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": 6,
  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": 139,
  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": 8,
  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": 8,
  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": 9,
  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": 9,
  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": 10,
 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": 10,
 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": 135,
 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": 136,
 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": 137,
 192    "metadata": {},
 193    "outputs": [
 194     {
 195      "name": "stdout",
 196      "output_type": "stream",
 197      "text": [
 198       "T . . . . .\n",
 199       "T . . . . .\n",
 200       "T T T T . .\n",
 201       ". T T T . .\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": 140,
 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": 140,
 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": 83,
 334    "metadata": {},
 335    "outputs": [],
 336    "source": [
 337     "def is_interleave(seq1, seq2, seq3, return_backpointers=False, return_table=False, debug=False):\n",
 338     "    \"\"\"Return true if seq3 is some interleaved merge of seq1 and seq2.\n",
 339     "    If return_backpointers, also return the set of backpointers to\n",
 340     "    reconstruct the interleaving\"\"\"\n",
 341     "    \n",
 342     "    # dp_table[i, j] is True if first i+j characters of seq is made up of \n",
 343     "    # an interleaving of the first i characters of seq1 and the \n",
 344     "    # first j characters of seq2\n",
 345     "    \n",
 346     "    if len(seq1) + len(seq2) != len(seq3):\n",
 347     "        if return_backpointers or return_table:\n",
 348     "            retval = [False]\n",
 349     "            if return_backpointers:\n",
 350     "                retval += [{}]\n",
 351     "            if return_table:\n",
 352     "                retval += [{}]\n",
 353     "            return tuple(retval)\n",
 354     "        else:\n",
 355     "            return False\n",
 356     "    \n",
 357     "    dp_table = {(i, j): False\n",
 358     "               for i in range(len(seq1)+1)\n",
 359     "               for j in range(len(seq2)+1)}\n",
 360     "\n",
 361     "    backpointers = {}\n",
 362     "\n",
 363     "    for i in range(len(seq1)+1):\n",
 364     "        for j in range(len(seq2)+1):\n",
 365     "            if i == 0 and j == 0:\n",
 366     "                dp_table[i, j] = True\n",
 367     "                if debug: print('xxxx', i, j, '!', '!', '!', dp_table[i, j])\n",
 368     "            elif i == 0:\n",
 369     "                # extend by character from seq2\n",
 370     "                if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
 371     "                    dp_table[i, j] = True\n",
 372     "                    backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
 373     "                if debug: print('seq2', i, j, '!', seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 374     "            elif j == 0:\n",
 375     "                # extend by character from seq1\n",
 376     "                if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
 377     "                    dp_table[i, j] = True\n",
 378     "                    backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')\n",
 379     "                if debug: print('seq1', i, j, seq1[i-1], '!', seq3[i+j-1], dp_table[i, j])\n",
 380     "            else:\n",
 381     "                # extend by character from seq2\n",
 382     "                if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
 383     "                    dp_table[i, j] = True\n",
 384     "                    backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
 385     "                    if debug: print('seq2', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])                \n",
 386     "                # extend by character from seq1\n",
 387     "                if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
 388     "                    dp_table[i, j] = True\n",
 389     "                    backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')                \n",
 390     "                    if debug: print('seq1', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 391     "                if not dp_table[i, j]:\n",
 392     "                    if debug: print('xxxx', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 393     "\n",
 394     "    if return_backpointers or return_table:\n",
 395     "        retval = [dp_table[len(seq1), len(seq2)]]\n",
 396     "        if return_backpointers:\n",
 397     "            retval += [backpointers]\n",
 398     "        if return_table:\n",
 399     "            retval += [dp_table]\n",
 400     "        return tuple(retval)\n",
 401     "    else:\n",
 402     "        return dp_table[len(seq1), len(seq2)]"
 403    ]
 404   },
 405   {
 406    "cell_type": "code",
 407    "execution_count": 67,
 408    "metadata": {},
 409    "outputs": [
 410     {
 411      "data": {
 412       "text/plain": [
 413        "True"
 414       ]
 415      },
 416      "execution_count": 67,
 417      "metadata": {},
 418      "output_type": "execute_result"
 419     }
 420    ],
 421    "source": [
 422     "is_interleave(s1, s2, s3t)"
 423    ]
 424   },
 425   {
 426    "cell_type": "code",
 427    "execution_count": 71,
 428    "metadata": {},
 429    "outputs": [
 430     {
 431      "data": {
 432       "text/plain": [
 433        "(True,\n",
 434        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 435        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 436        "  (2, 1): (2, 0, 'd', 'seq2'),\n",
 437        "  (2, 2): (2, 1, 'b', 'seq2'),\n",
 438        "  (2, 3): (2, 2, 'b', 'seq2'),\n",
 439        "  (2, 4): (2, 3, 'c', 'seq2'),\n",
 440        "  (3, 1): (2, 1, 'b', 'seq1'),\n",
 441        "  (3, 2): (2, 2, 'b', 'seq1'),\n",
 442        "  (3, 4): (2, 4, 'b', 'seq1'),\n",
 443        "  (4, 2): (3, 2, 'c', 'seq1'),\n",
 444        "  (4, 3): (4, 2, 'b', 'seq2'),\n",
 445        "  (4, 4): (3, 4, 'c', 'seq1'),\n",
 446        "  (4, 5): (4, 4, 'a', 'seq2'),\n",
 447        "  (5, 3): (4, 3, 'c', 'seq1'),\n",
 448        "  (5, 5): (4, 5, 'c', 'seq1')})"
 449       ]
 450      },
 451      "execution_count": 71,
 452      "metadata": {},
 453      "output_type": "execute_result"
 454     }
 455    ],
 456    "source": [
 457     "is_interleave(s1, s2, s3t, return_backpointers=True)"
 458    ]
 459   },
 460   {
 461    "cell_type": "code",
 462    "execution_count": 72,
 463    "metadata": {
 464     "scrolled": true
 465    },
 466    "outputs": [
 467     {
 468      "data": {
 469       "text/plain": [
 470        "(True,\n",
 471        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 472        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 473        "  (2, 1): (2, 0, 'd', 'seq2'),\n",
 474        "  (2, 2): (2, 1, 'b', 'seq2'),\n",
 475        "  (2, 3): (2, 2, 'b', 'seq2'),\n",
 476        "  (2, 4): (2, 3, 'c', 'seq2'),\n",
 477        "  (3, 1): (2, 1, 'b', 'seq1'),\n",
 478        "  (3, 2): (2, 2, 'b', 'seq1'),\n",
 479        "  (3, 4): (2, 4, 'b', 'seq1'),\n",
 480        "  (4, 2): (3, 2, 'c', 'seq1'),\n",
 481        "  (4, 3): (4, 2, 'b', 'seq2'),\n",
 482        "  (4, 4): (3, 4, 'c', 'seq1'),\n",
 483        "  (4, 5): (4, 4, 'a', 'seq2'),\n",
 484        "  (5, 3): (4, 3, 'c', 'seq1'),\n",
 485        "  (5, 5): (4, 5, 'c', 'seq1')},\n",
 486        " {(0, 0): True,\n",
 487        "  (0, 1): False,\n",
 488        "  (0, 2): False,\n",
 489        "  (0, 3): False,\n",
 490        "  (0, 4): False,\n",
 491        "  (0, 5): False,\n",
 492        "  (1, 0): True,\n",
 493        "  (1, 1): False,\n",
 494        "  (1, 2): False,\n",
 495        "  (1, 3): False,\n",
 496        "  (1, 4): False,\n",
 497        "  (1, 5): False,\n",
 498        "  (2, 0): True,\n",
 499        "  (2, 1): True,\n",
 500        "  (2, 2): True,\n",
 501        "  (2, 3): True,\n",
 502        "  (2, 4): True,\n",
 503        "  (2, 5): False,\n",
 504        "  (3, 0): False,\n",
 505        "  (3, 1): True,\n",
 506        "  (3, 2): True,\n",
 507        "  (3, 3): False,\n",
 508        "  (3, 4): True,\n",
 509        "  (3, 5): False,\n",
 510        "  (4, 0): False,\n",
 511        "  (4, 1): False,\n",
 512        "  (4, 2): True,\n",
 513        "  (4, 3): True,\n",
 514        "  (4, 4): True,\n",
 515        "  (4, 5): True,\n",
 516        "  (5, 0): False,\n",
 517        "  (5, 1): False,\n",
 518        "  (5, 2): False,\n",
 519        "  (5, 3): True,\n",
 520        "  (5, 4): False,\n",
 521        "  (5, 5): True})"
 522       ]
 523      },
 524      "execution_count": 72,
 525      "metadata": {},
 526      "output_type": "execute_result"
 527     }
 528    ],
 529    "source": [
 530     "is_interleave(s1, s2, s3t, return_backpointers=True, return_table=True)"
 531    ]
 532   },
 533   {
 534    "cell_type": "code",
 535    "execution_count": 17,
 536    "metadata": {},
 537    "outputs": [
 538     {
 539      "data": {
 540       "text/plain": [
 541        "False"
 542       ]
 543      },
 544      "execution_count": 17,
 545      "metadata": {},
 546      "output_type": "execute_result"
 547     }
 548    ],
 549    "source": [
 550     "is_interleave(s1, s2, s3f)"
 551    ]
 552   },
 553   {
 554    "cell_type": "code",
 555    "execution_count": 18,
 556    "metadata": {},
 557    "outputs": [
 558     {
 559      "name": "stdout",
 560      "output_type": "stream",
 561      "text": [
 562       "xxxx 0 0 ! ! ! True\n",
 563       "seq2 0 1 ! b a False\n",
 564       "seq2 0 2 ! b a False\n",
 565       "seq2 0 3 ! b a False\n",
 566       "seq1 1 0 a ! a True\n",
 567       "xxxx 1 1 a b a False\n",
 568       "xxxx 1 2 a b a False\n",
 569       "xxxx 1 3 a b b False\n",
 570       "seq1 2 0 a ! a True\n",
 571       "xxxx 2 1 a b a False\n",
 572       "xxxx 2 2 a b b False\n",
 573       "xxxx 2 3 a b a False\n",
 574       "seq1 3 0 a ! a True\n",
 575       "seq2 3 1 a b b True\n",
 576       "xxxx 3 2 a b a False\n",
 577       "xxxx 3 3 a b b False\n",
 578       "seq1 4 0 a ! b False\n",
 579       "seq1 4 1 a b a True\n",
 580       "seq2 4 2 a b b True\n",
 581       "seq2 4 3 a b b True\n"
 582      ]
 583     },
 584     {
 585      "data": {
 586       "text/plain": [
 587        "(True,\n",
 588        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 589        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 590        "  (3, 0): (2, 0, 'a', 'seq1'),\n",
 591        "  (3, 1): (3, 0, 'b', 'seq2'),\n",
 592        "  (4, 1): (3, 1, 'a', 'seq1'),\n",
 593        "  (4, 2): (4, 1, 'b', 'seq2'),\n",
 594        "  (4, 3): (4, 2, 'b', 'seq2')})"
 595       ]
 596      },
 597      "execution_count": 18,
 598      "metadata": {},
 599      "output_type": "execute_result"
 600     }
 601    ],
 602    "source": [
 603     "is_interleave('aaaa', 'bbb', 'aaababb', return_backpointers=True, debug=True)"
 604    ]
 605   },
 606   {
 607    "cell_type": "code",
 608    "execution_count": 109,
 609    "metadata": {},
 610    "outputs": [],
 611    "source": [
 612     "def show_backtrace(bps):\n",
 613     "    i = max([0] + [k[0] for k in bps])\n",
 614     "    j = max([0] + [k[1] for k in bps])\n",
 615     "    chars = ''\n",
 616     "    if (i, j) in bps:\n",
 617     "        while i != 0 or j != 0:\n",
 618     "            if bps[i, j][3] == 'seq1':\n",
 619     "                chars += bps[i, j][2].upper()\n",
 620     "            else:\n",
 621     "                chars += bps[i, j][2]\n",
 622     "            i, j = bps[i, j][0], bps[i, j][1] \n",
 623     "        return ''.join(list(reversed(chars)))\n",
 624     "    else:\n",
 625     "        return ''"
 626    ]
 627   },
 628   {
 629    "cell_type": "code",
 630    "execution_count": 20,
 631    "metadata": {
 632     "collapsed": true
 633    },
 634    "outputs": [],
 635    "source": [
 636     "def make_string(length, alphabet=None):\n",
 637     "    if not alphabet:\n",
 638     "        alphabet = 'abcdefgh'\n",
 639     "    return ''.join(random.choice(alphabet) for _ in range(length))    "
 640    ]
 641   },
 642   {
 643    "cell_type": "code",
 644    "execution_count": 24,
 645    "metadata": {},
 646    "outputs": [
 647     {
 648      "data": {
 649       "text/plain": [
 650        "'abgdfggfabffcagcagdhaedeeecedcdbaeaahdfgegacbhbdba'"
 651       ]
 652      },
 653      "execution_count": 24,
 654      "metadata": {},
 655      "output_type": "execute_result"
 656     }
 657    ],
 658    "source": [
 659     "make_string(50)"
 660    ]
 661   },
 662   {
 663    "cell_type": "code",
 664    "execution_count": 94,
 665    "metadata": {
 666     "collapsed": true
 667    },
 668    "outputs": [],
 669    "source": [
 670     "def interleave(s1, s2, wander_limit=10, debug=False):\n",
 671     "    i1 = i2 = wander = 0\n",
 672     "    interleaved = []\n",
 673     "    while i1 <= len(s1) and i2 <= len(s2):\n",
 674     "        if i1 == len(s1):\n",
 675     "            if debug: print(i1, i2, wander, 'remaining s2', s2[i2:])\n",
 676     "            interleaved += s2[i2:]\n",
 677     "            i2 = len(s2) + 1\n",
 678     "        elif i2 == len(s2):\n",
 679     "            if debug: print(i1, i2, wander, 'remaining s1', s1[i1:])\n",
 680     "            interleaved += s1[i1:]\n",
 681     "            i1 = len(s1) + 1\n",
 682     "        else:\n",
 683     "            if wander == wander_limit:\n",
 684     "                step = -1\n",
 685     "            elif wander == -wander_limit:\n",
 686     "                step = +1\n",
 687     "            else:\n",
 688     "                step = random.choice([+1, -1])\n",
 689     "            if step == +1:\n",
 690     "                if debug: print(i1, i2, wander, 'adding', s1[i1])\n",
 691     "                interleaved += s1[i1]\n",
 692     "                i1 += 1\n",
 693     "                wander += 1\n",
 694     "            else:\n",
 695     "                if debug: print(i1, i2, wander, 'adding', s2[i2])\n",
 696     "                interleaved += s2[i2]\n",
 697     "                i2 += 1\n",
 698     "                wander -= 1\n",
 699     "    return ''.join(interleaved)\n",
 700     "            "
 701    ]
 702   },
 703   {
 704    "cell_type": "code",
 705    "execution_count": 142,
 706    "metadata": {},
 707    "outputs": [
 708     {
 709      "name": "stdout",
 710      "output_type": "stream",
 711      "text": [
 712       "0 0 0 adding d\n",
 713       "1 0 1 adding v\n",
 714       "1 1 0 adding v\n",
 715       "1 2 -1 adding f\n",
 716       "2 2 0 adding v\n",
 717       "2 3 -1 adding w\n",
 718       "2 4 -2 adding g\n",
 719       "3 4 -1 adding y\n",
 720       "3 5 -2 adding a\n",
 721       "4 5 -1 adding w\n",
 722       "4 6 -2 adding w\n",
 723       "4 7 -3 adding w\n",
 724       "4 8 -4 adding g\n",
 725       "5 8 -3 adding h\n",
 726       "6 8 -2 adding u\n",
 727       "6 9 -3 adding v\n",
 728       "6 10 -4 adding w\n",
 729       "6 11 -5 adding f\n",
 730       "7 11 -4 adding z\n",
 731       "7 12 -5 adding f\n",
 732       "8 12 -4 adding d\n",
 733       "9 12 -3 adding x\n",
 734       "9 13 -4 adding y\n",
 735       "9 14 -5 adding g\n",
 736       "10 14 -4 adding h\n",
 737       "11 14 -3 adding u\n",
 738       "11 15 -4 adding g\n",
 739       "12 15 -3 adding b\n",
 740       "13 15 -2 adding u\n",
 741       "13 16 -3 adding z\n",
 742       "13 17 -4 adding a\n",
 743       "14 17 -3 adding u\n",
 744       "14 18 -4 adding x\n",
 745       "14 19 -5 adding a\n",
 746       "15 19 -4 adding d\n",
 747       "16 19 -3 adding g\n",
 748       "17 19 -2 adding c\n",
 749       "18 19 -1 adding x\n",
 750       "18 20 -2 remaining s1 cg\n"
 751      ]
 752     },
 753     {
 754      "data": {
 755       "text/plain": [
 756        "('dfgaghffdghgbaadgccg',\n",
 757        " 'vvvwywwwuvwzxyuuzuxx',\n",
 758        " 'dvvfvwgyawwwghuvwfzfdxyghugbuzauxadgcxcg',\n",
 759        " 40)"
 760       ]
 761      },
 762      "execution_count": 142,
 763      "metadata": {},
 764      "output_type": "execute_result"
 765     }
 766    ],
 767    "source": [
 768     "s1 = make_string(20)\n",
 769     "s2 = make_string(20, alphabet='uvwxyz')\n",
 770     "il = interleave(s1, s2, wander_limit=5, debug=True)\n",
 771     "s1, s2, il, len(il)"
 772    ]
 773   },
 774   {
 775    "cell_type": "code",
 776    "execution_count": 143,
 777    "metadata": {},
 778    "outputs": [
 779     {
 780      "name": "stdout",
 781      "output_type": "stream",
 782      "text": [
 783       "xxxx 0 0 ! ! ! True\n",
 784       "seq2 0 1 ! d d True\n",
 785       "seq2 0 2 ! f v False\n",
 786       "seq2 0 3 ! g v False\n",
 787       "seq2 0 4 ! a f False\n",
 788       "seq2 0 5 ! g v False\n",
 789       "seq2 0 6 ! h w False\n",
 790       "seq2 0 7 ! f g False\n",
 791       "seq2 0 8 ! f y False\n",
 792       "seq2 0 9 ! d a False\n",
 793       "seq2 0 10 ! g w False\n",
 794       "seq2 0 11 ! h w False\n",
 795       "seq2 0 12 ! g w False\n",
 796       "seq2 0 13 ! b g False\n",
 797       "seq2 0 14 ! a h False\n",
 798       "seq2 0 15 ! a u False\n",
 799       "seq2 0 16 ! d v False\n",
 800       "seq2 0 17 ! g w False\n",
 801       "seq2 0 18 ! c f False\n",
 802       "seq2 0 19 ! c z False\n",
 803       "seq2 0 20 ! g f False\n",
 804       "seq1 1 0 v ! d False\n",
 805       "seq1 1 1 v d v True\n",
 806       "xxxx 1 2 v f v False\n",
 807       "xxxx 1 3 v g f False\n",
 808       "xxxx 1 4 v a v False\n",
 809       "xxxx 1 5 v g w False\n",
 810       "xxxx 1 6 v h g False\n",
 811       "xxxx 1 7 v f y False\n",
 812       "xxxx 1 8 v f a False\n",
 813       "xxxx 1 9 v d w False\n",
 814       "xxxx 1 10 v g w False\n",
 815       "xxxx 1 11 v h w False\n",
 816       "xxxx 1 12 v g g False\n",
 817       "xxxx 1 13 v b h False\n",
 818       "xxxx 1 14 v a u False\n",
 819       "xxxx 1 15 v a v False\n",
 820       "xxxx 1 16 v d w False\n",
 821       "xxxx 1 17 v g f False\n",
 822       "xxxx 1 18 v c z False\n",
 823       "xxxx 1 19 v c f False\n",
 824       "xxxx 1 20 v g d False\n",
 825       "seq1 2 0 v ! v False\n",
 826       "seq1 2 1 v d v True\n",
 827       "seq2 2 2 v f f True\n",
 828       "xxxx 2 3 v g v False\n",
 829       "xxxx 2 4 v a w False\n",
 830       "xxxx 2 5 v g g False\n",
 831       "xxxx 2 6 v h y False\n",
 832       "xxxx 2 7 v f a False\n",
 833       "xxxx 2 8 v f w False\n",
 834       "xxxx 2 9 v d w False\n",
 835       "xxxx 2 10 v g w False\n",
 836       "xxxx 2 11 v h g False\n",
 837       "xxxx 2 12 v g h False\n",
 838       "xxxx 2 13 v b u False\n",
 839       "xxxx 2 14 v a v False\n",
 840       "xxxx 2 15 v a w False\n",
 841       "xxxx 2 16 v d f False\n",
 842       "xxxx 2 17 v g z False\n",
 843       "xxxx 2 18 v c f False\n",
 844       "xxxx 2 19 v c d False\n",
 845       "xxxx 2 20 v g x False\n",
 846       "seq1 3 0 v ! v False\n",
 847       "xxxx 3 1 v d f False\n",
 848       "seq1 3 2 v f v True\n",
 849       "xxxx 3 3 v g w False\n",
 850       "xxxx 3 4 v a g False\n",
 851       "xxxx 3 5 v g y False\n",
 852       "xxxx 3 6 v h a False\n",
 853       "xxxx 3 7 v f w False\n",
 854       "xxxx 3 8 v f w False\n",
 855       "xxxx 3 9 v d w False\n",
 856       "xxxx 3 10 v g g False\n",
 857       "xxxx 3 11 v h h False\n",
 858       "xxxx 3 12 v g u False\n",
 859       "xxxx 3 13 v b v False\n",
 860       "xxxx 3 14 v a w False\n",
 861       "xxxx 3 15 v a f False\n",
 862       "xxxx 3 16 v d z False\n",
 863       "xxxx 3 17 v g f False\n",
 864       "xxxx 3 18 v c d False\n",
 865       "xxxx 3 19 v c x False\n",
 866       "xxxx 3 20 v g y False\n",
 867       "seq1 4 0 w ! f False\n",
 868       "xxxx 4 1 w d v False\n",
 869       "seq1 4 2 w f w True\n",
 870       "seq2 4 3 w g g True\n",
 871       "xxxx 4 4 w a y False\n",
 872       "xxxx 4 5 w g a False\n",
 873       "xxxx 4 6 w h w False\n",
 874       "xxxx 4 7 w f w False\n",
 875       "xxxx 4 8 w f w False\n",
 876       "xxxx 4 9 w d g False\n",
 877       "xxxx 4 10 w g h False\n",
 878       "xxxx 4 11 w h u False\n",
 879       "xxxx 4 12 w g v False\n",
 880       "xxxx 4 13 w b w False\n",
 881       "xxxx 4 14 w a f False\n",
 882       "xxxx 4 15 w a z False\n",
 883       "xxxx 4 16 w d f False\n",
 884       "xxxx 4 17 w g d False\n",
 885       "xxxx 4 18 w c x False\n",
 886       "xxxx 4 19 w c y False\n",
 887       "xxxx 4 20 w g g False\n",
 888       "seq1 5 0 y ! v False\n",
 889       "xxxx 5 1 y d w False\n",
 890       "xxxx 5 2 y f g False\n",
 891       "seq1 5 3 y g y True\n",
 892       "seq2 5 4 y a a True\n",
 893       "xxxx 5 5 y g w False\n",
 894       "xxxx 5 6 y h w False\n",
 895       "xxxx 5 7 y f w False\n",
 896       "xxxx 5 8 y f g False\n",
 897       "xxxx 5 9 y d h False\n",
 898       "xxxx 5 10 y g u False\n",
 899       "xxxx 5 11 y h v False\n",
 900       "xxxx 5 12 y g w False\n",
 901       "xxxx 5 13 y b f False\n",
 902       "xxxx 5 14 y a z False\n",
 903       "xxxx 5 15 y a f False\n",
 904       "xxxx 5 16 y d d False\n",
 905       "xxxx 5 17 y g x False\n",
 906       "xxxx 5 18 y c y False\n",
 907       "xxxx 5 19 y c g False\n",
 908       "xxxx 5 20 y g h False\n",
 909       "seq1 6 0 w ! w False\n",
 910       "xxxx 6 1 w d g False\n",
 911       "xxxx 6 2 w f y False\n",
 912       "xxxx 6 3 w g a False\n",
 913       "seq1 6 4 w a w True\n",
 914       "xxxx 6 5 w g w False\n",
 915       "xxxx 6 6 w h w False\n",
 916       "xxxx 6 7 w f g False\n",
 917       "xxxx 6 8 w f h False\n",
 918       "xxxx 6 9 w d u False\n",
 919       "xxxx 6 10 w g v False\n",
 920       "xxxx 6 11 w h w False\n",
 921       "xxxx 6 12 w g f False\n",
 922       "xxxx 6 13 w b z False\n",
 923       "xxxx 6 14 w a f False\n",
 924       "xxxx 6 15 w a d False\n",
 925       "xxxx 6 16 w d x False\n",
 926       "xxxx 6 17 w g y False\n",
 927       "xxxx 6 18 w c g False\n",
 928       "xxxx 6 19 w c h False\n",
 929       "xxxx 6 20 w g u False\n",
 930       "seq1 7 0 w ! g False\n",
 931       "xxxx 7 1 w d y False\n",
 932       "xxxx 7 2 w f a False\n",
 933       "xxxx 7 3 w g w False\n",
 934       "seq1 7 4 w a w True\n",
 935       "xxxx 7 5 w g w False\n",
 936       "xxxx 7 6 w h g False\n",
 937       "xxxx 7 7 w f h False\n",
 938       "xxxx 7 8 w f u False\n",
 939       "xxxx 7 9 w d v False\n",
 940       "xxxx 7 10 w g w False\n",
 941       "xxxx 7 11 w h f False\n",
 942       "xxxx 7 12 w g z False\n",
 943       "xxxx 7 13 w b f False\n",
 944       "xxxx 7 14 w a d False\n",
 945       "xxxx 7 15 w a x False\n",
 946       "xxxx 7 16 w d y False\n",
 947       "xxxx 7 17 w g g False\n",
 948       "xxxx 7 18 w c h False\n",
 949       "xxxx 7 19 w c u False\n",
 950       "xxxx 7 20 w g g False\n",
 951       "seq1 8 0 w ! y False\n",
 952       "xxxx 8 1 w d a False\n",
 953       "xxxx 8 2 w f w False\n",
 954       "xxxx 8 3 w g w False\n",
 955       "seq1 8 4 w a w True\n",
 956       "seq2 8 5 w g g True\n",
 957       "seq2 8 6 w h h True\n",
 958       "xxxx 8 7 w f u False\n",
 959       "xxxx 8 8 w f v False\n",
 960       "xxxx 8 9 w d w False\n",
 961       "xxxx 8 10 w g f False\n",
 962       "xxxx 8 11 w h z False\n",
 963       "xxxx 8 12 w g f False\n",
 964       "xxxx 8 13 w b d False\n",
 965       "xxxx 8 14 w a x False\n",
 966       "xxxx 8 15 w a y False\n",
 967       "xxxx 8 16 w d g False\n",
 968       "xxxx 8 17 w g h False\n",
 969       "xxxx 8 18 w c u False\n",
 970       "xxxx 8 19 w c g False\n",
 971       "xxxx 8 20 w g b False\n",
 972       "seq1 9 0 u ! a False\n",
 973       "xxxx 9 1 u d w False\n",
 974       "xxxx 9 2 u f w False\n",
 975       "xxxx 9 3 u g w False\n",
 976       "xxxx 9 4 u a g False\n",
 977       "xxxx 9 5 u g h False\n",
 978       "seq1 9 6 u h u True\n",
 979       "xxxx 9 7 u f v False\n",
 980       "xxxx 9 8 u f w False\n",
 981       "xxxx 9 9 u d f False\n",
 982       "xxxx 9 10 u g z False\n",
 983       "xxxx 9 11 u h f False\n",
 984       "xxxx 9 12 u g d False\n",
 985       "xxxx 9 13 u b x False\n",
 986       "xxxx 9 14 u a y False\n",
 987       "xxxx 9 15 u a g False\n",
 988       "xxxx 9 16 u d h False\n",
 989       "xxxx 9 17 u g u False\n",
 990       "xxxx 9 18 u c g False\n",
 991       "xxxx 9 19 u c b False\n",
 992       "xxxx 9 20 u g u False\n",
 993       "seq1 10 0 v ! w False\n",
 994       "xxxx 10 1 v d w False\n",
 995       "xxxx 10 2 v f w False\n",
 996       "xxxx 10 3 v g g False\n",
 997       "xxxx 10 4 v a h False\n",
 998       "xxxx 10 5 v g u False\n",
 999       "seq1 10 6 v h v True\n",
1000       "xxxx 10 7 v f w False\n",
1001       "xxxx 10 8 v f f False\n",
1002       "xxxx 10 9 v d z False\n",
1003       "xxxx 10 10 v g f False\n",
1004       "xxxx 10 11 v h d False\n",
1005       "xxxx 10 12 v g x False\n",
1006       "xxxx 10 13 v b y False\n",
1007       "xxxx 10 14 v a g False\n",
1008       "xxxx 10 15 v a h False\n",
1009       "xxxx 10 16 v d u False\n",
1010       "xxxx 10 17 v g g False\n",
1011       "xxxx 10 18 v c b False\n",
1012       "xxxx 10 19 v c u False\n",
1013       "xxxx 10 20 v g z False\n",
1014       "seq1 11 0 w ! w False\n",
1015       "xxxx 11 1 w d w False\n",
1016       "xxxx 11 2 w f g False\n",
1017       "xxxx 11 3 w g h False\n",
1018       "xxxx 11 4 w a u False\n",
1019       "xxxx 11 5 w g v False\n",
1020       "seq1 11 6 w h w True\n",
1021       "seq2 11 7 w f f True\n",
1022       "xxxx 11 8 w f z False\n",
1023       "xxxx 11 9 w d f False\n",
1024       "xxxx 11 10 w g d False\n",
1025       "xxxx 11 11 w h x False\n",
1026       "xxxx 11 12 w g y False\n",
1027       "xxxx 11 13 w b g False\n",
1028       "xxxx 11 14 w a h False\n",
1029       "xxxx 11 15 w a u False\n",
1030       "xxxx 11 16 w d g False\n",
1031       "xxxx 11 17 w g b False\n",
1032       "xxxx 11 18 w c u False\n",
1033       "xxxx 11 19 w c z False\n",
1034       "xxxx 11 20 w g a False\n",
1035       "seq1 12 0 z ! w False\n",
1036       "xxxx 12 1 z d g False\n",
1037       "xxxx 12 2 z f h False\n",
1038       "xxxx 12 3 z g u False\n",
1039       "xxxx 12 4 z a v False\n",
1040       "xxxx 12 5 z g w False\n",
1041       "xxxx 12 6 z h f False\n",
1042       "seq1 12 7 z f z True\n",
1043       "seq2 12 8 z f f True\n",
1044       "seq2 12 9 z d d True\n",
1045       "xxxx 12 10 z g x False\n",
1046       "xxxx 12 11 z h y False\n",
1047       "xxxx 12 12 z g g False\n",
1048       "xxxx 12 13 z b h False\n",
1049       "xxxx 12 14 z a u False\n",
1050       "xxxx 12 15 z a g False\n",
1051       "xxxx 12 16 z d b False\n",
1052       "xxxx 12 17 z g u False\n",
1053       "xxxx 12 18 z c z False\n",
1054       "xxxx 12 19 z c a False\n",
1055       "xxxx 12 20 z g u False\n",
1056       "seq1 13 0 x ! g False\n",
1057       "xxxx 13 1 x d h False\n",
1058       "xxxx 13 2 x f u False\n",
1059       "xxxx 13 3 x g v False\n",
1060       "xxxx 13 4 x a w False\n",
1061       "xxxx 13 5 x g f False\n",
1062       "xxxx 13 6 x h z False\n",
1063       "xxxx 13 7 x f f False\n",
1064       "xxxx 13 8 x f d False\n",
1065       "seq1 13 9 x d x True\n",
1066       "xxxx 13 10 x g y False\n",
1067       "xxxx 13 11 x h g False\n",
1068       "xxxx 13 12 x g h False\n",
1069       "xxxx 13 13 x b u False\n",
1070       "xxxx 13 14 x a g False\n",
1071       "xxxx 13 15 x a b False\n",
1072       "xxxx 13 16 x d u False\n",
1073       "xxxx 13 17 x g z False\n",
1074       "xxxx 13 18 x c a False\n",
1075       "xxxx 13 19 x c u False\n",
1076       "xxxx 13 20 x g x False\n",
1077       "seq1 14 0 y ! h False\n",
1078       "xxxx 14 1 y d u False\n",
1079       "xxxx 14 2 y f v False\n",
1080       "xxxx 14 3 y g w False\n",
1081       "xxxx 14 4 y a f False\n",
1082       "xxxx 14 5 y g z False\n",
1083       "xxxx 14 6 y h f False\n",
1084       "xxxx 14 7 y f d False\n",
1085       "xxxx 14 8 y f x False\n",
1086       "seq1 14 9 y d y True\n",
1087       "seq2 14 10 y g g True\n",
1088       "seq2 14 11 y h h True\n",
1089       "xxxx 14 12 y g u False\n",
1090       "xxxx 14 13 y b g False\n",
1091       "xxxx 14 14 y a b False\n",
1092       "xxxx 14 15 y a u False\n",
1093       "xxxx 14 16 y d z False\n",
1094       "xxxx 14 17 y g a False\n",
1095       "xxxx 14 18 y c u False\n",
1096       "xxxx 14 19 y c x False\n",
1097       "xxxx 14 20 y g a False\n",
1098       "seq1 15 0 u ! u False\n",
1099       "xxxx 15 1 u d v False\n",
1100       "xxxx 15 2 u f w False\n",
1101       "xxxx 15 3 u g f False\n",
1102       "xxxx 15 4 u a z False\n",
1103       "xxxx 15 5 u g f False\n",
1104       "xxxx 15 6 u h d False\n",
1105       "xxxx 15 7 u f x False\n",
1106       "xxxx 15 8 u f y False\n",
1107       "xxxx 15 9 u d g False\n",
1108       "xxxx 15 10 u g h False\n",
1109       "seq1 15 11 u h u True\n",
1110       "seq2 15 12 u g g True\n",
1111       "seq2 15 13 u b b True\n",
1112       "xxxx 15 14 u a u False\n",
1113       "xxxx 15 15 u a z False\n",
1114       "xxxx 15 16 u d a False\n",
1115       "xxxx 15 17 u g u False\n",
1116       "xxxx 15 18 u c x False\n",
1117       "xxxx 15 19 u c a False\n",
1118       "xxxx 15 20 u g d False\n",
1119       "seq1 16 0 u ! v False\n",
1120       "xxxx 16 1 u d w False\n",
1121       "xxxx 16 2 u f f False\n",
1122       "xxxx 16 3 u g z False\n",
1123       "xxxx 16 4 u a f False\n",
1124       "xxxx 16 5 u g d False\n",
1125       "xxxx 16 6 u h x False\n",
1126       "xxxx 16 7 u f y False\n",
1127       "xxxx 16 8 u f g False\n",
1128       "xxxx 16 9 u d h False\n",
1129       "xxxx 16 10 u g u False\n",
1130       "xxxx 16 11 u h g False\n",
1131       "xxxx 16 12 u g b False\n",
1132       "seq1 16 13 u b u True\n",
1133       "xxxx 16 14 u a z False\n",
1134       "xxxx 16 15 u a a False\n",
1135       "xxxx 16 16 u d u False\n",
1136       "xxxx 16 17 u g x False\n",
1137       "xxxx 16 18 u c a False\n",
1138       "xxxx 16 19 u c d False\n",
1139       "xxxx 16 20 u g g False\n",
1140       "seq1 17 0 z ! w False\n",
1141       "xxxx 17 1 z d f False\n",
1142       "xxxx 17 2 z f z False\n",
1143       "xxxx 17 3 z g f False\n",
1144       "xxxx 17 4 z a d False\n",
1145       "xxxx 17 5 z g x False\n",
1146       "xxxx 17 6 z h y False\n",
1147       "xxxx 17 7 z f g False\n",
1148       "xxxx 17 8 z f h False\n",
1149       "xxxx 17 9 z d u False\n",
1150       "xxxx 17 10 z g g False\n",
1151       "xxxx 17 11 z h b False\n",
1152       "xxxx 17 12 z g u False\n",
1153       "seq1 17 13 z b z True\n",
1154       "seq2 17 14 z a a True\n",
1155       "xxxx 17 15 z a u False\n",
1156       "xxxx 17 16 z d x False\n",
1157       "xxxx 17 17 z g a False\n",
1158       "xxxx 17 18 z c d False\n",
1159       "xxxx 17 19 z c g False\n",
1160       "xxxx 17 20 z g c False\n",
1161       "seq1 18 0 u ! f False\n",
1162       "xxxx 18 1 u d z False\n",
1163       "xxxx 18 2 u f f False\n",
1164       "xxxx 18 3 u g d False\n",
1165       "xxxx 18 4 u a x False\n",
1166       "xxxx 18 5 u g y False\n",
1167       "xxxx 18 6 u h g False\n",
1168       "xxxx 18 7 u f h False\n",
1169       "xxxx 18 8 u f u False\n",
1170       "xxxx 18 9 u d g False\n",
1171       "xxxx 18 10 u g b False\n",
1172       "xxxx 18 11 u h u False\n",
1173       "xxxx 18 12 u g z False\n",
1174       "xxxx 18 13 u b a False\n",
1175       "seq1 18 14 u a u True\n",
1176       "xxxx 18 15 u a x False\n",
1177       "xxxx 18 16 u d a False\n",
1178       "xxxx 18 17 u g d False\n",
1179       "xxxx 18 18 u c g False\n",
1180       "xxxx 18 19 u c c False\n",
1181       "xxxx 18 20 u g x False\n",
1182       "seq1 19 0 x ! z False\n",
1183       "xxxx 19 1 x d f False\n",
1184       "xxxx 19 2 x f d False\n"
1185      ]
1186     },
1187     {
1188      "name": "stdout",
1189      "output_type": "stream",
1190      "text": [
1191       "xxxx 19 3 x g x False\n",
1192       "xxxx 19 4 x a y False\n",
1193       "xxxx 19 5 x g g False\n",
1194       "xxxx 19 6 x h h False\n",
1195       "xxxx 19 7 x f u False\n",
1196       "xxxx 19 8 x f g False\n",
1197       "xxxx 19 9 x d b False\n",
1198       "xxxx 19 10 x g u False\n",
1199       "xxxx 19 11 x h z False\n",
1200       "xxxx 19 12 x g a False\n",
1201       "xxxx 19 13 x b u False\n",
1202       "seq1 19 14 x a x True\n",
1203       "seq2 19 15 x a a True\n",
1204       "seq2 19 16 x d d True\n",
1205       "seq2 19 17 x g g True\n",
1206       "seq2 19 18 x c c True\n",
1207       "xxxx 19 19 x c x False\n",
1208       "xxxx 19 20 x g c False\n",
1209       "seq1 20 0 x ! f False\n",
1210       "xxxx 20 1 x d d False\n",
1211       "xxxx 20 2 x f x False\n",
1212       "xxxx 20 3 x g y False\n",
1213       "xxxx 20 4 x a g False\n",
1214       "xxxx 20 5 x g h False\n",
1215       "xxxx 20 6 x h u False\n",
1216       "xxxx 20 7 x f g False\n",
1217       "xxxx 20 8 x f b False\n",
1218       "xxxx 20 9 x d u False\n",
1219       "xxxx 20 10 x g z False\n",
1220       "xxxx 20 11 x h a False\n",
1221       "xxxx 20 12 x g u False\n",
1222       "xxxx 20 13 x b x False\n",
1223       "xxxx 20 14 x a a False\n",
1224       "xxxx 20 15 x a d False\n",
1225       "xxxx 20 16 x d g False\n",
1226       "xxxx 20 17 x g c False\n",
1227       "seq1 20 18 x c x True\n",
1228       "seq2 20 19 x c c True\n",
1229       "seq2 20 20 x g g True\n",
1230       "T T . . . . . . . . . . . . . . . . . . .\n",
1231       ". T . . . . . . . . . . . . . . . . . . .\n",
1232       ". T T . . . . . . . . . . . . . . . . . .\n",
1233       ". . T . . . . . . . . . . . . . . . . . .\n",
1234       ". . T T . . . . . . . . . . . . . . . . .\n",
1235       ". . . T T . . . . . . . . . . . . . . . .\n",
1236       ". . . . T . . . . . . . . . . . . . . . .\n",
1237       ". . . . T . . . . . . . . . . . . . . . .\n",
1238       ". . . . T T T . . . . . . . . . . . . . .\n",
1239       ". . . . . . T . . . . . . . . . . . . . .\n",
1240       ". . . . . . T . . . . . . . . . . . . . .\n",
1241       ". . . . . . T T . . . . . . . . . . . . .\n",
1242       ". . . . . . . T T T . . . . . . . . . . .\n",
1243       ". . . . . . . . . T . . . . . . . . . . .\n",
1244       ". . . . . . . . . T T T . . . . . . . . .\n",
1245       ". . . . . . . . . . . T T T . . . . . . .\n",
1246       ". . . . . . . . . . . . . T . . . . . . .\n",
1247       ". . . . . . . . . . . . . T T . . . . . .\n",
1248       ". . . . . . . . . . . . . . T . . . . . .\n",
1249       ". . . . . . . . . . . . . . T T T T T . .\n",
1250       ". . . . . . . . . . . . . . . . . . T T T\n"
1251      ]
1252     }
1253    ],
1254    "source": [
1255     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True, debug=True)\n",
1256     "print(show_table(t))"
1257    ]
1258   },
1259   {
1260    "cell_type": "code",
1261    "execution_count": 144,
1262    "metadata": {},
1263    "outputs": [
1264     {
1265      "data": {
1266       "text/plain": [
1267        "'dVVfVWgYaWWWghUVWfZfdXYghUgbUZaUXadgcXcg'"
1268       ]
1269      },
1270      "execution_count": 144,
1271      "metadata": {},
1272      "output_type": "execute_result"
1273     }
1274    ],
1275    "source": [
1276     "show_backtrace(bp)"
1277    ]
1278   },
1279   {
1280    "cell_type": "code",
1281    "execution_count": 145,
1282    "metadata": {},
1283    "outputs": [
1284     {
1285      "name": "stdout",
1286      "output_type": "stream",
1287      "text": [
1288       "T T . . . . . . . . . . . . . . . . . . .\n",
1289       ". T . . . . . . . . . . . . . . . . . . .\n",
1290       ". T T . . . . . . . . . . . . . . . . . .\n",
1291       ". . T . . . . . . . . . . . . . . . . . .\n",
1292       ". . T T . . . . . . . . . . . . . . . . .\n",
1293       ". . . T T . . . . . . . . . . . . . . . .\n",
1294       ". . . . T . . . . . . . . . . . . . . . .\n",
1295       ". . . . T . . . . . . . . . . . . . . . .\n",
1296       ". . . . T T T . . . . . . . . . . . . . .\n",
1297       ". . . . . . T . . . . . . . . . . . . . .\n",
1298       ". . . . . . T . . . . . . . . . . . . . .\n",
1299       ". . . . . . T T . . . . . . . . . . . . .\n",
1300       ". . . . . . . T T T . . . . . . . . . . .\n",
1301       ". . . . . . . . . T . . . . . . . . . . .\n",
1302       ". . . . . . . . . T T T . . . . . . . . .\n",
1303       ". . . . . . . . . . . T T T . . . . . . .\n",
1304       ". . . . . . . . . . . . . T . . . . . . .\n",
1305       ". . . . . . . . . . . . . T T . . . . . .\n",
1306       ". . . . . . . . . . . . . . T . . . . . .\n",
1307       ". . . . . . . . . . . . . . T T T T T . .\n",
1308       ". . . . . . . . . . . . . . . . . . T T T\n",
1309       "dVVfVWgYaWWWghUVWfZfdXYghUgbUZaUXadgcXcg\n"
1310      ]
1311     },
1312     {
1313      "data": {
1314       "text/plain": [
1315        "True"
1316       ]
1317      },
1318      "execution_count": 145,
1319      "metadata": {},
1320      "output_type": "execute_result"
1321     }
1322    ],
1323    "source": [
1324     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1325     "print(show_table(t))\n",
1326     "print(show_backtrace(bp))\n",
1327     "v"
1328    ]
1329   },
1330   {
1331    "cell_type": "code",
1332    "execution_count": 151,
1333    "metadata": {},
1334    "outputs": [
1335     {
1336      "data": {
1337       "text/plain": [
1338        "('cfhgbbfabcehcbfdfcafdfecefaecfagbdfeecfdbhebgbfhee',\n",
1339        " 'begacfabcgegaegefgcgaabeefahahgfhbdbhhdabbaaahhdcb',\n",
1340        " 'bcfehggacfbbabcgegfaeabgceefhcbgcgaabfdfcaefedfefacehahgffhbdbahechfagdabbbdaafeahechdfdcbbhebgbfhee',\n",
1341        " 100)"
1342       ]
1343      },
1344      "execution_count": 151,
1345      "metadata": {},
1346      "output_type": "execute_result"
1347     }
1348    ],
1349    "source": [
1350     "s1 = make_string(50)\n",
1351     "s2 = make_string(50)\n",
1352     "il = interleave(s1, s2)\n",
1353     "s1, s2, il, len(il)"
1354    ]
1355   },
1356   {
1357    "cell_type": "code",
1358    "execution_count": 152,
1359    "metadata": {},
1360    "outputs": [
1361     {
1362      "name": "stdout",
1363      "output_type": "stream",
1364      "text": [
1365       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1366       "T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1367       ". . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1368       ". . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1369       ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1370       ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1371       ". . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1372       ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1373       ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1374       ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1375       ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1376       ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1377       ". . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1378       ". . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1379       ". . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1380       ". . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1381       ". . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1382       ". . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1383       ". . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1384       ". . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1385       ". . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1386       ". . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1387       ". . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1388       ". . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1389       ". . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1390       ". . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1391       ". . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1392       ". . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1393       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1394       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1395       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1396       ". . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1397       ". . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1398       ". . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1399       ". . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1400       ". . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1401       ". . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1402       ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . .\n",
1403       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n",
1404       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . .\n",
1405       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . .\n",
1406       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . .\n",
1407       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . .\n",
1408       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1409       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . .\n",
1410       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . .\n",
1411       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . .\n",
1412       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
1413       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . .\n",
1414       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . .\n",
1415       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T T T T T\n",
1416       "BcfEhgGACFbbABCGEGfAEabGceEFhcbGCGAABfdfcaEfEdfeFAceHAHGfFHBDBaHecHfagDAbBBdAAfeAHecHDfdCbBhebgbfhee\n"
1417      ]
1418     },
1419     {
1420      "data": {
1421       "text/plain": [
1422        "True"
1423       ]
1424      },
1425      "execution_count": 152,
1426      "metadata": {},
1427      "output_type": "execute_result"
1428     }
1429    ],
1430    "source": [
1431     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1432     "print(show_table(t))\n",
1433     "print(show_backtrace(bp))\n",
1434     "v"
1435    ]
1436   },
1437   {
1438    "cell_type": "code",
1439    "execution_count": 157,
1440    "metadata": {},
1441    "outputs": [
1442     {
1443      "name": "stdout",
1444      "output_type": "stream",
1445      "text": [
1446       "1000 loops, best of 3: 1.24 ms per loop\n"
1447      ]
1448     }
1449    ],
1450    "source": [
1451     "%%timeit\n",
1452     "is_interleave(s2, s1, il)"
1453    ]
1454   },
1455   {
1456    "cell_type": "code",
1457    "execution_count": 148,
1458    "metadata": {},
1459    "outputs": [
1460     {
1461      "name": "stdout",
1462      "output_type": "stream",
1463      "text": [
1464       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1465       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1466       "T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1467       "T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1468       ". . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1469       ". . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1470       ". . . . T . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1471       ". . . . T . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1472       ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1473       ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1474       ". . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1475       ". . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1476       ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1477       ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1478       ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1479       ". . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1480       ". . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1481       ". . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1482       ". . . . . . . . . . . . . . . T T T T T T T T T T T T T T . . . . . . . . . . . . . . . . . . . . . .\n",
1483       ". . . . . . . . . . . . . . . T . . . . . . . . . T . . T T T . . . . . . . . . . . . . . . . . . . .\n",
1484       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . .\n",
1485       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n",
1486       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . .\n",
1487       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . .\n",
1488       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . .\n",
1489       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . .\n",
1490       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1491       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
1492       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
1493       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
1494       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
1495       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . .\n",
1496       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . .\n",
1497       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . .\n",
1498       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . .\n",
1499       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T . . . . . . . . . .\n",
1500       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . .\n",
1501       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . .\n",
1502       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . .\n",
1503       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . .\n",
1504       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . .\n",
1505       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . .\n",
1506       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . .\n",
1507       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T\n",
1508       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1509       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1510       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1511       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1512       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1513       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1514       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1515       "FCgcGdDEgebbEhBCCgEcehHDAFBebgGECehcgdfdadbeggEgFCfggGAGaAhEEHfAgGAGHeFdaDfEcbfGcBDEbHdEaaFdfBBCABHC\n"
1516      ]
1517     },
1518     {
1519      "data": {
1520       "text/plain": [
1521        "True"
1522       ]
1523      },
1524      "execution_count": 148,
1525      "metadata": {},
1526      "output_type": "execute_result"
1527     }
1528    ],
1529    "source": [
1530     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1531     "print(show_table(t))\n",
1532     "print(show_backtrace(bp))\n",
1533     "v"
1534    ]
1535   },
1536   {
1537    "cell_type": "code",
1538    "execution_count": 115,
1539    "metadata": {},
1540    "outputs": [
1541     {
1542      "data": {
1543       "text/plain": [
1544        "True"
1545       ]
1546      },
1547      "execution_count": 115,
1548      "metadata": {},
1549      "output_type": "execute_result"
1550     }
1551    ],
1552    "source": [
1553     "show_backtrace(bp).lower() == il"
1554    ]
1555   },
1556   {
1557    "cell_type": "code",
1558    "execution_count": 149,
1559    "metadata": {},
1560    "outputs": [
1561     {
1562      "data": {
1563       "text/plain": [
1564        "('hchdchbfgbfhfcadcdehgebefhebedbdadfbbcdadfgbefebeb', False, False)"
1565       ]
1566      },
1567      "execution_count": 149,
1568      "metadata": {},
1569      "output_type": "execute_result"
1570     }
1571    ],
1572    "source": [
1573     "s3 = make_string(50)\n",
1574     "s3, is_interleave(s1, s3, il), is_interleave(s2, s3, il)"
1575    ]
1576   },
1577   {
1578    "cell_type": "code",
1579    "execution_count": 150,
1580    "metadata": {},
1581    "outputs": [
1582     {
1583      "name": "stdout",
1584      "output_type": "stream",
1585      "text": [
1586       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1587       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1588       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1589       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1590       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1591       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1592       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1593       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1594       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1595       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1596       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1597       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1598       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1599       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1600       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1601       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1602       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1603       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1604       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1605       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1606       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1607       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1608       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1609       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1610       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1611       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1612       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1613       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1614       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1615       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1616       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1617       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1618       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1619       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1620       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1621       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1622       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1623       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1624       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1625       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1626       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1627       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1628       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1629       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1630       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1631       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1632       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1633       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1634       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1635       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1636       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1637       "FCG\n"
1638      ]
1639     },
1640     {
1641      "data": {
1642       "text/plain": [
1643        "False"
1644       ]
1645      },
1646      "execution_count": 150,
1647      "metadata": {},
1648      "output_type": "execute_result"
1649     }
1650    ],
1651    "source": [
1652     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1653     "print(show_table(t))\n",
1654     "print(show_backtrace(bp))\n",
1655     "v"
1656    ]
1657   },
1658   {
1659    "cell_type": "markdown",
1660    "metadata": {},
1661    "source": [
1662     "## Example"
1663    ]
1664   },
1665   {
1666    "cell_type": "code",
1667    "execution_count": 174,
1668    "metadata": {
1669     "collapsed": true
1670    },
1671    "outputs": [],
1672    "source": [
1673     "def show_annotated_table(table, bps):\n",
1674     "    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",
1675     "        for i in sorted(set([k[0] for k in table])))"
1676    ]
1677   },
1678   {
1679    "cell_type": "code",
1680    "execution_count": 195,
1681    "metadata": {
1682     "collapsed": true
1683    },
1684    "outputs": [],
1685    "source": [
1686     "def show_backtrace_star(bps):\n",
1687     "    i = max([0] + [k[0] for k in bps])\n",
1688     "    j = max([0] + [k[1] for k in bps])\n",
1689     "    chars = ''\n",
1690     "    stars = ''\n",
1691     "    if (i, j) in bps:\n",
1692     "        while i != 0 or j != 0:\n",
1693     "            chars += bps[i, j][2]\n",
1694     "            if bps[i, j][3] == 'seq1':\n",
1695     "                stars += '*'\n",
1696     "            else:\n",
1697     "                stars += ' '\n",
1698     "            i, j = bps[i, j][0], bps[i, j][1] \n",
1699     "        return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n",
1700     "    else:\n",
1701     "        return ''"
1702    ]
1703   },
1704   {
1705    "cell_type": "code",
1706    "execution_count": 203,
1707    "metadata": {},
1708    "outputs": [
1709     {
1710      "data": {
1711       "text/plain": [
1712        "('ddcbcaabac', 'abcaddcbcc', 'abddcbccaaadbadccbcc', 20)"
1713       ]
1714      },
1715      "execution_count": 203,
1716      "metadata": {},
1717      "output_type": "execute_result"
1718     }
1719    ],
1720    "source": [
1721     "s1 = make_string(10, alphabet='abcd')\n",
1722     "s2 = make_string(10, alphabet='abcd')\n",
1723     "s3 = make_string(10, alphabet='abcd')\n",
1724     "il = interleave(s1, s2)\n",
1725     "s1, s2, il, len(il)"
1726    ]
1727   },
1728   {
1729    "cell_type": "code",
1730    "execution_count": 204,
1731    "metadata": {},
1732    "outputs": [
1733     {
1734      "name": "stdout",
1735      "output_type": "stream",
1736      "text": [
1737       "* a b . . . . . . . .\n",
1738       ". . d . . . . . . . .\n",
1739       ". . d c . . . . . . .\n",
1740       ". . c . . . . . . . .\n",
1741       ". . b c . . . . . . .\n",
1742       ". . c c a . . . . . .\n",
1743       ". . . a a . . . . . .\n",
1744       ". . . a a d . . . . .\n",
1745       ". . . . . b . . . . .\n",
1746       ". . . . . a d c . . .\n",
1747       ". . . . . . c c b c c\n",
1748       "abDDCBcCaAAdBAdcCbcc\n",
1749       "abddcbccaaadbadccbcc\n",
1750       "  **** * ** **  *   \n"
1751      ]
1752     },
1753     {
1754      "data": {
1755       "text/plain": [
1756        "True"
1757       ]
1758      },
1759      "execution_count": 204,
1760      "metadata": {},
1761      "output_type": "execute_result"
1762     }
1763    ],
1764    "source": [
1765     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1766     "print(show_annotated_table(t, bp))\n",
1767     "print(show_backtrace(bp))\n",
1768     "print(show_backtrace_star(bp))\n",
1769     "v"
1770    ]
1771   },
1772   {
1773    "cell_type": "code",
1774    "execution_count": 198,
1775    "metadata": {},
1776    "outputs": [
1777     {
1778      "name": "stdout",
1779      "output_type": "stream",
1780      "text": [
1781       "* b . . . . . . . . .\n",
1782       "b b c a . . . . . . .\n",
1783       ". c . c . . . . . . .\n",
1784       ". a c . . . . . . . .\n",
1785       ". . b . . . . . . . .\n",
1786       ". . d a a . . . . . .\n",
1787       ". . a a . . . . . . .\n",
1788       ". . . d a . . . . . .\n",
1789       ". . . . b a d a . . .\n",
1790       ". . . . . . . c . . .\n",
1791       ". . . . . . . c b b b\n",
1792       "bBCAcBDaADaBadaCCbbb\n",
1793       "bbcacbdaadabadaccbbb\n",
1794       " *** ** ** *   **   \n"
1795      ]
1796     },
1797     {
1798      "data": {
1799       "text/plain": [
1800        "True"
1801       ]
1802      },
1803      "execution_count": 198,
1804      "metadata": {},
1805      "output_type": "execute_result"
1806     }
1807    ],
1808    "source": [
1809     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1810     "print(show_annotated_table(t, bp))\n",
1811     "print(show_backtrace(bp))\n",
1812     "print(show_backtrace_star(bp))\n",
1813     "v"
1814    ]
1815   },
1816   {
1817    "cell_type": "code",
1818    "execution_count": 199,
1819    "metadata": {},
1820    "outputs": [
1821     {
1822      "name": "stdout",
1823      "output_type": "stream",
1824      "text": [
1825       "* b . . . . . . . . .\n",
1826       "b b c . . . . . . . .\n",
1827       ". c . . . . . . . . .\n",
1828       ". a c . . . . . . . .\n",
1829       ". . . . . . . . . . .\n",
1830       ". . . . . . . . . . .\n",
1831       ". . . . . . . . . . .\n",
1832       ". . . . . . . . . . .\n",
1833       ". . . . . . . . . . .\n",
1834       ". . . . . . . . . . .\n",
1835       ". . . . . . . . . . .\n",
1836       "bBCAc\n",
1837       "bbcac\n",
1838       " *** \n"
1839      ]
1840     },
1841     {
1842      "data": {
1843       "text/plain": [
1844        "False"
1845       ]
1846      },
1847      "execution_count": 199,
1848      "metadata": {},
1849      "output_type": "execute_result"
1850     }
1851    ],
1852    "source": [
1853     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1854     "print(show_annotated_table(t, bp))\n",
1855     "print(show_backtrace(bp))\n",
1856     "print(show_backtrace_star(bp))\n",
1857     "v"
1858    ]
1859   },
1860   {
1861    "cell_type": "code",
1862    "execution_count": 200,
1863    "metadata": {},
1864    "outputs": [
1865     {
1866      "name": "stdout",
1867      "output_type": "stream",
1868      "text": [
1869       "* b . . . . . . . . .\n",
1870       "b b c . . . . . . . .\n",
1871       ". c . . . . . . . . .\n",
1872       ". a c . . . . . . . .\n",
1873       ". . b . . . . . . . .\n",
1874       ". . d . . . . . . . .\n",
1875       ". . a . . . . . . . .\n",
1876       ". . . . . . . . . . .\n",
1877       ". . . . . . . . . . .\n",
1878       ". . . . . . . . . . .\n",
1879       ". . . . . . . . . . .\n",
1880       "bBCAcBDA\n",
1881       "bbcacbda\n",
1882       " *** ***\n"
1883      ]
1884     },
1885     {
1886      "data": {
1887       "text/plain": [
1888        "False"
1889       ]
1890      },
1891      "execution_count": 200,
1892      "metadata": {},
1893      "output_type": "execute_result"
1894     }
1895    ],
1896    "source": [
1897     "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n",
1898     "print(show_annotated_table(t, bp))\n",
1899     "print(show_backtrace(bp))\n",
1900     "print(show_backtrace_star(bp))\n",
1901     "v"
1902    ]
1903   },
1904   {
1905    "cell_type": "code",
1906    "execution_count": null,
1907    "metadata": {
1908     "collapsed": true
1909    },
1910    "outputs": [],
1911    "source": []
1912   }
1913  ],
1914  "metadata": {
1915   "kernelspec": {
1916    "display_name": "Python 3",
1917    "language": "python",
1918    "name": "python3"
1919   },
1920   "language_info": {
1921    "codemirror_mode": {
1922     "name": "ipython",
1923     "version": 3
1924    },
1925    "file_extension": ".py",
1926    "mimetype": "text/x-python",
1927    "name": "python",
1928    "nbconvert_exporter": "python",
1929    "pygments_lexer": "ipython3",
1930    "version": "3.5.2+"
1931   }
1932  },
1933  "nbformat": 4,
1934  "nbformat_minor": 1
1935 }