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     "collapsed": false
  52    },
  53    "outputs": [
  54     {
  55      "data": {
  56       "text/plain": [
  57        "[(0, ''), (1, 'a'), (2, 'aa'), (3, 'aab'), (4, 'aabc'), (5, 'aabcc')]"
  58       ]
  59      },
  60      "execution_count": 3,
  61      "metadata": {},
  62      "output_type": "execute_result"
  63     }
  64    ],
  65    "source": [
  66     "[(i, s1[:i]) for i in range(len(s1)+1)]"
  67    ]
  68   },
  69   {
  70    "cell_type": "markdown",
  71    "metadata": {},
  72    "source": [
  73     "`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`."
  74    ]
  75   },
  76   {
  77    "cell_type": "code",
  78    "execution_count": 4,
  79    "metadata": {
  80     "collapsed": false
  81    },
  82    "outputs": [
  83     {
  84      "data": {
  85       "text/plain": [
  86        "[[True, False, False, False, False, False],\n",
  87        " [False, False, False, False, False, False],\n",
  88        " [False, False, False, False, False, False],\n",
  89        " [False, False, False, False, False, False],\n",
  90        " [False, False, False, False, False, False],\n",
  91        " [False, False, False, False, False, False]]"
  92       ]
  93      },
  94      "execution_count": 4,
  95      "metadata": {},
  96      "output_type": "execute_result"
  97     }
  98    ],
  99    "source": [
 100     "dp_table = [[False] * (len(s1) + 1) for _ in range(len(s2) + 1)]\n",
 101     "dp_table[0][0] = True\n",
 102     "dp_table"
 103    ]
 104   },
 105   {
 106    "cell_type": "code",
 107    "execution_count": 5,
 108    "metadata": {
 109     "collapsed": false,
 110     "scrolled": true
 111    },
 112    "outputs": [
 113     {
 114      "data": {
 115       "text/plain": [
 116        "{(0, 0): False,\n",
 117        " (0, 1): False,\n",
 118        " (0, 2): False,\n",
 119        " (0, 3): False,\n",
 120        " (0, 4): False,\n",
 121        " (0, 5): False,\n",
 122        " (1, 0): False,\n",
 123        " (1, 1): False,\n",
 124        " (1, 2): False,\n",
 125        " (1, 3): False,\n",
 126        " (1, 4): False,\n",
 127        " (1, 5): False,\n",
 128        " (2, 0): False,\n",
 129        " (2, 1): False,\n",
 130        " (2, 2): False,\n",
 131        " (2, 3): False,\n",
 132        " (2, 4): False,\n",
 133        " (2, 5): False,\n",
 134        " (3, 0): False,\n",
 135        " (3, 1): False,\n",
 136        " (3, 2): False,\n",
 137        " (3, 3): False,\n",
 138        " (3, 4): False,\n",
 139        " (3, 5): False,\n",
 140        " (4, 0): False,\n",
 141        " (4, 1): False,\n",
 142        " (4, 2): False,\n",
 143        " (4, 3): False,\n",
 144        " (4, 4): False,\n",
 145        " (4, 5): False,\n",
 146        " (5, 0): False,\n",
 147        " (5, 1): False,\n",
 148        " (5, 2): False,\n",
 149        " (5, 3): False,\n",
 150        " (5, 4): False,\n",
 151        " (5, 5): False}"
 152       ]
 153      },
 154      "execution_count": 5,
 155      "metadata": {},
 156      "output_type": "execute_result"
 157     }
 158    ],
 159    "source": [
 160     "dp_table = {(i, j): False\n",
 161     "           for i in range(len(s1)+1)\n",
 162     "           for j in range(len(s2)+1)}\n",
 163     "dp_table"
 164    ]
 165   },
 166   {
 167    "cell_type": "code",
 168    "execution_count": 6,
 169    "metadata": {
 170     "collapsed": true
 171    },
 172    "outputs": [],
 173    "source": [
 174     "def show_table(table):\n",
 175     "    return '\\n'.join(\n",
 176     "        ' '.join(str(table[i, j])[0] for j in sorted(set([k[1] for k in table])))\n",
 177     "        for i in sorted(set([k[0] for k in table])))        "
 178    ]
 179   },
 180   {
 181    "cell_type": "code",
 182    "execution_count": 7,
 183    "metadata": {
 184     "collapsed": true
 185    },
 186    "outputs": [],
 187    "source": [
 188     "def show_table(table):\n",
 189     "    return '\\n'.join(\n",
 190     "        ' '.join('T' if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n",
 191     "        for i in sorted(set([k[0] for k in table])))        "
 192    ]
 193   },
 194   {
 195    "cell_type": "code",
 196    "execution_count": 8,
 197    "metadata": {
 198     "collapsed": false
 199    },
 200    "outputs": [
 201     {
 202      "name": "stdout",
 203      "output_type": "stream",
 204      "text": [
 205       ". . . . . .\n",
 206       ". . . . . .\n",
 207       ". . . . . .\n",
 208       ". . . . . .\n",
 209       ". . . . . .\n",
 210       ". . . . . .\n"
 211      ]
 212     }
 213    ],
 214    "source": [
 215     "print(show_table(dp_table))"
 216    ]
 217   },
 218   {
 219    "cell_type": "code",
 220    "execution_count": 9,
 221    "metadata": {
 222     "collapsed": false
 223    },
 224    "outputs": [
 225     {
 226      "name": "stdout",
 227      "output_type": "stream",
 228      "text": [
 229       "aabcc dbbca aadbbbaccc\n",
 230       "aa 0 0 ! ! ! True\n",
 231       "s2 0 1 ! d a False\n",
 232       "s2 0 2 ! b a False\n",
 233       "s2 0 3 ! b d False\n",
 234       "s2 0 4 ! c b False\n",
 235       "s2 0 5 ! a b False\n",
 236       "s1 1 0 a ! a True\n",
 237       "xx 1 1 a d a False\n",
 238       "xx 1 2 a b d False\n",
 239       "xx 1 3 a b b False\n",
 240       "xx 1 4 a c b False\n",
 241       "xx 1 5 a a b False\n",
 242       "s1 2 0 a ! a True\n",
 243       "s2 2 1 a d d True\n",
 244       "s2 2 2 a b b True\n",
 245       "s2 2 3 a b b True\n",
 246       "xx 2 4 a c b False\n",
 247       "xx 2 5 a a a False\n",
 248       "s1 3 0 b ! d False\n",
 249       "s1 3 1 b d b True\n",
 250       "s2 3 2 b b b True\n",
 251       "s1 3 2 b b b True\n",
 252       "s2 3 3 b b b True\n",
 253       "s1 3 3 b b b True\n",
 254       "xx 3 4 b c a False\n",
 255       "xx 3 5 b a c False\n",
 256       "s1 4 0 c ! b False\n",
 257       "xx 4 1 c d b False\n",
 258       "xx 4 2 c b b False\n",
 259       "xx 4 3 c b a False\n",
 260       "xx 4 4 c c c False\n",
 261       "xx 4 5 c a c False\n",
 262       "s1 5 0 c ! b False\n",
 263       "xx 5 1 c d b False\n",
 264       "xx 5 2 c b a False\n",
 265       "xx 5 3 c b c False\n",
 266       "xx 5 4 c c c False\n",
 267       "xx 5 5 c a c False\n",
 268       "T . . . . .\n",
 269       "T . . . . .\n",
 270       "T T T T . .\n",
 271       ". T T T . .\n",
 272       ". . . . . .\n",
 273       ". . . . . .\n"
 274      ]
 275     },
 276     {
 277      "data": {
 278       "text/plain": [
 279        "{(1, 0): (0, 0, 'a', 's1'),\n",
 280        " (2, 0): (1, 0, 'a', 's1'),\n",
 281        " (2, 1): (2, 0, 'd', 's2'),\n",
 282        " (2, 2): (2, 1, 'b', 's2'),\n",
 283        " (2, 3): (2, 2, 'b', 's2'),\n",
 284        " (3, 1): (2, 1, 'b', 's1'),\n",
 285        " (3, 2): (2, 2, 'b', 's1'),\n",
 286        " (3, 3): (2, 3, 'b', 's1')}"
 287       ]
 288      },
 289      "execution_count": 9,
 290      "metadata": {},
 291      "output_type": "execute_result"
 292     }
 293    ],
 294    "source": [
 295     "s3 = s3f\n",
 296     "\n",
 297     "print(s1, s2, s3)\n",
 298     "\n",
 299     "dp_table = {(i, j): False\n",
 300     "           for i in range(len(s1)+1)\n",
 301     "           for j in range(len(s2)+1)}\n",
 302     "\n",
 303     "backpointers = {}\n",
 304     "\n",
 305     "for i in range(len(s1)+1):\n",
 306     "    for j in range(len(s2)+1):\n",
 307     "        if i == 0 and j == 0:\n",
 308     "            dp_table[i, j] = True\n",
 309     "            print('aa', i, j, '!', '!', '!', dp_table[i, j])\n",
 310     "        elif i == 0:\n",
 311     "            # extend by character from s2\n",
 312     "            if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
 313     "                dp_table[i, j] = True\n",
 314     "                backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
 315     "            print('s2', i, j, '!', s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 316     "        elif j == 0:\n",
 317     "            # extend by character from s1\n",
 318     "            if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
 319     "                dp_table[i, j] = True\n",
 320     "                backpointers[i, j] = (i-1, j, s1[i-1], 's1')\n",
 321     "            print('s1', i, j, s1[i-1], '!', s3[i+j-1], dp_table[i, j])\n",
 322     "        else:\n",
 323     "            # extend by character from s2\n",
 324     "            if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n",
 325     "                dp_table[i, j] = True\n",
 326     "                backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n",
 327     "                print('s2', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])                \n",
 328     "            # extend by character from s1\n",
 329     "            if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n",
 330     "                dp_table[i, j] = True\n",
 331     "                backpointers[i, j] = (i-1, j, s1[i-1], 's1')                \n",
 332     "                print('s1', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 333     "            if not dp_table[i, j]:\n",
 334     "                print('xx', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n",
 335     "\n",
 336     "print(show_table(dp_table))\n",
 337     "backpointers"
 338    ]
 339   },
 340   {
 341    "cell_type": "code",
 342    "execution_count": 10,
 343    "metadata": {
 344     "collapsed": true
 345    },
 346    "outputs": [],
 347    "source": [
 348     "def is_interleave(seq1, seq2, seq3, return_backpointers=False, return_table=False, debug=False):\n",
 349     "    \"\"\"Return true if seq3 is some interleaved merge of seq1 and seq2.\n",
 350     "    If return_backpointers, also return the set of backpointers to\n",
 351     "    reconstruct the interleaving\"\"\"\n",
 352     "    \n",
 353     "    # dp_table[i, j] is True if first i+j characters of seq is made up of \n",
 354     "    # an interleaving of the first i characters of seq1 and the \n",
 355     "    # first j characters of seq2\n",
 356     "    \n",
 357     "    if len(seq1) + len(seq2) != len(seq3):\n",
 358     "        if return_backpointers or return_table:\n",
 359     "            retval = [False]\n",
 360     "            if return_backpointers:\n",
 361     "                retval += [{}]\n",
 362     "            if return_table:\n",
 363     "                retval += [{}]\n",
 364     "            return tuple(retval)\n",
 365     "        else:\n",
 366     "            return False\n",
 367     "    \n",
 368     "    dp_table = {(i, j): False\n",
 369     "               for i in range(len(seq1)+1)\n",
 370     "               for j in range(len(seq2)+1)}\n",
 371     "\n",
 372     "    backpointers = {}\n",
 373     "\n",
 374     "    for i in range(len(seq1)+1):\n",
 375     "        for j in range(len(seq2)+1):\n",
 376     "            if i == 0 and j == 0:\n",
 377     "                dp_table[i, j] = True\n",
 378     "                if debug: print('xxxx', i, j, '!', '!', '!', dp_table[i, j])\n",
 379     "            elif i == 0:\n",
 380     "                # extend by character from seq2\n",
 381     "                if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
 382     "                    dp_table[i, j] = True\n",
 383     "                    backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
 384     "                if debug: print('seq2', i, j, '!', seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 385     "            elif j == 0:\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], '!', seq3[i+j-1], dp_table[i, j])\n",
 391     "            else:\n",
 392     "                # extend by character from seq2\n",
 393     "                if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n",
 394     "                    dp_table[i, j] = True\n",
 395     "                    backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n",
 396     "                    if debug: print('seq2', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])                \n",
 397     "                # extend by character from seq1\n",
 398     "                if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n",
 399     "                    dp_table[i, j] = True\n",
 400     "                    backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')                \n",
 401     "                    if debug: print('seq1', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 402     "                if not dp_table[i, j]:\n",
 403     "                    if debug: print('xxxx', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n",
 404     "\n",
 405     "    if return_backpointers or return_table:\n",
 406     "        retval = [dp_table[len(seq1), len(seq2)]]\n",
 407     "        if return_backpointers:\n",
 408     "            retval += [backpointers]\n",
 409     "        if return_table:\n",
 410     "            retval += [dp_table]\n",
 411     "        return tuple(retval)\n",
 412     "    else:\n",
 413     "        return dp_table[len(seq1), len(seq2)]"
 414    ]
 415   },
 416   {
 417    "cell_type": "code",
 418    "execution_count": 11,
 419    "metadata": {
 420     "collapsed": false
 421    },
 422    "outputs": [
 423     {
 424      "data": {
 425       "text/plain": [
 426        "True"
 427       ]
 428      },
 429      "execution_count": 11,
 430      "metadata": {},
 431      "output_type": "execute_result"
 432     }
 433    ],
 434    "source": [
 435     "is_interleave(s1, s2, s3t)"
 436    ]
 437   },
 438   {
 439    "cell_type": "code",
 440    "execution_count": 12,
 441    "metadata": {
 442     "collapsed": false
 443    },
 444    "outputs": [
 445     {
 446      "data": {
 447       "text/plain": [
 448        "(True,\n",
 449        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 450        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 451        "  (2, 1): (2, 0, 'd', 'seq2'),\n",
 452        "  (2, 2): (2, 1, 'b', 'seq2'),\n",
 453        "  (2, 3): (2, 2, 'b', 'seq2'),\n",
 454        "  (2, 4): (2, 3, 'c', 'seq2'),\n",
 455        "  (3, 1): (2, 1, 'b', 'seq1'),\n",
 456        "  (3, 2): (2, 2, 'b', 'seq1'),\n",
 457        "  (3, 4): (2, 4, 'b', 'seq1'),\n",
 458        "  (4, 2): (3, 2, 'c', 'seq1'),\n",
 459        "  (4, 3): (4, 2, 'b', 'seq2'),\n",
 460        "  (4, 4): (3, 4, 'c', 'seq1'),\n",
 461        "  (4, 5): (4, 4, 'a', 'seq2'),\n",
 462        "  (5, 3): (4, 3, 'c', 'seq1'),\n",
 463        "  (5, 5): (4, 5, 'c', 'seq1')})"
 464       ]
 465      },
 466      "execution_count": 12,
 467      "metadata": {},
 468      "output_type": "execute_result"
 469     }
 470    ],
 471    "source": [
 472     "is_interleave(s1, s2, s3t, return_backpointers=True)"
 473    ]
 474   },
 475   {
 476    "cell_type": "code",
 477    "execution_count": 13,
 478    "metadata": {
 479     "collapsed": false,
 480     "scrolled": true
 481    },
 482    "outputs": [
 483     {
 484      "data": {
 485       "text/plain": [
 486        "(True,\n",
 487        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 488        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 489        "  (2, 1): (2, 0, 'd', 'seq2'),\n",
 490        "  (2, 2): (2, 1, 'b', 'seq2'),\n",
 491        "  (2, 3): (2, 2, 'b', 'seq2'),\n",
 492        "  (2, 4): (2, 3, 'c', 'seq2'),\n",
 493        "  (3, 1): (2, 1, 'b', 'seq1'),\n",
 494        "  (3, 2): (2, 2, 'b', 'seq1'),\n",
 495        "  (3, 4): (2, 4, 'b', 'seq1'),\n",
 496        "  (4, 2): (3, 2, 'c', 'seq1'),\n",
 497        "  (4, 3): (4, 2, 'b', 'seq2'),\n",
 498        "  (4, 4): (3, 4, 'c', 'seq1'),\n",
 499        "  (4, 5): (4, 4, 'a', 'seq2'),\n",
 500        "  (5, 3): (4, 3, 'c', 'seq1'),\n",
 501        "  (5, 5): (4, 5, 'c', 'seq1')},\n",
 502        " {(0, 0): True,\n",
 503        "  (0, 1): False,\n",
 504        "  (0, 2): False,\n",
 505        "  (0, 3): False,\n",
 506        "  (0, 4): False,\n",
 507        "  (0, 5): False,\n",
 508        "  (1, 0): True,\n",
 509        "  (1, 1): False,\n",
 510        "  (1, 2): False,\n",
 511        "  (1, 3): False,\n",
 512        "  (1, 4): False,\n",
 513        "  (1, 5): False,\n",
 514        "  (2, 0): True,\n",
 515        "  (2, 1): True,\n",
 516        "  (2, 2): True,\n",
 517        "  (2, 3): True,\n",
 518        "  (2, 4): True,\n",
 519        "  (2, 5): False,\n",
 520        "  (3, 0): False,\n",
 521        "  (3, 1): True,\n",
 522        "  (3, 2): True,\n",
 523        "  (3, 3): False,\n",
 524        "  (3, 4): True,\n",
 525        "  (3, 5): False,\n",
 526        "  (4, 0): False,\n",
 527        "  (4, 1): False,\n",
 528        "  (4, 2): True,\n",
 529        "  (4, 3): True,\n",
 530        "  (4, 4): True,\n",
 531        "  (4, 5): True,\n",
 532        "  (5, 0): False,\n",
 533        "  (5, 1): False,\n",
 534        "  (5, 2): False,\n",
 535        "  (5, 3): True,\n",
 536        "  (5, 4): False,\n",
 537        "  (5, 5): True})"
 538       ]
 539      },
 540      "execution_count": 13,
 541      "metadata": {},
 542      "output_type": "execute_result"
 543     }
 544    ],
 545    "source": [
 546     "is_interleave(s1, s2, s3t, return_backpointers=True, return_table=True)"
 547    ]
 548   },
 549   {
 550    "cell_type": "code",
 551    "execution_count": 14,
 552    "metadata": {
 553     "collapsed": false
 554    },
 555    "outputs": [
 556     {
 557      "data": {
 558       "text/plain": [
 559        "False"
 560       ]
 561      },
 562      "execution_count": 14,
 563      "metadata": {},
 564      "output_type": "execute_result"
 565     }
 566    ],
 567    "source": [
 568     "is_interleave(s1, s2, s3f)"
 569    ]
 570   },
 571   {
 572    "cell_type": "code",
 573    "execution_count": 15,
 574    "metadata": {
 575     "collapsed": false
 576    },
 577    "outputs": [
 578     {
 579      "name": "stdout",
 580      "output_type": "stream",
 581      "text": [
 582       "xxxx 0 0 ! ! ! True\n",
 583       "seq2 0 1 ! b a False\n",
 584       "seq2 0 2 ! b a False\n",
 585       "seq2 0 3 ! b a False\n",
 586       "seq1 1 0 a ! a True\n",
 587       "xxxx 1 1 a b a False\n",
 588       "xxxx 1 2 a b a False\n",
 589       "xxxx 1 3 a b b False\n",
 590       "seq1 2 0 a ! a True\n",
 591       "xxxx 2 1 a b a False\n",
 592       "xxxx 2 2 a b b False\n",
 593       "xxxx 2 3 a b a False\n",
 594       "seq1 3 0 a ! a True\n",
 595       "seq2 3 1 a b b True\n",
 596       "xxxx 3 2 a b a False\n",
 597       "xxxx 3 3 a b b False\n",
 598       "seq1 4 0 a ! b False\n",
 599       "seq1 4 1 a b a True\n",
 600       "seq2 4 2 a b b True\n",
 601       "seq2 4 3 a b b True\n"
 602      ]
 603     },
 604     {
 605      "data": {
 606       "text/plain": [
 607        "(True,\n",
 608        " {(1, 0): (0, 0, 'a', 'seq1'),\n",
 609        "  (2, 0): (1, 0, 'a', 'seq1'),\n",
 610        "  (3, 0): (2, 0, 'a', 'seq1'),\n",
 611        "  (3, 1): (3, 0, 'b', 'seq2'),\n",
 612        "  (4, 1): (3, 1, 'a', 'seq1'),\n",
 613        "  (4, 2): (4, 1, 'b', 'seq2'),\n",
 614        "  (4, 3): (4, 2, 'b', 'seq2')})"
 615       ]
 616      },
 617      "execution_count": 15,
 618      "metadata": {},
 619      "output_type": "execute_result"
 620     }
 621    ],
 622    "source": [
 623     "is_interleave('aaaa', 'bbb', 'aaababb', return_backpointers=True, debug=True)"
 624    ]
 625   },
 626   {
 627    "cell_type": "code",
 628    "execution_count": 16,
 629    "metadata": {
 630     "collapsed": true
 631    },
 632    "outputs": [],
 633    "source": [
 634     "def show_backtrace(bps):\n",
 635     "    i = max([0] + [k[0] for k in bps])\n",
 636     "    j = max([0] + [k[1] for k in bps])\n",
 637     "    chars = ''\n",
 638     "    if (i, j) in bps:\n",
 639     "        while i != 0 or j != 0:\n",
 640     "            if bps[i, j][3] == 'seq1':\n",
 641     "                chars += bps[i, j][2].upper()\n",
 642     "            else:\n",
 643     "                chars += bps[i, j][2]\n",
 644     "            i, j = bps[i, j][0], bps[i, j][1] \n",
 645     "        return ''.join(list(reversed(chars)))\n",
 646     "    else:\n",
 647     "        return ''"
 648    ]
 649   },
 650   {
 651    "cell_type": "code",
 652    "execution_count": 17,
 653    "metadata": {
 654     "collapsed": true
 655    },
 656    "outputs": [],
 657    "source": [
 658     "def make_string(length, alphabet=None):\n",
 659     "    if not alphabet:\n",
 660     "        alphabet = 'abcdefgh'\n",
 661     "    return ''.join(random.choice(alphabet) for _ in range(length))    "
 662    ]
 663   },
 664   {
 665    "cell_type": "code",
 666    "execution_count": 18,
 667    "metadata": {
 668     "collapsed": false
 669    },
 670    "outputs": [
 671     {
 672      "data": {
 673       "text/plain": [
 674        "'acdcfgfcgdhagedbdccbgefgbfbgaacbfbdcebehaeccgadghe'"
 675       ]
 676      },
 677      "execution_count": 18,
 678      "metadata": {},
 679      "output_type": "execute_result"
 680     }
 681    ],
 682    "source": [
 683     "make_string(50)"
 684    ]
 685   },
 686   {
 687    "cell_type": "code",
 688    "execution_count": 19,
 689    "metadata": {
 690     "collapsed": true
 691    },
 692    "outputs": [],
 693    "source": [
 694     "def interleave(s1, s2, wander_limit=10, debug=False):\n",
 695     "    i1 = i2 = wander = 0\n",
 696     "    interleaved = []\n",
 697     "    while i1 <= len(s1) and i2 <= len(s2):\n",
 698     "        if i1 == len(s1):\n",
 699     "            if debug: print(i1, i2, wander, 'remaining s2', s2[i2:])\n",
 700     "            interleaved += s2[i2:]\n",
 701     "            i2 = len(s2) + 1\n",
 702     "        elif i2 == len(s2):\n",
 703     "            if debug: print(i1, i2, wander, 'remaining s1', s1[i1:])\n",
 704     "            interleaved += s1[i1:]\n",
 705     "            i1 = len(s1) + 1\n",
 706     "        else:\n",
 707     "            if wander == wander_limit:\n",
 708     "                step = -1\n",
 709     "            elif wander == -wander_limit:\n",
 710     "                step = +1\n",
 711     "            else:\n",
 712     "                step = random.choice([+1, -1])\n",
 713     "            if step == +1:\n",
 714     "                if debug: print(i1, i2, wander, 'adding', s1[i1])\n",
 715     "                interleaved += s1[i1]\n",
 716     "                i1 += 1\n",
 717     "                wander += 1\n",
 718     "            else:\n",
 719     "                if debug: print(i1, i2, wander, 'adding', s2[i2])\n",
 720     "                interleaved += s2[i2]\n",
 721     "                i2 += 1\n",
 722     "                wander -= 1\n",
 723     "    return ''.join(interleaved)\n",
 724     "            "
 725    ]
 726   },
 727   {
 728    "cell_type": "code",
 729    "execution_count": 20,
 730    "metadata": {
 731     "collapsed": false
 732    },
 733    "outputs": [
 734     {
 735      "name": "stdout",
 736      "output_type": "stream",
 737      "text": [
 738       "0 0 0 adding g\n",
 739       "1 0 1 adding w\n",
 740       "1 1 0 adding x\n",
 741       "1 2 -1 adding u\n",
 742       "1 3 -2 adding z\n",
 743       "1 4 -3 adding f\n",
 744       "2 4 -2 adding z\n",
 745       "2 5 -3 adding x\n",
 746       "2 6 -4 adding h\n",
 747       "3 6 -3 adding u\n",
 748       "3 7 -4 adding a\n",
 749       "4 7 -3 adding b\n",
 750       "5 7 -2 adding y\n",
 751       "5 8 -3 adding u\n",
 752       "5 9 -4 adding w\n",
 753       "5 10 -5 adding g\n",
 754       "6 10 -4 adding u\n",
 755       "6 11 -5 adding g\n",
 756       "7 11 -4 adding g\n",
 757       "8 11 -3 adding f\n",
 758       "9 11 -2 adding g\n",
 759       "10 11 -1 adding g\n",
 760       "11 11 0 adding w\n",
 761       "11 12 -1 adding y\n",
 762       "11 13 -2 adding w\n",
 763       "11 14 -3 adding y\n",
 764       "11 15 -4 adding a\n",
 765       "12 15 -3 adding e\n",
 766       "13 15 -2 adding z\n",
 767       "13 16 -3 adding x\n",
 768       "13 17 -4 adding x\n",
 769       "13 18 -5 adding f\n",
 770       "14 18 -4 adding y\n",
 771       "14 19 -5 adding b\n",
 772       "15 19 -4 adding x\n",
 773       "15 20 -5 remaining s1 fcbab\n"
 774      ]
 775     },
 776     {
 777      "data": {
 778       "text/plain": [
 779        "('gfhabgggfggaefbfcbab',\n",
 780        " 'wxuzzxuyuwuwywyzxxyx',\n",
 781        " 'gwxuzfzxhuabyuwguggfggwywyaezxxfybxfcbab',\n",
 782        " 40)"
 783       ]
 784      },
 785      "execution_count": 20,
 786      "metadata": {},
 787      "output_type": "execute_result"
 788     }
 789    ],
 790    "source": [
 791     "s1 = make_string(20)\n",
 792     "s2 = make_string(20, alphabet='uvwxyz')\n",
 793     "il = interleave(s1, s2, wander_limit=5, debug=True)\n",
 794     "s1, s2, il, len(il)"
 795    ]
 796   },
 797   {
 798    "cell_type": "code",
 799    "execution_count": 21,
 800    "metadata": {
 801     "collapsed": false
 802    },
 803    "outputs": [
 804     {
 805      "name": "stdout",
 806      "output_type": "stream",
 807      "text": [
 808       "xxxx 0 0 ! ! ! True\n",
 809       "seq2 0 1 ! g g True\n",
 810       "seq2 0 2 ! f w False\n",
 811       "seq2 0 3 ! h x False\n",
 812       "seq2 0 4 ! a u False\n",
 813       "seq2 0 5 ! b z False\n",
 814       "seq2 0 6 ! g f False\n",
 815       "seq2 0 7 ! g z False\n",
 816       "seq2 0 8 ! g x False\n",
 817       "seq2 0 9 ! f h False\n",
 818       "seq2 0 10 ! g u False\n",
 819       "seq2 0 11 ! g a False\n",
 820       "seq2 0 12 ! a b False\n",
 821       "seq2 0 13 ! e y False\n",
 822       "seq2 0 14 ! f u False\n",
 823       "seq2 0 15 ! b w False\n",
 824       "seq2 0 16 ! f g False\n",
 825       "seq2 0 17 ! c u False\n",
 826       "seq2 0 18 ! b g False\n",
 827       "seq2 0 19 ! a g False\n",
 828       "seq2 0 20 ! b f False\n",
 829       "seq1 1 0 w ! g False\n",
 830       "seq1 1 1 w g w True\n",
 831       "xxxx 1 2 w f x False\n",
 832       "xxxx 1 3 w h u False\n",
 833       "xxxx 1 4 w a z False\n",
 834       "xxxx 1 5 w b f False\n",
 835       "xxxx 1 6 w g z False\n",
 836       "xxxx 1 7 w g x False\n",
 837       "xxxx 1 8 w g h False\n",
 838       "xxxx 1 9 w f u False\n",
 839       "xxxx 1 10 w g a False\n",
 840       "xxxx 1 11 w g b False\n",
 841       "xxxx 1 12 w a y False\n",
 842       "xxxx 1 13 w e u False\n",
 843       "xxxx 1 14 w f w False\n",
 844       "xxxx 1 15 w b g False\n",
 845       "xxxx 1 16 w f u False\n",
 846       "xxxx 1 17 w c g False\n",
 847       "xxxx 1 18 w b g False\n",
 848       "xxxx 1 19 w a f False\n",
 849       "xxxx 1 20 w b g False\n",
 850       "seq1 2 0 x ! w False\n",
 851       "seq1 2 1 x g x True\n",
 852       "xxxx 2 2 x f u False\n",
 853       "xxxx 2 3 x h z False\n",
 854       "xxxx 2 4 x a f False\n",
 855       "xxxx 2 5 x b z False\n",
 856       "xxxx 2 6 x g x False\n",
 857       "xxxx 2 7 x g h False\n",
 858       "xxxx 2 8 x g u False\n",
 859       "xxxx 2 9 x f a False\n",
 860       "xxxx 2 10 x g b False\n",
 861       "xxxx 2 11 x g y False\n",
 862       "xxxx 2 12 x a u False\n",
 863       "xxxx 2 13 x e w False\n",
 864       "xxxx 2 14 x f g False\n",
 865       "xxxx 2 15 x b u False\n",
 866       "xxxx 2 16 x f g False\n",
 867       "xxxx 2 17 x c g False\n",
 868       "xxxx 2 18 x b f False\n",
 869       "xxxx 2 19 x a g False\n",
 870       "xxxx 2 20 x b g False\n",
 871       "seq1 3 0 u ! x False\n",
 872       "seq1 3 1 u g u True\n",
 873       "xxxx 3 2 u f z False\n",
 874       "xxxx 3 3 u h f False\n",
 875       "xxxx 3 4 u a z False\n",
 876       "xxxx 3 5 u b x False\n",
 877       "xxxx 3 6 u g h False\n",
 878       "xxxx 3 7 u g u False\n",
 879       "xxxx 3 8 u g a False\n",
 880       "xxxx 3 9 u f b False\n",
 881       "xxxx 3 10 u g y False\n",
 882       "xxxx 3 11 u g u False\n",
 883       "xxxx 3 12 u a w False\n",
 884       "xxxx 3 13 u e g False\n",
 885       "xxxx 3 14 u f u False\n",
 886       "xxxx 3 15 u b g False\n",
 887       "xxxx 3 16 u f g False\n",
 888       "xxxx 3 17 u c f False\n",
 889       "xxxx 3 18 u b g False\n",
 890       "xxxx 3 19 u a g False\n",
 891       "xxxx 3 20 u b w False\n",
 892       "seq1 4 0 z ! u False\n",
 893       "seq1 4 1 z g z True\n",
 894       "seq2 4 2 z f f True\n",
 895       "xxxx 4 3 z h z False\n",
 896       "xxxx 4 4 z a x False\n",
 897       "xxxx 4 5 z b h False\n",
 898       "xxxx 4 6 z g u False\n",
 899       "xxxx 4 7 z g a False\n",
 900       "xxxx 4 8 z g b False\n",
 901       "xxxx 4 9 z f y False\n",
 902       "xxxx 4 10 z g u False\n",
 903       "xxxx 4 11 z g w False\n",
 904       "xxxx 4 12 z a g False\n",
 905       "xxxx 4 13 z e u False\n",
 906       "xxxx 4 14 z f g False\n",
 907       "xxxx 4 15 z b g False\n",
 908       "xxxx 4 16 z f f False\n",
 909       "xxxx 4 17 z c g False\n",
 910       "xxxx 4 18 z b g False\n",
 911       "xxxx 4 19 z a w False\n",
 912       "xxxx 4 20 z b y False\n",
 913       "seq1 5 0 z ! z False\n",
 914       "xxxx 5 1 z g f False\n",
 915       "seq1 5 2 z f z True\n",
 916       "xxxx 5 3 z h x False\n",
 917       "xxxx 5 4 z a h False\n",
 918       "xxxx 5 5 z b u False\n",
 919       "xxxx 5 6 z g a False\n",
 920       "xxxx 5 7 z g b False\n",
 921       "xxxx 5 8 z g y False\n",
 922       "xxxx 5 9 z f u False\n",
 923       "xxxx 5 10 z g w False\n",
 924       "xxxx 5 11 z g g False\n",
 925       "xxxx 5 12 z a u False\n",
 926       "xxxx 5 13 z e g False\n",
 927       "xxxx 5 14 z f g False\n",
 928       "xxxx 5 15 z b f False\n",
 929       "xxxx 5 16 z f g False\n",
 930       "xxxx 5 17 z c g False\n",
 931       "xxxx 5 18 z b w False\n",
 932       "xxxx 5 19 z a y False\n",
 933       "xxxx 5 20 z b w False\n",
 934       "seq1 6 0 x ! f False\n",
 935       "xxxx 6 1 x g z False\n",
 936       "seq1 6 2 x f x True\n",
 937       "seq2 6 3 x h h True\n",
 938       "xxxx 6 4 x a u False\n",
 939       "xxxx 6 5 x b a False\n",
 940       "xxxx 6 6 x g b False\n",
 941       "xxxx 6 7 x g y False\n",
 942       "xxxx 6 8 x g u False\n",
 943       "xxxx 6 9 x f w False\n",
 944       "xxxx 6 10 x g g False\n",
 945       "xxxx 6 11 x g u False\n",
 946       "xxxx 6 12 x a g False\n",
 947       "xxxx 6 13 x e g False\n",
 948       "xxxx 6 14 x f f False\n",
 949       "xxxx 6 15 x b g False\n",
 950       "xxxx 6 16 x f g False\n",
 951       "xxxx 6 17 x c w False\n",
 952       "xxxx 6 18 x b y False\n",
 953       "xxxx 6 19 x a w False\n",
 954       "xxxx 6 20 x b y False\n",
 955       "seq1 7 0 u ! z False\n",
 956       "xxxx 7 1 u g x False\n",
 957       "xxxx 7 2 u f h False\n",
 958       "seq1 7 3 u h u True\n",
 959       "seq2 7 4 u a a True\n",
 960       "seq2 7 5 u b b True\n",
 961       "xxxx 7 6 u g y False\n",
 962       "xxxx 7 7 u g u False\n",
 963       "xxxx 7 8 u g w False\n",
 964       "xxxx 7 9 u f g False\n",
 965       "xxxx 7 10 u g u False\n",
 966       "xxxx 7 11 u g g False\n",
 967       "xxxx 7 12 u a g False\n",
 968       "xxxx 7 13 u e f False\n",
 969       "xxxx 7 14 u f g False\n",
 970       "xxxx 7 15 u b g False\n",
 971       "xxxx 7 16 u f w False\n",
 972       "xxxx 7 17 u c y False\n",
 973       "xxxx 7 18 u b w False\n",
 974       "xxxx 7 19 u a y False\n",
 975       "xxxx 7 20 u b a False\n",
 976       "seq1 8 0 y ! x False\n",
 977       "xxxx 8 1 y g h False\n",
 978       "xxxx 8 2 y f u False\n",
 979       "xxxx 8 3 y h a False\n",
 980       "xxxx 8 4 y a b False\n",
 981       "seq1 8 5 y b y True\n",
 982       "xxxx 8 6 y g u False\n",
 983       "xxxx 8 7 y g w False\n",
 984       "xxxx 8 8 y g g False\n",
 985       "xxxx 8 9 y f u False\n",
 986       "xxxx 8 10 y g g False\n",
 987       "xxxx 8 11 y g g False\n",
 988       "xxxx 8 12 y a f False\n",
 989       "xxxx 8 13 y e g False\n",
 990       "xxxx 8 14 y f g False\n",
 991       "xxxx 8 15 y b w False\n",
 992       "xxxx 8 16 y f y False\n",
 993       "xxxx 8 17 y c w False\n",
 994       "xxxx 8 18 y b y False\n",
 995       "xxxx 8 19 y a a False\n",
 996       "xxxx 8 20 y b e False\n",
 997       "seq1 9 0 u ! h False\n",
 998       "xxxx 9 1 u g u False\n",
 999       "xxxx 9 2 u f a False\n",
1000       "xxxx 9 3 u h b False\n",
1001       "xxxx 9 4 u a y False\n",
1002       "seq1 9 5 u b u True\n",
1003       "xxxx 9 6 u g w False\n",
1004       "xxxx 9 7 u g g False\n",
1005       "xxxx 9 8 u g u False\n",
1006       "xxxx 9 9 u f g False\n",
1007       "xxxx 9 10 u g g False\n",
1008       "xxxx 9 11 u g f False\n",
1009       "xxxx 9 12 u a g False\n",
1010       "xxxx 9 13 u e g False\n",
1011       "xxxx 9 14 u f w False\n",
1012       "xxxx 9 15 u b y False\n",
1013       "xxxx 9 16 u f w False\n",
1014       "xxxx 9 17 u c y False\n",
1015       "xxxx 9 18 u b a False\n",
1016       "xxxx 9 19 u a e False\n",
1017       "xxxx 9 20 u b z False\n",
1018       "seq1 10 0 w ! u False\n",
1019       "xxxx 10 1 w g a False\n",
1020       "xxxx 10 2 w f b False\n",
1021       "xxxx 10 3 w h y False\n",
1022       "xxxx 10 4 w a u False\n",
1023       "seq1 10 5 w b w True\n",
1024       "seq2 10 6 w g g True\n",
1025       "xxxx 10 7 w g u False\n",
1026       "xxxx 10 8 w g g False\n",
1027       "xxxx 10 9 w f g False\n",
1028       "xxxx 10 10 w g f False\n",
1029       "xxxx 10 11 w g g False\n",
1030       "xxxx 10 12 w a g False\n",
1031       "xxxx 10 13 w e w False\n",
1032       "xxxx 10 14 w f y False\n",
1033       "xxxx 10 15 w b w False\n",
1034       "xxxx 10 16 w f y False\n",
1035       "xxxx 10 17 w c a False\n",
1036       "xxxx 10 18 w b e False\n",
1037       "xxxx 10 19 w a z False\n",
1038       "xxxx 10 20 w b x False\n",
1039       "seq1 11 0 u ! a False\n",
1040       "xxxx 11 1 u g b False\n",
1041       "xxxx 11 2 u f y False\n",
1042       "xxxx 11 3 u h u False\n",
1043       "xxxx 11 4 u a w False\n",
1044       "xxxx 11 5 u b g False\n",
1045       "seq1 11 6 u g u True\n",
1046       "seq2 11 7 u g g True\n",
1047       "seq2 11 8 u g g True\n",
1048       "seq2 11 9 u f f True\n",
1049       "seq2 11 10 u g g True\n",
1050       "seq2 11 11 u g g True\n",
1051       "xxxx 11 12 u a w False\n",
1052       "xxxx 11 13 u e y False\n",
1053       "xxxx 11 14 u f w False\n",
1054       "xxxx 11 15 u b y False\n",
1055       "xxxx 11 16 u f a False\n",
1056       "xxxx 11 17 u c e False\n",
1057       "xxxx 11 18 u b z False\n",
1058       "xxxx 11 19 u a x False\n",
1059       "xxxx 11 20 u b x False\n",
1060       "seq1 12 0 w ! b False\n",
1061       "xxxx 12 1 w g y False\n",
1062       "xxxx 12 2 w f u False\n",
1063       "xxxx 12 3 w h w False\n",
1064       "xxxx 12 4 w a g False\n",
1065       "xxxx 12 5 w b u False\n",
1066       "xxxx 12 6 w g g False\n",
1067       "xxxx 12 7 w g g False\n",
1068       "xxxx 12 8 w g f False\n",
1069       "xxxx 12 9 w f g False\n",
1070       "xxxx 12 10 w g g False\n",
1071       "seq1 12 11 w g w True\n",
1072       "xxxx 12 12 w a y False\n",
1073       "xxxx 12 13 w e w False\n",
1074       "xxxx 12 14 w f y False\n",
1075       "xxxx 12 15 w b a False\n",
1076       "xxxx 12 16 w f e False\n",
1077       "xxxx 12 17 w c z False\n",
1078       "xxxx 12 18 w b x False\n",
1079       "xxxx 12 19 w a x False\n",
1080       "xxxx 12 20 w b f False\n",
1081       "seq1 13 0 y ! y False\n",
1082       "xxxx 13 1 y g u False\n",
1083       "xxxx 13 2 y f w False\n",
1084       "xxxx 13 3 y h g False\n",
1085       "xxxx 13 4 y a u False\n",
1086       "xxxx 13 5 y b g False\n",
1087       "xxxx 13 6 y g g False\n",
1088       "xxxx 13 7 y g f False\n",
1089       "xxxx 13 8 y g g False\n",
1090       "xxxx 13 9 y f g False\n",
1091       "xxxx 13 10 y g w False\n",
1092       "seq1 13 11 y g y True\n",
1093       "xxxx 13 12 y a w False\n",
1094       "xxxx 13 13 y e y False\n",
1095       "xxxx 13 14 y f a False\n",
1096       "xxxx 13 15 y b e False\n",
1097       "xxxx 13 16 y f z False\n",
1098       "xxxx 13 17 y c x False\n",
1099       "xxxx 13 18 y b x False\n",
1100       "xxxx 13 19 y a f False\n",
1101       "xxxx 13 20 y b y False\n",
1102       "seq1 14 0 w ! u False\n",
1103       "xxxx 14 1 w g w False\n",
1104       "xxxx 14 2 w f g False\n",
1105       "xxxx 14 3 w h u False\n",
1106       "xxxx 14 4 w a g False\n",
1107       "xxxx 14 5 w b g False\n",
1108       "xxxx 14 6 w g f False\n",
1109       "xxxx 14 7 w g g False\n",
1110       "xxxx 14 8 w g g False\n",
1111       "xxxx 14 9 w f w False\n",
1112       "xxxx 14 10 w g y False\n",
1113       "seq1 14 11 w g w True\n",
1114       "xxxx 14 12 w a y False\n",
1115       "xxxx 14 13 w e a False\n",
1116       "xxxx 14 14 w f e False\n",
1117       "xxxx 14 15 w b z False\n",
1118       "xxxx 14 16 w f x False\n",
1119       "xxxx 14 17 w c x False\n",
1120       "xxxx 14 18 w b f False\n",
1121       "xxxx 14 19 w a y False\n",
1122       "xxxx 14 20 w b b False\n",
1123       "seq1 15 0 y ! w False\n",
1124       "xxxx 15 1 y g g False\n",
1125       "xxxx 15 2 y f u False\n",
1126       "xxxx 15 3 y h g False\n",
1127       "xxxx 15 4 y a g False\n",
1128       "xxxx 15 5 y b f False\n",
1129       "xxxx 15 6 y g g False\n",
1130       "xxxx 15 7 y g g False\n",
1131       "xxxx 15 8 y g w False\n",
1132       "xxxx 15 9 y f y False\n",
1133       "xxxx 15 10 y g w False\n",
1134       "seq1 15 11 y g y True\n",
1135       "seq2 15 12 y a a True\n",
1136       "seq2 15 13 y e e True\n",
1137       "xxxx 15 14 y f z False\n",
1138       "xxxx 15 15 y b x False\n",
1139       "xxxx 15 16 y f x False\n",
1140       "xxxx 15 17 y c f False\n",
1141       "xxxx 15 18 y b y False\n",
1142       "xxxx 15 19 y a b False\n",
1143       "xxxx 15 20 y b x False\n",
1144       "seq1 16 0 z ! g False\n",
1145       "xxxx 16 1 z g u False\n",
1146       "xxxx 16 2 z f g False\n",
1147       "xxxx 16 3 z h g False\n",
1148       "xxxx 16 4 z a f False\n",
1149       "xxxx 16 5 z b g False\n",
1150       "xxxx 16 6 z g g False\n",
1151       "xxxx 16 7 z g w False\n",
1152       "xxxx 16 8 z g y False\n",
1153       "xxxx 16 9 z f w False\n",
1154       "xxxx 16 10 z g y False\n",
1155       "xxxx 16 11 z g a False\n",
1156       "xxxx 16 12 z a e False\n",
1157       "seq1 16 13 z e z True\n",
1158       "xxxx 16 14 z f x False\n",
1159       "xxxx 16 15 z b x False\n",
1160       "xxxx 16 16 z f f False\n",
1161       "xxxx 16 17 z c y False\n",
1162       "xxxx 16 18 z b b False\n",
1163       "xxxx 16 19 z a x False\n",
1164       "xxxx 16 20 z b f False\n",
1165       "seq1 17 0 x ! u False\n",
1166       "xxxx 17 1 x g g False\n",
1167       "xxxx 17 2 x f g False\n",
1168       "xxxx 17 3 x h f False\n",
1169       "xxxx 17 4 x a g False\n",
1170       "xxxx 17 5 x b g False\n",
1171       "xxxx 17 6 x g w False\n",
1172       "xxxx 17 7 x g y False\n",
1173       "xxxx 17 8 x g w False\n",
1174       "xxxx 17 9 x f y False\n",
1175       "xxxx 17 10 x g a False\n",
1176       "xxxx 17 11 x g e False\n",
1177       "xxxx 17 12 x a z False\n",
1178       "seq1 17 13 x e x True\n",
1179       "xxxx 17 14 x f x False\n",
1180       "xxxx 17 15 x b f False\n",
1181       "xxxx 17 16 x f y False\n",
1182       "xxxx 17 17 x c b False\n",
1183       "xxxx 17 18 x b x False\n",
1184       "xxxx 17 19 x a f False\n",
1185       "xxxx 17 20 x b c False\n",
1186       "seq1 18 0 x ! g False\n",
1187       "xxxx 18 1 x g g False\n",
1188       "xxxx 18 2 x f f False\n",
1189       "xxxx 18 3 x h g False\n",
1190       "xxxx 18 4 x a g False\n",
1191       "xxxx 18 5 x b w False\n",
1192       "xxxx 18 6 x g y False\n",
1193       "xxxx 18 7 x g w False\n",
1194       "xxxx 18 8 x g y False\n",
1195       "xxxx 18 9 x f a False\n",
1196       "xxxx 18 10 x g e False\n",
1197       "xxxx 18 11 x g z False\n",
1198       "xxxx 18 12 x a x False\n",
1199       "seq1 18 13 x e x True\n",
1200       "seq2 18 14 x f f True\n",
1201       "xxxx 18 15 x b y False\n",
1202       "xxxx 18 16 x f b False\n",
1203       "xxxx 18 17 x c x False\n",
1204       "xxxx 18 18 x b f False\n",
1205       "xxxx 18 19 x a c False\n",
1206       "xxxx 18 20 x b b False\n",
1207       "seq1 19 0 y ! g False\n",
1208       "xxxx 19 1 y g f False\n",
1209       "xxxx 19 2 y f g False\n",
1210       "xxxx 19 3 y h g False\n",
1211       "xxxx 19 4 y a w False\n",
1212       "xxxx 19 5 y b y False\n",
1213       "xxxx 19 6 y g w False\n",
1214       "xxxx 19 7 y g y False\n",
1215       "xxxx 19 8 y g a False\n",
1216       "xxxx 19 9 y f e False\n",
1217       "xxxx 19 10 y g z False\n",
1218       "xxxx 19 11 y g x False\n",
1219       "xxxx 19 12 y a x False\n",
1220       "xxxx 19 13 y e f False\n",
1221       "seq1 19 14 y f y True\n",
1222       "seq2 19 15 y b b True\n",
1223       "xxxx 19 16 y f x False\n",
1224       "xxxx 19 17 y c f False\n",
1225       "xxxx 19 18 y b c False\n",
1226       "xxxx 19 19 y a b False\n",
1227       "xxxx 19 20 y b a False\n",
1228       "seq1 20 0 x ! f False\n",
1229       "xxxx 20 1 x g g False\n",
1230       "xxxx 20 2 x f g False\n",
1231       "xxxx 20 3 x h w False\n",
1232       "xxxx 20 4 x a y False\n",
1233       "xxxx 20 5 x b w False\n",
1234       "xxxx 20 6 x g y False\n",
1235       "xxxx 20 7 x g a False\n",
1236       "xxxx 20 8 x g e False\n",
1237       "xxxx 20 9 x f z False\n",
1238       "xxxx 20 10 x g x False\n",
1239       "xxxx 20 11 x g x False\n",
1240       "xxxx 20 12 x a f False\n",
1241       "xxxx 20 13 x e y False\n",
1242       "xxxx 20 14 x f b False\n",
1243       "seq1 20 15 x b x True\n",
1244       "seq2 20 16 x f f True\n",
1245       "seq2 20 17 x c c True\n",
1246       "seq2 20 18 x b b True\n",
1247       "seq2 20 19 x a a True\n",
1248       "seq2 20 20 x b b True\n",
1249       "T T . . . . . . . . . . . . . . . . . . .\n",
1250       ". T . . . . . . . . . . . . . . . . . . .\n",
1251       ". T . . . . . . . . . . . . . . . . . . .\n",
1252       ". T . . . . . . . . . . . . . . . . . . .\n",
1253       ". T T . . . . . . . . . . . . . . . . . .\n",
1254       ". . T . . . . . . . . . . . . . . . . . .\n",
1255       ". . T T . . . . . . . . . . . . . . . . .\n",
1256       ". . . T T T . . . . . . . . . . . . . . .\n",
1257       ". . . . . T . . . . . . . . . . . . . . .\n",
1258       ". . . . . T . . . . . . . . . . . . . . .\n",
1259       ". . . . . T T . . . . . . . . . . . . . .\n",
1260       ". . . . . . T T T T T T . . . . . . . . .\n",
1261       ". . . . . . . . . . . T . . . . . . . . .\n",
1262       ". . . . . . . . . . . T . . . . . . . . .\n",
1263       ". . . . . . . . . . . T . . . . . . . . .\n",
1264       ". . . . . . . . . . . T T T . . . . . . .\n",
1265       ". . . . . . . . . . . . . T . . . . . . .\n",
1266       ". . . . . . . . . . . . . T . . . . . . .\n",
1267       ". . . . . . . . . . . . . T T . . . . . .\n",
1268       ". . . . . . . . . . . . . . T T . . . . .\n",
1269       ". . . . . . . . . . . . . . . T T T T T T\n"
1270      ]
1271     }
1272    ],
1273    "source": [
1274     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True, debug=True)\n",
1275     "print(show_table(t))"
1276    ]
1277   },
1278   {
1279    "cell_type": "code",
1280    "execution_count": 22,
1281    "metadata": {
1282     "collapsed": false
1283    },
1284    "outputs": [
1285     {
1286      "data": {
1287       "text/plain": [
1288        "'gWXUZfZXhUabYUWgUggfggWYWYaeZXXfYbXfcbab'"
1289       ]
1290      },
1291      "execution_count": 22,
1292      "metadata": {},
1293      "output_type": "execute_result"
1294     }
1295    ],
1296    "source": [
1297     "show_backtrace(bp)"
1298    ]
1299   },
1300   {
1301    "cell_type": "code",
1302    "execution_count": 23,
1303    "metadata": {
1304     "collapsed": false
1305    },
1306    "outputs": [
1307     {
1308      "name": "stdout",
1309      "output_type": "stream",
1310      "text": [
1311       "T T . . . . . . . . . . . . . . . . . . .\n",
1312       ". T . . . . . . . . . . . . . . . . . . .\n",
1313       ". T . . . . . . . . . . . . . . . . . . .\n",
1314       ". T . . . . . . . . . . . . . . . . . . .\n",
1315       ". T T . . . . . . . . . . . . . . . . . .\n",
1316       ". . T . . . . . . . . . . . . . . . . . .\n",
1317       ". . T T . . . . . . . . . . . . . . . . .\n",
1318       ". . . T T T . . . . . . . . . . . . . . .\n",
1319       ". . . . . T . . . . . . . . . . . . . . .\n",
1320       ". . . . . T . . . . . . . . . . . . . . .\n",
1321       ". . . . . T T . . . . . . . . . . . . . .\n",
1322       ". . . . . . T T T T T T . . . . . . . . .\n",
1323       ". . . . . . . . . . . T . . . . . . . . .\n",
1324       ". . . . . . . . . . . T . . . . . . . . .\n",
1325       ". . . . . . . . . . . T . . . . . . . . .\n",
1326       ". . . . . . . . . . . T T T . . . . . . .\n",
1327       ". . . . . . . . . . . . . T . . . . . . .\n",
1328       ". . . . . . . . . . . . . T . . . . . . .\n",
1329       ". . . . . . . . . . . . . T T . . . . . .\n",
1330       ". . . . . . . . . . . . . . T T . . . . .\n",
1331       ". . . . . . . . . . . . . . . T T T T T T\n",
1332       "gWXUZfZXhUabYUWgUggfggWYWYaeZXXfYbXfcbab\n"
1333      ]
1334     },
1335     {
1336      "data": {
1337       "text/plain": [
1338        "True"
1339       ]
1340      },
1341      "execution_count": 23,
1342      "metadata": {},
1343      "output_type": "execute_result"
1344     }
1345    ],
1346    "source": [
1347     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1348     "print(show_table(t))\n",
1349     "print(show_backtrace(bp))\n",
1350     "v"
1351    ]
1352   },
1353   {
1354    "cell_type": "code",
1355    "execution_count": 24,
1356    "metadata": {
1357     "collapsed": false
1358    },
1359    "outputs": [
1360     {
1361      "data": {
1362       "text/plain": [
1363        "('dcgegfedbddhhbgafhbgggcdhgbhbhghbfddbedcacbdhbafbg',\n",
1364        " 'bbbahedbceeebafgghffehgbeacgfcbhccffcacccfacgegcfc',\n",
1365        " 'dcgbbbegfeadhbedddbceheebahfbgaggfhhbgggfcdfhehggbbhbheghbfdadcgbfecbhdccacfcbdhfcabcaccffbgacgegcfc',\n",
1366        " 100)"
1367       ]
1368      },
1369      "execution_count": 24,
1370      "metadata": {},
1371      "output_type": "execute_result"
1372     }
1373    ],
1374    "source": [
1375     "s1 = make_string(50)\n",
1376     "s2 = make_string(50)\n",
1377     "il = interleave(s1, s2)\n",
1378     "s1, s2, il, len(il)"
1379    ]
1380   },
1381   {
1382    "cell_type": "code",
1383    "execution_count": 25,
1384    "metadata": {
1385     "collapsed": false
1386    },
1387    "outputs": [
1388     {
1389      "name": "stdout",
1390      "output_type": "stream",
1391      "text": [
1392       "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1393       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1394       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1395       ". . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1396       ". . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1397       ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1398       ". . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1399       ". . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1400       ". . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1401       ". . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1402       ". . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1403       ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1404       ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1405       ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1406       ". . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1407       ". . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1408       ". . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1409       ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1410       ". . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1411       ". . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1412       ". . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1413       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1414       ". . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1415       ". . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
1416       ". . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . .\n",
1417       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . .\n",
1418       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
1419       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . .\n",
1420       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . .\n",
1421       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
1422       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
1423       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
1424       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . .\n",
1425       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . .\n",
1426       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . .\n",
1427       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . .\n",
1428       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . .\n",
1429       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . .\n",
1430       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . .\n",
1431       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . .\n",
1432       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . .\n",
1433       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . .\n",
1434       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T\n",
1435       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1436       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1437       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1438       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1439       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1440       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1441       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1442       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
1443       "dcgBBBegfeAdHbEddDBCEhEEBAhFbgaGGfhHbgggFcdFhEHgGbBhbhEghbfdAdCGbFeCBHdcCaCFcbdhFCAbCaCCfFbgACGEGCFC\n"
1444      ]
1445     },
1446     {
1447      "data": {
1448       "text/plain": [
1449        "True"
1450       ]
1451      },
1452      "execution_count": 25,
1453      "metadata": {},
1454      "output_type": "execute_result"
1455     }
1456    ],
1457    "source": [
1458     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1459     "print(show_table(t))\n",
1460     "print(show_backtrace(bp))\n",
1461     "v"
1462    ]
1463   },
1464   {
1465    "cell_type": "code",
1466    "execution_count": 26,
1467    "metadata": {
1468     "collapsed": false
1469    },
1470    "outputs": [
1471     {
1472      "name": "stdout",
1473      "output_type": "stream",
1474      "text": [
1475       "100 loops, best of 3: 1.77 ms per loop\n"
1476      ]
1477     }
1478    ],
1479    "source": [
1480     "%%timeit\n",
1481     "is_interleave(s2, s1, il)"
1482    ]
1483   },
1484   {
1485    "cell_type": "code",
1486    "execution_count": 27,
1487    "metadata": {
1488     "collapsed": false
1489    },
1490    "outputs": [
1491     {
1492      "name": "stdout",
1493      "output_type": "stream",
1494      "text": [
1495       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1496       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1497       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1498       "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1499       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1500       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1501       ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1502       ". . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1503       ". . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1504       ". . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1505       ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1506       ". . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1507       ". . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1508       ". . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1509       ". . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1510       ". . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1511       ". . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1512       ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1513       ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1514       ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1515       ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1516       ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1517       ". . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1518       ". . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1519       ". . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1520       ". . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1521       ". . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1522       ". . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1523       ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1524       ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1525       ". . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1526       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1527       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1528       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1529       ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1530       ". . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
1531       ". . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . .\n",
1532       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
1533       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n",
1534       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . .\n",
1535       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . .\n",
1536       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . .\n",
1537       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . .\n",
1538       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
1539       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
1540       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . .\n",
1541       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . .\n",
1542       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . .\n",
1543       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . .\n",
1544       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
1545       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T T T\n",
1546       "DCGbbbEGFEaDhBedDDbceHeebaHfBGAggFhHBGGGfCDfHehgGbBHBHeGHBFDaDcgBfEcbhDcCAcfCBDHfcaBcAccfFBGacgegcfc\n"
1547      ]
1548     },
1549     {
1550      "data": {
1551       "text/plain": [
1552        "True"
1553       ]
1554      },
1555      "execution_count": 27,
1556      "metadata": {},
1557      "output_type": "execute_result"
1558     }
1559    ],
1560    "source": [
1561     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1562     "print(show_table(t))\n",
1563     "print(show_backtrace(bp))\n",
1564     "v"
1565    ]
1566   },
1567   {
1568    "cell_type": "code",
1569    "execution_count": 28,
1570    "metadata": {
1571     "collapsed": false
1572    },
1573    "outputs": [
1574     {
1575      "data": {
1576       "text/plain": [
1577        "True"
1578       ]
1579      },
1580      "execution_count": 28,
1581      "metadata": {},
1582      "output_type": "execute_result"
1583     }
1584    ],
1585    "source": [
1586     "show_backtrace(bp).lower() == il"
1587    ]
1588   },
1589   {
1590    "cell_type": "code",
1591    "execution_count": 29,
1592    "metadata": {
1593     "collapsed": false
1594    },
1595    "outputs": [
1596     {
1597      "data": {
1598       "text/plain": [
1599        "('aebeedbbfabfbddehbagecgaadbbedaedghchdaghhaghedhbe', False, False)"
1600       ]
1601      },
1602      "execution_count": 29,
1603      "metadata": {},
1604      "output_type": "execute_result"
1605     }
1606    ],
1607    "source": [
1608     "s3 = make_string(50)\n",
1609     "s3, is_interleave(s1, s3, il), is_interleave(s2, s3, il)"
1610    ]
1611   },
1612   {
1613    "cell_type": "code",
1614    "execution_count": 30,
1615    "metadata": {
1616     "collapsed": false
1617    },
1618    "outputs": [
1619     {
1620      "name": "stdout",
1621      "output_type": "stream",
1622      "text": [
1623       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1624       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1625       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1626       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1627       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1628       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1629       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1630       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1631       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1632       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1633       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1634       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1635       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1636       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1637       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1638       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1639       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1640       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1641       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1642       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1643       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1644       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1645       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1646       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1647       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1648       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1649       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1650       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1651       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1652       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1653       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1654       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1655       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1656       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1657       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1658       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1659       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1660       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1661       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1662       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1663       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1664       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1665       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1666       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1667       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1668       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1669       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1670       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1671       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1672       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1673       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
1674       "DCG\n"
1675      ]
1676     },
1677     {
1678      "data": {
1679       "text/plain": [
1680        "False"
1681       ]
1682      },
1683      "execution_count": 30,
1684      "metadata": {},
1685      "output_type": "execute_result"
1686     }
1687    ],
1688    "source": [
1689     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1690     "print(show_table(t))\n",
1691     "print(show_backtrace(bp))\n",
1692     "v"
1693    ]
1694   },
1695   {
1696    "cell_type": "code",
1697    "execution_count": 31,
1698    "metadata": {
1699     "collapsed": true
1700    },
1701    "outputs": [],
1702    "source": [
1703     "def is_interleave_recursive(s1, s2, s3):\n",
1704     "    if not s1:\n",
1705     "        return s2 == s3\n",
1706     "    elif not s2:\n",
1707     "        return s1 == s3\n",
1708     "    else:\n",
1709     "        if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
1710     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n",
1711     "        elif s1[-1] == s3[-1]:\n",
1712     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
1713     "        elif s2[-1] == s3[-1]:\n",
1714     "            return is_interleave(s1, s2[:-1], s3[:-1])\n",
1715     "        else:\n",
1716     "            return False"
1717    ]
1718   },
1719   {
1720    "cell_type": "code",
1721    "execution_count": 32,
1722    "metadata": {
1723     "collapsed": true
1724    },
1725    "outputs": [],
1726    "source": [
1727     "s1 = make_string(500)\n",
1728     "s2 = make_string(500)\n",
1729     "s3 = make_string(500)\n",
1730     "s12 = interleave(s1, s2)\n",
1731     "s23 = interleave(s2, s3)"
1732    ]
1733   },
1734   {
1735    "cell_type": "code",
1736    "execution_count": 33,
1737    "metadata": {
1738     "collapsed": false
1739    },
1740    "outputs": [
1741     {
1742      "data": {
1743       "text/plain": [
1744        "True"
1745       ]
1746      },
1747      "execution_count": 33,
1748      "metadata": {},
1749      "output_type": "execute_result"
1750     }
1751    ],
1752    "source": [
1753     "is_interleave_recursive(s1, s2, s12)"
1754    ]
1755   },
1756   {
1757    "cell_type": "code",
1758    "execution_count": 34,
1759    "metadata": {
1760     "collapsed": false
1761    },
1762    "outputs": [
1763     {
1764      "data": {
1765       "text/plain": [
1766        "False"
1767       ]
1768      },
1769      "execution_count": 34,
1770      "metadata": {},
1771      "output_type": "execute_result"
1772     }
1773    ],
1774    "source": [
1775     "is_interleave_recursive(s1, s2, s23)"
1776    ]
1777   },
1778   {
1779    "cell_type": "markdown",
1780    "metadata": {},
1781    "source": [
1782     "## Example"
1783    ]
1784   },
1785   {
1786    "cell_type": "code",
1787    "execution_count": 35,
1788    "metadata": {
1789     "collapsed": true
1790    },
1791    "outputs": [],
1792    "source": [
1793     "def show_annotated_table(table, bps):\n",
1794     "    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",
1795     "        for i in sorted(set([k[0] for k in table])))"
1796    ]
1797   },
1798   {
1799    "cell_type": "code",
1800    "execution_count": 36,
1801    "metadata": {
1802     "collapsed": true
1803    },
1804    "outputs": [],
1805    "source": [
1806     "def show_backtrace_star(bps):\n",
1807     "    i = max([0] + [k[0] for k in bps])\n",
1808     "    j = max([0] + [k[1] for k in bps])\n",
1809     "    chars = ''\n",
1810     "    stars = ''\n",
1811     "    if (i, j) in bps:\n",
1812     "        while i != 0 or j != 0:\n",
1813     "            chars += bps[i, j][2]\n",
1814     "            if bps[i, j][3] == 'seq1':\n",
1815     "                stars += '*'\n",
1816     "            else:\n",
1817     "                stars += ' '\n",
1818     "            i, j = bps[i, j][0], bps[i, j][1] \n",
1819     "        return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n",
1820     "    else:\n",
1821     "        return ''"
1822    ]
1823   },
1824   {
1825    "cell_type": "code",
1826    "execution_count": 37,
1827    "metadata": {
1828     "collapsed": false
1829    },
1830    "outputs": [
1831     {
1832      "data": {
1833       "text/plain": [
1834        "('badbabcddb', 'dcaacccbaa', 'bdacaacccdbbabacdadb', 20)"
1835       ]
1836      },
1837      "execution_count": 37,
1838      "metadata": {},
1839      "output_type": "execute_result"
1840     }
1841    ],
1842    "source": [
1843     "s1 = make_string(10, alphabet='abcd')\n",
1844     "s2 = make_string(10, alphabet='abcd')\n",
1845     "s3 = make_string(10, alphabet='abcd')\n",
1846     "il = interleave(s1, s2)\n",
1847     "s1, s2, il, len(il)"
1848    ]
1849   },
1850   {
1851    "cell_type": "code",
1852    "execution_count": 38,
1853    "metadata": {
1854     "collapsed": false
1855    },
1856    "outputs": [
1857     {
1858      "name": "stdout",
1859      "output_type": "stream",
1860      "text": [
1861       "* . . . . . . . . . .\n",
1862       "b d . . . . . . . . .\n",
1863       ". a c a a c c c . . .\n",
1864       ". . . . . . . d b . .\n",
1865       ". . . . . . . b b a .\n",
1866       ". . . . . . . . a . .\n",
1867       ". . . . . . . . b a .\n",
1868       ". . . . . . . . . c .\n",
1869       ". . . . . . . . . d a\n",
1870       ". . . . . . . . . . d\n",
1871       ". . . . . . . . . . b\n",
1872       "BdAcaacccDbBABaCDaDB\n",
1873       "bdacaacccdbbabacdadb\n",
1874       "* *      * *** ** **\n"
1875      ]
1876     },
1877     {
1878      "data": {
1879       "text/plain": [
1880        "True"
1881       ]
1882      },
1883      "execution_count": 38,
1884      "metadata": {},
1885      "output_type": "execute_result"
1886     }
1887    ],
1888    "source": [
1889     "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n",
1890     "print(show_annotated_table(t, bp))\n",
1891     "print(show_backtrace(bp))\n",
1892     "print(show_backtrace_star(bp))\n",
1893     "v"
1894    ]
1895   },
1896   {
1897    "cell_type": "code",
1898    "execution_count": 39,
1899    "metadata": {
1900     "collapsed": false
1901    },
1902    "outputs": [
1903     {
1904      "name": "stdout",
1905      "output_type": "stream",
1906      "text": [
1907       "* b . . . . . . . . .\n",
1908       ". d a . . . . . . . .\n",
1909       ". . c . . . . . . . .\n",
1910       ". . a . . . . . . . .\n",
1911       ". . a . . . . . . . .\n",
1912       ". . c . . . . . . . .\n",
1913       ". . c . . . . . . . .\n",
1914       ". . c d b . . . . . .\n",
1915       ". . . b b a b . . . .\n",
1916       ". . . . a . a c d . .\n",
1917       ". . . . . . . . a d b\n",
1918       "bDaCAACCCdbBabAcdAdb\n",
1919       "bdacaacccdbbabacdadb\n",
1920       " * ******  *  *  *  \n"
1921      ]
1922     },
1923     {
1924      "data": {
1925       "text/plain": [
1926        "True"
1927       ]
1928      },
1929      "execution_count": 39,
1930      "metadata": {},
1931      "output_type": "execute_result"
1932     }
1933    ],
1934    "source": [
1935     "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n",
1936     "print(show_annotated_table(t, bp))\n",
1937     "print(show_backtrace(bp))\n",
1938     "print(show_backtrace_star(bp))\n",
1939     "v"
1940    ]
1941   },
1942   {
1943    "cell_type": "code",
1944    "execution_count": 40,
1945    "metadata": {
1946     "collapsed": false
1947    },
1948    "outputs": [
1949     {
1950      "name": "stdout",
1951      "output_type": "stream",
1952      "text": [
1953       "* . . . . . . . . . .\n",
1954       "b . . . . . . . . . .\n",
1955       ". . . . . . . . . . .\n",
1956       ". . . . . . . . . . .\n",
1957       ". . . . . . . . . . .\n",
1958       ". . . . . . . . . . .\n",
1959       ". . . . . . . . . . .\n",
1960       ". . . . . . . . . . .\n",
1961       ". . . . . . . . . . .\n",
1962       ". . . . . . . . . . .\n",
1963       ". . . . . . . . . . .\n",
1964       "B\n",
1965       "b\n",
1966       "*\n"
1967      ]
1968     },
1969     {
1970      "data": {
1971       "text/plain": [
1972        "False"
1973       ]
1974      },
1975      "execution_count": 40,
1976      "metadata": {},
1977      "output_type": "execute_result"
1978     }
1979    ],
1980    "source": [
1981     "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n",
1982     "print(show_annotated_table(t, bp))\n",
1983     "print(show_backtrace(bp))\n",
1984     "print(show_backtrace_star(bp))\n",
1985     "v"
1986    ]
1987   },
1988   {
1989    "cell_type": "code",
1990    "execution_count": 41,
1991    "metadata": {
1992     "collapsed": false
1993    },
1994    "outputs": [
1995     {
1996      "name": "stdout",
1997      "output_type": "stream",
1998      "text": [
1999       "* . . . . . . . . . .\n",
2000       ". . . . . . . . . . .\n",
2001       ". . . . . . . . . . .\n",
2002       ". . . . . . . . . . .\n",
2003       ". . . . . . . . . . .\n",
2004       ". . . . . . . . . . .\n",
2005       ". . . . . . . . . . .\n",
2006       ". . . . . . . . . . .\n",
2007       ". . . . . . . . . . .\n",
2008       ". . . . . . . . . . .\n",
2009       ". . . . . . . . . . .\n",
2010       "\n",
2011       "\n"
2012      ]
2013     },
2014     {
2015      "data": {
2016       "text/plain": [
2017        "False"
2018       ]
2019      },
2020      "execution_count": 41,
2021      "metadata": {},
2022      "output_type": "execute_result"
2023     }
2024    ],
2025    "source": [
2026     "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n",
2027     "print(show_annotated_table(t, bp))\n",
2028     "print(show_backtrace(bp))\n",
2029     "print(show_backtrace_star(bp))\n",
2030     "v"
2031    ]
2032   },
2033   {
2034    "cell_type": "markdown",
2035    "metadata": {
2036     "collapsed": true
2037    },
2038    "source": [
2039     "# Make puzzle data"
2040    ]
2041   },
2042   {
2043    "cell_type": "code",
2044    "execution_count": 58,
2045    "metadata": {
2046     "collapsed": false
2047    },
2048    "outputs": [],
2049    "source": [
2050     "my_bill = make_string(200)\n",
2051     "friend_bill = make_string(200)\n",
2052     "other_bills = [make_string(200) for _ in range(98)]\n",
2053     "\n",
2054     "target_interleaved = interleave(my_bill, friend_bill)\n",
2055     "mine_interleaved = [interleave(my_bill, o) for o in random.sample(other_bills, 24)]\n",
2056     "friend_interleaved = [interleave(friend_bill, o) for o in random.sample(other_bills, 13)]\n",
2057     "other_interleaved = []\n",
2058     "for _ in range(103):\n",
2059     "    s1, s2 = random.sample(other_bills, 2)\n",
2060     "    other_interleaved += [interleave(s1, s2)]"
2061    ]
2062   },
2063   {
2064    "cell_type": "code",
2065    "execution_count": 59,
2066    "metadata": {
2067     "collapsed": false
2068    },
2069    "outputs": [],
2070    "source": [
2071     "all_targets = [target_interleaved] + mine_interleaved + friend_interleaved + other_interleaved"
2072    ]
2073   },
2074   {
2075    "cell_type": "code",
2076    "execution_count": 60,
2077    "metadata": {
2078     "collapsed": false
2079    },
2080    "outputs": [
2081     {
2082      "name": "stdout",
2083      "output_type": "stream",
2084      "text": [
2085       "CPU times: user 4.55 s, sys: 4 ms, total: 4.56 s\n",
2086       "Wall time: 4.56 s\n"
2087      ]
2088     },
2089     {
2090      "data": {
2091       "text/plain": [
2092        "[0]"
2093       ]
2094      },
2095      "execution_count": 60,
2096      "metadata": {},
2097      "output_type": "execute_result"
2098     }
2099    ],
2100    "source": [
2101     "%time [i for i, s12 in enumerate(all_targets) if is_interleave(my_bill, friend_bill, s12)]"
2102    ]
2103   },
2104   {
2105    "cell_type": "code",
2106    "execution_count": 61,
2107    "metadata": {
2108     "collapsed": false
2109    },
2110    "outputs": [
2111     {
2112      "name": "stdout",
2113      "output_type": "stream",
2114      "text": [
2115       "CPU times: user 1.03 s, sys: 4 ms, total: 1.04 s\n",
2116       "Wall time: 1.03 s\n"
2117      ]
2118     },
2119     {
2120      "data": {
2121       "text/plain": [
2122        "[0]"
2123       ]
2124      },
2125      "execution_count": 61,
2126      "metadata": {},
2127      "output_type": "execute_result"
2128     }
2129    ],
2130    "source": [
2131     "%time [i for i, s12 in enumerate(all_targets) if is_interleave_recursive(my_bill, friend_bill, s12)]"
2132    ]
2133   },
2134   {
2135    "cell_type": "code",
2136    "execution_count": 62,
2137    "metadata": {
2138     "collapsed": true
2139    },
2140    "outputs": [],
2141    "source": [
2142     "bill_set = all_targets + random.sample(other_bills, 8)\n",
2143     "random.shuffle(bill_set)\n",
2144     "bill_set = [my_bill, friend_bill] + bill_set\n",
2145     "\n",
2146     "with open('09-bills.txt', 'w') as f:\n",
2147     "    for i, b in enumerate(bill_set):\n",
2148     "        f.write('{}: {}\\n'.format(i, b))\n"
2149    ]
2150   },
2151   {
2152    "cell_type": "code",
2153    "execution_count": null,
2154    "metadata": {
2155     "collapsed": true
2156    },
2157    "outputs": [],
2158    "source": []
2159   }
2160  ],
2161  "metadata": {
2162   "kernelspec": {
2163    "display_name": "Python 3",
2164    "language": "python",
2165    "name": "python3"
2166   },
2167   "language_info": {
2168    "codemirror_mode": {
2169     "name": "ipython",
2170     "version": 3
2171    },
2172    "file_extension": ".py",
2173    "mimetype": "text/x-python",
2174    "name": "python",
2175    "nbconvert_exporter": "python",
2176    "pygments_lexer": "ipython3",
2177    "version": "3.5.2"
2178   }
2179  },
2180  "nbformat": 4,
2181  "nbformat_minor": 1
2182 }