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": 3,
  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": 4,
  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": 5,
  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": 5,
  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": 6,
  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": 6,
  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": 7,
 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": 7,
 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": 8,
 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": 9,
 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": 10,
 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": 11,
 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": 11,
 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": 12,
 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": 13,
 417    "metadata": {},
 418    "outputs": [
 419     {
 420      "data": {
 421       "text/plain": [
 422        "True"
 423       ]
 424      },
 425      "execution_count": 13,
 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": 14,
 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": 14,
 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": 15,
 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": 15,
 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": 16,
 545    "metadata": {},
 546    "outputs": [
 547     {
 548      "data": {
 549       "text/plain": [
 550        "False"
 551       ]
 552      },
 553      "execution_count": 16,
 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": 17,
 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": 17,
 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": 18,
 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": 19,
 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": 20,
 656    "metadata": {},
 657    "outputs": [
 658     {
 659      "data": {
 660       "text/plain": [
 661        "'fcdafhachbgaheghbbcehecbgfgbbbedcgcgcagdcgcbffdgbg'"
 662       ]
 663      },
 664      "execution_count": 20,
 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": 21,
 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": 22,
 717    "metadata": {},
 718    "outputs": [
 719     {
 720      "name": "stdout",
 721      "output_type": "stream",
 722      "text": [
 723       "0 0 0 adding b\n",
 724       "1 0 1 adding x\n",
 725       "1 1 0 adding z\n",
 726       "1 2 -1 adding h\n",
 727       "2 2 0 adding v\n",
 728       "2 3 -1 adding w\n",
 729       "2 4 -2 adding f\n",
 730       "3 4 -1 adding g\n",
 731       "4 4 0 adding g\n",
 732       "5 4 1 adding w\n",
 733       "5 5 0 adding z\n",
 734       "5 6 -1 adding x\n",
 735       "5 7 -2 adding w\n",
 736       "5 8 -3 adding w\n",
 737       "5 9 -4 adding e\n",
 738       "6 9 -3 adding h\n",
 739       "7 9 -2 adding c\n",
 740       "8 9 -1 adding x\n",
 741       "8 10 -2 adding y\n",
 742       "8 11 -3 adding d\n",
 743       "9 11 -2 adding x\n",
 744       "9 12 -3 adding a\n",
 745       "10 12 -2 adding e\n",
 746       "11 12 -1 adding a\n",
 747       "12 12 0 adding z\n",
 748       "12 13 -1 adding y\n",
 749       "12 14 -2 adding x\n",
 750       "12 15 -3 adding h\n",
 751       "13 15 -2 adding x\n",
 752       "13 16 -3 adding x\n",
 753       "13 17 -4 adding u\n",
 754       "13 18 -5 adding d\n",
 755       "14 18 -4 adding w\n",
 756       "14 19 -5 adding e\n",
 757       "15 19 -4 adding b\n",
 758       "16 19 -3 adding w\n",
 759       "16 20 -4 remaining s1 eaca\n"
 760      ]
 761     },
 762     {
 763      "data": {
 764       "text/plain": [
 765        "('bhfggehcdaeahdebeaca',\n",
 766        " 'xzvwwzxwwxyxzyxxxuww',\n",
 767        " 'bxzhvwfggwzxwwehcxydxaeazyxhxxudwebweaca',\n",
 768        " 40)"
 769       ]
 770      },
 771      "execution_count": 22,
 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": 23,
 786    "metadata": {},
 787    "outputs": [
 788     {
 789      "name": "stdout",
 790      "output_type": "stream",
 791      "text": [
 792       "xxxx 0 0 ! ! ! True\n",
 793       "seq2 0 1 ! b b True\n",
 794       "seq2 0 2 ! h x False\n",
 795       "seq2 0 3 ! f z False\n",
 796       "seq2 0 4 ! g h False\n",
 797       "seq2 0 5 ! g v False\n",
 798       "seq2 0 6 ! e w False\n",
 799       "seq2 0 7 ! h f False\n",
 800       "seq2 0 8 ! c g False\n",
 801       "seq2 0 9 ! d g False\n",
 802       "seq2 0 10 ! a w False\n",
 803       "seq2 0 11 ! e z False\n",
 804       "seq2 0 12 ! a x False\n",
 805       "seq2 0 13 ! h w False\n",
 806       "seq2 0 14 ! d w False\n",
 807       "seq2 0 15 ! e e False\n",
 808       "seq2 0 16 ! b h False\n",
 809       "seq2 0 17 ! e c False\n",
 810       "seq2 0 18 ! a x False\n",
 811       "seq2 0 19 ! c y False\n",
 812       "seq2 0 20 ! a d False\n",
 813       "seq1 1 0 x ! b False\n",
 814       "seq1 1 1 x b x True\n",
 815       "xxxx 1 2 x h z False\n",
 816       "xxxx 1 3 x f h False\n",
 817       "xxxx 1 4 x g v False\n",
 818       "xxxx 1 5 x g w False\n",
 819       "xxxx 1 6 x e f False\n",
 820       "xxxx 1 7 x h g False\n",
 821       "xxxx 1 8 x c g False\n",
 822       "xxxx 1 9 x d w False\n",
 823       "xxxx 1 10 x a z False\n",
 824       "xxxx 1 11 x e x False\n",
 825       "xxxx 1 12 x a w False\n",
 826       "xxxx 1 13 x h w False\n",
 827       "xxxx 1 14 x d e False\n",
 828       "xxxx 1 15 x e h False\n",
 829       "xxxx 1 16 x b c False\n",
 830       "xxxx 1 17 x e x False\n",
 831       "xxxx 1 18 x a y False\n",
 832       "xxxx 1 19 x c d False\n",
 833       "xxxx 1 20 x a x False\n",
 834       "seq1 2 0 z ! x False\n",
 835       "seq1 2 1 z b z True\n",
 836       "seq2 2 2 z h h True\n",
 837       "xxxx 2 3 z f v False\n",
 838       "xxxx 2 4 z g w False\n",
 839       "xxxx 2 5 z g f False\n",
 840       "xxxx 2 6 z e g False\n",
 841       "xxxx 2 7 z h g False\n",
 842       "xxxx 2 8 z c w False\n",
 843       "xxxx 2 9 z d z False\n",
 844       "xxxx 2 10 z a x False\n",
 845       "xxxx 2 11 z e w False\n",
 846       "xxxx 2 12 z a w False\n",
 847       "xxxx 2 13 z h e False\n",
 848       "xxxx 2 14 z d h False\n",
 849       "xxxx 2 15 z e c False\n",
 850       "xxxx 2 16 z b x False\n",
 851       "xxxx 2 17 z e y False\n",
 852       "xxxx 2 18 z a d False\n",
 853       "xxxx 2 19 z c x False\n",
 854       "xxxx 2 20 z a a False\n",
 855       "seq1 3 0 v ! z False\n",
 856       "xxxx 3 1 v b h False\n",
 857       "seq1 3 2 v h v True\n",
 858       "xxxx 3 3 v f w False\n",
 859       "xxxx 3 4 v g f False\n",
 860       "xxxx 3 5 v g g False\n",
 861       "xxxx 3 6 v e g False\n",
 862       "xxxx 3 7 v h w False\n",
 863       "xxxx 3 8 v c z False\n",
 864       "xxxx 3 9 v d x False\n",
 865       "xxxx 3 10 v a w False\n",
 866       "xxxx 3 11 v e w False\n",
 867       "xxxx 3 12 v a e False\n",
 868       "xxxx 3 13 v h h False\n",
 869       "xxxx 3 14 v d c False\n",
 870       "xxxx 3 15 v e x False\n",
 871       "xxxx 3 16 v b y False\n",
 872       "xxxx 3 17 v e d False\n",
 873       "xxxx 3 18 v a x False\n",
 874       "xxxx 3 19 v c a False\n",
 875       "xxxx 3 20 v a e False\n",
 876       "seq1 4 0 w ! h False\n",
 877       "xxxx 4 1 w b v False\n",
 878       "seq1 4 2 w h w True\n",
 879       "seq2 4 3 w f f True\n",
 880       "seq2 4 4 w g g True\n",
 881       "seq2 4 5 w g g True\n",
 882       "xxxx 4 6 w e w False\n",
 883       "xxxx 4 7 w h z False\n",
 884       "xxxx 4 8 w c x False\n",
 885       "xxxx 4 9 w d w False\n",
 886       "xxxx 4 10 w a w False\n",
 887       "xxxx 4 11 w e e False\n",
 888       "xxxx 4 12 w a h False\n",
 889       "xxxx 4 13 w h c False\n",
 890       "xxxx 4 14 w d x False\n",
 891       "xxxx 4 15 w e y False\n",
 892       "xxxx 4 16 w b d False\n",
 893       "xxxx 4 17 w e x False\n",
 894       "xxxx 4 18 w a a False\n",
 895       "xxxx 4 19 w c e False\n",
 896       "xxxx 4 20 w a a False\n",
 897       "seq1 5 0 w ! v False\n",
 898       "xxxx 5 1 w b w False\n",
 899       "xxxx 5 2 w h f False\n",
 900       "xxxx 5 3 w f g False\n",
 901       "xxxx 5 4 w g g False\n",
 902       "seq1 5 5 w g w True\n",
 903       "xxxx 5 6 w e z False\n",
 904       "xxxx 5 7 w h x False\n",
 905       "xxxx 5 8 w c w False\n",
 906       "xxxx 5 9 w d w False\n",
 907       "xxxx 5 10 w a e False\n",
 908       "xxxx 5 11 w e h False\n",
 909       "xxxx 5 12 w a c False\n",
 910       "xxxx 5 13 w h x False\n",
 911       "xxxx 5 14 w d y False\n",
 912       "xxxx 5 15 w e d False\n",
 913       "xxxx 5 16 w b x False\n",
 914       "xxxx 5 17 w e a False\n",
 915       "xxxx 5 18 w a e False\n",
 916       "xxxx 5 19 w c a False\n",
 917       "xxxx 5 20 w a z False\n",
 918       "seq1 6 0 z ! w False\n",
 919       "xxxx 6 1 z b f False\n",
 920       "xxxx 6 2 z h g False\n",
 921       "xxxx 6 3 z f g False\n",
 922       "xxxx 6 4 z g w False\n",
 923       "seq1 6 5 z g z True\n",
 924       "xxxx 6 6 z e x False\n",
 925       "xxxx 6 7 z h w False\n",
 926       "xxxx 6 8 z c w False\n",
 927       "xxxx 6 9 z d e False\n",
 928       "xxxx 6 10 z a h False\n",
 929       "xxxx 6 11 z e c False\n",
 930       "xxxx 6 12 z a x False\n",
 931       "xxxx 6 13 z h y False\n",
 932       "xxxx 6 14 z d d False\n",
 933       "xxxx 6 15 z e x False\n",
 934       "xxxx 6 16 z b a False\n",
 935       "xxxx 6 17 z e e False\n",
 936       "xxxx 6 18 z a a False\n",
 937       "xxxx 6 19 z c z False\n",
 938       "xxxx 6 20 z a y False\n",
 939       "seq1 7 0 x ! f False\n",
 940       "xxxx 7 1 x b g False\n",
 941       "xxxx 7 2 x h g False\n",
 942       "xxxx 7 3 x f w False\n",
 943       "xxxx 7 4 x g z False\n",
 944       "seq1 7 5 x g x True\n",
 945       "xxxx 7 6 x e w False\n",
 946       "xxxx 7 7 x h w False\n",
 947       "xxxx 7 8 x c e False\n",
 948       "xxxx 7 9 x d h False\n",
 949       "xxxx 7 10 x a c False\n",
 950       "xxxx 7 11 x e x False\n",
 951       "xxxx 7 12 x a y False\n",
 952       "xxxx 7 13 x h d False\n",
 953       "xxxx 7 14 x d x False\n",
 954       "xxxx 7 15 x e a False\n",
 955       "xxxx 7 16 x b e False\n",
 956       "xxxx 7 17 x e a False\n",
 957       "xxxx 7 18 x a z False\n",
 958       "xxxx 7 19 x c y False\n",
 959       "xxxx 7 20 x a x False\n",
 960       "seq1 8 0 w ! g False\n",
 961       "xxxx 8 1 w b g False\n",
 962       "xxxx 8 2 w h w False\n",
 963       "xxxx 8 3 w f z False\n",
 964       "xxxx 8 4 w g x False\n",
 965       "seq1 8 5 w g w True\n",
 966       "xxxx 8 6 w e w False\n",
 967       "xxxx 8 7 w h e False\n",
 968       "xxxx 8 8 w c h False\n",
 969       "xxxx 8 9 w d c False\n",
 970       "xxxx 8 10 w a x False\n",
 971       "xxxx 8 11 w e y False\n",
 972       "xxxx 8 12 w a d False\n",
 973       "xxxx 8 13 w h x False\n",
 974       "xxxx 8 14 w d a False\n",
 975       "xxxx 8 15 w e e False\n",
 976       "xxxx 8 16 w b a False\n",
 977       "xxxx 8 17 w e z False\n",
 978       "xxxx 8 18 w a y False\n",
 979       "xxxx 8 19 w c x False\n",
 980       "xxxx 8 20 w a h False\n",
 981       "seq1 9 0 w ! g False\n",
 982       "xxxx 9 1 w b w False\n",
 983       "xxxx 9 2 w h z False\n",
 984       "xxxx 9 3 w f x False\n",
 985       "xxxx 9 4 w g w False\n",
 986       "seq1 9 5 w g w True\n",
 987       "seq2 9 6 w e e True\n",
 988       "seq2 9 7 w h h True\n",
 989       "seq2 9 8 w c c True\n",
 990       "xxxx 9 9 w d x False\n",
 991       "xxxx 9 10 w a y False\n",
 992       "xxxx 9 11 w e d False\n",
 993       "xxxx 9 12 w a x False\n",
 994       "xxxx 9 13 w h a False\n",
 995       "xxxx 9 14 w d e False\n",
 996       "xxxx 9 15 w e a False\n",
 997       "xxxx 9 16 w b z False\n",
 998       "xxxx 9 17 w e y False\n",
 999       "xxxx 9 18 w a x False\n",
1000       "xxxx 9 19 w c h False\n",
1001       "xxxx 9 20 w a x False\n",
1002       "seq1 10 0 x ! w False\n",
1003       "xxxx 10 1 x b z False\n",
1004       "xxxx 10 2 x h x False\n",
1005       "xxxx 10 3 x f w False\n",
1006       "xxxx 10 4 x g w False\n",
1007       "xxxx 10 5 x g e False\n",
1008       "xxxx 10 6 x e h False\n",
1009       "xxxx 10 7 x h c False\n",
1010       "seq1 10 8 x c x True\n",
1011       "xxxx 10 9 x d y False\n",
1012       "xxxx 10 10 x a d False\n",
1013       "xxxx 10 11 x e x False\n",
1014       "xxxx 10 12 x a a False\n",
1015       "xxxx 10 13 x h e False\n",
1016       "xxxx 10 14 x d a False\n",
1017       "xxxx 10 15 x e z False\n",
1018       "xxxx 10 16 x b y False\n",
1019       "xxxx 10 17 x e x False\n",
1020       "xxxx 10 18 x a h False\n",
1021       "xxxx 10 19 x c x False\n",
1022       "xxxx 10 20 x a x False\n",
1023       "seq1 11 0 y ! z False\n",
1024       "xxxx 11 1 y b x False\n",
1025       "xxxx 11 2 y h w False\n",
1026       "xxxx 11 3 y f w False\n",
1027       "xxxx 11 4 y g e False\n",
1028       "xxxx 11 5 y g h False\n",
1029       "xxxx 11 6 y e c False\n",
1030       "xxxx 11 7 y h x False\n",
1031       "seq1 11 8 y c y True\n",
1032       "seq2 11 9 y d d True\n",
1033       "xxxx 11 10 y a x False\n",
1034       "xxxx 11 11 y e a False\n",
1035       "xxxx 11 12 y a e False\n",
1036       "xxxx 11 13 y h a False\n",
1037       "xxxx 11 14 y d z False\n",
1038       "xxxx 11 15 y e y False\n",
1039       "xxxx 11 16 y b x False\n",
1040       "xxxx 11 17 y e h False\n",
1041       "xxxx 11 18 y a x False\n",
1042       "xxxx 11 19 y c x False\n",
1043       "xxxx 11 20 y a u False\n",
1044       "seq1 12 0 x ! x False\n",
1045       "xxxx 12 1 x b w False\n",
1046       "xxxx 12 2 x h w False\n",
1047       "xxxx 12 3 x f e False\n",
1048       "xxxx 12 4 x g h False\n",
1049       "xxxx 12 5 x g c False\n",
1050       "xxxx 12 6 x e x False\n",
1051       "xxxx 12 7 x h y False\n",
1052       "xxxx 12 8 x c d False\n",
1053       "seq1 12 9 x d x True\n",
1054       "seq2 12 10 x a a True\n",
1055       "seq2 12 11 x e e True\n",
1056       "seq2 12 12 x a a True\n",
1057       "xxxx 12 13 x h z False\n",
1058       "xxxx 12 14 x d y False\n",
1059       "xxxx 12 15 x e x False\n",
1060       "xxxx 12 16 x b h False\n",
1061       "xxxx 12 17 x e x False\n",
1062       "xxxx 12 18 x a x False\n",
1063       "xxxx 12 19 x c u False\n",
1064       "xxxx 12 20 x a d False\n",
1065       "seq1 13 0 z ! w False\n",
1066       "xxxx 13 1 z b w False\n",
1067       "xxxx 13 2 z h e False\n",
1068       "xxxx 13 3 z f h False\n",
1069       "xxxx 13 4 z g c False\n",
1070       "xxxx 13 5 z g x False\n",
1071       "xxxx 13 6 z e y False\n",
1072       "xxxx 13 7 z h d False\n",
1073       "xxxx 13 8 z c x False\n",
1074       "xxxx 13 9 z d a False\n",
1075       "xxxx 13 10 z a e False\n",
1076       "xxxx 13 11 z e a False\n",
1077       "seq1 13 12 z a z True\n",
1078       "xxxx 13 13 z h y False\n",
1079       "xxxx 13 14 z d x False\n",
1080       "xxxx 13 15 z e h False\n",
1081       "xxxx 13 16 z b x False\n",
1082       "xxxx 13 17 z e x False\n",
1083       "xxxx 13 18 z a u False\n",
1084       "xxxx 13 19 z c d False\n",
1085       "xxxx 13 20 z a w False\n",
1086       "seq1 14 0 y ! w False\n",
1087       "xxxx 14 1 y b e False\n",
1088       "xxxx 14 2 y h h False\n",
1089       "xxxx 14 3 y f c False\n",
1090       "xxxx 14 4 y g x False\n",
1091       "xxxx 14 5 y g y False\n",
1092       "xxxx 14 6 y e d False\n",
1093       "xxxx 14 7 y h x False\n",
1094       "xxxx 14 8 y c a False\n",
1095       "xxxx 14 9 y d e False\n",
1096       "xxxx 14 10 y a a False\n",
1097       "xxxx 14 11 y e z False\n",
1098       "seq1 14 12 y a y True\n",
1099       "xxxx 14 13 y h x False\n",
1100       "xxxx 14 14 y d h False\n",
1101       "xxxx 14 15 y e x False\n",
1102       "xxxx 14 16 y b x False\n",
1103       "xxxx 14 17 y e u False\n",
1104       "xxxx 14 18 y a d False\n",
1105       "xxxx 14 19 y c w False\n",
1106       "xxxx 14 20 y a e False\n",
1107       "seq1 15 0 x ! e False\n",
1108       "xxxx 15 1 x b h False\n",
1109       "xxxx 15 2 x h c False\n",
1110       "xxxx 15 3 x f x False\n",
1111       "xxxx 15 4 x g y False\n",
1112       "xxxx 15 5 x g d False\n",
1113       "xxxx 15 6 x e x False\n",
1114       "xxxx 15 7 x h a False\n",
1115       "xxxx 15 8 x c e False\n",
1116       "xxxx 15 9 x d a False\n",
1117       "xxxx 15 10 x a z False\n",
1118       "xxxx 15 11 x e y False\n",
1119       "seq1 15 12 x a x True\n",
1120       "seq2 15 13 x h h True\n",
1121       "xxxx 15 14 x d x False\n",
1122       "xxxx 15 15 x e x False\n",
1123       "xxxx 15 16 x b u False\n",
1124       "xxxx 15 17 x e d False\n",
1125       "xxxx 15 18 x a w False\n",
1126       "xxxx 15 19 x c e False\n",
1127       "xxxx 15 20 x a b False\n",
1128       "seq1 16 0 x ! h False\n",
1129       "xxxx 16 1 x b c False\n",
1130       "xxxx 16 2 x h x False\n",
1131       "xxxx 16 3 x f y False\n",
1132       "xxxx 16 4 x g d False\n",
1133       "xxxx 16 5 x g x False\n",
1134       "xxxx 16 6 x e a False\n",
1135       "xxxx 16 7 x h e False\n",
1136       "xxxx 16 8 x c a False\n",
1137       "xxxx 16 9 x d z False\n",
1138       "xxxx 16 10 x a y False\n",
1139       "xxxx 16 11 x e x False\n",
1140       "xxxx 16 12 x a h False\n",
1141       "seq1 16 13 x h x True\n",
1142       "xxxx 16 14 x d x False\n",
1143       "xxxx 16 15 x e u False\n",
1144       "xxxx 16 16 x b d False\n",
1145       "xxxx 16 17 x e w False\n",
1146       "xxxx 16 18 x a e False\n",
1147       "xxxx 16 19 x c b False\n",
1148       "xxxx 16 20 x a w False\n",
1149       "seq1 17 0 x ! c False\n",
1150       "xxxx 17 1 x b x False\n",
1151       "xxxx 17 2 x h y False\n",
1152       "xxxx 17 3 x f d False\n",
1153       "xxxx 17 4 x g x False\n",
1154       "xxxx 17 5 x g a False\n",
1155       "xxxx 17 6 x e e False\n",
1156       "xxxx 17 7 x h a False\n",
1157       "xxxx 17 8 x c z False\n",
1158       "xxxx 17 9 x d y False\n",
1159       "xxxx 17 10 x a x False\n",
1160       "xxxx 17 11 x e h False\n",
1161       "xxxx 17 12 x a x False\n",
1162       "seq1 17 13 x h x True\n",
1163       "xxxx 17 14 x d u False\n",
1164       "xxxx 17 15 x e d False\n",
1165       "xxxx 17 16 x b w False\n",
1166       "xxxx 17 17 x e e False\n",
1167       "xxxx 17 18 x a b False\n",
1168       "xxxx 17 19 x c w False\n",
1169       "xxxx 17 20 x a e False\n",
1170       "seq1 18 0 u ! x False\n",
1171       "xxxx 18 1 u b y False\n",
1172       "xxxx 18 2 u h d False\n",
1173       "xxxx 18 3 u f x False\n",
1174       "xxxx 18 4 u g a False\n",
1175       "xxxx 18 5 u g e False\n",
1176       "xxxx 18 6 u e a False\n",
1177       "xxxx 18 7 u h z False\n",
1178       "xxxx 18 8 u c y False\n",
1179       "xxxx 18 9 u d x False\n",
1180       "xxxx 18 10 u a h False\n",
1181       "xxxx 18 11 u e x False\n",
1182       "xxxx 18 12 u a x False\n",
1183       "seq1 18 13 u h u True\n",
1184       "seq2 18 14 u d d True\n",
1185       "xxxx 18 15 u e w False\n",
1186       "xxxx 18 16 u b e False\n",
1187       "xxxx 18 17 u e b False\n",
1188       "xxxx 18 18 u a w False\n",
1189       "xxxx 18 19 u c e False\n",
1190       "xxxx 18 20 u a a False\n",
1191       "seq1 19 0 w ! y False\n",
1192       "xxxx 19 1 w b d False\n",
1193       "xxxx 19 2 w h x False\n",
1194       "xxxx 19 3 w f a False\n",
1195       "xxxx 19 4 w g e False\n",
1196       "xxxx 19 5 w g a False\n",
1197       "xxxx 19 6 w e z False\n",
1198       "xxxx 19 7 w h y False\n",
1199       "xxxx 19 8 w c x False\n",
1200       "xxxx 19 9 w d h False\n",
1201       "xxxx 19 10 w a x False\n",
1202       "xxxx 19 11 w e x False\n",
1203       "xxxx 19 12 w a u False\n",
1204       "xxxx 19 13 w h d False\n",
1205       "seq1 19 14 w d w True\n",
1206       "seq2 19 15 w e e True\n",
1207       "seq2 19 16 w b b True\n",
1208       "xxxx 19 17 w e w False\n",
1209       "xxxx 19 18 w a e False\n",
1210       "xxxx 19 19 w c a False\n",
1211       "xxxx 19 20 w a c False\n",
1212       "seq1 20 0 w ! d False\n",
1213       "xxxx 20 1 w b x False\n",
1214       "xxxx 20 2 w h a False\n",
1215       "xxxx 20 3 w f e False\n",
1216       "xxxx 20 4 w g a False\n",
1217       "xxxx 20 5 w g z False\n",
1218       "xxxx 20 6 w e y False\n",
1219       "xxxx 20 7 w h x False\n",
1220       "xxxx 20 8 w c h False\n",
1221       "xxxx 20 9 w d x False\n",
1222       "xxxx 20 10 w a x False\n",
1223       "xxxx 20 11 w e u False\n",
1224       "xxxx 20 12 w a d False\n",
1225       "xxxx 20 13 w h w False\n",
1226       "xxxx 20 14 w d e False\n",
1227       "xxxx 20 15 w e b False\n",
1228       "seq1 20 16 w b w True\n",
1229       "seq2 20 17 w e e True\n",
1230       "seq2 20 18 w a a True\n",
1231       "seq2 20 19 w c c True\n",
1232       "seq2 20 20 w a a True\n",
1233       "T T . . . . . . . . . . . . . . . . . . .\n",
1234       ". T . . . . . . . . . . . . . . . . . . .\n",
1235       ". T T . . . . . . . . . . . . . . . . . .\n",
1236       ". . T . . . . . . . . . . . . . . . . . .\n",
1237       ". . T T T T . . . . . . . . . . . . . . .\n",
1238       ". . . . . T . . . . . . . . . . . . . . .\n",
1239       ". . . . . T . . . . . . . . . . . . . . .\n",
1240       ". . . . . T . . . . . . . . . . . . . . .\n",
1241       ". . . . . T . . . . . . . . . . . . . . .\n",
1242       ". . . . . T T T T . . . . . . . . . . . .\n",
1243       ". . . . . . . . T . . . . . . . . . . . .\n",
1244       ". . . . . . . . T T . . . . . . . . . . .\n",
1245       ". . . . . . . . . T T T T . . . . . . . .\n",
1246       ". . . . . . . . . . . . T . . . . . . . .\n",
1247       ". . . . . . . . . . . . T . . . . . . . .\n",
1248       ". . . . . . . . . . . . T T . . . . . . .\n",
1249       ". . . . . . . . . . . . . T . . . . . . .\n",
1250       ". . . . . . . . . . . . . T . . . . . . .\n",
1251       ". . . . . . . . . . . . . T T . . . . . .\n",
1252       ". . . . . . . . . . . . . . T T T . . . .\n",
1253       ". . . . . . . . . . . . . . . . T T T T 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": 24,
1265    "metadata": {},
1266    "outputs": [
1267     {
1268      "data": {
1269       "text/plain": [
1270        "'bXZhVWfggWZXWWehcXYdXaeaZYXhXXUdWebWeaca'"
1271       ]
1272      },
1273      "execution_count": 24,
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": 25,
1285    "metadata": {},
1286    "outputs": [
1287     {
1288      "name": "stdout",
1289      "output_type": "stream",
1290      "text": [
1291       "T T . . . . . . . . . . . . . . . . . . .\n",
1292       ". T . . . . . . . . . . . . . . . . . . .\n",
1293       ". T T . . . . . . . . . . . . . . . . . .\n",
1294       ". . T . . . . . . . . . . . . . . . . . .\n",
1295       ". . T T T T . . . . . . . . . . . . . . .\n",
1296       ". . . . . T . . . . . . . . . . . . . . .\n",
1297       ". . . . . T . . . . . . . . . . . . . . .\n",
1298       ". . . . . T . . . . . . . . . . . . . . .\n",
1299       ". . . . . T . . . . . . . . . . . . . . .\n",
1300       ". . . . . T T T T . . . . . . . . . . . .\n",
1301       ". . . . . . . . T . . . . . . . . . . . .\n",
1302       ". . . . . . . . T T . . . . . . . . . . .\n",
1303       ". . . . . . . . . T T T T . . . . . . . .\n",
1304       ". . . . . . . . . . . . T . . . . . . . .\n",
1305       ". . . . . . . . . . . . T . . . . . . . .\n",
1306       ". . . . . . . . . . . . T T . . . . . . .\n",
1307       ". . . . . . . . . . . . . T . . . . . . .\n",
1308       ". . . . . . . . . . . . . T . . . . . . .\n",
1309       ". . . . . . . . . . . . . T T . . . . . .\n",
1310       ". . . . . . . . . . . . . . T T T . . . .\n",
1311       ". . . . . . . . . . . . . . . . T T T T T\n",
1312       "bXZhVWfggWZXWWehcXYdXaeaZYXhXXUdWebWeaca\n"
1313      ]
1314     },
1315     {
1316      "data": {
1317       "text/plain": [
1318        "True"
1319       ]
1320      },
1321      "execution_count": 25,
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": 26,
1336    "metadata": {},
1337    "outputs": [
1338     {
1339      "data": {
1340       "text/plain": [
1341        "('baffeeecaecbfghedbgbddbcdchbefeddgdbecbaacbdedbeca',\n",
1342        " 'affdffbahedebhaagaaahebdeechbfhedcdgcccdcgfbdhaghe',\n",
1343        " 'affbaffedeecfaefcbbfaghhededebbhgaagbdaaadbhebdeechbcdchfbehfedcdgecddcgcdcgdfbbdehacgbhaaecbdedbeca',\n",
1344        " 100)"
1345       ]
1346      },
1347      "execution_count": 26,
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": 27,
1362    "metadata": {},
1363    "outputs": [
1364     {
1365      "name": "stdout",
1366      "output_type": "stream",
1367      "text": [
1368       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1369       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1370       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1371       "T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1372       ". . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1373       ". . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1374       ". . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1375       ". . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1376       ". . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1377       ". . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1378       ". . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1379       ". . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1380       ". . . . . . . . . . . . . . . T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1381       ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1382       ". . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1383       ". . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1384       ". . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1385       ". . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1386       ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1387       ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1388       ". . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1389       ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1390       ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1391       ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1392       ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1393       ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1394       ". . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1395       ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1396       ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1397       ". . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1398       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . .\n",
1399       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n",
1400       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
1401       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
1402       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
1403       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
1404       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . .\n",
1405       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . .\n",
1406       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . .\n",
1407       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
1408       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1409       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1410       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
1411       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
1412       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
1413       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . .\n",
1414       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1415       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
1416       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . .\n",
1417       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . .\n",
1418       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T T T T\n",
1419       "AFFbaffeDeecFaeFcbBfAghHedEDEbBHgAAGbdAAAdbHEBDEECHBcdchFbeHfEDCDGeCddCgCDCGdFbBDeHAcGbHaaEcbdedbeca\n"
1420      ]
1421     },
1422     {
1423      "data": {
1424       "text/plain": [
1425        "True"
1426       ]
1427      },
1428      "execution_count": 27,
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": 28,
1443    "metadata": {},
1444    "outputs": [
1445     {
1446      "name": "stdout",
1447      "output_type": "stream",
1448      "text": [
1449       "1000 loops, best of 3: 1.48 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": 29,
1461    "metadata": {},
1462    "outputs": [
1463     {
1464      "name": "stdout",
1465      "output_type": "stream",
1466      "text": [
1467       "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1468       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1469       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1470       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1471       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1472       ". . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1473       ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1474       ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1475       ". . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1476       ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1477       ". . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1478       ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1479       ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1480       ". . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1481       ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1482       ". . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1483       ". . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1484       ". . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1485       ". . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1486       ". . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1487       ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1488       ". . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1489       ". . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1490       ". . . . . . . . . . . . . . . . . . . . T T T T T T T T T T . . . . . . . . . . . . . . . . . . . . .\n",
1491       ". . . . . . . . . . . . . . . . . . . . . . . . . . T . . T . . . . . . . . . . . . . . . . . . . . .\n",
1492       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . .\n",
1493       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . .\n",
1494       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
1495       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
1496       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . .\n",
1497       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . .\n",
1498       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . T T . . . . . . . . . . . . .\n",
1499       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . T . . . . . . . . . . . . .\n",
1500       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
1501       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . .\n",
1502       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . T T T . . . . . .\n",
1503       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . .\n",
1504       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . .\n",
1505       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . .\n",
1506       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T .\n",
1507       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T .\n",
1508       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T\n",
1509       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1510       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1511       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1512       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1513       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1514       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1515       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1516       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1517       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1518       "affBAFFEdEECfAEfCbBFaGhHedEDebBhGaagBDaaaDBhebdeechbCDCHfBEhFedcdgEcDDcGcdcgDfbBdEhaCgBhAAeCBDEDBECA\n"
1519      ]
1520     },
1521     {
1522      "data": {
1523       "text/plain": [
1524        "True"
1525       ]
1526      },
1527      "execution_count": 29,
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": 30,
1542    "metadata": {},
1543    "outputs": [
1544     {
1545      "data": {
1546       "text/plain": [
1547        "True"
1548       ]
1549      },
1550      "execution_count": 30,
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": 31,
1562    "metadata": {},
1563    "outputs": [
1564     {
1565      "data": {
1566       "text/plain": [
1567        "('bgcbeceebhdgegdfehfccbfbagadhbddfbbgecdhegdaegdheh', False, False)"
1568       ]
1569      },
1570      "execution_count": 31,
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": 32,
1583    "metadata": {},
1584    "outputs": [
1585     {
1586      "name": "stdout",
1587      "output_type": "stream",
1588      "text": [
1589       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1590       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1591       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1592       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1593       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1594       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1595       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1596       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1597       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1598       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1599       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1600       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1601       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1602       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1603       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1604       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1605       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1606       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1607       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1608       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1609       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1610       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1611       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1612       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1613       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1614       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1615       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1616       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1617       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1618       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1619       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1620       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1621       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1622       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1623       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1624       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1625       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1626       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1627       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1628       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1629       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1630       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1631       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1632       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1633       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1634       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1635       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1636       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1637       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1638       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1639       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1640       "\n"
1641      ]
1642     },
1643     {
1644      "data": {
1645       "text/plain": [
1646        "False"
1647       ]
1648      },
1649      "execution_count": 32,
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": 33,
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": 34,
1688    "metadata": {
1689     "collapsed": true
1690    },
1691    "outputs": [],
1692    "source": [
1693     "import uuid"
1694    ]
1695   },
1696   {
1697    "cell_type": "code",
1698    "execution_count": 35,
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": 36,
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": 62,
1791    "metadata": {},
1792    "outputs": [
1793     {
1794      "name": "stdout",
1795      "output_type": "stream",
1796      "text": [
1797       "T . . . . .\n",
1798       "T . . . . .\n",
1799       "T T T T T .\n",
1800       ". T T . T .\n",
1801       ". . T T T T\n",
1802       ". . . T . T\n",
1803       "AAdbbcBCaC\n"
1804      ]
1805     }
1806    ],
1807    "source": [
1808     "v, bp, t = is_interleave(s1, s2, s3t, return_backpointers=True, return_table=True)\n",
1809     "print(show_table(t))\n",
1810     "print(show_backtrace(bp))"
1811    ]
1812   },
1813   {
1814    "cell_type": "code",
1815    "execution_count": 63,
1816    "metadata": {
1817     "collapsed": true
1818    },
1819    "outputs": [],
1820    "source": [
1821     "def show_table_md(table, s1, s2, s3):\n",
1822     "    header = '|   |' + '|'.join('{}<br />{}'.format('<br />'.join(str(s2[:i])), i) for i in range(len(s2) + 1)) + '|'\n",
1823     "    separator = '|:---:' * (len(s2) + 2) + '|'\n",
1824     "    rows = []\n",
1825     "    columns = sorted(set(k[1] for k in table))\n",
1826     "    for r in range(len(s1) + 1):\n",
1827     "        row = '|**{}<br />{}**|'.format(r, s1[:r])\n",
1828     "        row += '|'.join('{}<br />T'.format(s3[:(r+c)]) if table[r, c] else '{}<br />.'.format(s3[:(r+c)]) for c in columns)\n",
1829     "        row += '|'\n",
1830     "        rows += [row]\n",
1831     "    return '\\n'.join([header] + [separator] + rows)"
1832    ]
1833   },
1834   {
1835    "cell_type": "code",
1836    "execution_count": 64,
1837    "metadata": {},
1838    "outputs": [
1839     {
1840      "name": "stdout",
1841      "output_type": "stream",
1842      "text": [
1843       "|   |<br />0|d<br />1|d<br />b<br />2|d<br />b<br />b<br />3|d<br />b<br />b<br />c<br />4|d<br />b<br />b<br />c<br />a<br />5|\n",
1844       "|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n",
1845       "|**0<br />**|<br />T|a<br />.|aa<br />.|aad<br />.|aadb<br />.|aadbb<br />.|\n",
1846       "|**1<br />a**|a<br />T|aa<br />.|aad<br />.|aadb<br />.|aadbb<br />.|aadbbc<br />.|\n",
1847       "|**2<br />aa**|aa<br />T|aad<br />T|aadb<br />T|aadbb<br />T|aadbbc<br />T|aadbbcb<br />.|\n",
1848       "|**3<br />aab**|aad<br />.|aadb<br />T|aadbb<br />T|aadbbc<br />.|aadbbcb<br />T|aadbbcbc<br />.|\n",
1849       "|**4<br />aabc**|aadb<br />.|aadbb<br />.|aadbbc<br />T|aadbbcb<br />T|aadbbcbc<br />T|aadbbcbca<br />T|\n",
1850       "|**5<br />aabcc**|aadbb<br />.|aadbbc<br />.|aadbbcb<br />.|aadbbcbc<br />T|aadbbcbca<br />.|aadbbcbcac<br />T|\n"
1851      ]
1852     }
1853    ],
1854    "source": [
1855     "print(show_table_md(t, s1, s2, s3t))"
1856    ]
1857   },
1858   {
1859    "cell_type": "markdown",
1860    "metadata": {},
1861    "source": [
1862     "|   |<br />0|d<br />1|d<br />b<br />2|d<br />b<br />b<br />3|d<br />b<br />b<br />c<br />4|d<br />b<br />b<br />c<br />a<br />5|\n",
1863     "|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n",
1864     "|**0<br />**|<br />T|a<br />.|aa<br />.|aad<br />.|aadb<br />.|aadbb<br />.|\n",
1865     "|**1<br />a**|a<br />T|aa<br />.|aad<br />.|aadb<br />.|aadbb<br />.|aadbbc<br />.|\n",
1866     "|**2<br />aa**|aa<br />T|aad<br />T|aadb<br />T|aadbb<br />T|aadbbc<br />T|aadbbcb<br />.|\n",
1867     "|**3<br />aab**|aad<br />.|aadb<br />T|aadbb<br />T|aadbbc<br />.|aadbbcb<br />T|aadbbcbc<br />.|\n",
1868     "|**4<br />aabc**|aadb<br />.|aadbb<br />.|aadbbc<br />T|aadbbcb<br />T|aadbbcbc<br />T|aadbbcbca<br />T|\n",
1869     "|**5<br />aabcc**|aadbb<br />.|aadbbc<br />.|aadbbcb<br />.|aadbbcbc<br />T|aadbbcbca<br />.|aadbbcbcac<br />T|"
1870    ]
1871   },
1872   {
1873    "cell_type": "code",
1874    "execution_count": 68,
1875    "metadata": {},
1876    "outputs": [
1877     {
1878      "name": "stdout",
1879      "output_type": "stream",
1880      "text": [
1881       "T T T T\n",
1882       "T . T .\n",
1883       ". . T T\n",
1884       ". . . T\n",
1885       "abACaB\n"
1886      ]
1887     }
1888    ],
1889    "source": [
1890     "e1 = 'acb'\n",
1891     "e2 = 'aba'\n",
1892     "e3 = 'abacab'\n",
1893     "v, bp, et = is_interleave(e1, e2, e3, return_backpointers=True, return_table=True)\n",
1894     "print(show_table(et))\n",
1895     "print(show_backtrace(bp))"
1896    ]
1897   },
1898   {
1899    "cell_type": "code",
1900    "execution_count": 69,
1901    "metadata": {},
1902    "outputs": [
1903     {
1904      "name": "stdout",
1905      "output_type": "stream",
1906      "text": [
1907       "|   |<br />0|a<br />1|a<br />b<br />2|a<br />b<br />a<br />3|\n",
1908       "|:---:|:---:|:---:|:---:|:---:|\n",
1909       "|**0<br />**|<br />T|a<br />T|ab<br />T|aba<br />T|\n",
1910       "|**1<br />a**|a<br />T|ab<br />.|aba<br />T|abac<br />.|\n",
1911       "|**2<br />ac**|ab<br />.|aba<br />.|abac<br />T|abaca<br />T|\n",
1912       "|**3<br />acb**|aba<br />.|abac<br />.|abaca<br />.|abacab<br />T|\n"
1913      ]
1914     }
1915    ],
1916    "source": [
1917     "print(show_table_md(et, e1, e2, e3))"
1918    ]
1919   },
1920   {
1921    "cell_type": "markdown",
1922    "metadata": {},
1923    "source": [
1924     "|   |<br />0|a<br />1|a<br />b<br />2|a<br />b<br />a<br />3|\n",
1925     "|:---:|:---:|:---:|:---:|:---:|\n",
1926     "|**0<br />**|<br />T|a<br />T|ab<br />T|aba<br />T|\n",
1927     "|**1<br />a**|a<br />T|ab<br />.|aba<br />T|abac<br />.|\n",
1928     "|**2<br />ac**|ab<br />.|aba<br />.|abac<br />T|abaca<br />T|\n",
1929     "|**3<br />acb**|aba<br />.|abac<br />.|abaca<br />.|abacab<br />T|"
1930    ]
1931   },
1932   {
1933    "cell_type": "code",
1934    "execution_count": 70,
1935    "metadata": {
1936     "scrolled": true
1937    },
1938    "outputs": [
1939     {
1940      "name": "stdout",
1941      "output_type": "stream",
1942      "text": [
1943       "n825af3fb1bf441a3b97d8fbfcdce6f3d [label=\"aabcc\\ndbbca\\naadbbcbcac\"];\n",
1944       "n825af3fb1bf441a3b97d8fbfcdce6f3d -> n944a00ca9b134f3c98aeef34526ff17d;\n",
1945       "n944a00ca9b134f3c98aeef34526ff17d [label=\"aabc\\ndbbca\\naadbbcbca\"];\n",
1946       "n944a00ca9b134f3c98aeef34526ff17d -> n1586862dcfb74b1a9e9f964b7de102ef;\n",
1947       "n1586862dcfb74b1a9e9f964b7de102ef [label=\"aabc\\ndbbc\\naadbbcbc\"];\n",
1948       "n1586862dcfb74b1a9e9f964b7de102ef -> nf59278631d8047e7b0cca670e412297b;\n",
1949       "n1586862dcfb74b1a9e9f964b7de102ef -> nd83e9c32d1fa43bab45dc21d46830924;\n",
1950       "nf59278631d8047e7b0cca670e412297b [label=\"aab\\ndbbc\\naadbbcb\"];\n",
1951       "nf59278631d8047e7b0cca670e412297b -> nb0424588e9354d2aa61b587a7edfb7f6;\n",
1952       "nb0424588e9354d2aa61b587a7edfb7f6 [label=\"aa\\ndbbc\\naadbbc\"];\n",
1953       "nb0424588e9354d2aa61b587a7edfb7f6 -> nb73d85cfb09e43d692de22a49de48b35;\n",
1954       "nb73d85cfb09e43d692de22a49de48b35 [label=\"aa\\ndbb\\naadbb\"];\n",
1955       "nb73d85cfb09e43d692de22a49de48b35 -> n9e34f866ae1746d797cebd4e1fc73af9;\n",
1956       "n9e34f866ae1746d797cebd4e1fc73af9 [label=\"aa\\ndb\\naadb\"];\n",
1957       "n9e34f866ae1746d797cebd4e1fc73af9 -> n5c7027bfea9f494894cea01fd5e25387;\n",
1958       "n5c7027bfea9f494894cea01fd5e25387 [label=\"aa\\nd\\naad\"];\n",
1959       "n5c7027bfea9f494894cea01fd5e25387 -> n650da0feb2624011a20e209bada2445c;\n",
1960       "n650da0feb2624011a20e209bada2445c [label=\"aa\\n-\\naa\\nTrue\"];\n",
1961       "nd83e9c32d1fa43bab45dc21d46830924 [label=\"aabc\\ndbb\\naadbbcb\"];\n",
1962       "nd83e9c32d1fa43bab45dc21d46830924 -> n1c4772b660f24d6da9194d16be602b3a;\n",
1963       "n1c4772b660f24d6da9194d16be602b3a [label=\"aabc\\ndb\\naadbbc\"];\n",
1964       "n1c4772b660f24d6da9194d16be602b3a -> n0393745322e447c79515cffb4afc4d5b;\n",
1965       "n0393745322e447c79515cffb4afc4d5b [label=\"aab\\ndb\\naadbb\"];\n",
1966       "n0393745322e447c79515cffb4afc4d5b -> na9ae42f3b7dd415886e78bb960b94184;\n",
1967       "n0393745322e447c79515cffb4afc4d5b -> nccaf23a4e311415cbe42bedd8a3727c2;\n",
1968       "na9ae42f3b7dd415886e78bb960b94184 [label=\"aa\\ndb\\naadb\"];\n",
1969       "na9ae42f3b7dd415886e78bb960b94184 -> nab2d4f76a75c4c6686166212cad4b4a3;\n",
1970       "nab2d4f76a75c4c6686166212cad4b4a3 [label=\"aa\\nd\\naad\"];\n",
1971       "nab2d4f76a75c4c6686166212cad4b4a3 -> nee8a56cc920943e0a2593a8ee863c53c;\n",
1972       "nee8a56cc920943e0a2593a8ee863c53c [label=\"aa\\n-\\naa\\nTrue\"];\n",
1973       "nccaf23a4e311415cbe42bedd8a3727c2 [label=\"aab\\nd\\naadb\"];\n",
1974       "nccaf23a4e311415cbe42bedd8a3727c2 -> ne1d3cf2b04074c10986fdefb464e5da8;\n",
1975       "ne1d3cf2b04074c10986fdefb464e5da8 [label=\"aa\\nd\\naad\"];\n",
1976       "ne1d3cf2b04074c10986fdefb464e5da8 -> n9091b74bc8a64b91a9e75aef6b016a64;\n",
1977       "n9091b74bc8a64b91a9e75aef6b016a64 [label=\"aa\\n-\\naa\\nTrue\"];\n"
1978      ]
1979     }
1980    ],
1981    "source": [
1982     "root, graph = is_interleave_recursive_dot(s1, s2, s3t)\n",
1983     "print('\\n'.join(graph))"
1984    ]
1985   },
1986   {
1987    "cell_type": "code",
1988    "execution_count": 71,
1989    "metadata": {
1990     "scrolled": true
1991    },
1992    "outputs": [
1993     {
1994      "name": "stdout",
1995      "output_type": "stream",
1996      "text": [
1997       "n894a2781e978478699af2875308ec4ad [label=\"aaa\\naaa\\naaaaaa\"];\n",
1998       "n894a2781e978478699af2875308ec4ad -> n863e03f8030547bf9f4e7a4815c4e027;\n",
1999       "n894a2781e978478699af2875308ec4ad -> n4c492e6eb94741d2b11567b1b4c729fa;\n",
2000       "n863e03f8030547bf9f4e7a4815c4e027 [label=\"aa\\naaa\\naaaaa\"];\n",
2001       "n863e03f8030547bf9f4e7a4815c4e027 -> n8f044087a7324ef69d5cf2ae120c0902;\n",
2002       "n863e03f8030547bf9f4e7a4815c4e027 -> n5510c6a96018480ba0fc2315d34a69e6;\n",
2003       "n8f044087a7324ef69d5cf2ae120c0902 [label=\"a\\naaa\\naaaa\"];\n",
2004       "n8f044087a7324ef69d5cf2ae120c0902 -> n6f3153ef68384ebbbe5860a48c774d55;\n",
2005       "n8f044087a7324ef69d5cf2ae120c0902 -> n4d068ce52cf248adb3b537805a233dda;\n",
2006       "n6f3153ef68384ebbbe5860a48c774d55 [label=\"-\\naaa\\naaa\\nTrue\"];\n",
2007       "n4d068ce52cf248adb3b537805a233dda [label=\"a\\naa\\naaa\"];\n",
2008       "n4d068ce52cf248adb3b537805a233dda -> nb85aee31625f4998b596d9b6ea3b77fd;\n",
2009       "n4d068ce52cf248adb3b537805a233dda -> nec2837ce384246ffb06e3d4090adfb37;\n",
2010       "nb85aee31625f4998b596d9b6ea3b77fd [label=\"-\\naa\\naa\\nTrue\"];\n",
2011       "nec2837ce384246ffb06e3d4090adfb37 [label=\"a\\na\\naa\"];\n",
2012       "nec2837ce384246ffb06e3d4090adfb37 -> n9c395901af2d4e67a7e5a370f759bce6;\n",
2013       "nec2837ce384246ffb06e3d4090adfb37 -> nff84b0c784744901afb3ac8a5aef3c23;\n",
2014       "n9c395901af2d4e67a7e5a370f759bce6 [label=\"-\\na\\na\\nTrue\"];\n",
2015       "nff84b0c784744901afb3ac8a5aef3c23 [label=\"a\\n-\\na\\nTrue\"];\n",
2016       "n5510c6a96018480ba0fc2315d34a69e6 [label=\"aa\\naa\\naaaa\"];\n",
2017       "n5510c6a96018480ba0fc2315d34a69e6 -> n5eaaabd1caef4c3f8f6607a8bb254906;\n",
2018       "n5510c6a96018480ba0fc2315d34a69e6 -> n6041081af67d4f57968572aa2051d1bc;\n",
2019       "n5eaaabd1caef4c3f8f6607a8bb254906 [label=\"a\\naa\\naaa\"];\n",
2020       "n5eaaabd1caef4c3f8f6607a8bb254906 -> n6dd23a9ed026429fb57cbf94e6283364;\n",
2021       "n5eaaabd1caef4c3f8f6607a8bb254906 -> n3042bda75e7c4d8f8a9ccc464f0ba724;\n",
2022       "n6dd23a9ed026429fb57cbf94e6283364 [label=\"-\\naa\\naa\\nTrue\"];\n",
2023       "n3042bda75e7c4d8f8a9ccc464f0ba724 [label=\"a\\na\\naa\"];\n",
2024       "n3042bda75e7c4d8f8a9ccc464f0ba724 -> n5e702eeee87042deb3157b6663b1f07a;\n",
2025       "n3042bda75e7c4d8f8a9ccc464f0ba724 -> n37928d6516f942008c5e89b5c37098ee;\n",
2026       "n5e702eeee87042deb3157b6663b1f07a [label=\"-\\na\\na\\nTrue\"];\n",
2027       "n37928d6516f942008c5e89b5c37098ee [label=\"a\\n-\\na\\nTrue\"];\n",
2028       "n6041081af67d4f57968572aa2051d1bc [label=\"aa\\na\\naaa\"];\n",
2029       "n6041081af67d4f57968572aa2051d1bc -> nbb96e07d3c89450cb92ad725f6fc4845;\n",
2030       "n6041081af67d4f57968572aa2051d1bc -> n0dbe764d7e4a429298f2d3583e8c84b1;\n",
2031       "nbb96e07d3c89450cb92ad725f6fc4845 [label=\"a\\na\\naa\"];\n",
2032       "nbb96e07d3c89450cb92ad725f6fc4845 -> nbe5a7be2ec824370a293e7aa8f3a5467;\n",
2033       "nbb96e07d3c89450cb92ad725f6fc4845 -> ndc15a7d84b734bb793055e4712a82d5c;\n",
2034       "nbe5a7be2ec824370a293e7aa8f3a5467 [label=\"-\\na\\na\\nTrue\"];\n",
2035       "ndc15a7d84b734bb793055e4712a82d5c [label=\"a\\n-\\na\\nTrue\"];\n",
2036       "n0dbe764d7e4a429298f2d3583e8c84b1 [label=\"aa\\n-\\naa\\nTrue\"];\n",
2037       "n4c492e6eb94741d2b11567b1b4c729fa [label=\"aaa\\naa\\naaaaa\"];\n",
2038       "n4c492e6eb94741d2b11567b1b4c729fa -> n0e78dd2900a34a7297cc0ea2bb27e30c;\n",
2039       "n4c492e6eb94741d2b11567b1b4c729fa -> nc18fe2c53e9e4209a9af9c0678465b1f;\n",
2040       "n0e78dd2900a34a7297cc0ea2bb27e30c [label=\"aa\\naa\\naaaa\"];\n",
2041       "n0e78dd2900a34a7297cc0ea2bb27e30c -> n1b98c16a65994faaa980d9c530383c77;\n",
2042       "n0e78dd2900a34a7297cc0ea2bb27e30c -> n33dbe313802045f8895d0e904d588881;\n",
2043       "n1b98c16a65994faaa980d9c530383c77 [label=\"a\\naa\\naaa\"];\n",
2044       "n1b98c16a65994faaa980d9c530383c77 -> n5e7c6dff46ff49f7903eb543c02fa22b;\n",
2045       "n1b98c16a65994faaa980d9c530383c77 -> n33391a1fab3849cf9823ccc7396aa7d4;\n",
2046       "n5e7c6dff46ff49f7903eb543c02fa22b [label=\"-\\naa\\naa\\nTrue\"];\n",
2047       "n33391a1fab3849cf9823ccc7396aa7d4 [label=\"a\\na\\naa\"];\n",
2048       "n33391a1fab3849cf9823ccc7396aa7d4 -> n13b4732016804c3986853f6d2fe4a28b;\n",
2049       "n33391a1fab3849cf9823ccc7396aa7d4 -> n767be985e5a5469da7cfeea0272705b3;\n",
2050       "n13b4732016804c3986853f6d2fe4a28b [label=\"-\\na\\na\\nTrue\"];\n",
2051       "n767be985e5a5469da7cfeea0272705b3 [label=\"a\\n-\\na\\nTrue\"];\n",
2052       "n33dbe313802045f8895d0e904d588881 [label=\"aa\\na\\naaa\"];\n",
2053       "n33dbe313802045f8895d0e904d588881 -> nf59143762fc643f0bd58507b5097b837;\n",
2054       "n33dbe313802045f8895d0e904d588881 -> n30d968450bf147b68a8d7df49177722c;\n",
2055       "nf59143762fc643f0bd58507b5097b837 [label=\"a\\na\\naa\"];\n",
2056       "nf59143762fc643f0bd58507b5097b837 -> ncd2168bdc52c459d821427219fb885d1;\n",
2057       "nf59143762fc643f0bd58507b5097b837 -> nc6011f3f746f425ab01fd89e1f17cbb4;\n",
2058       "ncd2168bdc52c459d821427219fb885d1 [label=\"-\\na\\na\\nTrue\"];\n",
2059       "nc6011f3f746f425ab01fd89e1f17cbb4 [label=\"a\\n-\\na\\nTrue\"];\n",
2060       "n30d968450bf147b68a8d7df49177722c [label=\"aa\\n-\\naa\\nTrue\"];\n",
2061       "nc18fe2c53e9e4209a9af9c0678465b1f [label=\"aaa\\na\\naaaa\"];\n",
2062       "nc18fe2c53e9e4209a9af9c0678465b1f -> n38a7aa8aab21444d8b9d50ca71871b7e;\n",
2063       "nc18fe2c53e9e4209a9af9c0678465b1f -> n1ec1cf69ce3c4798b305338648a6e46b;\n",
2064       "n38a7aa8aab21444d8b9d50ca71871b7e [label=\"aa\\na\\naaa\"];\n",
2065       "n38a7aa8aab21444d8b9d50ca71871b7e -> nad5433a86522484e85d560ac7d202b3d;\n",
2066       "n38a7aa8aab21444d8b9d50ca71871b7e -> n6bfb83c32f9e46a19e9408fc087e74ae;\n",
2067       "nad5433a86522484e85d560ac7d202b3d [label=\"a\\na\\naa\"];\n",
2068       "nad5433a86522484e85d560ac7d202b3d -> n292f0206736a40ac8f6045ac0d8a0a07;\n",
2069       "nad5433a86522484e85d560ac7d202b3d -> n07c65e03d3bd473f97579a2c63f922c7;\n",
2070       "n292f0206736a40ac8f6045ac0d8a0a07 [label=\"-\\na\\na\\nTrue\"];\n",
2071       "n07c65e03d3bd473f97579a2c63f922c7 [label=\"a\\n-\\na\\nTrue\"];\n",
2072       "n6bfb83c32f9e46a19e9408fc087e74ae [label=\"aa\\n-\\naa\\nTrue\"];\n",
2073       "n1ec1cf69ce3c4798b305338648a6e46b [label=\"aaa\\n-\\naaa\\nTrue\"];\n"
2074      ]
2075     }
2076    ],
2077    "source": [
2078     "root, graph = is_interleave_recursive_dot('aaa', 'aaa', 'aaaaaa')\n",
2079     "print('\\n'.join(graph))"
2080    ]
2081   },
2082   {
2083    "cell_type": "code",
2084    "execution_count": 70,
2085    "metadata": {
2086     "scrolled": true
2087    },
2088    "outputs": [
2089     {
2090      "name": "stdout",
2091      "output_type": "stream",
2092      "text": [
2093       "nd6df1effdb85482db276ea5fea364b79 [label=\"acb\\naba\\nabacab\"];\n",
2094       "nd6df1effdb85482db276ea5fea364b79 -> necd79ad17e9d435c9f49c1c1ae26b524;\n",
2095       "necd79ad17e9d435c9f49c1c1ae26b524 [label=\"ac\\naba\\nabaca\"];\n",
2096       "necd79ad17e9d435c9f49c1c1ae26b524 -> n369b759fead243e0b35621ac1dbc09de;\n",
2097       "n369b759fead243e0b35621ac1dbc09de [label=\"ac\\nab\\nabac\"];\n",
2098       "n369b759fead243e0b35621ac1dbc09de -> nc4a2401f9791408ba2bb7b4052c27f11;\n",
2099       "nc4a2401f9791408ba2bb7b4052c27f11 [label=\"a\\nab\\naba\"];\n",
2100       "nc4a2401f9791408ba2bb7b4052c27f11 -> n71b5737da5e54fcb9dfdee6085091a01;\n",
2101       "n71b5737da5e54fcb9dfdee6085091a01 [label=\"-\\nab\\nab\\nTrue\"];\n"
2102      ]
2103     }
2104    ],
2105    "source": [
2106     "root, graph = is_interleave_recursive_dot(e1, e2, e3)\n",
2107     "print('\\n'.join(graph))"
2108    ]
2109   },
2110   {
2111    "cell_type": "code",
2112    "execution_count": 35,
2113    "metadata": {
2114     "collapsed": true
2115    },
2116    "outputs": [],
2117    "source": [
2118     "s1 = make_string(500)\n",
2119     "s2 = make_string(500)\n",
2120     "s3 = make_string(500)\n",
2121     "s12 = interleave(s1, s2)\n",
2122     "s23 = interleave(s2, s3)"
2123    ]
2124   },
2125   {
2126    "cell_type": "code",
2127    "execution_count": 36,
2128    "metadata": {},
2129    "outputs": [
2130     {
2131      "data": {
2132       "text/plain": [
2133        "True"
2134       ]
2135      },
2136      "execution_count": 36,
2137      "metadata": {},
2138      "output_type": "execute_result"
2139     }
2140    ],
2141    "source": [
2142     "is_interleave_recursive(s1, s2, s12)"
2143    ]
2144   },
2145   {
2146    "cell_type": "code",
2147    "execution_count": 37,
2148    "metadata": {},
2149    "outputs": [
2150     {
2151      "data": {
2152       "text/plain": [
2153        "False"
2154       ]
2155      },
2156      "execution_count": 37,
2157      "metadata": {},
2158      "output_type": "execute_result"
2159     }
2160    ],
2161    "source": [
2162     "is_interleave_recursive(s1, s2, s23)"
2163    ]
2164   },
2165   {
2166    "cell_type": "markdown",
2167    "metadata": {},
2168    "source": [
2169     "## Example"
2170    ]
2171   },
2172   {
2173    "cell_type": "code",
2174    "execution_count": 38,
2175    "metadata": {
2176     "collapsed": true
2177    },
2178    "outputs": [],
2179    "source": [
2180     "def show_annotated_table(table, bps):\n",
2181     "    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",
2182     "        for i in sorted(set([k[0] for k in table])))"
2183    ]
2184   },
2185   {
2186    "cell_type": "code",
2187    "execution_count": 39,
2188    "metadata": {
2189     "collapsed": true
2190    },
2191    "outputs": [],
2192    "source": [
2193     "def show_backtrace_star(bps):\n",
2194     "    i = max([0] + [k[0] for k in bps])\n",
2195     "    j = max([0] + [k[1] for k in bps])\n",
2196     "    chars = ''\n",
2197     "    stars = ''\n",
2198     "    if (i, j) in bps:\n",
2199     "        while i != 0 or j != 0:\n",
2200     "            chars += bps[i, j][2]\n",
2201     "            if bps[i, j][3] == 'seq1':\n",
2202     "                stars += '*'\n",
2203     "            else:\n",
2204     "                stars += ' '\n",
2205     "            i, j = bps[i, j][0], bps[i, j][1] \n",
2206     "        return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n",
2207     "    else:\n",
2208     "        return ''"
2209    ]
2210   },
2211   {
2212    "cell_type": "code",
2213    "execution_count": 40,
2214    "metadata": {},
2215    "outputs": [
2216     {
2217      "name": "stdout",
2218      "output_type": "stream",
2219      "text": [
2220       "0: baddacaddb\n",
2221       "1: bcccacbacb\n",
2222       "2: cdcddbcccacbacbaabcc\n",
2223       "3: cdccdbadcaacbbcccaac\n",
2224       "4: bbacccdacdacadbdbacb\n",
2225       "5: cbaccbbcadadaaccaddb\n",
2226       "6: cbaccbcaac\n"
2227      ]
2228     },
2229     {
2230      "data": {
2231       "text/plain": [
2232        "['bbacccdacdacadbdbacb']"
2233       ]
2234      },
2235      "execution_count": 40,
2236      "metadata": {},
2237      "output_type": "execute_result"
2238     }
2239    ],
2240    "source": [
2241     "s1 = make_string(10, alphabet='abcd')\n",
2242     "s2 = make_string(10, alphabet='abcd')\n",
2243     "s3 = make_string(10, alphabet='abcd')\n",
2244     "s4 = make_string(10, alphabet='abcd')\n",
2245     "il = interleave(s1, s2)\n",
2246     "bs = [s3, il, interleave(s3, s4), interleave(s2, s4), interleave(s1, s3)]\n",
2247     "random.shuffle(bs)\n",
2248     "bs = [s1, s2] + bs\n",
2249     "tg = [l for l in bs if is_interleave(s1, s2, l)]\n",
2250     "print('\\n'.join(['{}: {}'.format(i, s) for i, s in enumerate(bs)]))\n",
2251     "tg"
2252    ]
2253   },
2254   {
2255    "cell_type": "code",
2256    "execution_count": 41,
2257    "metadata": {},
2258    "outputs": [
2259     {
2260      "name": "stdout",
2261      "output_type": "stream",
2262      "text": [
2263       "* b . . . . . . . . .\n",
2264       "b b . . . . . . . . .\n",
2265       ". a c c c . . . . . .\n",
2266       ". . . . d a c . . . .\n",
2267       ". . . . . . d . . . .\n",
2268       ". . . . . . a . . . .\n",
2269       ". . . . . . c . . . .\n",
2270       ". . . . . . a . . . .\n",
2271       ". . . . . . d b . . .\n",
2272       ". . . . . . . d . . .\n",
2273       ". . . . . . . b a c b\n",
2274       "bBAcccDacDACADbDBacb\n",
2275       "bbacccdacdacadbdbacb\n",
2276       " **   *  ***** **   \n"
2277      ]
2278     },
2279     {
2280      "data": {
2281       "text/plain": [
2282        "True"
2283       ]
2284      },
2285      "execution_count": 41,
2286      "metadata": {},
2287      "output_type": "execute_result"
2288     }
2289    ],
2290    "source": [
2291     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
2292     "print(show_annotated_table(t, bp))\n",
2293     "print(show_backtrace(bp))\n",
2294     "print(show_backtrace_star(bp))\n",
2295     "v"
2296    ]
2297   },
2298   {
2299    "cell_type": "code",
2300    "execution_count": 42,
2301    "metadata": {},
2302    "outputs": [
2303     {
2304      "name": "stdout",
2305      "output_type": "stream",
2306      "text": [
2307       "cbaccbbcadadaaccaddb\n",
2308       "      * ** * * *****\n"
2309      ]
2310     },
2311     {
2312      "data": {
2313       "text/plain": [
2314        "5"
2315       ]
2316      },
2317      "execution_count": 42,
2318      "metadata": {},
2319      "output_type": "execute_result"
2320     }
2321    ],
2322    "source": [
2323     "ind = [i for i, b in enumerate(bs) if is_interleave(s1, s3, b)][0]\n",
2324     "v, bp = is_interleave(s1, s3, bs[ind], return_backpointers=True)\n",
2325     "print(show_backtrace_star(bp))\n",
2326     "ind"
2327    ]
2328   },
2329   {
2330    "cell_type": "code",
2331    "execution_count": 43,
2332    "metadata": {},
2333    "outputs": [
2334     {
2335      "name": "stdout",
2336      "output_type": "stream",
2337      "text": [
2338       "* b . . . . . . . . .\n",
2339       "b b a . . . . . . . .\n",
2340       ". . c . . . . . . . .\n",
2341       ". . c . . . . . . . .\n",
2342       ". . c d . . . . . . .\n",
2343       ". . . a . . . . . . .\n",
2344       ". . . c d a c a d . .\n",
2345       ". . . . . . . . b d b\n",
2346       ". . . . . . . . . . a\n",
2347       ". . . . . . . . . . c\n",
2348       ". . . . . . . . . . b\n",
2349       "bBaCCCdACdacadBdbACB\n",
2350       "bbacccdacdacadbdbacb\n",
2351       " * *** **     *  ***\n"
2352      ]
2353     },
2354     {
2355      "data": {
2356       "text/plain": [
2357        "True"
2358       ]
2359      },
2360      "execution_count": 43,
2361      "metadata": {},
2362      "output_type": "execute_result"
2363     }
2364    ],
2365    "source": [
2366     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
2367     "print(show_annotated_table(t, bp))\n",
2368     "print(show_backtrace(bp))\n",
2369     "print(show_backtrace_star(bp))\n",
2370     "v"
2371    ]
2372   },
2373   {
2374    "cell_type": "code",
2375    "execution_count": 44,
2376    "metadata": {},
2377    "outputs": [
2378     {
2379      "name": "stdout",
2380      "output_type": "stream",
2381      "text": [
2382       "* . . . . . . . . . .\n",
2383       "b . . . . . . . . . .\n",
2384       ". . . . . . . . . . .\n",
2385       ". . . . . . . . . . .\n",
2386       ". . . . . . . . . . .\n",
2387       ". . . . . . . . . . .\n",
2388       ". . . . . . . . . . .\n",
2389       ". . . . . . . . . . .\n",
2390       ". . . . . . . . . . .\n",
2391       ". . . . . . . . . . .\n",
2392       ". . . . . . . . . . .\n",
2393       "B\n",
2394       "b\n",
2395       "*\n"
2396      ]
2397     },
2398     {
2399      "data": {
2400       "text/plain": [
2401        "False"
2402       ]
2403      },
2404      "execution_count": 44,
2405      "metadata": {},
2406      "output_type": "execute_result"
2407     }
2408    ],
2409    "source": [
2410     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
2411     "print(show_annotated_table(t, bp))\n",
2412     "print(show_backtrace(bp))\n",
2413     "print(show_backtrace_star(bp))\n",
2414     "v"
2415    ]
2416   },
2417   {
2418    "cell_type": "code",
2419    "execution_count": 45,
2420    "metadata": {},
2421    "outputs": [
2422     {
2423      "name": "stdout",
2424      "output_type": "stream",
2425      "text": [
2426       "* . . . . . . . . . .\n",
2427       "b . . . . . . . . . .\n",
2428       ". . . . . . . . . . .\n",
2429       ". . . . . . . . . . .\n",
2430       ". . . . . . . . . . .\n",
2431       ". . . . . . . . . . .\n",
2432       ". . . . . . . . . . .\n",
2433       ". . . . . . . . . . .\n",
2434       ". . . . . . . . . . .\n",
2435       ". . . . . . . . . . .\n",
2436       ". . . . . . . . . . .\n",
2437       "B\n",
2438       "b\n",
2439       "*\n"
2440      ]
2441     },
2442     {
2443      "data": {
2444       "text/plain": [
2445        "False"
2446       ]
2447      },
2448      "execution_count": 45,
2449      "metadata": {},
2450      "output_type": "execute_result"
2451     }
2452    ],
2453    "source": [
2454     "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n",
2455     "print(show_annotated_table(t, bp))\n",
2456     "print(show_backtrace(bp))\n",
2457     "print(show_backtrace_star(bp))\n",
2458     "v"
2459    ]
2460   },
2461   {
2462    "cell_type": "markdown",
2463    "metadata": {
2464     "collapsed": true
2465    },
2466    "source": [
2467     "# Make puzzle data\n",
2468     "\n",
2469     "## Note to self\n",
2470     "Include some distractors in the test set, such that:\n",
2471     "* subsequence(my_bill, distractor) is true\n",
2472     "* subsequence(friend_bill, distractor) is true\n",
2473     "* interleave(my_bill, friend_bill, distractor) is false\n",
2474     "\n",
2475     "(i.e. characters are shared between my_bill and friend_bill)\n",
2476     "\n",
2477     "Students are taking a greedy approach to subsequence, and saying the interleave is true if both bills are subsequences of the distractor.\n",
2478     "\n",
2479     "i.e. \"aaa\" and \"aab\" are both subsequences of \"aaabbb\", but cannot be interleaved to form \"aaabbb\".\n"
2480    ]
2481   },
2482   {
2483    "cell_type": "code",
2484    "execution_count": 46,
2485    "metadata": {
2486     "collapsed": true
2487    },
2488    "outputs": [],
2489    "source": [
2490     "my_bill = make_string(200)\n",
2491     "friend_bill = make_string(200)\n",
2492     "other_bills = [make_string(200) for _ in range(98)]\n",
2493     "\n",
2494     "target_interleaved = interleave(my_bill, friend_bill)\n",
2495     "mine_interleaved = [interleave(my_bill, o) for o in random.sample(other_bills, 21)]\n",
2496     "friend_interleaved = [interleave(friend_bill, o) for o in random.sample(other_bills, 13)]\n",
2497     "other_interleaved = []\n",
2498     "for _ in range(103):\n",
2499     "    s1, s2 = random.sample(other_bills, 2)\n",
2500     "    other_interleaved += [interleave(s1, s2)]"
2501    ]
2502   },
2503   {
2504    "cell_type": "code",
2505    "execution_count": 47,
2506    "metadata": {
2507     "collapsed": true
2508    },
2509    "outputs": [],
2510    "source": [
2511     "all_targets = [target_interleaved] + mine_interleaved + friend_interleaved + other_interleaved"
2512    ]
2513   },
2514   {
2515    "cell_type": "code",
2516    "execution_count": 48,
2517    "metadata": {},
2518    "outputs": [
2519     {
2520      "name": "stdout",
2521      "output_type": "stream",
2522      "text": [
2523       "CPU times: user 2.96 s, sys: 4 ms, total: 2.97 s\n",
2524       "Wall time: 2.97 s\n"
2525      ]
2526     },
2527     {
2528      "data": {
2529       "text/plain": [
2530        "[0]"
2531       ]
2532      },
2533      "execution_count": 48,
2534      "metadata": {},
2535      "output_type": "execute_result"
2536     }
2537    ],
2538    "source": [
2539     "%time [i for i, s12 in enumerate(all_targets) if is_interleave(my_bill, friend_bill, s12)]"
2540    ]
2541   },
2542   {
2543    "cell_type": "code",
2544    "execution_count": 49,
2545    "metadata": {},
2546    "outputs": [
2547     {
2548      "name": "stdout",
2549      "output_type": "stream",
2550      "text": [
2551       "CPU times: user 660 ms, sys: 0 ns, total: 660 ms\n",
2552       "Wall time: 658 ms\n"
2553      ]
2554     },
2555     {
2556      "data": {
2557       "text/plain": [
2558        "[0]"
2559       ]
2560      },
2561      "execution_count": 49,
2562      "metadata": {},
2563      "output_type": "execute_result"
2564     }
2565    ],
2566    "source": [
2567     "%time [i for i, s12 in enumerate(all_targets) if is_interleave_recursive(my_bill, friend_bill, s12)]"
2568    ]
2569   },
2570   {
2571    "cell_type": "code",
2572    "execution_count": 50,
2573    "metadata": {
2574     "collapsed": true
2575    },
2576    "outputs": [],
2577    "source": [
2578     "bill_set = all_targets + random.sample(other_bills, 8)\n",
2579     "random.shuffle(bill_set)\n",
2580     "bill_set = [my_bill, friend_bill] + bill_set\n",
2581     "\n",
2582     "# with open('09-bills.txt', 'w') as f:\n",
2583     "#     for i, b in enumerate(bill_set):\n",
2584     "#         f.write('{}: {}\\n'.format(i, b))"
2585    ]
2586   },
2587   {
2588    "cell_type": "code",
2589    "execution_count": 51,
2590    "metadata": {
2591     "collapsed": true
2592    },
2593    "outputs": [],
2594    "source": [
2595     "def is_subseq_greedy(s1, s2):\n",
2596     "    i = j = 0\n",
2597     "    while i < len(s1) and j < len(s2):\n",
2598     "        if s1[i] == s2[j]:\n",
2599     "            i += 1\n",
2600     "        j += 1\n",
2601     "    return i == len(s1)"
2602    ]
2603   },
2604   {
2605    "cell_type": "code",
2606    "execution_count": 52,
2607    "metadata": {
2608     "collapsed": true
2609    },
2610    "outputs": [],
2611    "source": [
2612     "def subseq_partition(s1, s2):\n",
2613     "    i = j = 0\n",
2614     "    remainder = ''\n",
2615     "    while i < len(s1) and j < len(s2):\n",
2616     "        if s1[i] == s2[j]:\n",
2617     "            i += 1\n",
2618     "        else:\n",
2619     "            remainder += s2[j]\n",
2620     "        j += 1\n",
2621     "    return i == len(s1), remainder"
2622    ]
2623   },
2624   {
2625    "cell_type": "code",
2626    "execution_count": 53,
2627    "metadata": {},
2628    "outputs": [
2629     {
2630      "data": {
2631       "text/plain": [
2632        "(40, 40, 20, 20)"
2633       ]
2634      },
2635      "execution_count": 53,
2636      "metadata": {},
2637      "output_type": "execute_result"
2638     }
2639    ],
2640    "source": [
2641     "common = make_string(10)\n",
2642     "padding = make_string(10)\n",
2643     "middle = interleave(common, padding)\n",
2644     "\n",
2645     "pre1 = make_string(5)\n",
2646     "suf1 = make_string(5)\n",
2647     "\n",
2648     "pre2 = make_string(5)\n",
2649     "suf2 = make_string(5)\n",
2650     "\n",
2651     "pre = interleave(pre1, pre2)\n",
2652     "suf = interleave(suf1, suf2)\n",
2653     "\n",
2654     "distractor = pre + middle + suf\n",
2655     "\n",
2656     "sub1 = pre1 + common + suf1\n",
2657     "sub2 = pre2 + common + suf2\n",
2658     "\n",
2659     "valid = interleave(sub1, sub2)\n",
2660     "\n",
2661     "len(distractor), len(valid), len(sub1), len(sub2)"
2662    ]
2663   },
2664   {
2665    "cell_type": "code",
2666    "execution_count": 54,
2667    "metadata": {},
2668    "outputs": [
2669     {
2670      "data": {
2671       "text/plain": [
2672        "(True, True)"
2673       ]
2674      },
2675      "execution_count": 54,
2676      "metadata": {},
2677      "output_type": "execute_result"
2678     }
2679    ],
2680    "source": [
2681     "is_subseq_greedy(sub1, distractor), is_subseq_greedy(sub2, distractor)"
2682    ]
2683   },
2684   {
2685    "cell_type": "code",
2686    "execution_count": 55,
2687    "metadata": {},
2688    "outputs": [
2689     {
2690      "data": {
2691       "text/plain": [
2692        "(True, True)"
2693       ]
2694      },
2695      "execution_count": 55,
2696      "metadata": {},
2697      "output_type": "execute_result"
2698     }
2699    ],
2700    "source": [
2701     "is_subseq_greedy(sub1, valid), is_subseq_greedy(sub2, valid)"
2702    ]
2703   },
2704   {
2705    "cell_type": "code",
2706    "execution_count": 56,
2707    "metadata": {},
2708    "outputs": [
2709     {
2710      "data": {
2711       "text/plain": [
2712        "(False, True)"
2713       ]
2714      },
2715      "execution_count": 56,
2716      "metadata": {},
2717      "output_type": "execute_result"
2718     }
2719    ],
2720    "source": [
2721     "is_interleave(sub1, sub2, distractor), is_interleave(sub1, sub2, valid)"
2722    ]
2723   },
2724   {
2725    "cell_type": "code",
2726    "execution_count": 57,
2727    "metadata": {},
2728    "outputs": [
2729     {
2730      "data": {
2731       "text/plain": [
2732        "('echgeaeeefdcebeaahaf',\n",
2733        " 'eeahaaeeefdcebedghbg',\n",
2734        " 'eeecahahgeaaeeebafaadgceadabefdaghbgahaf',\n",
2735        " 'eecheagehaaaeeeeeefdcebefadahcaebfedghbg')"
2736       ]
2737      },
2738      "execution_count": 57,
2739      "metadata": {},
2740      "output_type": "execute_result"
2741     }
2742    ],
2743    "source": [
2744     "sub1, sub2, distractor, valid"
2745    ]
2746   },
2747   {
2748    "cell_type": "code",
2749    "execution_count": 58,
2750    "metadata": {},
2751    "outputs": [
2752     {
2753      "data": {
2754       "text/plain": [
2755        "False"
2756       ]
2757      },
2758      "execution_count": 58,
2759      "metadata": {},
2760      "output_type": "execute_result"
2761     }
2762    ],
2763    "source": [
2764     "a, b = subseq_partition(sub1, distractor)\n",
2765     "b == sub2"
2766    ]
2767   },
2768   {
2769    "cell_type": "code",
2770    "execution_count": 59,
2771    "metadata": {},
2772    "outputs": [
2773     {
2774      "data": {
2775       "text/plain": [
2776        "('eeahaaeeefdceb', 'eeahaaeeefdcebedghbg')"
2777       ]
2778      },
2779      "execution_count": 59,
2780      "metadata": {},
2781      "output_type": "execute_result"
2782     }
2783    ],
2784    "source": [
2785     "a, b = subseq_partition(sub1, valid)\n",
2786     "b, sub2"
2787    ]
2788   },
2789   {
2790    "cell_type": "code",
2791    "execution_count": null,
2792    "metadata": {
2793     "collapsed": true
2794    },
2795    "outputs": [],
2796    "source": []
2797   }
2798  ],
2799  "metadata": {
2800   "kernelspec": {
2801    "display_name": "Python 3",
2802    "language": "python",
2803    "name": "python3"
2804   },
2805   "language_info": {
2806    "codemirror_mode": {
2807     "name": "ipython",
2808     "version": 3
2809    },
2810    "file_extension": ".py",
2811    "mimetype": "text/x-python",
2812    "name": "python",
2813    "nbconvert_exporter": "python",
2814    "pygments_lexer": "ipython3",
2815    "version": "3.5.2+"
2816   }
2817  },
2818  "nbformat": 4,
2819  "nbformat_minor": 1
2820 }