09-resolving-the-bill/interleaving.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "markdown",
   5    "metadata": {},
   6    "source": [
   7     "# Interleaved strings\n",
   8     "\n",
   9     "Given two strings a and b and a target c, could c be formed form some interleaving/merge of a and b?\n",
  10     "\n",
  11     "For example,\n",
  12     "Given:\n",
  13     "s1 = \"aabcc\",\n",
  14     "s2 = \"dbbca\",\n",
  15     "\n",
  16     "When s3 = \"aadbbcbcac\", return true.\n",
  17     "When s3 = \"aadbbbaccc\", return false."
  18    ]
  19   },
  20   {
  21    "cell_type": "code",
  22    "execution_count": 1,
  23    "metadata": {
  24     "collapsed": true
  25    },
  26    "outputs": [],
  27    "source": [
  28     "import random\n",
  29     "import string"
  30    ]
  31   },
  32   {
  33    "cell_type": "code",
  34    "execution_count": 2,
  35    "metadata": {
  36     "collapsed": true
  37    },
  38    "outputs": [],
  39    "source": [
  40     "s1 = \"aabcc\"\n",
  41     "s2 = \"dbbca\"\n",
  42     "\n",
  43     "s3t = \"aadbbcbcac\"\n",
  44     "s3f = \"aadbbbaccc\""
  45    ]
  46   },
  47   {
  48    "cell_type": "code",
  49    "execution_count": 3,
  50    "metadata": {},
  51    "outputs": [
  52     {
  53      "data": {
  54       "text/plain": [
  55        "[(0, ''), (1, 'a'), (2, 'aa'), (3, 'aab'), (4, 'aabc'), (5, 'aabcc')]"
  56       ]
  57      },
  58      "execution_count": 3,
  59      "metadata": {},
  60      "output_type": "execute_result"
  61     }
  62    ],
  63    "source": [
  64     "[(i, s1[:i]) for i in range(len(s1)+1)]"
  65    ]
  66   },
  67   {
  68    "cell_type": "markdown",
  69    "metadata": {},
  70    "source": [
  71     "`dp_table[i, j]` is True if first `i` + `j` characters of `s3` can be formed from interleaving of first `i` characters of `s1` and first `j` characters of `s2`."
  72    ]
  73   },
  74   {
  75    "cell_type": "code",
  76    "execution_count": 4,
  77    "metadata": {},
  78    "outputs": [
  79     {
  80      "data": {
  81       "text/plain": [
  82        "[[True, False, False, False, False, False],\n",
  83        " [False, False, False, False, False, False],\n",
  84        " [False, False, False, False, False, False],\n",
  85        " [False, False, False, False, False, False],\n",
  86        " [False, False, False, False, False, False],\n",
  87        " [False, False, False, False, False, False]]"
  88       ]
  89      },
  90      "execution_count": 4,
  91      "metadata": {},
  92      "output_type": "execute_result"
  93     }
  94    ],
  95    "source": [
  96     "dp_table = [[False] * (len(s1) + 1) for _ in range(len(s2) + 1)]\n",
  97     "dp_table[0][0] = True\n",
  98     "dp_table"
  99    ]
 100   },
 101   {
 102    "cell_type": "code",
 103    "execution_count": 5,
 104    "metadata": {
 105     "scrolled": true
 106    },
 107    "outputs": [
 108     {
 109      "data": {
 110       "text/plain": [
 111        "{(0, 0): False,\n",
 112        " (0, 1): False,\n",
 113        " (0, 2): False,\n",
 114        " (0, 3): False,\n",
 115        " (0, 4): False,\n",
 116        " (0, 5): False,\n",
 117        " (1, 0): False,\n",
 118        " (1, 1): False,\n",
 119        " (1, 2): False,\n",
 120        " (1, 3): False,\n",
 121        " (1, 4): False,\n",
 122        " (1, 5): False,\n",
 123        " (2, 0): False,\n",
 124        " (2, 1): False,\n",
 125        " (2, 2): False,\n",
 126        " (2, 3): False,\n",
 127        " (2, 4): False,\n",
 128        " (2, 5): False,\n",
 129        " (3, 0): False,\n",
 130        " (3, 1): False,\n",
 131        " (3, 2): False,\n",
 132        " (3, 3): False,\n",
 133        " (3, 4): False,\n",
 134        " (3, 5): False,\n",
 135        " (4, 0): False,\n",
 136        " (4, 1): False,\n",
 137        " (4, 2): False,\n",
 138        " (4, 3): False,\n",
 139        " (4, 4): False,\n",
 140        " (4, 5): False,\n",
 141        " (5, 0): False,\n",
 142        " (5, 1): False,\n",
 143        " (5, 2): False,\n",
 144        " (5, 3): False,\n",
 145        " (5, 4): False,\n",
 146        " (5, 5): False}"
 147       ]
 148      },
 149      "execution_count": 5,
 150      "metadata": {},
 151      "output_type": "execute_result"
 152     }
 153    ],
 154    "source": [
 155     "dp_table = {(i, j): False\n",
 156     "           for i in range(len(s1)+1)\n",
 157     "           for j in range(len(s2)+1)}\n",
 158     "dp_table"
 159    ]
 160   },
 161   {
 162    "cell_type": "code",
 163    "execution_count": 6,
 164    "metadata": {
 165     "collapsed": true
 166    },
 167    "outputs": [],
 168    "source": [
 169     "def show_table(table):\n",
 170     "    return '\\n'.join(\n",
 171     "        ' '.join(str(table[i, j])[0] for j in sorted(set([k[1] for k in table])))\n",
 172     "        for i in sorted(set([k[0] for k in table])))        "
 173    ]
 174   },
 175   {
 176    "cell_type": "code",
 177    "execution_count": 7,
 178    "metadata": {
 179     "collapsed": true
 180    },
 181    "outputs": [],
 182    "source": [
 183     "def show_table(table):\n",
 184     "    return '\\n'.join(\n",
 185     "        ' '.join('T' if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n",
 186     "        for i in sorted(set([k[0] for k in table])))        "
 187    ]
 188   },
 189   {
 190    "cell_type": "code",
 191    "execution_count": 8,
 192    "metadata": {},
 193    "outputs": [
 194     {
 195      "name": "stdout",
 196      "output_type": "stream",
 197      "text": [
 198       ". . . . . .\n",
 199       ". . . . . .\n",
 200       ". . . . . .\n",
 201       ". . . . . .\n",
 202       ". . . . . .\n",
 203       ". . . . . .\n"
 204      ]
 205     }
 206    ],
 207    "source": [
 208     "print(show_table(dp_table))"
 209    ]
 210   },
 211   {
 212    "cell_type": "code",
 213    "execution_count": 9,
 214    "metadata": {},
 215    "outputs": [
 216     {
 217      "name": "stdout",
 218      "output_type": "stream",
 219      "text": [
 220       "aabcc dbbca aadbbbaccc\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 b 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       "xx 2 4 a c b False\n",
 238       "xx 2 5 a a a 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       "s2 3 3 b b b True\n",
 244       "s1 3 3 b b b True\n",
 245       "xx 3 4 b c a False\n",
 246       "xx 3 5 b a c False\n",
 247       "s1 4 0 c ! b False\n",
 248       "xx 4 1 c d b False\n",
 249       "xx 4 2 c b b False\n",
 250       "xx 4 3 c b a False\n",
 251       "xx 4 4 c c c False\n",
 252       "xx 4 5 c a c False\n",
 253       "s1 5 0 c ! b False\n",
 254       "xx 5 1 c d b False\n",
 255       "xx 5 2 c b a False\n",
 256       "xx 5 3 c b c False\n",
 257       "xx 5 4 c c c False\n",
 258       "xx 5 5 c a c False\n",
 259       "T . . . . .\n",
 260       "T . . . . .\n",
 261       "T T T T . .\n",
 262       ". T T T . .\n",
 263       ". . . . . .\n",
 264       ". . . . . .\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        " (3, 1): (2, 1, 'b', 's1'),\n",
 276        " (3, 2): (2, 2, 'b', 's1'),\n",
 277        " (3, 3): (2, 3, 'b', 's1')}"
 278       ]
 279      },
 280      "execution_count": 9,
 281      "metadata": {},
 282      "output_type": "execute_result"
 283     }
 284    ],
 285    "source": [
 286     "s3 = s3f\n",
 287     "\n",
 288     "print(s1, s2, s3)\n",
 289     "\n",
 290     "dp_table = {(i, j): False\n",
 291     "           for i in range(len(s1)+1)\n",
 292     "           for j in range(len(s2)+1)}\n",
 293     "\n",
 294     "backpointers = {}\n",
 295     "\n",
 296     "for i in range(len(s1)+1):\n",
 297     "    for j in range(len(s2)+1):\n",
 298     "        if i == 0 and j == 0:\n",
 299     "            dp_table[i, j] = True\n",
 300     "            print('aa', i, j, '!', '!', '!', dp_table[i, j])\n",
 301     "        elif i == 0:\n",
 302     "            # extend by character from s2\n",
 303     "            if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
 304     "                dp_table[i, j] = True\n",
 305     "                backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
 306     "            print('s2', i, j, '!', s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 307     "        elif j == 0:\n",
 308     "            # extend by character from s1\n",
 309     "            if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
 310     "                dp_table[i, j] = True\n",
 311     "                backpointers[i, j] = (i-1, j, s1[i-1], 's1')\n",
 312     "            print('s1', i, j, s1[i-1], '!', s3[i+j-1], dp_table[i, j])\n",
 313     "        else:\n",
 314     "            # extend by character from s2\n",
 315     "            if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
 316     "                dp_table[i, j] = True\n",
 317     "                backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
 318     "                print('s2', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])                \n",
 319     "            # extend by character from s1\n",
 320     "            if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
 321     "                dp_table[i, j] = True\n",
 322     "                backpointers[i, j] = (i-1, j, s1[i-1], 's1')                \n",
 323     "                print('s1', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 324     "            if not dp_table[i, j]:\n",
 325     "                print('xx', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 326     "\n",
 327     "print(show_table(dp_table))\n",
 328     "backpointers"
 329    ]
 330   },
 331   {
 332    "cell_type": "code",
 333    "execution_count": 10,
 334    "metadata": {
 335     "collapsed": true
 336    },
 337    "outputs": [],
 338    "source": [
 339     "def is_interleave(seq1, seq2, seq3, return_backpointers=False, return_table=False, debug=False):\n",
 340     "    \"\"\"Return true if seq3 is some interleaved merge of seq1 and seq2.\n",
 341     "    If return_backpointers, also return the set of backpointers to\n",
 342     "    reconstruct the interleaving\"\"\"\n",
 343     "    \n",
 344     "    # dp_table[i, j] is True if first i+j characters of seq is made up of \n",
 345     "    # an interleaving of the first i characters of seq1 and the \n",
 346     "    # first j characters of seq2\n",
 347     "    \n",
 348     "    if len(seq1) + len(seq2) != len(seq3):\n",
 349     "        if return_backpointers or return_table:\n",
 350     "            retval = [False]\n",
 351     "            if return_backpointers:\n",
 352     "                retval += [{}]\n",
 353     "            if return_table:\n",
 354     "                retval += [{}]\n",
 355     "            return tuple(retval)\n",
 356     "        else:\n",
 357     "            return False\n",
 358     "    \n",
 359     "    dp_table = {(i, j): False\n",
 360     "               for i in range(len(seq1)+1)\n",
 361     "               for j in range(len(seq2)+1)}\n",
 362     "\n",
 363     "    backpointers = {}\n",
 364     "\n",
 365     "    for i in range(len(seq1)+1):\n",
 366     "        for j in range(len(seq2)+1):\n",
 367     "            if i == 0 and j == 0:\n",
 368     "                dp_table[i, j] = True\n",
 369     "                if debug: print('xxxx', i, j, '!', '!', '!', dp_table[i, j])\n",
 370     "            elif i == 0:\n",
 371     "                # extend by character from seq2\n",
 372     "                if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
 373     "                    dp_table[i, j] = True\n",
 374     "                    backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
 375     "                if debug: print('seq2', i, j, '!', seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 376     "            elif j == 0:\n",
 377     "                # extend by character from seq1\n",
 378     "                if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
 379     "                    dp_table[i, j] = True\n",
 380     "                    backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')\n",
 381     "                if debug: print('seq1', i, j, seq1[i-1], '!', seq3[i+j-1], dp_table[i, j])\n",
 382     "            else:\n",
 383     "                # extend by character from seq2\n",
 384     "                if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
 385     "                    dp_table[i, j] = True\n",
 386     "                    backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
 387     "                    if debug: print('seq2', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])                \n",
 388     "                # extend by character from seq1\n",
 389     "                if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
 390     "                    dp_table[i, j] = True\n",
 391     "                    backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')                \n",
 392     "                    if debug: print('seq1', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 393     "                if not dp_table[i, j]:\n",
 394     "                    if debug: print('xxxx', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 395     "\n",
 396     "    if return_backpointers or return_table:\n",
 397     "        retval = [dp_table[len(seq1), len(seq2)]]\n",
 398     "        if return_backpointers:\n",
 399     "            retval += [backpointers]\n",
 400     "        if return_table:\n",
 401     "            retval += [dp_table]\n",
 402     "        return tuple(retval)\n",
 403     "    else:\n",
 404     "        return dp_table[len(seq1), len(seq2)]"
 405    ]
 406   },
 407   {
 408    "cell_type": "code",
 409    "execution_count": 11,
 410    "metadata": {},
 411    "outputs": [
 412     {
 413      "data": {
 414       "text/plain": [
 415        "True"
 416       ]
 417      },
 418      "execution_count": 11,
 419      "metadata": {},
 420      "output_type": "execute_result"
 421     }
 422    ],
 423    "source": [
 424     "is_interleave(s1, s2, s3t)"
 425    ]
 426   },
 427   {
 428    "cell_type": "code",
 429    "execution_count": 12,
 430    "metadata": {},
 431    "outputs": [
 432     {
 433      "data": {
 434       "text/plain": [
 435        "(True,\n",
 436        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 437        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 438        "  (2, 1): (2, 0, 'd', 'seq2'),\n",
 439        "  (2, 2): (2, 1, 'b', 'seq2'),\n",
 440        "  (2, 3): (2, 2, 'b', 'seq2'),\n",
 441        "  (2, 4): (2, 3, 'c', 'seq2'),\n",
 442        "  (3, 1): (2, 1, 'b', 'seq1'),\n",
 443        "  (3, 2): (2, 2, 'b', 'seq1'),\n",
 444        "  (3, 4): (2, 4, 'b', 'seq1'),\n",
 445        "  (4, 2): (3, 2, 'c', 'seq1'),\n",
 446        "  (4, 3): (4, 2, 'b', 'seq2'),\n",
 447        "  (4, 4): (3, 4, 'c', 'seq1'),\n",
 448        "  (4, 5): (4, 4, 'a', 'seq2'),\n",
 449        "  (5, 3): (4, 3, 'c', 'seq1'),\n",
 450        "  (5, 5): (4, 5, 'c', 'seq1')})"
 451       ]
 452      },
 453      "execution_count": 12,
 454      "metadata": {},
 455      "output_type": "execute_result"
 456     }
 457    ],
 458    "source": [
 459     "is_interleave(s1, s2, s3t, return_backpointers=True)"
 460    ]
 461   },
 462   {
 463    "cell_type": "code",
 464    "execution_count": 13,
 465    "metadata": {
 466     "scrolled": true
 467    },
 468    "outputs": [
 469     {
 470      "data": {
 471       "text/plain": [
 472        "(True,\n",
 473        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 474        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 475        "  (2, 1): (2, 0, 'd', 'seq2'),\n",
 476        "  (2, 2): (2, 1, 'b', 'seq2'),\n",
 477        "  (2, 3): (2, 2, 'b', 'seq2'),\n",
 478        "  (2, 4): (2, 3, 'c', 'seq2'),\n",
 479        "  (3, 1): (2, 1, 'b', 'seq1'),\n",
 480        "  (3, 2): (2, 2, 'b', 'seq1'),\n",
 481        "  (3, 4): (2, 4, 'b', 'seq1'),\n",
 482        "  (4, 2): (3, 2, 'c', 'seq1'),\n",
 483        "  (4, 3): (4, 2, 'b', 'seq2'),\n",
 484        "  (4, 4): (3, 4, 'c', 'seq1'),\n",
 485        "  (4, 5): (4, 4, 'a', 'seq2'),\n",
 486        "  (5, 3): (4, 3, 'c', 'seq1'),\n",
 487        "  (5, 5): (4, 5, 'c', 'seq1')},\n",
 488        " {(0, 0): True,\n",
 489        "  (0, 1): False,\n",
 490        "  (0, 2): False,\n",
 491        "  (0, 3): False,\n",
 492        "  (0, 4): False,\n",
 493        "  (0, 5): False,\n",
 494        "  (1, 0): True,\n",
 495        "  (1, 1): False,\n",
 496        "  (1, 2): False,\n",
 497        "  (1, 3): False,\n",
 498        "  (1, 4): False,\n",
 499        "  (1, 5): False,\n",
 500        "  (2, 0): True,\n",
 501        "  (2, 1): True,\n",
 502        "  (2, 2): True,\n",
 503        "  (2, 3): True,\n",
 504        "  (2, 4): True,\n",
 505        "  (2, 5): False,\n",
 506        "  (3, 0): False,\n",
 507        "  (3, 1): True,\n",
 508        "  (3, 2): True,\n",
 509        "  (3, 3): False,\n",
 510        "  (3, 4): True,\n",
 511        "  (3, 5): False,\n",
 512        "  (4, 0): False,\n",
 513        "  (4, 1): False,\n",
 514        "  (4, 2): True,\n",
 515        "  (4, 3): True,\n",
 516        "  (4, 4): True,\n",
 517        "  (4, 5): True,\n",
 518        "  (5, 0): False,\n",
 519        "  (5, 1): False,\n",
 520        "  (5, 2): False,\n",
 521        "  (5, 3): True,\n",
 522        "  (5, 4): False,\n",
 523        "  (5, 5): True})"
 524       ]
 525      },
 526      "execution_count": 13,
 527      "metadata": {},
 528      "output_type": "execute_result"
 529     }
 530    ],
 531    "source": [
 532     "is_interleave(s1, s2, s3t, return_backpointers=True, return_table=True)"
 533    ]
 534   },
 535   {
 536    "cell_type": "code",
 537    "execution_count": 14,
 538    "metadata": {},
 539    "outputs": [
 540     {
 541      "data": {
 542       "text/plain": [
 543        "False"
 544       ]
 545      },
 546      "execution_count": 14,
 547      "metadata": {},
 548      "output_type": "execute_result"
 549     }
 550    ],
 551    "source": [
 552     "is_interleave(s1, s2, s3f)"
 553    ]
 554   },
 555   {
 556    "cell_type": "code",
 557    "execution_count": 15,
 558    "metadata": {},
 559    "outputs": [
 560     {
 561      "name": "stdout",
 562      "output_type": "stream",
 563      "text": [
 564       "xxxx 0 0 ! ! ! True\n",
 565       "seq2 0 1 ! b a False\n",
 566       "seq2 0 2 ! b a False\n",
 567       "seq2 0 3 ! b a False\n",
 568       "seq1 1 0 a ! a True\n",
 569       "xxxx 1 1 a b a False\n",
 570       "xxxx 1 2 a b a False\n",
 571       "xxxx 1 3 a b b False\n",
 572       "seq1 2 0 a ! a True\n",
 573       "xxxx 2 1 a b a False\n",
 574       "xxxx 2 2 a b b False\n",
 575       "xxxx 2 3 a b a False\n",
 576       "seq1 3 0 a ! a True\n",
 577       "seq2 3 1 a b b True\n",
 578       "xxxx 3 2 a b a False\n",
 579       "xxxx 3 3 a b b False\n",
 580       "seq1 4 0 a ! b False\n",
 581       "seq1 4 1 a b a True\n",
 582       "seq2 4 2 a b b True\n",
 583       "seq2 4 3 a b b True\n"
 584      ]
 585     },
 586     {
 587      "data": {
 588       "text/plain": [
 589        "(True,\n",
 590        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 591        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 592        "  (3, 0): (2, 0, 'a', 'seq1'),\n",
 593        "  (3, 1): (3, 0, 'b', 'seq2'),\n",
 594        "  (4, 1): (3, 1, 'a', 'seq1'),\n",
 595        "  (4, 2): (4, 1, 'b', 'seq2'),\n",
 596        "  (4, 3): (4, 2, 'b', 'seq2')})"
 597       ]
 598      },
 599      "execution_count": 15,
 600      "metadata": {},
 601      "output_type": "execute_result"
 602     }
 603    ],
 604    "source": [
 605     "is_interleave('aaaa', 'bbb', 'aaababb', return_backpointers=True, debug=True)"
 606    ]
 607   },
 608   {
 609    "cell_type": "code",
 610    "execution_count": 16,
 611    "metadata": {
 612     "collapsed": true
 613    },
 614    "outputs": [],
 615    "source": [
 616     "def show_backtrace(bps):\n",
 617     "    i = max([0] + [k[0] for k in bps])\n",
 618     "    j = max([0] + [k[1] for k in bps])\n",
 619     "    chars = ''\n",
 620     "    if (i, j) in bps:\n",
 621     "        while i != 0 or j != 0:\n",
 622     "            if bps[i, j][3] == 'seq1':\n",
 623     "                chars += bps[i, j][2].upper()\n",
 624     "            else:\n",
 625     "                chars += bps[i, j][2]\n",
 626     "            i, j = bps[i, j][0], bps[i, j][1] \n",
 627     "        return ''.join(list(reversed(chars)))\n",
 628     "    else:\n",
 629     "        return ''"
 630    ]
 631   },
 632   {
 633    "cell_type": "code",
 634    "execution_count": 17,
 635    "metadata": {
 636     "collapsed": true
 637    },
 638    "outputs": [],
 639    "source": [
 640     "def make_string(length, alphabet=None):\n",
 641     "    if not alphabet:\n",
 642     "        alphabet = 'abcdefgh'\n",
 643     "    return ''.join(random.choice(alphabet) for _ in range(length))    "
 644    ]
 645   },
 646   {
 647    "cell_type": "code",
 648    "execution_count": 18,
 649    "metadata": {},
 650    "outputs": [
 651     {
 652      "data": {
 653       "text/plain": [
 654        "'fgcebagebfhfbadbgggacgeebbfceffhbhbgdfhhbahgbchbhe'"
 655       ]
 656      },
 657      "execution_count": 18,
 658      "metadata": {},
 659      "output_type": "execute_result"
 660     }
 661    ],
 662    "source": [
 663     "make_string(50)"
 664    ]
 665   },
 666   {
 667    "cell_type": "code",
 668    "execution_count": 19,
 669    "metadata": {
 670     "collapsed": true
 671    },
 672    "outputs": [],
 673    "source": [
 674     "def interleave(s1, s2, wander_limit=10, debug=False):\n",
 675     "    i1 = i2 = wander = 0\n",
 676     "    interleaved = []\n",
 677     "    while i1 <= len(s1) and i2 <= len(s2):\n",
 678     "        if i1 == len(s1):\n",
 679     "            if debug: print(i1, i2, wander, 'remaining s2', s2[i2:])\n",
 680     "            interleaved += s2[i2:]\n",
 681     "            i2 = len(s2) + 1\n",
 682     "        elif i2 == len(s2):\n",
 683     "            if debug: print(i1, i2, wander, 'remaining s1', s1[i1:])\n",
 684     "            interleaved += s1[i1:]\n",
 685     "            i1 = len(s1) + 1\n",
 686     "        else:\n",
 687     "            if wander == wander_limit:\n",
 688     "                step = -1\n",
 689     "            elif wander == -wander_limit:\n",
 690     "                step = +1\n",
 691     "            else:\n",
 692     "                step = random.choice([+1, -1])\n",
 693     "            if step == +1:\n",
 694     "                if debug: print(i1, i2, wander, 'adding', s1[i1])\n",
 695     "                interleaved += s1[i1]\n",
 696     "                i1 += 1\n",
 697     "                wander += 1\n",
 698     "            else:\n",
 699     "                if debug: print(i1, i2, wander, 'adding', s2[i2])\n",
 700     "                interleaved += s2[i2]\n",
 701     "                i2 += 1\n",
 702     "                wander -= 1\n",
 703     "    return ''.join(interleaved)\n",
 704     "            "
 705    ]
 706   },
 707   {
 708    "cell_type": "code",
 709    "execution_count": 20,
 710    "metadata": {},
 711    "outputs": [
 712     {
 713      "name": "stdout",
 714      "output_type": "stream",
 715      "text": [
 716       "0 0 0 adding y\n",
 717       "0 1 -1 adding a\n",
 718       "1 1 0 adding z\n",
 719       "1 2 -1 adding v\n",
 720       "1 3 -2 adding x\n",
 721       "1 4 -3 adding z\n",
 722       "1 5 -4 adding w\n",
 723       "1 6 -5 adding e\n",
 724       "2 6 -4 adding h\n",
 725       "3 6 -3 adding b\n",
 726       "4 6 -2 adding a\n",
 727       "5 6 -1 adding b\n",
 728       "6 6 0 adding u\n",
 729       "6 7 -1 adding x\n",
 730       "6 8 -2 adding e\n",
 731       "7 8 -1 adding y\n",
 732       "7 9 -2 adding x\n",
 733       "7 10 -3 adding x\n",
 734       "7 11 -4 adding x\n",
 735       "7 12 -5 adding e\n",
 736       "8 12 -4 adding e\n",
 737       "9 12 -3 adding z\n",
 738       "9 13 -4 adding z\n",
 739       "9 14 -5 adding a\n",
 740       "10 14 -4 adding c\n",
 741       "11 14 -3 adding y\n",
 742       "11 15 -4 adding d\n",
 743       "12 15 -3 adding g\n",
 744       "13 15 -2 adding g\n",
 745       "14 15 -1 adding c\n",
 746       "15 15 0 adding x\n",
 747       "15 16 -1 adding e\n",
 748       "16 16 0 adding f\n",
 749       "17 16 1 adding w\n",
 750       "17 17 0 adding w\n",
 751       "17 18 -1 adding v\n",
 752       "17 19 -2 adding f\n",
 753       "18 19 -1 adding a\n",
 754       "19 19 0 adding g\n",
 755       "20 19 1 remaining s2 z\n"
 756      ]
 757     },
 758     {
 759      "data": {
 760       "text/plain": [
 761        "('aehbabeeeacdggceffag',\n",
 762        " 'yzvxzwuxyxxxzzyxwwvz',\n",
 763        " 'yazvxzwehbabuxeyxxxeezzacydggcxefwwvfagz',\n",
 764        " 40)"
 765       ]
 766      },
 767      "execution_count": 20,
 768      "metadata": {},
 769      "output_type": "execute_result"
 770     }
 771    ],
 772    "source": [
 773     "s1 = make_string(20)\n",
 774     "s2 = make_string(20, alphabet='uvwxyz')\n",
 775     "il = interleave(s1, s2, wander_limit=5, debug=True)\n",
 776     "s1, s2, il, len(il)"
 777    ]
 778   },
 779   {
 780    "cell_type": "code",
 781    "execution_count": 21,
 782    "metadata": {},
 783    "outputs": [
 784     {
 785      "name": "stdout",
 786      "output_type": "stream",
 787      "text": [
 788       "xxxx 0 0 ! ! ! True\n",
 789       "seq2 0 1 ! a y False\n",
 790       "seq2 0 2 ! e a False\n",
 791       "seq2 0 3 ! h z False\n",
 792       "seq2 0 4 ! b v False\n",
 793       "seq2 0 5 ! a x False\n",
 794       "seq2 0 6 ! b z False\n",
 795       "seq2 0 7 ! e w False\n",
 796       "seq2 0 8 ! e e False\n",
 797       "seq2 0 9 ! e h False\n",
 798       "seq2 0 10 ! a b False\n",
 799       "seq2 0 11 ! c a False\n",
 800       "seq2 0 12 ! d b False\n",
 801       "seq2 0 13 ! g u False\n",
 802       "seq2 0 14 ! g x False\n",
 803       "seq2 0 15 ! c e False\n",
 804       "seq2 0 16 ! e y False\n",
 805       "seq2 0 17 ! f x False\n",
 806       "seq2 0 18 ! f x False\n",
 807       "seq2 0 19 ! a x False\n",
 808       "seq2 0 20 ! g e False\n",
 809       "seq1 1 0 y ! y True\n",
 810       "seq2 1 1 y a a True\n",
 811       "xxxx 1 2 y e z False\n",
 812       "xxxx 1 3 y h v False\n",
 813       "xxxx 1 4 y b x False\n",
 814       "xxxx 1 5 y a z False\n",
 815       "xxxx 1 6 y b w False\n",
 816       "xxxx 1 7 y e e False\n",
 817       "xxxx 1 8 y e h False\n",
 818       "xxxx 1 9 y e b False\n",
 819       "xxxx 1 10 y a a False\n",
 820       "xxxx 1 11 y c b False\n",
 821       "xxxx 1 12 y d u False\n",
 822       "xxxx 1 13 y g x False\n",
 823       "xxxx 1 14 y g e False\n",
 824       "xxxx 1 15 y c y False\n",
 825       "xxxx 1 16 y e x False\n",
 826       "xxxx 1 17 y f x False\n",
 827       "xxxx 1 18 y f x False\n",
 828       "xxxx 1 19 y a e False\n",
 829       "xxxx 1 20 y g e False\n",
 830       "seq1 2 0 z ! a False\n",
 831       "seq1 2 1 z a z True\n",
 832       "xxxx 2 2 z e v False\n",
 833       "xxxx 2 3 z h x False\n",
 834       "xxxx 2 4 z b z False\n",
 835       "xxxx 2 5 z a w False\n",
 836       "xxxx 2 6 z b e False\n",
 837       "xxxx 2 7 z e h False\n",
 838       "xxxx 2 8 z e b False\n",
 839       "xxxx 2 9 z e a False\n",
 840       "xxxx 2 10 z a b False\n",
 841       "xxxx 2 11 z c u False\n",
 842       "xxxx 2 12 z d x False\n",
 843       "xxxx 2 13 z g e False\n",
 844       "xxxx 2 14 z g y False\n",
 845       "xxxx 2 15 z c x False\n",
 846       "xxxx 2 16 z e x False\n",
 847       "xxxx 2 17 z f x False\n",
 848       "xxxx 2 18 z f e False\n",
 849       "xxxx 2 19 z a e False\n",
 850       "xxxx 2 20 z g z False\n",
 851       "seq1 3 0 v ! z False\n",
 852       "seq1 3 1 v a v True\n",
 853       "xxxx 3 2 v e x False\n",
 854       "xxxx 3 3 v h z False\n",
 855       "xxxx 3 4 v b w False\n",
 856       "xxxx 3 5 v a e False\n",
 857       "xxxx 3 6 v b h False\n",
 858       "xxxx 3 7 v e b False\n",
 859       "xxxx 3 8 v e a False\n",
 860       "xxxx 3 9 v e b False\n",
 861       "xxxx 3 10 v a u False\n",
 862       "xxxx 3 11 v c x False\n",
 863       "xxxx 3 12 v d e False\n",
 864       "xxxx 3 13 v g y False\n",
 865       "xxxx 3 14 v g x False\n",
 866       "xxxx 3 15 v c x False\n",
 867       "xxxx 3 16 v e x False\n",
 868       "xxxx 3 17 v f e False\n",
 869       "xxxx 3 18 v f e False\n",
 870       "xxxx 3 19 v a z False\n",
 871       "xxxx 3 20 v g z False\n",
 872       "seq1 4 0 x ! v False\n",
 873       "seq1 4 1 x a x True\n",
 874       "xxxx 4 2 x e z False\n",
 875       "xxxx 4 3 x h w False\n",
 876       "xxxx 4 4 x b e False\n",
 877       "xxxx 4 5 x a h False\n",
 878       "xxxx 4 6 x b b False\n",
 879       "xxxx 4 7 x e a False\n",
 880       "xxxx 4 8 x e b False\n",
 881       "xxxx 4 9 x e u False\n",
 882       "xxxx 4 10 x a x False\n",
 883       "xxxx 4 11 x c e False\n",
 884       "xxxx 4 12 x d y False\n",
 885       "xxxx 4 13 x g x False\n",
 886       "xxxx 4 14 x g x False\n",
 887       "xxxx 4 15 x c x False\n",
 888       "xxxx 4 16 x e e False\n",
 889       "xxxx 4 17 x f e False\n",
 890       "xxxx 4 18 x f z False\n",
 891       "xxxx 4 19 x a z False\n",
 892       "xxxx 4 20 x g a False\n",
 893       "seq1 5 0 z ! x False\n",
 894       "seq1 5 1 z a z True\n",
 895       "xxxx 5 2 z e w False\n",
 896       "xxxx 5 3 z h e False\n",
 897       "xxxx 5 4 z b h False\n",
 898       "xxxx 5 5 z a b False\n",
 899       "xxxx 5 6 z b a False\n",
 900       "xxxx 5 7 z e b False\n",
 901       "xxxx 5 8 z e u False\n",
 902       "xxxx 5 9 z e x False\n",
 903       "xxxx 5 10 z a e False\n",
 904       "xxxx 5 11 z c y False\n",
 905       "xxxx 5 12 z d x False\n",
 906       "xxxx 5 13 z g x False\n",
 907       "xxxx 5 14 z g x False\n",
 908       "xxxx 5 15 z c e False\n",
 909       "xxxx 5 16 z e e False\n",
 910       "xxxx 5 17 z f z False\n",
 911       "xxxx 5 18 z f z False\n",
 912       "xxxx 5 19 z a a False\n",
 913       "xxxx 5 20 z g c False\n",
 914       "seq1 6 0 w ! z False\n",
 915       "seq1 6 1 w a w True\n",
 916       "seq2 6 2 w e e True\n",
 917       "seq2 6 3 w h h True\n",
 918       "seq2 6 4 w b b True\n",
 919       "seq2 6 5 w a a True\n",
 920       "seq2 6 6 w b b True\n",
 921       "xxxx 6 7 w e u False\n",
 922       "xxxx 6 8 w e x False\n",
 923       "xxxx 6 9 w e e False\n",
 924       "xxxx 6 10 w a y False\n",
 925       "xxxx 6 11 w c x False\n",
 926       "xxxx 6 12 w d x False\n",
 927       "xxxx 6 13 w g x False\n",
 928       "xxxx 6 14 w g e False\n",
 929       "xxxx 6 15 w c e False\n",
 930       "xxxx 6 16 w e z False\n",
 931       "xxxx 6 17 w f z False\n",
 932       "xxxx 6 18 w f a False\n",
 933       "xxxx 6 19 w a c False\n",
 934       "xxxx 6 20 w g y False\n",
 935       "seq1 7 0 u ! w False\n",
 936       "xxxx 7 1 u a e False\n",
 937       "xxxx 7 2 u e h False\n",
 938       "xxxx 7 3 u h b False\n",
 939       "xxxx 7 4 u b a False\n",
 940       "xxxx 7 5 u a b False\n",
 941       "seq1 7 6 u b u True\n",
 942       "xxxx 7 7 u e x False\n",
 943       "xxxx 7 8 u e e False\n",
 944       "xxxx 7 9 u e y False\n",
 945       "xxxx 7 10 u a x False\n",
 946       "xxxx 7 11 u c x False\n",
 947       "xxxx 7 12 u d x False\n",
 948       "xxxx 7 13 u g e False\n",
 949       "xxxx 7 14 u g e False\n",
 950       "xxxx 7 15 u c z False\n",
 951       "xxxx 7 16 u e z False\n",
 952       "xxxx 7 17 u f a False\n",
 953       "xxxx 7 18 u f c False\n",
 954       "xxxx 7 19 u a y False\n",
 955       "xxxx 7 20 u g d False\n",
 956       "seq1 8 0 x ! e False\n",
 957       "xxxx 8 1 x a h False\n",
 958       "xxxx 8 2 x e b False\n",
 959       "xxxx 8 3 x h a False\n",
 960       "xxxx 8 4 x b b False\n",
 961       "xxxx 8 5 x a u False\n",
 962       "seq1 8 6 x b x True\n",
 963       "seq2 8 7 x e e True\n",
 964       "xxxx 8 8 x e y False\n",
 965       "xxxx 8 9 x e x False\n",
 966       "xxxx 8 10 x a x False\n",
 967       "xxxx 8 11 x c x False\n",
 968       "xxxx 8 12 x d e False\n",
 969       "xxxx 8 13 x g e False\n",
 970       "xxxx 8 14 x g z False\n",
 971       "xxxx 8 15 x c z False\n",
 972       "xxxx 8 16 x e a False\n",
 973       "xxxx 8 17 x f c False\n",
 974       "xxxx 8 18 x f y False\n",
 975       "xxxx 8 19 x a d False\n",
 976       "xxxx 8 20 x g g False\n",
 977       "seq1 9 0 y ! h False\n",
 978       "xxxx 9 1 y a b False\n",
 979       "xxxx 9 2 y e a False\n",
 980       "xxxx 9 3 y h b False\n",
 981       "xxxx 9 4 y b u False\n",
 982       "xxxx 9 5 y a x False\n",
 983       "xxxx 9 6 y b e False\n",
 984       "seq1 9 7 y e y True\n",
 985       "xxxx 9 8 y e x False\n",
 986       "xxxx 9 9 y e x False\n",
 987       "xxxx 9 10 y a x False\n",
 988       "xxxx 9 11 y c e False\n",
 989       "xxxx 9 12 y d e False\n",
 990       "xxxx 9 13 y g z False\n",
 991       "xxxx 9 14 y g z False\n",
 992       "xxxx 9 15 y c a False\n",
 993       "xxxx 9 16 y e c False\n",
 994       "xxxx 9 17 y f y False\n",
 995       "xxxx 9 18 y f d False\n",
 996       "xxxx 9 19 y a g False\n",
 997       "xxxx 9 20 y g g False\n",
 998       "seq1 10 0 x ! b False\n",
 999       "xxxx 10 1 x a a False\n",
1000       "xxxx 10 2 x e b False\n",
1001       "xxxx 10 3 x h u False\n",
1002       "xxxx 10 4 x b x False\n",
1003       "xxxx 10 5 x a e False\n",
1004       "xxxx 10 6 x b y False\n",
1005       "seq1 10 7 x e x True\n",
1006       "xxxx 10 8 x e x False\n",
1007       "xxxx 10 9 x e x False\n",
1008       "xxxx 10 10 x a e False\n",
1009       "xxxx 10 11 x c e False\n",
1010       "xxxx 10 12 x d z False\n",
1011       "xxxx 10 13 x g z False\n",
1012       "xxxx 10 14 x g a False\n",
1013       "xxxx 10 15 x c c False\n",
1014       "xxxx 10 16 x e y False\n",
1015       "xxxx 10 17 x f d False\n",
1016       "xxxx 10 18 x f g False\n",
1017       "xxxx 10 19 x a g False\n",
1018       "xxxx 10 20 x g c False\n",
1019       "seq1 11 0 x ! a False\n",
1020       "xxxx 11 1 x a b False\n",
1021       "xxxx 11 2 x e u False\n",
1022       "xxxx 11 3 x h x False\n",
1023       "xxxx 11 4 x b e False\n",
1024       "xxxx 11 5 x a y False\n",
1025       "xxxx 11 6 x b x False\n",
1026       "seq1 11 7 x e x True\n",
1027       "xxxx 11 8 x e x False\n",
1028       "xxxx 11 9 x e e False\n",
1029       "xxxx 11 10 x a e False\n",
1030       "xxxx 11 11 x c z False\n",
1031       "xxxx 11 12 x d z False\n",
1032       "xxxx 11 13 x g a False\n",
1033       "xxxx 11 14 x g c False\n",
1034       "xxxx 11 15 x c y False\n",
1035       "xxxx 11 16 x e d False\n",
1036       "xxxx 11 17 x f g False\n",
1037       "xxxx 11 18 x f g False\n",
1038       "xxxx 11 19 x a c False\n",
1039       "xxxx 11 20 x g x False\n",
1040       "seq1 12 0 x ! b False\n",
1041       "xxxx 12 1 x a u False\n",
1042       "xxxx 12 2 x e x False\n",
1043       "xxxx 12 3 x h e False\n",
1044       "xxxx 12 4 x b y False\n",
1045       "xxxx 12 5 x a x False\n",
1046       "xxxx 12 6 x b x False\n",
1047       "seq1 12 7 x e x True\n",
1048       "seq2 12 8 x e e True\n",
1049       "seq2 12 9 x e e True\n",
1050       "xxxx 12 10 x a z False\n",
1051       "xxxx 12 11 x c z False\n",
1052       "xxxx 12 12 x d a False\n",
1053       "xxxx 12 13 x g c False\n",
1054       "xxxx 12 14 x g y False\n",
1055       "xxxx 12 15 x c d False\n",
1056       "xxxx 12 16 x e g False\n",
1057       "xxxx 12 17 x f g False\n",
1058       "xxxx 12 18 x f c False\n",
1059       "xxxx 12 19 x a x False\n",
1060       "xxxx 12 20 x g e False\n",
1061       "seq1 13 0 z ! u False\n",
1062       "xxxx 13 1 z a x False\n",
1063       "xxxx 13 2 z e e False\n",
1064       "xxxx 13 3 z h y False\n",
1065       "xxxx 13 4 z b x False\n",
1066       "xxxx 13 5 z a x False\n",
1067       "xxxx 13 6 z b x False\n",
1068       "xxxx 13 7 z e e False\n",
1069       "xxxx 13 8 z e e False\n",
1070       "seq1 13 9 z e z True\n",
1071       "xxxx 13 10 z a z False\n",
1072       "xxxx 13 11 z c a False\n",
1073       "xxxx 13 12 z d c False\n",
1074       "xxxx 13 13 z g y False\n",
1075       "xxxx 13 14 z g d False\n",
1076       "xxxx 13 15 z c g False\n",
1077       "xxxx 13 16 z e g False\n",
1078       "xxxx 13 17 z f c False\n",
1079       "xxxx 13 18 z f x False\n",
1080       "xxxx 13 19 z a e False\n",
1081       "xxxx 13 20 z g f False\n",
1082       "seq1 14 0 z ! x False\n",
1083       "xxxx 14 1 z a e False\n",
1084       "xxxx 14 2 z e y False\n",
1085       "xxxx 14 3 z h x False\n",
1086       "xxxx 14 4 z b x False\n",
1087       "xxxx 14 5 z a x False\n",
1088       "xxxx 14 6 z b e False\n",
1089       "xxxx 14 7 z e e False\n",
1090       "xxxx 14 8 z e z False\n",
1091       "seq1 14 9 z e z True\n",
1092       "seq2 14 10 z a a True\n",
1093       "seq2 14 11 z c c True\n",
1094       "xxxx 14 12 z d y False\n",
1095       "xxxx 14 13 z g d False\n",
1096       "xxxx 14 14 z g g False\n",
1097       "xxxx 14 15 z c g False\n",
1098       "xxxx 14 16 z e c False\n",
1099       "xxxx 14 17 z f x False\n",
1100       "xxxx 14 18 z f e False\n",
1101       "xxxx 14 19 z a f False\n",
1102       "xxxx 14 20 z g w False\n",
1103       "seq1 15 0 y ! e False\n",
1104       "xxxx 15 1 y a y False\n",
1105       "xxxx 15 2 y e x False\n",
1106       "xxxx 15 3 y h x False\n",
1107       "xxxx 15 4 y b x False\n",
1108       "xxxx 15 5 y a e False\n",
1109       "xxxx 15 6 y b e False\n",
1110       "xxxx 15 7 y e z False\n",
1111       "xxxx 15 8 y e z False\n",
1112       "xxxx 15 9 y e a False\n",
1113       "xxxx 15 10 y a c False\n",
1114       "seq1 15 11 y c y True\n",
1115       "seq2 15 12 y d d True\n",
1116       "seq2 15 13 y g g True\n",
1117       "seq2 15 14 y g g True\n",
1118       "seq2 15 15 y c c True\n",
1119       "xxxx 15 16 y e x False\n",
1120       "xxxx 15 17 y f e False\n",
1121       "xxxx 15 18 y f f False\n",
1122       "xxxx 15 19 y a w False\n",
1123       "xxxx 15 20 y g w False\n",
1124       "seq1 16 0 x ! y False\n",
1125       "xxxx 16 1 x a x False\n",
1126       "xxxx 16 2 x e x False\n",
1127       "xxxx 16 3 x h x False\n",
1128       "xxxx 16 4 x b e False\n",
1129       "xxxx 16 5 x a e False\n",
1130       "xxxx 16 6 x b z False\n",
1131       "xxxx 16 7 x e z False\n",
1132       "xxxx 16 8 x e a False\n",
1133       "xxxx 16 9 x e c False\n",
1134       "xxxx 16 10 x a y False\n",
1135       "xxxx 16 11 x c d False\n",
1136       "xxxx 16 12 x d g False\n",
1137       "xxxx 16 13 x g g False\n",
1138       "xxxx 16 14 x g c False\n",
1139       "seq1 16 15 x c x True\n",
1140       "seq2 16 16 x e e True\n",
1141       "seq2 16 17 x f f True\n",
1142       "xxxx 16 18 x f w False\n",
1143       "xxxx 16 19 x a w False\n",
1144       "xxxx 16 20 x g v False\n",
1145       "seq1 17 0 w ! x False\n",
1146       "xxxx 17 1 w a x False\n",
1147       "xxxx 17 2 w e x False\n",
1148       "xxxx 17 3 w h e False\n",
1149       "xxxx 17 4 w b e False\n",
1150       "xxxx 17 5 w a z False\n",
1151       "xxxx 17 6 w b z False\n",
1152       "xxxx 17 7 w e a False\n",
1153       "xxxx 17 8 w e c False\n",
1154       "xxxx 17 9 w e y False\n",
1155       "xxxx 17 10 w a d False\n",
1156       "xxxx 17 11 w c g False\n",
1157       "xxxx 17 12 w d g False\n",
1158       "xxxx 17 13 w g c False\n",
1159       "xxxx 17 14 w g x False\n",
1160       "xxxx 17 15 w c e False\n",
1161       "xxxx 17 16 w e f False\n",
1162       "seq1 17 17 w f w True\n",
1163       "xxxx 17 18 w f w False\n",
1164       "xxxx 17 19 w a v False\n",
1165       "xxxx 17 20 w g f False\n",
1166       "seq1 18 0 w ! x False\n"
1167      ]
1168     },
1169     {
1170      "name": "stdout",
1171      "output_type": "stream",
1172      "text": [
1173       "xxxx 18 1 w a x False\n",
1174       "xxxx 18 2 w e e False\n",
1175       "xxxx 18 3 w h e False\n",
1176       "xxxx 18 4 w b z False\n",
1177       "xxxx 18 5 w a z False\n",
1178       "xxxx 18 6 w b a False\n",
1179       "xxxx 18 7 w e c False\n",
1180       "xxxx 18 8 w e y False\n",
1181       "xxxx 18 9 w e d False\n",
1182       "xxxx 18 10 w a g False\n",
1183       "xxxx 18 11 w c g False\n",
1184       "xxxx 18 12 w d c False\n",
1185       "xxxx 18 13 w g x False\n",
1186       "xxxx 18 14 w g e False\n",
1187       "xxxx 18 15 w c f False\n",
1188       "xxxx 18 16 w e w False\n",
1189       "seq1 18 17 w f w True\n",
1190       "xxxx 18 18 w f v False\n",
1191       "xxxx 18 19 w a f False\n",
1192       "xxxx 18 20 w g a False\n",
1193       "seq1 19 0 v ! x False\n",
1194       "xxxx 19 1 v a e False\n",
1195       "xxxx 19 2 v e e False\n",
1196       "xxxx 19 3 v h z False\n",
1197       "xxxx 19 4 v b z False\n",
1198       "xxxx 19 5 v a a False\n",
1199       "xxxx 19 6 v b c False\n",
1200       "xxxx 19 7 v e y False\n",
1201       "xxxx 19 8 v e d False\n",
1202       "xxxx 19 9 v e g False\n",
1203       "xxxx 19 10 v a g False\n",
1204       "xxxx 19 11 v c c False\n",
1205       "xxxx 19 12 v d x False\n",
1206       "xxxx 19 13 v g e False\n",
1207       "xxxx 19 14 v g f False\n",
1208       "xxxx 19 15 v c w False\n",
1209       "xxxx 19 16 v e w False\n",
1210       "seq1 19 17 v f v True\n",
1211       "seq2 19 18 v f f True\n",
1212       "seq2 19 19 v a a True\n",
1213       "seq2 19 20 v g g True\n",
1214       "seq1 20 0 z ! e False\n",
1215       "xxxx 20 1 z a e False\n",
1216       "xxxx 20 2 z e z False\n",
1217       "xxxx 20 3 z h z False\n",
1218       "xxxx 20 4 z b a False\n",
1219       "xxxx 20 5 z a c False\n",
1220       "xxxx 20 6 z b y False\n",
1221       "xxxx 20 7 z e d False\n",
1222       "xxxx 20 8 z e g False\n",
1223       "xxxx 20 9 z e g False\n",
1224       "xxxx 20 10 z a c False\n",
1225       "xxxx 20 11 z c x False\n",
1226       "xxxx 20 12 z d e False\n",
1227       "xxxx 20 13 z g f False\n",
1228       "xxxx 20 14 z g w False\n",
1229       "xxxx 20 15 z c w False\n",
1230       "xxxx 20 16 z e v False\n",
1231       "xxxx 20 17 z f f False\n",
1232       "xxxx 20 18 z f a False\n",
1233       "xxxx 20 19 z a g False\n",
1234       "seq1 20 20 z g z True\n",
1235       "T . . . . . . . . . . . . . . . . . . . .\n",
1236       "T T . . . . . . . . . . . . . . . . . . .\n",
1237       ". T . . . . . . . . . . . . . . . . . . .\n",
1238       ". T . . . . . . . . . . . . . . . . . . .\n",
1239       ". T . . . . . . . . . . . . . . . . . . .\n",
1240       ". T . . . . . . . . . . . . . . . . . . .\n",
1241       ". T T T T T T . . . . . . . . . . . . . .\n",
1242       ". . . . . . T . . . . . . . . . . . . . .\n",
1243       ". . . . . . T T . . . . . . . . . . . . .\n",
1244       ". . . . . . . T . . . . . . . . . . . . .\n",
1245       ". . . . . . . T . . . . . . . . . . . . .\n",
1246       ". . . . . . . T . . . . . . . . . . . . .\n",
1247       ". . . . . . . T T T . . . . . . . . . . .\n",
1248       ". . . . . . . . . T . . . . . . . . . . .\n",
1249       ". . . . . . . . . T T T . . . . . . . . .\n",
1250       ". . . . . . . . . . . T T T T T . . . . .\n",
1251       ". . . . . . . . . . . . . . . T T T . . .\n",
1252       ". . . . . . . . . . . . . . . . . T . . .\n",
1253       ". . . . . . . . . . . . . . . . . T . . .\n",
1254       ". . . . . . . . . . . . . . . . . T T T T\n",
1255       ". . . . . . . . . . . . . . . . . . . . T\n"
1256      ]
1257     }
1258    ],
1259    "source": [
1260     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True, debug=True)\n",
1261     "print(show_table(t))"
1262    ]
1263   },
1264   {
1265    "cell_type": "code",
1266    "execution_count": 22,
1267    "metadata": {},
1268    "outputs": [
1269     {
1270      "data": {
1271       "text/plain": [
1272        "'YaZVXZWehbabUXeYXXXeeZZacYdggcXefWWVfagZ'"
1273       ]
1274      },
1275      "execution_count": 22,
1276      "metadata": {},
1277      "output_type": "execute_result"
1278     }
1279    ],
1280    "source": [
1281     "show_backtrace(bp)"
1282    ]
1283   },
1284   {
1285    "cell_type": "code",
1286    "execution_count": 23,
1287    "metadata": {},
1288    "outputs": [
1289     {
1290      "name": "stdout",
1291      "output_type": "stream",
1292      "text": [
1293       "T . . . . . . . . . . . . . . . . . . . .\n",
1294       "T T . . . . . . . . . . . . . . . . . . .\n",
1295       ". T . . . . . . . . . . . . . . . . . . .\n",
1296       ". T . . . . . . . . . . . . . . . . . . .\n",
1297       ". T . . . . . . . . . . . . . . . . . . .\n",
1298       ". T . . . . . . . . . . . . . . . . . . .\n",
1299       ". T T T T T T . . . . . . . . . . . . . .\n",
1300       ". . . . . . T . . . . . . . . . . . . . .\n",
1301       ". . . . . . T T . . . . . . . . . . . . .\n",
1302       ". . . . . . . T . . . . . . . . . . . . .\n",
1303       ". . . . . . . T . . . . . . . . . . . . .\n",
1304       ". . . . . . . T . . . . . . . . . . . . .\n",
1305       ". . . . . . . T T T . . . . . . . . . . .\n",
1306       ". . . . . . . . . T . . . . . . . . . . .\n",
1307       ". . . . . . . . . T T T . . . . . . . . .\n",
1308       ". . . . . . . . . . . T T T T T . . . . .\n",
1309       ". . . . . . . . . . . . . . . T T T . . .\n",
1310       ". . . . . . . . . . . . . . . . . T . . .\n",
1311       ". . . . . . . . . . . . . . . . . T . . .\n",
1312       ". . . . . . . . . . . . . . . . . T T T T\n",
1313       ". . . . . . . . . . . . . . . . . . . . T\n",
1314       "YaZVXZWehbabUXeYXXXeeZZacYdggcXefWWVfagZ\n"
1315      ]
1316     },
1317     {
1318      "data": {
1319       "text/plain": [
1320        "True"
1321       ]
1322      },
1323      "execution_count": 23,
1324      "metadata": {},
1325      "output_type": "execute_result"
1326     }
1327    ],
1328    "source": [
1329     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1330     "print(show_table(t))\n",
1331     "print(show_backtrace(bp))\n",
1332     "v"
1333    ]
1334   },
1335   {
1336    "cell_type": "code",
1337    "execution_count": 24,
1338    "metadata": {},
1339    "outputs": [
1340     {
1341      "data": {
1342       "text/plain": [
1343        "('ehcceddeafddffefgffdfbbedabhbadebdchfabhhbfghdggcd',\n",
1344        " 'hdahagaefhadaaaeehdhfaeafgcgcdfbegehdfchbfecgbgfbe',\n",
1345        " 'hehcdahceddageaaefddfffefgfhafddaafaebbehedhdfabaeahbadfgcgecbddcfbhfegeahbhdhbfcfhgbfhdgecgbgcgdfbe',\n",
1346        " 100)"
1347       ]
1348      },
1349      "execution_count": 24,
1350      "metadata": {},
1351      "output_type": "execute_result"
1352     }
1353    ],
1354    "source": [
1355     "s1 = make_string(50)\n",
1356     "s2 = make_string(50)\n",
1357     "il = interleave(s1, s2)\n",
1358     "s1, s2, il, len(il)"
1359    ]
1360   },
1361   {
1362    "cell_type": "code",
1363    "execution_count": 25,
1364    "metadata": {},
1365    "outputs": [
1366     {
1367      "name": "stdout",
1368      "output_type": "stream",
1369      "text": [
1370       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1371       "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1372       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1373       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1374       ". . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1375       ". . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1376       ". . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1377       ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1378       ". . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1379       ". . . . . . . . . T . . T T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1380       ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1381       ". . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1382       ". . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1383       ". . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1384       ". . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1385       ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1386       ". . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1387       ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1388       ". . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1389       ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1390       ". . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1391       ". . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1392       ". . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1393       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
1394       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . .\n",
1395       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
1396       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
1397       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
1398       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . .\n",
1399       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . .\n",
1400       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . .\n",
1401       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
1402       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . .\n",
1403       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1404       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1405       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
1406       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . .\n",
1407       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . .\n",
1408       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
1409       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
1410       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . .\n",
1411       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . .\n",
1412       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . .\n",
1413       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . .\n",
1414       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . .\n",
1415       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . .\n",
1416       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T .\n",
1417       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T\n",
1418       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1419       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1420       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1421       "HehcDAHceddAGeaAEfddffFefgfHAfdDAAfAEbbEHeDHdFabAEAhbadFGCGeCbdDcFBhfEGEaHbhDhbFCfHgBFhdgECGBgcGdFBE\n"
1422      ]
1423     },
1424     {
1425      "data": {
1426       "text/plain": [
1427        "True"
1428       ]
1429      },
1430      "execution_count": 25,
1431      "metadata": {},
1432      "output_type": "execute_result"
1433     }
1434    ],
1435    "source": [
1436     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1437     "print(show_table(t))\n",
1438     "print(show_backtrace(bp))\n",
1439     "v"
1440    ]
1441   },
1442   {
1443    "cell_type": "code",
1444    "execution_count": 26,
1445    "metadata": {},
1446    "outputs": [
1447     {
1448      "name": "stdout",
1449      "output_type": "stream",
1450      "text": [
1451       "1000 loops, best of 3: 1.25 ms per loop\n"
1452      ]
1453     }
1454    ],
1455    "source": [
1456     "%%timeit\n",
1457     "is_interleave(s2, s1, il)"
1458    ]
1459   },
1460   {
1461    "cell_type": "code",
1462    "execution_count": 27,
1463    "metadata": {},
1464    "outputs": [
1465     {
1466      "name": "stdout",
1467      "output_type": "stream",
1468      "text": [
1469       "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1470       ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1471       ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1472       ". T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1473       ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1474       ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1475       ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1476       ". . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1477       ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1478       ". . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1479       ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1480       ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1481       ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1482       ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1483       ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1484       ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1485       ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1486       ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1487       ". . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1488       ". . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1489       ". . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1490       ". . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1491       ". . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1492       ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1493       ". . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1494       ". . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1495       ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1496       ". . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1497       ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1498       ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1499       ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1500       ". . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . .\n",
1501       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
1502       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
1503       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
1504       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . .\n",
1505       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . .\n",
1506       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . .\n",
1507       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
1508       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . .\n",
1509       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . .\n",
1510       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1511       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . .\n",
1512       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T . . . . . . . . . .\n",
1513       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . .\n",
1514       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
1515       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
1516       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . .\n",
1517       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . .\n",
1518       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . .\n",
1519       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T\n",
1520       "hEHCdahCEDDagEaAeFDDfFFEFGFhaFdDaaFaeBBehEdhDfABaeaHBADfgcgEcBdDCfbHFegeAhBHdHBfcFhGbfHDGecgbGCgDfbe\n"
1521      ]
1522     },
1523     {
1524      "data": {
1525       "text/plain": [
1526        "True"
1527       ]
1528      },
1529      "execution_count": 27,
1530      "metadata": {},
1531      "output_type": "execute_result"
1532     }
1533    ],
1534    "source": [
1535     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1536     "print(show_table(t))\n",
1537     "print(show_backtrace(bp))\n",
1538     "v"
1539    ]
1540   },
1541   {
1542    "cell_type": "code",
1543    "execution_count": 28,
1544    "metadata": {},
1545    "outputs": [
1546     {
1547      "data": {
1548       "text/plain": [
1549        "True"
1550       ]
1551      },
1552      "execution_count": 28,
1553      "metadata": {},
1554      "output_type": "execute_result"
1555     }
1556    ],
1557    "source": [
1558     "show_backtrace(bp).lower() == il"
1559    ]
1560   },
1561   {
1562    "cell_type": "code",
1563    "execution_count": 29,
1564    "metadata": {},
1565    "outputs": [
1566     {
1567      "data": {
1568       "text/plain": [
1569        "('ahgafgaagdgccegafedggefddeaabhffchdgeabcfaacahcgge', False, False)"
1570       ]
1571      },
1572      "execution_count": 29,
1573      "metadata": {},
1574      "output_type": "execute_result"
1575     }
1576    ],
1577    "source": [
1578     "s3 = make_string(50)\n",
1579     "s3, is_interleave(s1, s3, il), is_interleave(s2, s3, il)"
1580    ]
1581   },
1582   {
1583    "cell_type": "code",
1584    "execution_count": 30,
1585    "metadata": {},
1586    "outputs": [
1587     {
1588      "name": "stdout",
1589      "output_type": "stream",
1590      "text": [
1591       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\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       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1642       "\n"
1643      ]
1644     },
1645     {
1646      "data": {
1647       "text/plain": [
1648        "False"
1649       ]
1650      },
1651      "execution_count": 30,
1652      "metadata": {},
1653      "output_type": "execute_result"
1654     }
1655    ],
1656    "source": [
1657     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1658     "print(show_table(t))\n",
1659     "print(show_backtrace(bp))\n",
1660     "v"
1661    ]
1662   },
1663   {
1664    "cell_type": "code",
1665    "execution_count": 31,
1666    "metadata": {
1667     "collapsed": true
1668    },
1669    "outputs": [],
1670    "source": [
1671     "def is_interleave_recursive(s1, s2, s3):\n",
1672     "    if not s1:\n",
1673     "        return s2 == s3\n",
1674     "    elif not s2:\n",
1675     "        return s1 == s3\n",
1676     "    else:\n",
1677     "        if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
1678     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n",
1679     "        elif s1[-1] == s3[-1]:\n",
1680     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
1681     "        elif s2[-1] == s3[-1]:\n",
1682     "            return is_interleave(s1, s2[:-1], s3[:-1])\n",
1683     "        else:\n",
1684     "            return False"
1685    ]
1686   },
1687   {
1688    "cell_type": "code",
1689    "execution_count": 48,
1690    "metadata": {
1691     "collapsed": true
1692    },
1693    "outputs": [],
1694    "source": [
1695     "s1 = make_string(500)\n",
1696     "s2 = make_string(500)\n",
1697     "s3 = make_string(500)\n",
1698     "s12 = interleave(s1, s2)\n",
1699     "s23 = interleave(s2, s3)"
1700    ]
1701   },
1702   {
1703    "cell_type": "code",
1704    "execution_count": 49,
1705    "metadata": {},
1706    "outputs": [
1707     {
1708      "data": {
1709       "text/plain": [
1710        "True"
1711       ]
1712      },
1713      "execution_count": 49,
1714      "metadata": {},
1715      "output_type": "execute_result"
1716     }
1717    ],
1718    "source": [
1719     "is_interleave_recursive(s1, s2, s12)"
1720    ]
1721   },
1722   {
1723    "cell_type": "code",
1724    "execution_count": 50,
1725    "metadata": {},
1726    "outputs": [
1727     {
1728      "data": {
1729       "text/plain": [
1730        "False"
1731       ]
1732      },
1733      "execution_count": 50,
1734      "metadata": {},
1735      "output_type": "execute_result"
1736     }
1737    ],
1738    "source": [
1739     "is_interleave_recursive(s1, s2, s23)"
1740    ]
1741   },
1742   {
1743    "cell_type": "markdown",
1744    "metadata": {},
1745    "source": [
1746     "## Example"
1747    ]
1748   },
1749   {
1750    "cell_type": "code",
1751    "execution_count": 32,
1752    "metadata": {
1753     "collapsed": true
1754    },
1755    "outputs": [],
1756    "source": [
1757     "def show_annotated_table(table, bps):\n",
1758     "    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",
1759     "        for i in sorted(set([k[0] for k in table])))"
1760    ]
1761   },
1762   {
1763    "cell_type": "code",
1764    "execution_count": 33,
1765    "metadata": {
1766     "collapsed": true
1767    },
1768    "outputs": [],
1769    "source": [
1770     "def show_backtrace_star(bps):\n",
1771     "    i = max([0] + [k[0] for k in bps])\n",
1772     "    j = max([0] + [k[1] for k in bps])\n",
1773     "    chars = ''\n",
1774     "    stars = ''\n",
1775     "    if (i, j) in bps:\n",
1776     "        while i != 0 or j != 0:\n",
1777     "            chars += bps[i, j][2]\n",
1778     "            if bps[i, j][3] == 'seq1':\n",
1779     "                stars += '*'\n",
1780     "            else:\n",
1781     "                stars += ' '\n",
1782     "            i, j = bps[i, j][0], bps[i, j][1] \n",
1783     "        return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n",
1784     "    else:\n",
1785     "        return ''"
1786    ]
1787   },
1788   {
1789    "cell_type": "code",
1790    "execution_count": 34,
1791    "metadata": {},
1792    "outputs": [
1793     {
1794      "data": {
1795       "text/plain": [
1796        "('acabcbccaa', 'cabcadddca', 'acabcbcccaaabcadddca', 20)"
1797       ]
1798      },
1799      "execution_count": 34,
1800      "metadata": {},
1801      "output_type": "execute_result"
1802     }
1803    ],
1804    "source": [
1805     "s1 = make_string(10, alphabet='abcd')\n",
1806     "s2 = make_string(10, alphabet='abcd')\n",
1807     "s3 = make_string(10, alphabet='abcd')\n",
1808     "il = interleave(s1, s2)\n",
1809     "s1, s2, il, len(il)"
1810    ]
1811   },
1812   {
1813    "cell_type": "code",
1814    "execution_count": 35,
1815    "metadata": {},
1816    "outputs": [
1817     {
1818      "name": "stdout",
1819      "output_type": "stream",
1820      "text": [
1821       "* . . . . . . . . . .\n",
1822       "a c a b c . . . . . .\n",
1823       "c . . c . . . . . . .\n",
1824       "a . . . . . . . . . .\n",
1825       "b c . . . . . . . . .\n",
1826       "c . . . . . . . . . .\n",
1827       "b c . . . . . . . . .\n",
1828       "c c . . . . . . . . .\n",
1829       "c c a . . . . . . . .\n",
1830       ". a a . . . . . . . .\n",
1831       ". a a b c a d d d c a\n",
1832       "ACABCBcCCaAAbcadddca\n",
1833       "acabcbcccaaabcadddca\n",
1834       "****** ** **        \n"
1835      ]
1836     },
1837     {
1838      "data": {
1839       "text/plain": [
1840        "True"
1841       ]
1842      },
1843      "execution_count": 35,
1844      "metadata": {},
1845      "output_type": "execute_result"
1846     }
1847    ],
1848    "source": [
1849     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1850     "print(show_annotated_table(t, bp))\n",
1851     "print(show_backtrace(bp))\n",
1852     "print(show_backtrace_star(bp))\n",
1853     "v"
1854    ]
1855   },
1856   {
1857    "cell_type": "code",
1858    "execution_count": 36,
1859    "metadata": {},
1860    "outputs": [
1861     {
1862      "name": "stdout",
1863      "output_type": "stream",
1864      "text": [
1865       "* a c a b c b c c . .\n",
1866       ". c . . c . c c c a a\n",
1867       ". a . . . . . . a a a\n",
1868       ". b c . . . . . . . b\n",
1869       ". c . . . . . . . . c\n",
1870       ". . . . . . . . . . a\n",
1871       ". . . . . . . . . . d\n",
1872       ". . . . . . . . . . d\n",
1873       ". . . . . . . . . . d\n",
1874       ". . . . . . . . . . c\n",
1875       ". . . . . . . . . . a\n",
1876       "acabcbccCaaABCADDDCA\n",
1877       "acabcbcccaaabcadddca\n",
1878       "        *  *********\n"
1879      ]
1880     },
1881     {
1882      "data": {
1883       "text/plain": [
1884        "True"
1885       ]
1886      },
1887      "execution_count": 36,
1888      "metadata": {},
1889      "output_type": "execute_result"
1890     }
1891    ],
1892    "source": [
1893     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1894     "print(show_annotated_table(t, bp))\n",
1895     "print(show_backtrace(bp))\n",
1896     "print(show_backtrace_star(bp))\n",
1897     "v"
1898    ]
1899   },
1900   {
1901    "cell_type": "code",
1902    "execution_count": 37,
1903    "metadata": {},
1904    "outputs": [
1905     {
1906      "name": "stdout",
1907      "output_type": "stream",
1908      "text": [
1909       "* a . . . . . . . . .\n",
1910       "a . . . . . . . . . .\n",
1911       "c a . . . . . . . . .\n",
1912       "a . . . . . . . . . .\n",
1913       "b . . . . . . . . . .\n",
1914       "c . . . . . . . . . .\n",
1915       "b . . . . . . . . . .\n",
1916       "c . . . . . . . . . .\n",
1917       "c . . . . . . . . . .\n",
1918       ". . . . . . . . . . .\n",
1919       ". . . . . . . . . . .\n",
1920       "\n",
1921       "\n"
1922      ]
1923     },
1924     {
1925      "data": {
1926       "text/plain": [
1927        "False"
1928       ]
1929      },
1930      "execution_count": 37,
1931      "metadata": {},
1932      "output_type": "execute_result"
1933     }
1934    ],
1935    "source": [
1936     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1937     "print(show_annotated_table(t, bp))\n",
1938     "print(show_backtrace(bp))\n",
1939     "print(show_backtrace_star(bp))\n",
1940     "v"
1941    ]
1942   },
1943   {
1944    "cell_type": "code",
1945    "execution_count": 38,
1946    "metadata": {},
1947    "outputs": [
1948     {
1949      "name": "stdout",
1950      "output_type": "stream",
1951      "text": [
1952       "* a . . . . . . . . .\n",
1953       ". c . . . . . . . . .\n",
1954       ". a . . . . . . . . .\n",
1955       ". b . . . . . . . . .\n",
1956       ". c . . . . . . . . .\n",
1957       ". . . . . . . . . . .\n",
1958       ". . . . . . . . . . .\n",
1959       ". . . . . . . . . . .\n",
1960       ". . . . . . . . . . .\n",
1961       ". . . . . . . . . . .\n",
1962       ". . . . . . . . . . .\n",
1963       "aCABC\n",
1964       "acabc\n",
1965       " ****\n"
1966      ]
1967     },
1968     {
1969      "data": {
1970       "text/plain": [
1971        "False"
1972       ]
1973      },
1974      "execution_count": 38,
1975      "metadata": {},
1976      "output_type": "execute_result"
1977     }
1978    ],
1979    "source": [
1980     "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n",
1981     "print(show_annotated_table(t, bp))\n",
1982     "print(show_backtrace(bp))\n",
1983     "print(show_backtrace_star(bp))\n",
1984     "v"
1985    ]
1986   },
1987   {
1988    "cell_type": "code",
1989    "execution_count": null,
1990    "metadata": {
1991     "collapsed": true
1992    },
1993    "outputs": [],
1994    "source": []
1995   }
1996  ],
1997  "metadata": {
1998   "kernelspec": {
1999    "display_name": "Python 3",
2000    "language": "python",
2001    "name": "python3"
2002   },
2003   "language_info": {
2004    "codemirror_mode": {
2005     "name": "ipython",
2006     "version": 3
2007    },
2008    "file_extension": ".py",
2009    "mimetype": "text/x-python",
2010    "name": "python",
2011    "nbconvert_exporter": "python",
2012    "pygments_lexer": "ipython3",
2013    "version": "3.5.2+"
2014   }
2015  },
2016  "nbformat": 4,
2017  "nbformat_minor": 1
2018 }