interleaved"
2089    ]
2090   },
2091   {
2092    "cell_type": "code",
2093    "execution_count": 45,
2094    "metadata": {},
2095    "outputs": [
2096     {
2097      "name": "stdout",
2098      "output_type": "stream",
2099      "text": [
2100       "CPU times: user 3.4 s, sys: 0 ns, total: 3.4 s\n",
2101       "Wall time: 3.4 s\n"
2102      ]
2103     },
2104     {
2105      "data": {
2106       "text/plain": [
2107        "[0]"
2108       ]
2109      },
2110      "execution_count": 45,
2111      "metadata": {},
2112      "output_type": "execute_result"
2113     }
2114    ],
2115    "source": [
2116     "%time [i for i, s12 in enumerate(all_targets) if is_interleave(my_bill, friend_bill, s12)]"
2117    ]
2118   },
2119   {
2120    "cell_type": "code",
2121    "execution_count": 46,
2122    "metadata": {},
2123    "outputs": [
2124     {
2125      "name": "stdout",
2126      "output_type": "stream",
2127      "text": [
2128       "CPU times: user 932 ms, sys: 0 ns, total: 932 ms\n",
2129       "Wall time: 932 ms\n"
2130      ]
2131     },
2132     {
2133      "data": {
2134       "text/plain": [
2135        "[0]"
2136       ]
2137      },
2138      "execution_count": 46,
2139      "metadata": {},
2140      "output_type": "execute_result"
2141     }
2142    ],
2143    "source": [
2144     "%time [i for i, s12 in enumerate(all_targets) if is_interleave_recursive(my_bill, friend_bill, s12)]"
2145    ]
2146   },
2147   {
2148    "cell_type": "code",
2149    "execution_count": 47,
2150    "metadata": {
2151     "collapsed": true
2152    },
2153    "outputs": [],
2154    "source": [
2155     "bill_set = all_targets + random.sample(other_bills, 8)\n",
2156     "random.shuffle(bill_set)\n",
2157     "bill_set = [my_bill, friend_bill] + bill_set\n",
2158     "\n",
2159     "# with open('09-bills.txt', 'w') as f:\n",
2160     "#     for i, b in enumerate(bill_set):\n",
2161     "#         f.write('{}: {}\\n'.format(i, b))"
2162    ]
2163   },
2164   {
2165    "cell_type": "code",
2166    "execution_count": 51,
2167    "metadata": {
2168     "collapsed": true
2169    },
2170    "outputs": [],
2171    "source": [
2172     "def is_subseq_greedy(s1, s2):\n",
2173     "    i = j = 0\n",
2174     "    while i < len(s1) and j < len(s2):\n",
2175     "        if s1[i] == s2[j]:\n",
2176     "            i += 1\n",
2177     "        j += 1\n",
2178     "    return i == len(s1)"
2179    ]
2180   },
2181   {
2182    "cell_type": "code",
2183    "execution_count": 94,
2184    "metadata": {
2185     "collapsed": true
2186    },
2187    "outputs": [],
2188    "source": [
2189     "def subseq_partition(s1, s2):\n",
2190     "    i = j = 0\n",
2191     "    remainder = ''\n",
2192     "    while i < len(s1) and j < len(s2):\n",
2193     "        if s1[i] == s2[j]:\n",
2194     "            i += 1\n",
2195     "        else:\n",
2196     "            remainder += s2[j]\n",
2197     "        j += 1\n",
2198     "    return i == len(s1), remainder"
2199    ]
2200   },
2201   {
2202    "cell_type": "code",
2203    "execution_count": 88,
2204    "metadata": {},
2205    "outputs": [
2206     {
2207      "data": {
2208       "text/plain": [
2209        "(40, 40, 20, 20)"
2210       ]
2211      },
2212      "execution_count": 88,
2213      "metadata": {},
2214      "output_type": "execute_result"
2215     }
2216    ],
2217    "source": [
2218     "common = make_string(10)\n",
2219     "padding = make_string(10)\n",
2220     "middle = interleave(common, padding)\n",
2221     "\n",
2222     "pre1 = make_string(5)\n",
2223     "suf1 = make_string(5)\n",
2224     "\n",
2225     "pre2 = make_string(5)\n",
2226     "suf2 = make_string(5)\n",
2227     "\n",
2228     "pre = interleave(pre1, pre2)\n",
2229     "suf = interleave(suf1, suf2)\n",
2230     "\n",
2231     "distractor = pre + middle + suf\n",
2232     "\n",
2233     "sub1 = pre1 + common + suf1\n",
2234     "sub2 = pre2 + common + suf2\n",
2235     "\n",
2236     "valid = interleave(sub1, sub2)\n",
2237     "\n",
2238     "len(distractor), len(valid), len(sub1), len(sub2)"
2239    ]
2240   },
2241   {
2242    "cell_type": "code",
2243    "execution_count": 89,
2244    "metadata": {},
2245    "outputs": [
2246     {
2247      "data": {
2248       "text/plain": [
2249        "(True, True)"
2250       ]
2251      },
2252      "execution_count": 89,
2253      "metadata": {},
2254      "output_type": "execute_result"
2255     }
2256    ],
2257    "source": [
2258     "is_subseq_greedy(sub1, distractor), is_subseq_greedy(sub2, distractor)"
2259    ]
2260   },
2261   {
2262    "cell_type": "code",
2263    "execution_count": 90,
2264    "metadata": {},
2265    "outputs": [
2266     {
2267      "data": {
2268       "text/plain": [
2269        "(True, True)"
2270       ]
2271      },
2272      "execution_count": 90,
2273      "metadata": {},
2274      "output_type": "execute_result"
2275     }
2276    ],
2277    "source": [
2278     "is_subseq_greedy(sub1, valid), is_subseq_greedy(sub2, valid)"
2279    ]
2280   },
2281   {
2282    "cell_type": "code",
2283    "execution_count": 91,
2284    "metadata": {},
2285    "outputs": [
2286     {
2287      "data": {
2288       "text/plain": [
2289        "(False, True)"
2290       ]
2291      },
2292      "execution_count": 91,
2293      "metadata": {},
2294      "output_type": "execute_result"
2295     }
2296    ],
2297    "source": [
2298     "is_interleave(sub1, sub2, distractor), is_interleave(sub1, sub2, valid)"
2299    ]
2300   },
2301   {
2302    "cell_type": "code",
2303    "execution_count": 93,
2304    "metadata": {},
2305    "outputs": [
2306     {
2307      "data": {
2308       "text/plain": [
2309        "('efcfdffcdbcehdffghch',\n",
2310        " 'hhdgeffcdbcehdfhfded',\n",
2311        " 'hhefdcgefdffdhgcdbcdbbeebhdefgfhgfdehdch',\n",
2312        " 'hhdegeffcffcdfdbcefchdfdbchehfddeffghdch')"
2313       ]
2314      },
2315      "execution_count": 93,
2316      "metadata": {},
2317      "output_type": "execute_result"
2318     }
2319    ],
2320    "source": [
2321     "sub1, sub2, distractor, valid"
2322    ]
2323   },
2324   {
2325    "cell_type": "code",
2326    "execution_count": 96,
2327    "metadata": {},
2328    "outputs": [
2329     {
2330      "data": {
2331       "text/plain": [
2332        "False"
2333       ]
2334      },
2335      "execution_count": 96,
2336      "metadata": {},
2337      "output_type": "execute_result"
2338     }
2339    ],
2340    "source": [
2341     "a, b = subseq_partition(sub1, distractor)\n",
2342     "b == sub2"
2343    ]
2344   },
2345   {
2346    "cell_type": "code",
2347    "execution_count": 98,
2348    "metadata": {},
2349    "outputs": [
2350     {
2351      "data": {
2352       "text/plain": [
2353        "('hhdgeffcdbcehfdhfded', 'hhdgeffcdbcehdfhfded')"
2354       ]
2355      },
2356      "execution_count": 98,
2357      "metadata": {},
2358      "output_type": "execute_result"
2359     }
2360    ],
2361    "source": [
2362     "a, b = subseq_partition(sub1, valid)\n",
2363     "b, sub2"
2364    ]
2365   },
2366   {
2367    "cell_type": "code",
2368    "execution_count": null,
2369    "metadata": {
2370     "collapsed": true
2371    },
2372    "outputs": [],
2373    "source": []
2374   }
2375  ],
2376  "metadata": {
2377   "kernelspec": {
2378    "display_name": "Python 3",
2379    "language": "python",
2380    "name": "python3"
2381   },
2382   "language_info": {
2383    "codemirror_mode": {
2384     "name": "ipython",
2385     "version": 3
2386    },
2387    "file_extension": ".py",
2388    "mimetype": "text/x-python",
2389    "name": "python",
2390    "nbconvert_exporter": "python",
2391    "pygments_lexer": "ipython3",
2392    "version": "3.5.2+"
2393   }
2394  },
2395  "nbformat": 4,
2396  "nbformat_minor": 1
2397 }