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        "'gbbdffedehgebaaeghbggcfeegfaccdhaaaachhdhhchfcfdfb'"
 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 u\n",
 717       "0 1 -1 adding a\n",
 718       "1 1 0 adding c\n",
 719       "2 1 1 adding v\n",
 720       "2 2 0 adding h\n",
 721       "3 2 1 adding e\n",
 722       "4 2 2 adding v\n",
 723       "4 3 1 adding e\n",
 724       "5 3 2 adding u\n",
 725       "5 4 1 adding f\n",
 726       "6 4 2 adding u\n",
 727       "6 5 1 adding v\n",
 728       "6 6 0 adding u\n",
 729       "6 7 -1 adding x\n",
 730       "6 8 -2 adding z\n",
 731       "6 9 -3 adding u\n",
 732       "6 10 -4 adding a\n",
 733       "7 10 -3 adding e\n",
 734       "8 10 -2 adding d\n",
 735       "9 10 -1 adding h\n",
 736       "10 10 0 adding v\n",
 737       "10 11 -1 adding u\n",
 738       "10 12 -2 adding h\n",
 739       "11 12 -1 adding g\n",
 740       "12 12 0 adding x\n",
 741       "12 13 -1 adding e\n",
 742       "13 13 0 adding f\n",
 743       "14 13 1 adding w\n",
 744       "14 14 0 adding y\n",
 745       "14 15 -1 adding u\n",
 746       "14 16 -2 adding d\n",
 747       "15 16 -1 adding g\n",
 748       "16 16 0 adding h\n",
 749       "17 16 1 adding g\n",
 750       "18 16 2 adding g\n",
 751       "19 16 3 adding g\n",
 752       "20 16 4 remaining s2 yyuz\n"
 753      ]
 754     },
 755     {
 756      "data": {
 757       "text/plain": [
 758        "('acheefaedhhgefdghggg',\n",
 759        " 'uvvuuvuxzuvuxwyuyyuz',\n",
 760        " 'uacvheveufuvuxzuaedhvuhgxefwyudghgggyyuz',\n",
 761        " 40)"
 762       ]
 763      },
 764      "execution_count": 20,
 765      "metadata": {},
 766      "output_type": "execute_result"
 767     }
 768    ],
 769    "source": [
 770     "s1 = make_string(20)\n",
 771     "s2 = make_string(20, alphabet='uvwxyz')\n",
 772     "il = interleave(s1, s2, wander_limit=5, debug=True)\n",
 773     "s1, s2, il, len(il)"
 774    ]
 775   },
 776   {
 777    "cell_type": "code",
 778    "execution_count": 21,
 779    "metadata": {},
 780    "outputs": [
 781     {
 782      "name": "stdout",
 783      "output_type": "stream",
 784      "text": [
 785       "xxxx 0 0 ! ! ! True\n",
 786       "seq2 0 1 ! a u False\n",
 787       "seq2 0 2 ! c a False\n",
 788       "seq2 0 3 ! h c False\n",
 789       "seq2 0 4 ! e v False\n",
 790       "seq2 0 5 ! e h False\n",
 791       "seq2 0 6 ! f e False\n",
 792       "seq2 0 7 ! a v False\n",
 793       "seq2 0 8 ! e e False\n",
 794       "seq2 0 9 ! d u False\n",
 795       "seq2 0 10 ! h f False\n",
 796       "seq2 0 11 ! h u False\n",
 797       "seq2 0 12 ! g v False\n",
 798       "seq2 0 13 ! e u False\n",
 799       "seq2 0 14 ! f x False\n",
 800       "seq2 0 15 ! d z False\n",
 801       "seq2 0 16 ! g u False\n",
 802       "seq2 0 17 ! h a False\n",
 803       "seq2 0 18 ! g e False\n",
 804       "seq2 0 19 ! g d False\n",
 805       "seq2 0 20 ! g h False\n",
 806       "seq1 1 0 u ! u True\n",
 807       "seq2 1 1 u a a True\n",
 808       "seq2 1 2 u c c True\n",
 809       "xxxx 1 3 u h v False\n",
 810       "xxxx 1 4 u e h False\n",
 811       "xxxx 1 5 u e e False\n",
 812       "xxxx 1 6 u f v False\n",
 813       "xxxx 1 7 u a e False\n",
 814       "xxxx 1 8 u e u False\n",
 815       "xxxx 1 9 u d f False\n",
 816       "xxxx 1 10 u h u False\n",
 817       "xxxx 1 11 u h v False\n",
 818       "xxxx 1 12 u g u False\n",
 819       "xxxx 1 13 u e x False\n",
 820       "xxxx 1 14 u f z False\n",
 821       "xxxx 1 15 u d u False\n",
 822       "xxxx 1 16 u g a False\n",
 823       "xxxx 1 17 u h e False\n",
 824       "xxxx 1 18 u g d False\n",
 825       "xxxx 1 19 u g h False\n",
 826       "xxxx 1 20 u g v False\n",
 827       "seq1 2 0 v ! a False\n",
 828       "xxxx 2 1 v a c False\n",
 829       "seq1 2 2 v c v True\n",
 830       "seq2 2 3 v h h True\n",
 831       "seq2 2 4 v e e True\n",
 832       "xxxx 2 5 v e v False\n",
 833       "xxxx 2 6 v f e False\n",
 834       "xxxx 2 7 v a u False\n",
 835       "xxxx 2 8 v e f False\n",
 836       "xxxx 2 9 v d u False\n",
 837       "xxxx 2 10 v h v False\n",
 838       "xxxx 2 11 v h u False\n",
 839       "xxxx 2 12 v g x False\n",
 840       "xxxx 2 13 v e z False\n",
 841       "xxxx 2 14 v f u False\n",
 842       "xxxx 2 15 v d a False\n",
 843       "xxxx 2 16 v g e False\n",
 844       "xxxx 2 17 v h d False\n",
 845       "xxxx 2 18 v g h False\n",
 846       "xxxx 2 19 v g v False\n",
 847       "xxxx 2 20 v g u False\n",
 848       "seq1 3 0 v ! c False\n",
 849       "xxxx 3 1 v a v False\n",
 850       "xxxx 3 2 v c h False\n",
 851       "xxxx 3 3 v h e False\n",
 852       "seq1 3 4 v e v True\n",
 853       "seq2 3 5 v e e True\n",
 854       "xxxx 3 6 v f u False\n",
 855       "xxxx 3 7 v a f False\n",
 856       "xxxx 3 8 v e u False\n",
 857       "xxxx 3 9 v d v False\n",
 858       "xxxx 3 10 v h u False\n",
 859       "xxxx 3 11 v h x False\n",
 860       "xxxx 3 12 v g z False\n",
 861       "xxxx 3 13 v e u False\n",
 862       "xxxx 3 14 v f a False\n",
 863       "xxxx 3 15 v d e False\n",
 864       "xxxx 3 16 v g d False\n",
 865       "xxxx 3 17 v h h False\n",
 866       "xxxx 3 18 v g v False\n",
 867       "xxxx 3 19 v g u False\n",
 868       "xxxx 3 20 v g h False\n",
 869       "seq1 4 0 u ! v False\n",
 870       "xxxx 4 1 u a h False\n",
 871       "xxxx 4 2 u c e False\n",
 872       "xxxx 4 3 u h v False\n",
 873       "xxxx 4 4 u e e False\n",
 874       "seq1 4 5 u e u True\n",
 875       "seq2 4 6 u f f True\n",
 876       "xxxx 4 7 u a u False\n",
 877       "xxxx 4 8 u e v False\n",
 878       "xxxx 4 9 u d u False\n",
 879       "xxxx 4 10 u h x False\n",
 880       "xxxx 4 11 u h z False\n",
 881       "xxxx 4 12 u g u False\n",
 882       "xxxx 4 13 u e a False\n",
 883       "xxxx 4 14 u f e False\n",
 884       "xxxx 4 15 u d d False\n",
 885       "xxxx 4 16 u g h False\n",
 886       "xxxx 4 17 u h v False\n",
 887       "xxxx 4 18 u g u False\n",
 888       "xxxx 4 19 u g h False\n",
 889       "xxxx 4 20 u g g False\n",
 890       "seq1 5 0 u ! h False\n",
 891       "xxxx 5 1 u a e False\n",
 892       "xxxx 5 2 u c v False\n",
 893       "xxxx 5 3 u h e False\n",
 894       "xxxx 5 4 u e u False\n",
 895       "xxxx 5 5 u e f False\n",
 896       "seq1 5 6 u f u True\n",
 897       "xxxx 5 7 u a v False\n",
 898       "xxxx 5 8 u e u False\n",
 899       "xxxx 5 9 u d x False\n",
 900       "xxxx 5 10 u h z False\n",
 901       "xxxx 5 11 u h u False\n",
 902       "xxxx 5 12 u g a False\n",
 903       "xxxx 5 13 u e e False\n",
 904       "xxxx 5 14 u f d False\n",
 905       "xxxx 5 15 u d h False\n",
 906       "xxxx 5 16 u g v False\n",
 907       "xxxx 5 17 u h u False\n",
 908       "xxxx 5 18 u g h False\n",
 909       "xxxx 5 19 u g g False\n",
 910       "xxxx 5 20 u g x False\n",
 911       "seq1 6 0 v ! e False\n",
 912       "xxxx 6 1 v a v False\n",
 913       "xxxx 6 2 v c e False\n",
 914       "xxxx 6 3 v h u False\n",
 915       "xxxx 6 4 v e f False\n",
 916       "xxxx 6 5 v e u False\n",
 917       "seq1 6 6 v f v True\n",
 918       "xxxx 6 7 v a u False\n",
 919       "xxxx 6 8 v e x False\n",
 920       "xxxx 6 9 v d z False\n",
 921       "xxxx 6 10 v h u False\n",
 922       "xxxx 6 11 v h a False\n",
 923       "xxxx 6 12 v g e False\n",
 924       "xxxx 6 13 v e d False\n",
 925       "xxxx 6 14 v f h False\n",
 926       "xxxx 6 15 v d v False\n",
 927       "xxxx 6 16 v g u False\n",
 928       "xxxx 6 17 v h h False\n",
 929       "xxxx 6 18 v g g False\n",
 930       "xxxx 6 19 v g x False\n",
 931       "xxxx 6 20 v g e False\n",
 932       "seq1 7 0 u ! v False\n",
 933       "xxxx 7 1 u a e False\n",
 934       "xxxx 7 2 u c u False\n",
 935       "xxxx 7 3 u h f False\n",
 936       "xxxx 7 4 u e u False\n",
 937       "xxxx 7 5 u e v False\n",
 938       "seq1 7 6 u f u True\n",
 939       "xxxx 7 7 u a x False\n",
 940       "xxxx 7 8 u e z False\n",
 941       "xxxx 7 9 u d u False\n",
 942       "xxxx 7 10 u h a False\n",
 943       "xxxx 7 11 u h e False\n",
 944       "xxxx 7 12 u g d False\n",
 945       "xxxx 7 13 u e h False\n",
 946       "xxxx 7 14 u f v False\n",
 947       "xxxx 7 15 u d u False\n",
 948       "xxxx 7 16 u g h False\n",
 949       "xxxx 7 17 u h g False\n",
 950       "xxxx 7 18 u g x False\n",
 951       "xxxx 7 19 u g e False\n",
 952       "xxxx 7 20 u g f False\n",
 953       "seq1 8 0 x ! e False\n",
 954       "xxxx 8 1 x a u False\n",
 955       "xxxx 8 2 x c f False\n",
 956       "xxxx 8 3 x h u False\n",
 957       "xxxx 8 4 x e v False\n",
 958       "xxxx 8 5 x e u False\n",
 959       "seq1 8 6 x f x True\n",
 960       "xxxx 8 7 x a z False\n",
 961       "xxxx 8 8 x e u False\n",
 962       "xxxx 8 9 x d a False\n",
 963       "xxxx 8 10 x h e False\n",
 964       "xxxx 8 11 x h d False\n",
 965       "xxxx 8 12 x g h False\n",
 966       "xxxx 8 13 x e v False\n",
 967       "xxxx 8 14 x f u False\n",
 968       "xxxx 8 15 x d h False\n",
 969       "xxxx 8 16 x g g False\n",
 970       "xxxx 8 17 x h x False\n",
 971       "xxxx 8 18 x g e False\n",
 972       "xxxx 8 19 x g f False\n",
 973       "xxxx 8 20 x g w False\n",
 974       "seq1 9 0 z ! u False\n",
 975       "xxxx 9 1 z a f False\n",
 976       "xxxx 9 2 z c u False\n",
 977       "xxxx 9 3 z h v False\n",
 978       "xxxx 9 4 z e u False\n",
 979       "xxxx 9 5 z e x False\n",
 980       "seq1 9 6 z f z True\n",
 981       "xxxx 9 7 z a u False\n",
 982       "xxxx 9 8 z e a False\n",
 983       "xxxx 9 9 z d e False\n",
 984       "xxxx 9 10 z h d False\n",
 985       "xxxx 9 11 z h h False\n",
 986       "xxxx 9 12 z g v False\n",
 987       "xxxx 9 13 z e u False\n",
 988       "xxxx 9 14 z f h False\n",
 989       "xxxx 9 15 z d g False\n",
 990       "xxxx 9 16 z g x False\n",
 991       "xxxx 9 17 z h e False\n",
 992       "xxxx 9 18 z g f False\n",
 993       "xxxx 9 19 z g w False\n",
 994       "xxxx 9 20 z g y False\n",
 995       "seq1 10 0 u ! f False\n",
 996       "xxxx 10 1 u a u False\n",
 997       "xxxx 10 2 u c v False\n",
 998       "xxxx 10 3 u h u False\n",
 999       "xxxx 10 4 u e x False\n",
1000       "xxxx 10 5 u e z False\n",
1001       "seq1 10 6 u f u True\n",
1002       "seq2 10 7 u a a True\n",
1003       "seq2 10 8 u e e True\n",
1004       "seq2 10 9 u d d True\n",
1005       "seq2 10 10 u h h True\n",
1006       "xxxx 10 11 u h v False\n",
1007       "xxxx 10 12 u g u False\n",
1008       "xxxx 10 13 u e h False\n",
1009       "xxxx 10 14 u f g False\n",
1010       "xxxx 10 15 u d x False\n",
1011       "xxxx 10 16 u g e False\n",
1012       "xxxx 10 17 u h f False\n",
1013       "xxxx 10 18 u g w False\n",
1014       "xxxx 10 19 u g y False\n",
1015       "xxxx 10 20 u g u False\n",
1016       "seq1 11 0 v ! u False\n",
1017       "xxxx 11 1 v a v False\n",
1018       "xxxx 11 2 v c u False\n",
1019       "xxxx 11 3 v h x False\n",
1020       "xxxx 11 4 v e z False\n",
1021       "xxxx 11 5 v e u False\n",
1022       "xxxx 11 6 v f a False\n",
1023       "xxxx 11 7 v a e False\n",
1024       "xxxx 11 8 v e d False\n",
1025       "xxxx 11 9 v d h False\n",
1026       "seq1 11 10 v h v True\n",
1027       "xxxx 11 11 v h u False\n",
1028       "xxxx 11 12 v g h False\n",
1029       "xxxx 11 13 v e g False\n",
1030       "xxxx 11 14 v f x False\n",
1031       "xxxx 11 15 v d e False\n",
1032       "xxxx 11 16 v g f False\n",
1033       "xxxx 11 17 v h w False\n",
1034       "xxxx 11 18 v g y False\n",
1035       "xxxx 11 19 v g u False\n",
1036       "xxxx 11 20 v g d False\n",
1037       "seq1 12 0 u ! v False\n",
1038       "xxxx 12 1 u a u False\n",
1039       "xxxx 12 2 u c x False\n",
1040       "xxxx 12 3 u h z False\n",
1041       "xxxx 12 4 u e u False\n",
1042       "xxxx 12 5 u e a False\n",
1043       "xxxx 12 6 u f e False\n",
1044       "xxxx 12 7 u a d False\n",
1045       "xxxx 12 8 u e h False\n",
1046       "xxxx 12 9 u d v False\n",
1047       "seq1 12 10 u h u True\n",
1048       "seq2 12 11 u h h True\n",
1049       "seq2 12 12 u g g True\n",
1050       "xxxx 12 13 u e x False\n",
1051       "xxxx 12 14 u f e False\n",
1052       "xxxx 12 15 u d f False\n",
1053       "xxxx 12 16 u g w False\n",
1054       "xxxx 12 17 u h y False\n",
1055       "xxxx 12 18 u g u False\n",
1056       "xxxx 12 19 u g d False\n",
1057       "xxxx 12 20 u g g False\n",
1058       "seq1 13 0 x ! u False\n",
1059       "xxxx 13 1 x a x False\n",
1060       "xxxx 13 2 x c z False\n",
1061       "xxxx 13 3 x h u False\n",
1062       "xxxx 13 4 x e a False\n",
1063       "xxxx 13 5 x e e False\n",
1064       "xxxx 13 6 x f d False\n",
1065       "xxxx 13 7 x a h False\n",
1066       "xxxx 13 8 x e v False\n",
1067       "xxxx 13 9 x d u False\n",
1068       "xxxx 13 10 x h h False\n",
1069       "xxxx 13 11 x h g False\n",
1070       "seq1 13 12 x g x True\n",
1071       "seq2 13 13 x e e True\n",
1072       "seq2 13 14 x f f True\n",
1073       "xxxx 13 15 x d w False\n",
1074       "xxxx 13 16 x g y False\n",
1075       "xxxx 13 17 x h u False\n",
1076       "xxxx 13 18 x g d False\n",
1077       "xxxx 13 19 x g g False\n",
1078       "xxxx 13 20 x g h False\n",
1079       "seq1 14 0 w ! x False\n",
1080       "xxxx 14 1 w a z False\n",
1081       "xxxx 14 2 w c u False\n",
1082       "xxxx 14 3 w h a False\n",
1083       "xxxx 14 4 w e e False\n",
1084       "xxxx 14 5 w e d False\n",
1085       "xxxx 14 6 w f h False\n",
1086       "xxxx 14 7 w a v False\n",
1087       "xxxx 14 8 w e u False\n",
1088       "xxxx 14 9 w d h False\n",
1089       "xxxx 14 10 w h g False\n",
1090       "xxxx 14 11 w h x False\n",
1091       "xxxx 14 12 w g e False\n",
1092       "xxxx 14 13 w e f False\n",
1093       "seq1 14 14 w f w True\n",
1094       "xxxx 14 15 w d y False\n",
1095       "xxxx 14 16 w g u False\n",
1096       "xxxx 14 17 w h d False\n",
1097       "xxxx 14 18 w g g False\n",
1098       "xxxx 14 19 w g h False\n",
1099       "xxxx 14 20 w g g False\n",
1100       "seq1 15 0 y ! z False\n",
1101       "xxxx 15 1 y a u False\n",
1102       "xxxx 15 2 y c a False\n",
1103       "xxxx 15 3 y h e False\n",
1104       "xxxx 15 4 y e d False\n",
1105       "xxxx 15 5 y e h False\n",
1106       "xxxx 15 6 y f v False\n",
1107       "xxxx 15 7 y a u False\n",
1108       "xxxx 15 8 y e h False\n",
1109       "xxxx 15 9 y d g False\n",
1110       "xxxx 15 10 y h x False\n",
1111       "xxxx 15 11 y h e False\n",
1112       "xxxx 15 12 y g f False\n",
1113       "xxxx 15 13 y e w False\n",
1114       "seq1 15 14 y f y True\n",
1115       "xxxx 15 15 y d u False\n",
1116       "xxxx 15 16 y g d False\n",
1117       "xxxx 15 17 y h g False\n",
1118       "xxxx 15 18 y g h False\n",
1119       "xxxx 15 19 y g g False\n",
1120       "xxxx 15 20 y g g False\n",
1121       "seq1 16 0 u ! u False\n",
1122       "xxxx 16 1 u a a False\n",
1123       "xxxx 16 2 u c e False\n",
1124       "xxxx 16 3 u h d False\n",
1125       "xxxx 16 4 u e h False\n",
1126       "xxxx 16 5 u e v False\n",
1127       "xxxx 16 6 u f u False\n",
1128       "xxxx 16 7 u a h False\n",
1129       "xxxx 16 8 u e g False\n",
1130       "xxxx 16 9 u d x False\n",
1131       "xxxx 16 10 u h e False\n",
1132       "xxxx 16 11 u h f False\n",
1133       "xxxx 16 12 u g w False\n",
1134       "xxxx 16 13 u e y False\n",
1135       "seq1 16 14 u f u True\n",
1136       "seq2 16 15 u d d True\n",
1137       "seq2 16 16 u g g True\n",
1138       "seq2 16 17 u h h True\n",
1139       "seq2 16 18 u g g True\n",
1140       "seq2 16 19 u g g True\n",
1141       "seq2 16 20 u g g True\n",
1142       "seq1 17 0 y ! a False\n",
1143       "xxxx 17 1 y a e False\n",
1144       "xxxx 17 2 y c d False\n",
1145       "xxxx 17 3 y h h False\n",
1146       "xxxx 17 4 y e v False\n",
1147       "xxxx 17 5 y e u False\n",
1148       "xxxx 17 6 y f h False\n",
1149       "xxxx 17 7 y a g False\n",
1150       "xxxx 17 8 y e x False\n",
1151       "xxxx 17 9 y d e False\n",
1152       "xxxx 17 10 y h f False\n",
1153       "xxxx 17 11 y h w False\n",
1154       "xxxx 17 12 y g y False\n",
1155       "xxxx 17 13 y e u False\n",
1156       "xxxx 17 14 y f d False\n",
1157       "xxxx 17 15 y d g False\n",
1158       "xxxx 17 16 y g h False\n",
1159       "xxxx 17 17 y h g False\n",
1160       "xxxx 17 18 y g g False\n",
1161       "xxxx 17 19 y g g False\n",
1162       "seq1 17 20 y g y True\n",
1163       "seq1 18 0 y ! e False\n",
1164       "xxxx 18 1 y a d False\n",
1165       "xxxx 18 2 y c h False\n",
1166       "xxxx 18 3 y h v False\n",
1167       "xxxx 18 4 y e u False\n",
1168       "xxxx 18 5 y e h False\n",
1169       "xxxx 18 6 y f g False\n",
1170       "xxxx 18 7 y a x False\n",
1171       "xxxx 18 8 y e e False\n",
1172       "xxxx 18 9 y d f False\n",
1173       "xxxx 18 10 y h w False\n",
1174       "xxxx 18 11 y h y False\n",
1175       "xxxx 18 12 y g u False\n",
1176       "xxxx 18 13 y e d False\n",
1177       "xxxx 18 14 y f g False\n",
1178       "xxxx 18 15 y d h False\n",
1179       "xxxx 18 16 y g g False\n",
1180       "xxxx 18 17 y h g False\n",
1181       "xxxx 18 18 y g g False\n",
1182       "xxxx 18 19 y g y False\n",
1183       "seq1 18 20 y g y True\n",
1184       "seq1 19 0 u ! d False\n",
1185       "xxxx 19 1 u a h False\n",
1186       "xxxx 19 2 u c v False\n",
1187       "xxxx 19 3 u h u False\n",
1188       "xxxx 19 4 u e h False\n",
1189       "xxxx 19 5 u e g False\n",
1190       "xxxx 19 6 u f x False\n",
1191       "xxxx 19 7 u a e False\n",
1192       "xxxx 19 8 u e f False\n",
1193       "xxxx 19 9 u d w False\n",
1194       "xxxx 19 10 u h y False\n",
1195       "xxxx 19 11 u h u False\n",
1196       "xxxx 19 12 u g d False\n",
1197       "xxxx 19 13 u e g False\n",
1198       "xxxx 19 14 u f h False\n",
1199       "xxxx 19 15 u d g False\n",
1200       "xxxx 19 16 u g g False\n",
1201       "xxxx 19 17 u h g False\n",
1202       "xxxx 19 18 u g y False\n",
1203       "xxxx 19 19 u g y False\n",
1204       "seq1 19 20 u g u True\n",
1205       "seq1 20 0 z ! h False\n",
1206       "xxxx 20 1 z a v False\n",
1207       "xxxx 20 2 z c u False\n",
1208       "xxxx 20 3 z h h False\n",
1209       "xxxx 20 4 z e g False\n",
1210       "xxxx 20 5 z e x False\n",
1211       "xxxx 20 6 z f e False\n",
1212       "xxxx 20 7 z a f False\n",
1213       "xxxx 20 8 z e w False\n",
1214       "xxxx 20 9 z d y False\n",
1215       "xxxx 20 10 z h u False\n",
1216       "xxxx 20 11 z h d False\n",
1217       "xxxx 20 12 z g g False\n",
1218       "xxxx 20 13 z e h False\n",
1219       "xxxx 20 14 z f g False\n",
1220       "xxxx 20 15 z d g False\n",
1221       "xxxx 20 16 z g g False\n",
1222       "xxxx 20 17 z h y False\n",
1223       "xxxx 20 18 z g y False\n",
1224       "xxxx 20 19 z g u False\n",
1225       "seq1 20 20 z g z True\n",
1226       "T . . . . . . . . . . . . . . . . . . . .\n",
1227       "T T T . . . . . . . . . . . . . . . . . .\n",
1228       ". . T T T . . . . . . . . . . . . . . . .\n",
1229       ". . . . T T . . . . . . . . . . . . . . .\n",
1230       ". . . . . T T . . . . . . . . . . . . . .\n",
1231       ". . . . . . T . . . . . . . . . . . . . .\n",
1232       ". . . . . . T . . . . . . . . . . . . . .\n",
1233       ". . . . . . T . . . . . . . . . . . . . .\n",
1234       ". . . . . . T . . . . . . . . . . . . . .\n",
1235       ". . . . . . T . . . . . . . . . . . . . .\n",
1236       ". . . . . . T T T T T . . . . . . . . . .\n",
1237       ". . . . . . . . . . T . . . . . . . . . .\n",
1238       ". . . . . . . . . . T T T . . . . . . . .\n",
1239       ". . . . . . . . . . . . T T T . . . . . .\n",
1240       ". . . . . . . . . . . . . . T . . . . . .\n",
1241       ". . . . . . . . . . . . . . T . . . . . .\n",
1242       ". . . . . . . . . . . . . . T T T T T T T\n",
1243       ". . . . . . . . . . . . . . . . . . . . T\n",
1244       ". . . . . . . . . . . . . . . . . . . . T\n",
1245       ". . . . . . . . . . . . . . . . . . . . T\n",
1246       ". . . . . . . . . . . . . . . . . . . . T\n"
1247      ]
1248     }
1249    ],
1250    "source": [
1251     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True, debug=True)\n",
1252     "print(show_table(t))"
1253    ]
1254   },
1255   {
1256    "cell_type": "code",
1257    "execution_count": 22,
1258    "metadata": {},
1259    "outputs": [
1260     {
1261      "data": {
1262       "text/plain": [
1263        "'UacVheVeUfUVUXZUaedhVUhgXefWYUdghgggYYUZ'"
1264       ]
1265      },
1266      "execution_count": 22,
1267      "metadata": {},
1268      "output_type": "execute_result"
1269     }
1270    ],
1271    "source": [
1272     "show_backtrace(bp)"
1273    ]
1274   },
1275   {
1276    "cell_type": "code",
1277    "execution_count": 23,
1278    "metadata": {},
1279    "outputs": [
1280     {
1281      "name": "stdout",
1282      "output_type": "stream",
1283      "text": [
1284       "T . . . . . . . . . . . . . . . . . . . .\n",
1285       "T T T . . . . . . . . . . . . . . . . . .\n",
1286       ". . T T T . . . . . . . . . . . . . . . .\n",
1287       ". . . . T T . . . . . . . . . . . . . . .\n",
1288       ". . . . . T T . . . . . . . . . . . . . .\n",
1289       ". . . . . . T . . . . . . . . . . . . . .\n",
1290       ". . . . . . T . . . . . . . . . . . . . .\n",
1291       ". . . . . . T . . . . . . . . . . . . . .\n",
1292       ". . . . . . T . . . . . . . . . . . . . .\n",
1293       ". . . . . . T . . . . . . . . . . . . . .\n",
1294       ". . . . . . T T T T T . . . . . . . . . .\n",
1295       ". . . . . . . . . . T . . . . . . . . . .\n",
1296       ". . . . . . . . . . T T T . . . . . . . .\n",
1297       ". . . . . . . . . . . . T T T . . . . . .\n",
1298       ". . . . . . . . . . . . . . T . . . . . .\n",
1299       ". . . . . . . . . . . . . . T . . . . . .\n",
1300       ". . . . . . . . . . . . . . T T T T T T T\n",
1301       ". . . . . . . . . . . . . . . . . . . . T\n",
1302       ". . . . . . . . . . . . . . . . . . . . T\n",
1303       ". . . . . . . . . . . . . . . . . . . . T\n",
1304       ". . . . . . . . . . . . . . . . . . . . T\n",
1305       "UacVheVeUfUVUXZUaedhVUhgXefWYUdghgggYYUZ\n"
1306      ]
1307     },
1308     {
1309      "data": {
1310       "text/plain": [
1311        "True"
1312       ]
1313      },
1314      "execution_count": 23,
1315      "metadata": {},
1316      "output_type": "execute_result"
1317     }
1318    ],
1319    "source": [
1320     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1321     "print(show_table(t))\n",
1322     "print(show_backtrace(bp))\n",
1323     "v"
1324    ]
1325   },
1326   {
1327    "cell_type": "code",
1328    "execution_count": 24,
1329    "metadata": {},
1330    "outputs": [
1331     {
1332      "data": {
1333       "text/plain": [
1334        "('gfccbgegegaccfcgeehbgcafchgbfdfbggbcachfdfaccfbffb',\n",
1335        " 'accfcfbdaabcabbbegdfffhcgcefbddegghgfdgcgdcffcfdcd',\n",
1336        " 'acgcfcffbdcacbabcagbbbegegegadcfcffcgfeehbgchacfchggcbefbfddfbdggbegcgachhfgfdfdgcgdacccfbffcffbfdcd',\n",
1337        " 100)"
1338       ]
1339      },
1340      "execution_count": 24,
1341      "metadata": {},
1342      "output_type": "execute_result"
1343     }
1344    ],
1345    "source": [
1346     "s1 = make_string(50)\n",
1347     "s2 = make_string(50)\n",
1348     "il = interleave(s1, s2)\n",
1349     "s1, s2, il, len(il)"
1350    ]
1351   },
1352   {
1353    "cell_type": "code",
1354    "execution_count": 25,
1355    "metadata": {},
1356    "outputs": [
1357     {
1358      "name": "stdout",
1359      "output_type": "stream",
1360      "text": [
1361       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1362       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1363       "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1364       ". T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1365       ". T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1366       ". T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1367       ". T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1368       ". . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1369       ". . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1370       ". . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1371       ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1372       ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1373       ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1374       ". . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1375       ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1376       ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1377       ". . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1378       ". . . . . . T . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1379       ". . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1380       ". . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1381       ". . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1382       ". . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1383       ". . . . . . . . . . . . . T . . T T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1384       ". . . . . . . . . . . . . . . . . . T . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1385       ". . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1386       ". . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1387       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . .\n",
1388       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
1389       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . .\n",
1390       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . .\n",
1391       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n",
1392       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . T T T T . . . . . . . . . . . . . . .\n",
1393       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
1394       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
1395       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . .\n",
1396       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . .\n",
1397       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . .\n",
1398       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . .\n",
1399       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . .\n",
1400       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
1401       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
1402       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
1403       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . .\n",
1404       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T .\n",
1405       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T . .\n",
1406       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . .\n",
1407       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T\n",
1408       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . T\n",
1409       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1410       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1411       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1412       "ACgCFCfFBDcAcbABCAgBBBegegEGaDcFcfFcgFeehbgcHaCfchgGCbEFBfdDfbDggbEGcGachHfGFdfDGCGDaccCfbFFCffbFDCD\n"
1413      ]
1414     },
1415     {
1416      "data": {
1417       "text/plain": [
1418        "True"
1419       ]
1420      },
1421      "execution_count": 25,
1422      "metadata": {},
1423      "output_type": "execute_result"
1424     }
1425    ],
1426    "source": [
1427     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1428     "print(show_table(t))\n",
1429     "print(show_backtrace(bp))\n",
1430     "v"
1431    ]
1432   },
1433   {
1434    "cell_type": "code",
1435    "execution_count": 26,
1436    "metadata": {},
1437    "outputs": [
1438     {
1439      "name": "stdout",
1440      "output_type": "stream",
1441      "text": [
1442       "1000 loops, best of 3: 1.25 ms per loop\n"
1443      ]
1444     }
1445    ],
1446    "source": [
1447     "%%timeit\n",
1448     "is_interleave(s2, s1, il)"
1449    ]
1450   },
1451   {
1452    "cell_type": "code",
1453    "execution_count": 27,
1454    "metadata": {},
1455    "outputs": [
1456     {
1457      "name": "stdout",
1458      "output_type": "stream",
1459      "text": [
1460       "T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1461       ". . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1462       ". . . T . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1463       ". . . T T . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1464       ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1465       ". . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1466       ". . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1467       ". . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1468       ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1469       ". . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1470       ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1471       ". . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1472       ". . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1473       ". . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1474       ". . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1475       ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1476       ". . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1477       ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1478       ". . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1479       ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1480       ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1481       ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1482       ". . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1483       ". . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1484       ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1485       ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1486       ". . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1487       ". . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1488       ". . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . .\n",
1489       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . .\n",
1490       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
1491       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
1492       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . .\n",
1493       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
1494       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
1495       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . .\n",
1496       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . .\n",
1497       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1498       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
1499       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
1500       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . .\n",
1501       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
1502       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . .\n",
1503       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
1504       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
1505       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . .\n",
1506       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . .\n",
1507       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . .\n",
1508       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . T T . . .\n",
1509       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . T . . . .\n",
1510       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T\n",
1511       "acGcfcfFbdCaCBabcaGbbbegEGEGAdCfCfFCGfEEHBGChAcFCHgGcBefbFdDFBdGGBegCgAChHFgfDFdgcgdAcCCFBffcFFBfdcd\n"
1512      ]
1513     },
1514     {
1515      "data": {
1516       "text/plain": [
1517        "True"
1518       ]
1519      },
1520      "execution_count": 27,
1521      "metadata": {},
1522      "output_type": "execute_result"
1523     }
1524    ],
1525    "source": [
1526     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1527     "print(show_table(t))\n",
1528     "print(show_backtrace(bp))\n",
1529     "v"
1530    ]
1531   },
1532   {
1533    "cell_type": "code",
1534    "execution_count": 28,
1535    "metadata": {},
1536    "outputs": [
1537     {
1538      "data": {
1539       "text/plain": [
1540        "True"
1541       ]
1542      },
1543      "execution_count": 28,
1544      "metadata": {},
1545      "output_type": "execute_result"
1546     }
1547    ],
1548    "source": [
1549     "show_backtrace(bp).lower() == il"
1550    ]
1551   },
1552   {
1553    "cell_type": "code",
1554    "execution_count": 29,
1555    "metadata": {},
1556    "outputs": [
1557     {
1558      "data": {
1559       "text/plain": [
1560        "('adadhfgacgbahfchffghdfffcfcdccchedahggdffhgbacghbe', False, False)"
1561       ]
1562      },
1563      "execution_count": 29,
1564      "metadata": {},
1565      "output_type": "execute_result"
1566     }
1567    ],
1568    "source": [
1569     "s3 = make_string(50)\n",
1570     "s3, is_interleave(s1, s3, il), is_interleave(s2, s3, il)"
1571    ]
1572   },
1573   {
1574    "cell_type": "code",
1575    "execution_count": 30,
1576    "metadata": {},
1577    "outputs": [
1578     {
1579      "name": "stdout",
1580      "output_type": "stream",
1581      "text": [
1582       "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1583       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1584       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1585       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1586       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1587       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1588       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1589       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\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       "a\n"
1634      ]
1635     },
1636     {
1637      "data": {
1638       "text/plain": [
1639        "False"
1640       ]
1641      },
1642      "execution_count": 30,
1643      "metadata": {},
1644      "output_type": "execute_result"
1645     }
1646    ],
1647    "source": [
1648     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1649     "print(show_table(t))\n",
1650     "print(show_backtrace(bp))\n",
1651     "v"
1652    ]
1653   },
1654   {
1655    "cell_type": "markdown",
1656    "metadata": {},
1657    "source": [
1658     "## Example"
1659    ]
1660   },
1661   {
1662    "cell_type": "code",
1663    "execution_count": 31,
1664    "metadata": {
1665     "collapsed": true
1666    },
1667    "outputs": [],
1668    "source": [
1669     "def show_annotated_table(table, bps):\n",
1670     "    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",
1671     "        for i in sorted(set([k[0] for k in table])))"
1672    ]
1673   },
1674   {
1675    "cell_type": "code",
1676    "execution_count": 32,
1677    "metadata": {
1678     "collapsed": true
1679    },
1680    "outputs": [],
1681    "source": [
1682     "def show_backtrace_star(bps):\n",
1683     "    i = max([0] + [k[0] for k in bps])\n",
1684     "    j = max([0] + [k[1] for k in bps])\n",
1685     "    chars = ''\n",
1686     "    stars = ''\n",
1687     "    if (i, j) in bps:\n",
1688     "        while i != 0 or j != 0:\n",
1689     "            chars += bps[i, j][2]\n",
1690     "            if bps[i, j][3] == 'seq1':\n",
1691     "                stars += '*'\n",
1692     "            else:\n",
1693     "                stars += ' '\n",
1694     "            i, j = bps[i, j][0], bps[i, j][1] \n",
1695     "        return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n",
1696     "    else:\n",
1697     "        return ''"
1698    ]
1699   },
1700   {
1701    "cell_type": "code",
1702    "execution_count": 33,
1703    "metadata": {},
1704    "outputs": [
1705     {
1706      "data": {
1707       "text/plain": [
1708        "('badbbdcadc', 'bdaadcadab', 'bdabaadbdcbadcaddacb', 20)"
1709       ]
1710      },
1711      "execution_count": 33,
1712      "metadata": {},
1713      "output_type": "execute_result"
1714     }
1715    ],
1716    "source": [
1717     "s1 = make_string(10, alphabet='abcd')\n",
1718     "s2 = make_string(10, alphabet='abcd')\n",
1719     "s3 = make_string(10, alphabet='abcd')\n",
1720     "il = interleave(s1, s2)\n",
1721     "s1, s2, il, len(il)"
1722    ]
1723   },
1724   {
1725    "cell_type": "code",
1726    "execution_count": 34,
1727    "metadata": {},
1728    "outputs": [
1729     {
1730      "name": "stdout",
1731      "output_type": "stream",
1732      "text": [
1733       "* b d a . . . . . . .\n",
1734       "b . . b a . . . . . .\n",
1735       ". . . a a d . . . . .\n",
1736       ". . . . d . . . . . .\n",
1737       ". . . . b d c . . . .\n",
1738       ". . . . . . b a d . .\n",
1739       ". . . . . . . d . . .\n",
1740       ". . . . . . . c . . .\n",
1741       ". . . . . . . a d . .\n",
1742       ". . . . . . . d d a .\n",
1743       ". . . . . . . . . c b\n",
1744       "bdaBaADBdcBaDCAdDaCb\n",
1745       "bdabaadbdcbadcaddacb\n",
1746       "   * ***  * *** * * \n"
1747      ]
1748     },
1749     {
1750      "data": {
1751       "text/plain": [
1752        "True"
1753       ]
1754      },
1755      "execution_count": 34,
1756      "metadata": {},
1757      "output_type": "execute_result"
1758     }
1759    ],
1760    "source": [
1761     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1762     "print(show_annotated_table(t, bp))\n",
1763     "print(show_backtrace(bp))\n",
1764     "print(show_backtrace_star(bp))\n",
1765     "v"
1766    ]
1767   },
1768   {
1769    "cell_type": "code",
1770    "execution_count": 35,
1771    "metadata": {},
1772    "outputs": [
1773     {
1774      "name": "stdout",
1775      "output_type": "stream",
1776      "text": [
1777       "* b . . . . . . . . .\n",
1778       "b . . . . . . . . . .\n",
1779       "d . . . . . . . . . .\n",
1780       "a b a . . . . . . . .\n",
1781       ". a a d b . . . . . .\n",
1782       ". . d . d . . . . . .\n",
1783       ". . . . c b . . . . .\n",
1784       ". . . . . a d c a d .\n",
1785       ". . . . . d . . d d .\n",
1786       ". . . . . . . . . a c\n",
1787       ". . . . . . . . . . b\n",
1788       "BDAbaAdbDCbAdcadDAcB\n",
1789       "bdabaadbdcbadcaddacb\n",
1790       "***  *  ** *    ** *\n"
1791      ]
1792     },
1793     {
1794      "data": {
1795       "text/plain": [
1796        "True"
1797       ]
1798      },
1799      "execution_count": 35,
1800      "metadata": {},
1801      "output_type": "execute_result"
1802     }
1803    ],
1804    "source": [
1805     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1806     "print(show_annotated_table(t, bp))\n",
1807     "print(show_backtrace(bp))\n",
1808     "print(show_backtrace_star(bp))\n",
1809     "v"
1810    ]
1811   },
1812   {
1813    "cell_type": "code",
1814    "execution_count": 36,
1815    "metadata": {},
1816    "outputs": [
1817     {
1818      "name": "stdout",
1819      "output_type": "stream",
1820      "text": [
1821       "* . . . . . . . . . .\n",
1822       "b . . . . . . . . . .\n",
1823       ". . . . . . . . . . .\n",
1824       ". . . . . . . . . . .\n",
1825       ". . . . . . . . . . .\n",
1826       ". . . . . . . . . . .\n",
1827       ". . . . . . . . . . .\n",
1828       ". . . . . . . . . . .\n",
1829       ". . . . . . . . . . .\n",
1830       ". . . . . . . . . . .\n",
1831       ". . . . . . . . . . .\n",
1832       "B\n",
1833       "b\n",
1834       "*\n"
1835      ]
1836     },
1837     {
1838      "data": {
1839       "text/plain": [
1840        "False"
1841       ]
1842      },
1843      "execution_count": 36,
1844      "metadata": {},
1845      "output_type": "execute_result"
1846     }
1847    ],
1848    "source": [
1849     "v, bp, t = is_interleave(s1, s3, 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": 37,
1859    "metadata": {},
1860    "outputs": [
1861     {
1862      "name": "stdout",
1863      "output_type": "stream",
1864      "text": [
1865       "* . . . . . . . . . .\n",
1866       "b . . . . . . . . . .\n",
1867       "d a . . . . . . . . .\n",
1868       "a . . . . . . . . . .\n",
1869       ". . . . . . . . . . .\n",
1870       ". . . . . . . . . . .\n",
1871       ". . . . . . . . . . .\n",
1872       ". . . . . . . . . . .\n",
1873       ". . . . . . . . . . .\n",
1874       ". . . . . . . . . . .\n",
1875       ". . . . . . . . . . .\n",
1876       "\n",
1877       "\n"
1878      ]
1879     },
1880     {
1881      "data": {
1882       "text/plain": [
1883        "False"
1884       ]
1885      },
1886      "execution_count": 37,
1887      "metadata": {},
1888      "output_type": "execute_result"
1889     }
1890    ],
1891    "source": [
1892     "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n",
1893     "print(show_annotated_table(t, bp))\n",
1894     "print(show_backtrace(bp))\n",
1895     "print(show_backtrace_star(bp))\n",
1896     "v"
1897    ]
1898   },
1899   {
1900    "cell_type": "code",
1901    "execution_count": null,
1902    "metadata": {
1903     "collapsed": true
1904    },
1905    "outputs": [],
1906    "source": []
1907   }
1908  ],
1909  "metadata": {
1910   "kernelspec": {
1911    "display_name": "Python 3",
1912    "language": "python",
1913    "name": "python3"
1914   },
1915   "language_info": {
1916    "codemirror_mode": {
1917     "name": "ipython",
1918     "version": 3
1919    },
1920    "file_extension": ".py",
1921    "mimetype": "text/x-python",
1922    "name": "python",
1923    "nbconvert_exporter": "python",
1924    "pygments_lexer": "ipython3",
1925    "version": "3.5.2+"
1926   }
1927  },
1928  "nbformat": 4,
1929  "nbformat_minor": 1
1930 }