06-tour-shapes/tour-shapes-problem-creation.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "markdown",
   5    "metadata": {},
   6    "source": [
   7     "Given a sequence of {F|L|R}, each of which is \"move forward one step\", \"turn left, then move forward one step\", \"turn right, then move forward one step\":\n",
   8     "1. which tours are closed?\n",
   9     "2. what is the area enclosed by the tour?"
  10    ]
  11   },
  12   {
  13    "cell_type": "code",
  14    "execution_count": 69,
  15    "metadata": {
  16     "collapsed": true
  17    },
  18    "outputs": [],
  19    "source": [
  20     "import collections\n",
  21     "import enum\n",
  22     "import random"
  23    ]
  24   },
  25   {
  26    "cell_type": "code",
  27    "execution_count": 20,
  28    "metadata": {
  29     "collapsed": true
  30    },
  31    "outputs": [],
  32    "source": [
  33     "class Direction(enum.Enum):\n",
  34     "    UP = 1\n",
  35     "    RIGHT = 2\n",
  36     "    DOWN = 3\n",
  37     "    LEFT = 4\n",
  38     "    \n",
  39     "turn_lefts = {Direction.UP: Direction.LEFT, Direction.LEFT: Direction.DOWN,\n",
  40     "              Direction.DOWN: Direction.RIGHT, Direction.RIGHT: Direction.UP}\n",
  41     "\n",
  42     "turn_rights = {Direction.UP: Direction.RIGHT, Direction.RIGHT: Direction.DOWN,\n",
  43     "               Direction.DOWN: Direction.LEFT, Direction.LEFT: Direction.UP}\n",
  44     "\n",
  45     "def turn_left(d):\n",
  46     "    return turn_lefts[d]\n",
  47     "\n",
  48     "def turn_right(d):\n",
  49     "    return turn_rights[d]\n"
  50    ]
  51   },
  52   {
  53    "cell_type": "code",
  54    "execution_count": 8,
  55    "metadata": {
  56     "collapsed": true
  57    },
  58    "outputs": [],
  59    "source": [
  60     "Step = collections.namedtuple('Step', ['x', 'y', 'dir'])"
  61    ]
  62   },
  63   {
  64    "cell_type": "code",
  65    "execution_count": 30,
  66    "metadata": {
  67     "collapsed": true
  68    },
  69    "outputs": [],
  70    "source": [
  71     "def advance(step, d):\n",
  72     "    if d == Direction.UP:\n",
  73     "        return Step(step.x, step.y+1, d)\n",
  74     "    elif d == Direction.DOWN:\n",
  75     "        return Step(step.x, step.y-1, d)\n",
  76     "    elif d == Direction.LEFT:\n",
  77     "        return Step(step.x-1, step.y, d)\n",
  78     "    elif d == Direction.RIGHT:\n",
  79     "        return Step(step.x+1, step.y, d)"
  80    ]
  81   },
  82   {
  83    "cell_type": "code",
  84    "execution_count": 28,
  85    "metadata": {
  86     "collapsed": true
  87    },
  88    "outputs": [],
  89    "source": [
  90     "def trace_tour(tour):\n",
  91     "    current = Step(0, 0, Direction.RIGHT)\n",
  92     "    trace = [current]\n",
  93     "    for s in tour:\n",
  94     "        if s == 'F':\n",
  95     "            current = advance(current, current.dir)\n",
  96     "        elif s == 'L':\n",
  97     "            current = advance(current, turn_left(current.dir))\n",
  98     "        elif s == 'R':\n",
  99     "            current = advance(current, turn_right(current.dir))\n",
 100     "        trace += [current]\n",
 101     "    return trace    "
 102    ]
 103   },
 104   {
 105    "cell_type": "code",
 106    "execution_count": 9,
 107    "metadata": {
 108     "collapsed": true
 109    },
 110    "outputs": [],
 111    "source": [
 112     "k = Step(1, 2, 3)"
 113    ]
 114   },
 115   {
 116    "cell_type": "code",
 117    "execution_count": 10,
 118    "metadata": {},
 119    "outputs": [
 120     {
 121      "data": {
 122       "text/plain": [
 123        "Step(x=1, y=2, dir=3)"
 124       ]
 125      },
 126      "execution_count": 10,
 127      "metadata": {},
 128      "output_type": "execute_result"
 129     }
 130    ],
 131    "source": [
 132     "k"
 133    ]
 134   },
 135   {
 136    "cell_type": "code",
 137    "execution_count": 11,
 138    "metadata": {},
 139    "outputs": [
 140     {
 141      "data": {
 142       "text/plain": [
 143        "__main__.Step"
 144       ]
 145      },
 146      "execution_count": 11,
 147      "metadata": {},
 148      "output_type": "execute_result"
 149     }
 150    ],
 151    "source": [
 152     "Step"
 153    ]
 154   },
 155   {
 156    "cell_type": "code",
 157    "execution_count": 22,
 158    "metadata": {},
 159    "outputs": [
 160     {
 161      "data": {
 162       "text/plain": [
 163        "<Direction.UP: 1>"
 164       ]
 165      },
 166      "execution_count": 22,
 167      "metadata": {},
 168      "output_type": "execute_result"
 169     }
 170    ],
 171    "source": [
 172     "d = Direction.UP\n",
 173     "d"
 174    ]
 175   },
 176   {
 177    "cell_type": "code",
 178    "execution_count": 23,
 179    "metadata": {},
 180    "outputs": [
 181     {
 182      "data": {
 183       "text/plain": [
 184        "<Direction.RIGHT: 2>"
 185       ]
 186      },
 187      "execution_count": 23,
 188      "metadata": {},
 189      "output_type": "execute_result"
 190     }
 191    ],
 192    "source": [
 193     "turn_right(d)"
 194    ]
 195   },
 196   {
 197    "cell_type": "code",
 198    "execution_count": 21,
 199    "metadata": {},
 200    "outputs": [
 201     {
 202      "data": {
 203       "text/plain": [
 204        "{<Direction.LEFT: 4>: <Direction.UP: 1>,\n",
 205        " <Direction.UP: 1>: <Direction.RIGHT: 2>,\n",
 206        " <Direction.DOWN: 3>: <Direction.LEFT: 4>,\n",
 207        " <Direction.RIGHT: 2>: <Direction.DOWN: 3>}"
 208       ]
 209      },
 210      "execution_count": 21,
 211      "metadata": {},
 212      "output_type": "execute_result"
 213     }
 214    ],
 215    "source": [
 216     "turn_rights"
 217    ]
 218   },
 219   {
 220    "cell_type": "code",
 221    "execution_count": 31,
 222    "metadata": {},
 223    "outputs": [
 224     {
 225      "data": {
 226       "text/plain": [
 227        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 228        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 229        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 230        " Step(x=2, y=1, dir=<Direction.RIGHT: 2>),\n",
 231        " Step(x=2, y=2, dir=<Direction.UP: 1>)]"
 232       ]
 233      },
 234      "execution_count": 31,
 235      "metadata": {},
 236      "output_type": "execute_result"
 237     }
 238    ],
 239    "source": [
 240     "trace_tour('FLRL')"
 241    ]
 242   },
 243   {
 244    "cell_type": "code",
 245    "execution_count": 33,
 246    "metadata": {},
 247    "outputs": [
 248     {
 249      "data": {
 250       "text/plain": [
 251        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 252        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 253        " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
 254        " Step(x=2, y=1, dir=<Direction.UP: 1>),\n",
 255        " Step(x=3, y=1, dir=<Direction.RIGHT: 2>),\n",
 256        " Step(x=3, y=2, dir=<Direction.UP: 1>),\n",
 257        " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
 258        " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
 259        " Step(x=1, y=1, dir=<Direction.DOWN: 3>),\n",
 260        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
 261        " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
 262       ]
 263      },
 264      "execution_count": 33,
 265      "metadata": {},
 266      "output_type": "execute_result"
 267     }
 268    ],
 269    "source": [
 270     "trace_tour('FFLRLLFLRL')"
 271    ]
 272   },
 273   {
 274    "cell_type": "code",
 275    "execution_count": 34,
 276    "metadata": {},
 277    "outputs": [
 278     {
 279      "data": {
 280       "text/plain": [
 281        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 282        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 283        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 284        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
 285        " Step(x=-1, y=1, dir=<Direction.LEFT: 4>),\n",
 286        " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
 287        " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
 288        " Step(x=-2, y=-1, dir=<Direction.DOWN: 3>),\n",
 289        " Step(x=-2, y=-2, dir=<Direction.DOWN: 3>),\n",
 290        " Step(x=-2, y=-3, dir=<Direction.DOWN: 3>),\n",
 291        " Step(x=-1, y=-3, dir=<Direction.RIGHT: 2>),\n",
 292        " Step(x=0, y=-3, dir=<Direction.RIGHT: 2>),\n",
 293        " Step(x=1, y=-3, dir=<Direction.RIGHT: 2>),\n",
 294        " Step(x=1, y=-2, dir=<Direction.UP: 1>),\n",
 295        " Step(x=1, y=-1, dir=<Direction.UP: 1>),\n",
 296        " Step(x=0, y=-1, dir=<Direction.LEFT: 4>),\n",
 297        " Step(x=0, y=-2, dir=<Direction.DOWN: 3>),\n",
 298        " Step(x=-1, y=-2, dir=<Direction.LEFT: 4>),\n",
 299        " Step(x=-1, y=-1, dir=<Direction.UP: 1>),\n",
 300        " Step(x=-1, y=0, dir=<Direction.UP: 1>),\n",
 301        " Step(x=0, y=0, dir=<Direction.RIGHT: 2>)]"
 302       ]
 303      },
 304      "execution_count": 34,
 305      "metadata": {},
 306      "output_type": "execute_result"
 307     }
 308    ],
 309    "source": [
 310     "trace_tour('FLLFFLFFFLFFLFLLRRFR')"
 311    ]
 312   },
 313   {
 314    "cell_type": "code",
 315    "execution_count": 35,
 316    "metadata": {},
 317    "outputs": [
 318     {
 319      "data": {
 320       "text/plain": [
 321        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 322        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 323        " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
 324        " Step(x=2, y=-1, dir=<Direction.DOWN: 3>),\n",
 325        " Step(x=3, y=-1, dir=<Direction.RIGHT: 2>),\n",
 326        " Step(x=3, y=0, dir=<Direction.UP: 1>),\n",
 327        " Step(x=3, y=1, dir=<Direction.UP: 1>),\n",
 328        " Step(x=4, y=1, dir=<Direction.RIGHT: 2>),\n",
 329        " Step(x=4, y=2, dir=<Direction.UP: 1>),\n",
 330        " Step(x=3, y=2, dir=<Direction.LEFT: 4>),\n",
 331        " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
 332        " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
 333        " Step(x=0, y=2, dir=<Direction.LEFT: 4>),\n",
 334        " Step(x=0, y=3, dir=<Direction.UP: 1>),\n",
 335        " Step(x=0, y=4, dir=<Direction.UP: 1>),\n",
 336        " Step(x=-1, y=4, dir=<Direction.LEFT: 4>),\n",
 337        " Step(x=-1, y=3, dir=<Direction.DOWN: 3>),\n",
 338        " Step(x=-2, y=3, dir=<Direction.LEFT: 4>),\n",
 339        " Step(x=-2, y=2, dir=<Direction.DOWN: 3>),\n",
 340        " Step(x=-1, y=2, dir=<Direction.RIGHT: 2>),\n",
 341        " Step(x=-1, y=1, dir=<Direction.DOWN: 3>),\n",
 342        " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
 343        " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
 344        " Step(x=-1, y=0, dir=<Direction.RIGHT: 2>),\n",
 345        " Step(x=-1, y=-1, dir=<Direction.DOWN: 3>),\n",
 346        " Step(x=0, y=-1, dir=<Direction.RIGHT: 2>),\n",
 347        " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
 348       ]
 349      },
 350      "execution_count": 35,
 351      "metadata": {},
 352      "output_type": "execute_result"
 353     }
 354    ],
 355    "source": [
 356     "trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL')"
 357    ]
 358   },
 359   {
 360    "cell_type": "code",
 361    "execution_count": 112,
 362    "metadata": {
 363     "collapsed": true
 364    },
 365    "outputs": [],
 366    "source": [
 367     "def positions(trace):\n",
 368     "    return [(s.x, s.y) for s in trace]"
 369    ]
 370   },
 371   {
 372    "cell_type": "code",
 373    "execution_count": 113,
 374    "metadata": {},
 375    "outputs": [
 376     {
 377      "data": {
 378       "text/plain": [
 379        "[(0, 0),\n",
 380        " (1, 0),\n",
 381        " (2, 0),\n",
 382        " (2, -1),\n",
 383        " (3, -1),\n",
 384        " (3, 0),\n",
 385        " (3, 1),\n",
 386        " (4, 1),\n",
 387        " (4, 2),\n",
 388        " (3, 2),\n",
 389        " (2, 2),\n",
 390        " (1, 2),\n",
 391        " (0, 2),\n",
 392        " (0, 3),\n",
 393        " (0, 4),\n",
 394        " (-1, 4),\n",
 395        " (-1, 3),\n",
 396        " (-2, 3),\n",
 397        " (-2, 2),\n",
 398        " (-1, 2),\n",
 399        " (-1, 1),\n",
 400        " (-2, 1),\n",
 401        " (-2, 0),\n",
 402        " (-1, 0),\n",
 403        " (-1, -1),\n",
 404        " (0, -1),\n",
 405        " (0, 0)]"
 406       ]
 407      },
 408      "execution_count": 113,
 409      "metadata": {},
 410      "output_type": "execute_result"
 411     }
 412    ],
 413    "source": [
 414     "positions(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 415    ]
 416   },
 417   {
 418    "cell_type": "code",
 419    "execution_count": 114,
 420    "metadata": {
 421     "collapsed": true
 422    },
 423    "outputs": [],
 424    "source": [
 425     "def valid(trace):\n",
 426     "    return (trace[-1].x == 0 \n",
 427     "            and trace[-1].y == 0 \n",
 428     "            and len(set(positions(trace))) + 1 == len(trace))"
 429    ]
 430   },
 431   {
 432    "cell_type": "code",
 433    "execution_count": 115,
 434    "metadata": {},
 435    "outputs": [
 436     {
 437      "data": {
 438       "text/plain": [
 439        "True"
 440       ]
 441      },
 442      "execution_count": 115,
 443      "metadata": {},
 444      "output_type": "execute_result"
 445     }
 446    ],
 447    "source": [
 448     "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 449    ]
 450   },
 451   {
 452    "cell_type": "code",
 453    "execution_count": 116,
 454    "metadata": {},
 455    "outputs": [
 456     {
 457      "data": {
 458       "text/plain": [
 459        "False"
 460       ]
 461      },
 462      "execution_count": 116,
 463      "metadata": {},
 464      "output_type": "execute_result"
 465     }
 466    ],
 467    "source": [
 468     "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLLFF'))"
 469    ]
 470   },
 471   {
 472    "cell_type": "code",
 473    "execution_count": 117,
 474    "metadata": {},
 475    "outputs": [
 476     {
 477      "data": {
 478       "text/plain": [
 479        "False"
 480       ]
 481      },
 482      "execution_count": 117,
 483      "metadata": {},
 484      "output_type": "execute_result"
 485     }
 486    ],
 487    "source": [
 488     "valid(trace_tour('FFLLLFRR'))"
 489    ]
 490   },
 491   {
 492    "cell_type": "code",
 493    "execution_count": 118,
 494    "metadata": {},
 495    "outputs": [
 496     {
 497      "data": {
 498       "text/plain": [
 499        "False"
 500       ]
 501      },
 502      "execution_count": 118,
 503      "metadata": {},
 504      "output_type": "execute_result"
 505     }
 506    ],
 507    "source": [
 508     "valid(trace_tour('F'))"
 509    ]
 510   },
 511   {
 512    "cell_type": "code",
 513    "execution_count": 119,
 514    "metadata": {},
 515    "outputs": [
 516     {
 517      "data": {
 518       "text/plain": [
 519        "True"
 520       ]
 521      },
 522      "execution_count": 119,
 523      "metadata": {},
 524      "output_type": "execute_result"
 525     }
 526    ],
 527    "source": [
 528     "valid(trace_tour('LLLL'))"
 529    ]
 530   },
 531   {
 532    "cell_type": "code",
 533    "execution_count": 120,
 534    "metadata": {
 535     "collapsed": true
 536    },
 537    "outputs": [],
 538    "source": [
 539     "def chunks(items, n=2):\n",
 540     "    return [items[i:i+n] for i in range(len(items) - n + 1)]"
 541    ]
 542   },
 543   {
 544    "cell_type": "code",
 545    "execution_count": 121,
 546    "metadata": {},
 547    "outputs": [
 548     {
 549      "data": {
 550       "text/plain": [
 551        "['abcdefg',\n",
 552        " 'bcdefgh',\n",
 553        " 'cdefghi',\n",
 554        " 'defghij',\n",
 555        " 'efghijk',\n",
 556        " 'fghijkl',\n",
 557        " 'ghijklm',\n",
 558        " 'hijklmn',\n",
 559        " 'ijklmno',\n",
 560        " 'jklmnop',\n",
 561        " 'klmnopq',\n",
 562        " 'lmnopqr',\n",
 563        " 'mnopqrs',\n",
 564        " 'nopqrst',\n",
 565        " 'opqrstu',\n",
 566        " 'pqrstuv',\n",
 567        " 'qrstuvw',\n",
 568        " 'rstuvwx',\n",
 569        " 'stuvwxy',\n",
 570        " 'tuvwxyz']"
 571       ]
 572      },
 573      "execution_count": 121,
 574      "metadata": {},
 575      "output_type": "execute_result"
 576     }
 577    ],
 578    "source": [
 579     "import string\n",
 580     "chunks(string.ascii_lowercase, 7)"
 581    ]
 582   },
 583   {
 584    "cell_type": "markdown",
 585    "metadata": {},
 586    "source": [
 587     "Using the [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula)"
 588    ]
 589   },
 590   {
 591    "cell_type": "code",
 592    "execution_count": 122,
 593    "metadata": {
 594     "collapsed": true
 595    },
 596    "outputs": [],
 597    "source": [
 598     "def shoelace(trace):\n",
 599     "    return abs(sum(s.x * t.y - t.x * s.y for s, t in chunks(trace, 2))) // 2"
 600    ]
 601   },
 602   {
 603    "cell_type": "code",
 604    "execution_count": 123,
 605    "metadata": {},
 606    "outputs": [
 607     {
 608      "data": {
 609       "text/plain": [
 610        "4"
 611       ]
 612      },
 613      "execution_count": 123,
 614      "metadata": {},
 615      "output_type": "execute_result"
 616     }
 617    ],
 618    "source": [
 619     "shoelace(trace_tour('FFLRLLFLRL'))"
 620    ]
 621   },
 622   {
 623    "cell_type": "code",
 624    "execution_count": 124,
 625    "metadata": {},
 626    "outputs": [
 627     {
 628      "data": {
 629       "text/plain": [
 630        "9"
 631       ]
 632      },
 633      "execution_count": 124,
 634      "metadata": {},
 635      "output_type": "execute_result"
 636     }
 637    ],
 638    "source": [
 639     "shoelace(trace_tour('FLLFFLFFFLFFLFLLRRFR'))"
 640    ]
 641   },
 642   {
 643    "cell_type": "code",
 644    "execution_count": 125,
 645    "metadata": {},
 646    "outputs": [
 647     {
 648      "data": {
 649       "text/plain": [
 650        "15"
 651       ]
 652      },
 653      "execution_count": 125,
 654      "metadata": {},
 655      "output_type": "execute_result"
 656     }
 657    ],
 658    "source": [
 659     "shoelace(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 660    ]
 661   },
 662   {
 663    "cell_type": "code",
 664    "execution_count": 329,
 665    "metadata": {},
 666    "outputs": [],
 667    "source": [
 668     "def step(s, current):\n",
 669     "    if s == 'F':\n",
 670     "        return advance(current, current.dir)\n",
 671     "    elif s == 'L':\n",
 672     "        return advance(current, turn_left(current.dir))\n",
 673     "    elif s == 'R':\n",
 674     "        return advance(current, turn_right(current.dir))\n",
 675     "    else:\n",
 676     "        raise ValueError"
 677    ]
 678   },
 679   {
 680    "cell_type": "code",
 681    "execution_count": 507,
 682    "metadata": {},
 683    "outputs": [],
 684    "source": [
 685     "def valid_prefix(tour):\n",
 686     "    current = Step(0, 0, Direction.RIGHT)\n",
 687     "    prefix = []\n",
 688     "    posns = []\n",
 689     "    for s in tour:\n",
 690     "        current = step(s, current)\n",
 691     "        prefix += [s]\n",
 692     "        if (current.x, current.y) in posns:\n",
 693     "            return ''\n",
 694     "        elif current.x == 0 and current.y == 0: \n",
 695     "            return ''.join(prefix)\n",
 696     "        posns += [(current.x, current.y)]\n",
 697     "    if current.x == 0 and current.y == 0:\n",
 698     "        return ''.join(prefix)\n",
 699     "    else:\n",
 700     "        return ''"
 701    ]
 702   },
 703   {
 704    "cell_type": "code",
 705    "execution_count": 552,
 706    "metadata": {},
 707    "outputs": [],
 708    "source": [
 709     "def mistake_positions(tour, debug=False):\n",
 710     "    mistakes = []\n",
 711     "    current = Step(0, 0, Direction.RIGHT)\n",
 712     "    posns = [(0, 0)]\n",
 713     "    for i, s in enumerate(tour):\n",
 714     "        current = step(s, current)\n",
 715     "        if (current.x, current.y) in posns:\n",
 716     "            if debug: print(i, current)\n",
 717     "            mistakes += [(i+1, current)]\n",
 718     "        posns += [(current.x, current.y)]\n",
 719     "    if (current.x, current.y) == (0, 0):\n",
 720     "        return mistakes[:-1]\n",
 721     "    else:\n",
 722     "        return mistakes + [(len(tour)+1, current)]"
 723    ]
 724   },
 725   {
 726    "cell_type": "code",
 727    "execution_count": 550,
 728    "metadata": {
 729     "collapsed": true
 730    },
 731    "outputs": [],
 732    "source": [
 733     "def returns_to_origin(mistake_positions):\n",
 734     "    return [i for i, m in mistake_positions\n",
 735     "           if (m.x, m.y) == (0, 0)]"
 736    ]
 737   },
 738   {
 739    "cell_type": "code",
 740    "execution_count": 492,
 741    "metadata": {
 742     "collapsed": true
 743    },
 744    "outputs": [],
 745    "source": [
 746     "sample_tours = ['FFLRLLFLRL', 'FLLFFLFFFLFFLFLLRRFR', 'FFRLLFRLLFFFRFLLRLLRRLLRLL']"
 747    ]
 748   },
 749   {
 750    "cell_type": "code",
 751    "execution_count": 493,
 752    "metadata": {},
 753    "outputs": [
 754     {
 755      "data": {
 756       "text/plain": [
 757        "'FFLRLLFLRL'"
 758       ]
 759      },
 760      "execution_count": 493,
 761      "metadata": {},
 762      "output_type": "execute_result"
 763     }
 764    ],
 765    "source": [
 766     "valid_prefix(sample_tours[0])"
 767    ]
 768   },
 769   {
 770    "cell_type": "code",
 771    "execution_count": 494,
 772    "metadata": {
 773     "scrolled": true
 774    },
 775    "outputs": [
 776     {
 777      "data": {
 778       "text/plain": [
 779        "True"
 780       ]
 781      },
 782      "execution_count": 494,
 783      "metadata": {},
 784      "output_type": "execute_result"
 785     }
 786    ],
 787    "source": [
 788     "all(valid_prefix(t) == t for t in sample_tours)"
 789    ]
 790   },
 791   {
 792    "cell_type": "code",
 793    "execution_count": 495,
 794    "metadata": {},
 795    "outputs": [
 796     {
 797      "data": {
 798       "text/plain": [
 799        "False"
 800       ]
 801      },
 802      "execution_count": 495,
 803      "metadata": {},
 804      "output_type": "execute_result"
 805     }
 806    ],
 807    "source": [
 808     "valid_prefix(sample_tours[0] + 'FLLLL') == sample_tours[0]"
 809    ]
 810   },
 811   {
 812    "cell_type": "code",
 813    "execution_count": 526,
 814    "metadata": {},
 815    "outputs": [
 816     {
 817      "name": "stdout",
 818      "output_type": "stream",
 819      "text": [
 820       "9 Step(x=0, y=0, dir=<Direction.DOWN: 3>)\n"
 821      ]
 822     },
 823     {
 824      "data": {
 825       "text/plain": [
 826        "[(10, Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
 827        " (12, Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
 828       ]
 829      },
 830      "execution_count": 526,
 831      "metadata": {},
 832      "output_type": "execute_result"
 833     }
 834    ],
 835    "source": [
 836     "mistake_positions(sample_tours[0] + 'F')"
 837    ]
 838   },
 839   {
 840    "cell_type": "code",
 841    "execution_count": 527,
 842    "metadata": {},
 843    "outputs": [
 844     {
 845      "name": "stdout",
 846      "output_type": "stream",
 847      "text": [
 848       "9 Step(x=0, y=0, dir=<Direction.DOWN: 3>)\n",
 849       "12 Step(x=1, y=0, dir=<Direction.UP: 1>)\n",
 850       "13 Step(x=0, y=0, dir=<Direction.LEFT: 4>)\n",
 851       "14 Step(x=0, y=-1, dir=<Direction.DOWN: 3>)\n"
 852      ]
 853     },
 854     {
 855      "data": {
 856       "text/plain": [
 857        "[(10, Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
 858        " (13, Step(x=1, y=0, dir=<Direction.UP: 1>)),\n",
 859        " (14, Step(x=0, y=0, dir=<Direction.LEFT: 4>)),\n",
 860        " (15, Step(x=0, y=-1, dir=<Direction.DOWN: 3>)),\n",
 861        " (16, Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
 862       ]
 863      },
 864      "execution_count": 527,
 865      "metadata": {},
 866      "output_type": "execute_result"
 867     }
 868    ],
 869    "source": [
 870     "mistake_positions(sample_tours[0] + 'FLLLL')"
 871    ]
 872   },
 873   {
 874    "cell_type": "code",
 875    "execution_count": 528,
 876    "metadata": {},
 877    "outputs": [
 878     {
 879      "data": {
 880       "text/plain": [
 881        "'FFLRLLFLRL'"
 882       ]
 883      },
 884      "execution_count": 528,
 885      "metadata": {},
 886      "output_type": "execute_result"
 887     }
 888    ],
 889    "source": [
 890     "(sample_tours[0] + 'FLLLL')[:10]"
 891    ]
 892   },
 893   {
 894    "cell_type": "code",
 895    "execution_count": 375,
 896    "metadata": {
 897     "collapsed": true
 898    },
 899    "outputs": [],
 900    "source": [
 901     "def random_walk(steps=1000):\n",
 902     "    return ''.join(random.choice('FLR') for _ in range(steps))"
 903    ]
 904   },
 905   {
 906    "cell_type": "code",
 907    "execution_count": 548,
 908    "metadata": {},
 909    "outputs": [
 910     {
 911      "data": {
 912       "text/plain": [
 913        "''"
 914       ]
 915      },
 916      "execution_count": 548,
 917      "metadata": {},
 918      "output_type": "execute_result"
 919     }
 920    ],
 921    "source": [
 922     "valid_prefix(random_walk(1000))"
 923    ]
 924   },
 925   {
 926    "cell_type": "code",
 927    "execution_count": 342,
 928    "metadata": {},
 929    "outputs": [
 930     {
 931      "data": {
 932       "text/plain": [
 933        "'FLFFLRFRLFRRRR'"
 934       ]
 935      },
 936      "execution_count": 342,
 937      "metadata": {},
 938      "output_type": "execute_result"
 939     }
 940    ],
 941    "source": [
 942     "valid_prefix(random_walk(1000), allowed_mistakes=1)"
 943    ]
 944   },
 945   {
 946    "cell_type": "code",
 947    "execution_count": 440,
 948    "metadata": {
 949     "scrolled": true
 950    },
 951    "outputs": [],
 952    "source": [
 953     "walks = []\n",
 954     "while len(walks) < 10:\n",
 955     "    w = valid_prefix(random_walk())\n",
 956     "    if len(w) > 30: walks += [w]"
 957    ]
 958   },
 959   {
 960    "cell_type": "code",
 961    "execution_count": 441,
 962    "metadata": {},
 963    "outputs": [
 964     {
 965      "data": {
 966       "text/plain": [
 967        "['LFRRFLLRFLRLLRFLRLFLRFLFFFRLLRLL',\n",
 968        " 'LRFFLFFFRLLRFRFFLRRFRLFLRFRLFRLRFFFF',\n",
 969        " 'FFFLRFRLRLFLRLFLFFFFFRFFRLLFFFLRLFFLRF',\n",
 970        " 'LFRLFFFFRLLRFFLLFFFRFFLLRFRLFLRFLF',\n",
 971        " 'LFLRRFLLRRFRFLFFRFFFFRRLLRFLRFRRLF',\n",
 972        " 'FLRLRLRFRLRFRLLFRFFRRLFRFLFLRRLR',\n",
 973        " 'RFRRFFFFRLRFLFRRLRFFFFRRFFLLFFRF',\n",
 974        " 'FFLFLRLFRLFFRFFLLFFRLLFRRLLRLFFF',\n",
 975        " 'RFFLFRRLRRLRLLFRFRLLRRLRFRLLRRFFRLFFLR',\n",
 976        " 'RFLFFLFRLFLRLFLRRLFFLRFLFLFRLLRF']"
 977       ]
 978      },
 979      "execution_count": 441,
 980      "metadata": {},
 981      "output_type": "execute_result"
 982     }
 983    ],
 984    "source": [
 985     "walks"
 986    ]
 987   },
 988   {
 989    "cell_type": "code",
 990    "execution_count": 350,
 991    "metadata": {},
 992    "outputs": [
 993     {
 994      "data": {
 995       "text/plain": [
 996        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 997        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 998        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 999        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
1000        " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
1001       ]
1002      },
1003      "execution_count": 350,
1004      "metadata": {},
1005      "output_type": "execute_result"
1006     }
1007    ],
1008    "source": [
1009     "trace_tour('FLLL')"
1010    ]
1011   },
1012   {
1013    "cell_type": "code",
1014    "execution_count": 147,
1015    "metadata": {},
1016    "outputs": [
1017     {
1018      "data": {
1019       "text/plain": [
1020        "(-1, 3)"
1021       ]
1022      },
1023      "execution_count": 147,
1024      "metadata": {},
1025      "output_type": "execute_result"
1026     },
1027     {
1028      "data": {
1029       "image/png": 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aZghIUsMMAUlqmCEgSQ3rFAJJPpzkn5McTXLeceo2J9mb5IdJru3SpiSpP11nAnuA/wz8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\n",
1030       "text/plain": [
1031        "<matplotlib.figure.Figure at 0x7fc85ef4c240>"
1032       ]
1033      },
1034      "metadata": {},
1035      "output_type": "display_data"
1036     }
1037    ],
1038    "source": [
1039     "import matplotlib.pyplot as plt\n",
1040     "%matplotlib inline\n",
1041     "plt.axis('on')\n",
1042     "plt.arrow(0, 0, 0.8, 0, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
1043     "plt.arrow(0.2, 0, 0, 1, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
1044     "plt.xlim([-1, 2])\n",
1045     "plt.ylim([-1, 3])"
1046    ]
1047   },
1048   {
1049    "cell_type": "code",
1050    "execution_count": 135,
1051    "metadata": {
1052     "collapsed": true
1053    },
1054    "outputs": [],
1055    "source": [
1056     "def bounds(trace):\n",
1057     "    return (max(s.x for s in trace),\n",
1058     "            max(s.y for s in trace),\n",
1059     "            min(s.x for s in trace),\n",
1060     "            min(s.y for s in trace))"
1061    ]
1062   },
1063   {
1064    "cell_type": "code",
1065    "execution_count": 136,
1066    "metadata": {},
1067    "outputs": [
1068     {
1069      "data": {
1070       "text/plain": [
1071        "(0, 2, -13, -13)"
1072       ]
1073      },
1074      "execution_count": 136,
1075      "metadata": {},
1076      "output_type": "execute_result"
1077     }
1078    ],
1079    "source": [
1080     "bounds(trace_tour('RFRFFLRFLFFRRFFRRRRLLLRRRRRRFRLFRFFRFFRRFRLRRFLLFRLLFRFLFLFRFRLLFRLFRFLRRLLFRRRFRRRRLLFLFRFRRFFRRLLLRLRRFRLRRFFRRFLFRRLLRRFFRFRRRRRFLLLLLRRFFFLLFFFRRLFLFFLRRRFRFLLFFRRLLRFLLRRF'))"
1081    ]
1082   },
1083   {
1084    "cell_type": "code",
1085    "execution_count": 148,
1086    "metadata": {
1087     "collapsed": true
1088    },
1089    "outputs": [],
1090    "source": [
1091     "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
1092     "           Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
1093    ]
1094   },
1095   {
1096    "cell_type": "code",
1097    "execution_count": 214,
1098    "metadata": {
1099     "collapsed": true
1100    },
1101    "outputs": [],
1102    "source": [
1103     "def plot_trace(trace):\n",
1104     "    plt.axis('on')\n",
1105     "    plt.axes().set_aspect('equal')\n",
1106     "    for s, t in chunks(trace, 2):\n",
1107     "        w, h = plot_wh[t.dir]\n",
1108     "        plt.arrow(s.x, s.y, w, h, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
1109     "    xh, yh, xl, yl = bounds(trace)\n",
1110     "    plt.xlim([xl-1, xh+1])\n",
1111     "    plt.ylim([yl-1, yh+1])"
1112    ]
1113   },
1114   {
1115    "cell_type": "code",
1116    "execution_count": 514,
1117    "metadata": {},
1118    "outputs": [
1119     {
1120      "data": {
1121       "image/png": 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kP1LxyGazsUcYkVKbFzRzMckrBu6+2d37wsMXgIb8RyoepfafXmrzgmYuJkleM/gnYGOC\n+xORAkoPt4GZbQLOP/lDgAMPuvtPwzYPAsfcfe1ZmVJEzjpz9/x2YPaPwNeAme7eM8R2+R1IRM6Y\nu9tw2wy7MhiKmd0A3AfMGCoEuQ4jIvHktTIws71ABXAgfOgFd789icFEpLDyPk0QkdGhoO9ANLNb\nzey3ZnbCzD5XyGOPhJndYGZ7zOx/zGxJ7HmGY2ZPmtk+M9sRe5ZcmFmDmW0xs11mttPM7oo903DM\nrNLMXjSzV8PMzbFnyoWZlZnZb8zsP4fbttBvR94J3AxsLfBxc2ZmZcBjwBxgCrDQzCbHnWpYT9E/\nb6k4Dtzj7pcCXwDuKPbvcbgmdp27XwFcDtxoZtMij5WLRcCuXDYsaAzcvcPd99L/8mSxmgbsdfc/\nuPsx4MfA/MgzDcndtwEHY8+RK3d/z923h/tdwG6gPu5Uw3P3w+FuJf0X34v6HNvMGoAvAz/MZXv9\nodKp6oG3T3r8DiXwg1qqzGwi/b9pX4w7yfDCkvtV4D1gk7v/OvZMw/gXoIkco5V4DMxsk5ntOOm2\nM/z7N0kf6ywZbNVS1L8BSpWZjQXWA4vCCqGouXtfOE1oAK42s0tjz3Q6ZnYTsC+swIwcVuN5vc9g\nMO4+K+l9Ftg7wKdPetwAvBtpllHLzNL0h2CNuz8be56RcPdOM8sCN5Dj+XgEjcA8M/syUA2cY2b/\n7u7/cLoviHmaUKzXDX4NTDKzz5hZBfC3wLBXYotATvUvIj8Cdrn7d2MPkgszqzOzceF+NXA9sCfu\nVKfn7kvd/dPufhH9P8NbhgoBFP6lxa+Y2dvAdKDNzIruD5vc/QTwz/T/efbrwI/dfXfcqYZmZmuB\nduCvzOwtM7st9kxDMbNG4O+AmeGlut+Ed7MWs08CvzSz7fRf3/gvd/955JkSpTcdiQigVxNEJFAM\nRARQDEQkUAxEBFAMRCRQDEQEUAxEJFAMRASA/wNQM89DiBxhRAAAAABJRU5ErkJggg==\n",
1122       "text/plain": [
1123        "<matplotlib.figure.Figure at 0x7fc85ef71c50>"
1124       ]
1125      },
1126      "metadata": {},
1127      "output_type": "display_data"
1128     }
1129    ],
1130    "source": [
1131     "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'))"
1132    ]
1133   },
1134   {
1135    "cell_type": "code",
1136    "execution_count": 215,
1137    "metadata": {},
1138    "outputs": [
1139     {
1140      "data": {
1141       "image/png": 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+ACSCwAeARJQU+LbPsv2Y7c22f2t7QAftmmyvsf2s7V+U0icA4NQ4Ik79w/Y3JL0WEXNt\n3ynprIiY3U67v0ZE/yLuF6XUAwApsq2IcKftSgz8TZKujIjdtt8lKR8RF7bT7vWIeGcR9yPwAaCL\nig38UtfwB0fEbkmKiJclDeqgXY3t1bZX2J5UYp8AgFPQp7MGth+XNKT1KUkh6etd6GdERLxs+zxJ\ny2yvi4g/tdewoaGhZT+XyymXy3WhGwDo/fL5vPL5fJc/V+qSzkZJuVZLOr+PiPd18pkHJf0yIv63\nnWss6QBAF3XXks4SSZ8r7H9W0uJ2CjnT9hmF/YGSPixpQ4n9AgC6qNQZ/tmSFkkaLmm7pGkRsd/2\nxZJujYhbbF8u6QeSmtT8gPl2RPx3B/djhg8AXdQtv9IpNwIfALquu5Z0AAA9BIEPAIkg8AEgEQQ+\nACSCwAeARBD4AJAIAh8AEkHgA0AiCHwASASBDwCJIPABIBEEPgAkgsAHgEQQ+ACQCAIfABJB4ANA\nIgh8AEgEgQ8AiSDwASARBD4AJILAB4BEEPgAkAgCHwASQeADQCJKCnzbN9h+wXaT7X84SbtxtjfZ\n3mL7zlL6BACcmlJn+M9LmiJpeUcNbFdJul/SxyRdJGm67QtL7LfXy+fzWZdQMRiL4xiL4xiLrisp\n8CNic0RsleSTNLtU0taIeCkijkhaKGlSKf2mgD/MxzEWxzEWxzEWXdcda/hDJe1oddxYOAcA6EZ9\nOmtg+3FJQ1qfkhSS/j0ifllEH+3N/qO48gAA5eKI0rPX9u8lzYqINe1cGyupISLGFY5nS4qI+EY7\nbXkQAMApiIiTLa1LKmKG3wUddfaMpPfYHinp/yTdJGl6ew2LKRgAcGpK/VnmZNs7JI2VtNT2rwvn\n3217qSRFRJOkGZIek7Re0sKI2Fha2QCArirLkg4AoPJV3Ju2xb7M1Zvxoloz2/Nt77a9LutasmZ7\nmO1ltjfYft72bVnXlBXbNbZX2X62MBZzsq4pa7arbK+xveRk7Sou8FXEy1y9GS+qneBBNY8DpLck\nfSUi3i/pckn/luqfi4g4LOkfI+KDksZIGm/70ozLytpMSRs6a1RxgV/ky1y9GS+qFUTEHyTty7qO\nShARL0fE2sL+AUkblfD7LBHxZmG3Rs0/Pkl2bdr2MEkTJD3QWduKC3zwohpOzva5ap7Zrsq2kuwU\nljCelfSypMcj4pmsa8rQtyXdoSIeepkEvu3Hba9rtT1f+O91WdRTYXhRDR2yXS/pEUkzCzP9JEXE\n0cKSzjBJl9l+f9Y1ZcH2REm7C//6szpZGSnn7/CLFhHXZNFvD9EoaUSr42GSdmVUCyqI7T5qDvuH\nI2Jx1vVUgoj4q+28pHEqYg27F7pC0vW2J0iqk/RO2w9FxGfaa1zpSzopruO3vKhm+ww1v6h20m/e\ne7lOZy0J+ZGkDRHxnawLyZLtgbYHFPbrJF0taVO2VWUjIu6KiBER8XdqzoplHYW9VIGB39HLXKng\nRbXjbC+QtELSe21vt/35rGvKiu0rJH1K0lWFnyOusT0u67oy8m5Jv7e9Vs3fY/w2Ih7NuKYegRev\nACARFTfDBwCcHgQ+ACSCwAeARBD4AJAIAh8AEkHgA0AiCHwASASBDwCJ+H/mh3TR5lLJjgAAAABJ\nRU5ErkJggg==\n",
1142       "text/plain": [
1143        "<matplotlib.figure.Figure at 0x7fc85ef505f8>"
1144       ]
1145      },
1146      "metadata": {},
1147      "output_type": "display_data"
1148     }
1149    ],
1150    "source": [
1151     "plot_trace(trace_tour('FFFLLFFL'))"
1152    ]
1153   },
1154   {
1155    "cell_type": "code",
1156    "execution_count": 216,
1157    "metadata": {},
1158    "outputs": [
1159     {
1160      "data": {
1161       "text/plain": [
1162        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
1163        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
1164        " Step(x=1, y=-1, dir=<Direction.DOWN: 3>),\n",
1165        " Step(x=1, y=-2, dir=<Direction.DOWN: 3>),\n",
1166        " Step(x=0, y=-2, dir=<Direction.LEFT: 4>),\n",
1167        " Step(x=-1, y=-2, dir=<Direction.LEFT: 4>),\n",
1168        " Step(x=-1, y=-3, dir=<Direction.DOWN: 3>),\n",
1169        " Step(x=-2, y=-3, dir=<Direction.LEFT: 4>),\n",
1170        " Step(x=-2, y=-2, dir=<Direction.UP: 1>),\n",
1171        " Step(x=-2, y=-1, dir=<Direction.UP: 1>),\n",
1172        " Step(x=-1, y=-1, dir=<Direction.RIGHT: 2>),\n",
1173        " Step(x=-1, y=0, dir=<Direction.UP: 1>),\n",
1174        " Step(x=0, y=0, dir=<Direction.RIGHT: 2>)]"
1175       ]
1176      },
1177      "execution_count": 216,
1178      "metadata": {},
1179      "output_type": "execute_result"
1180     }
1181    ],
1182    "source": [
1183     "trace_tour(walks[3])"
1184    ]
1185   },
1186   {
1187    "cell_type": "code",
1188    "execution_count": 405,
1189    "metadata": {},
1190    "outputs": [
1191     {
1192      "data": {
1193       "image/png": 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uvSSeEHJ5KC0tZcuWLZgZ1dXVrFy5MumROqRnh4hIAFTGIiIBUBmLiARAZSwiEgCVsYhI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\nsYhIAFTGIiIB+C+pi+rYc+DkNgAAAABJRU5ErkJggg==\n",
1194       "text/plain": [
1195        "<matplotlib.figure.Figure at 0x7fc85eaef0f0>"
1196       ]
1197      },
1198      "metadata": {},
1199      "output_type": "display_data"
1200     }
1201    ],
1202    "source": [
1203     "plot_trace(trace_tour(walks[3]))"
1204    ]
1205   },
1206   {
1207    "cell_type": "code",
1208    "execution_count": 442,
1209    "metadata": {},
1210    "outputs": [
1211     {
1212      "data": {
1213       "text/plain": [
1214        "10"
1215       ]
1216      },
1217      "execution_count": 442,
1218      "metadata": {},
1219      "output_type": "execute_result"
1220     }
1221    ],
1222    "source": [
1223     "long_walks = [w for w in walks if len(w) >= 30]\n",
1224     "len(long_walks)"
1225    ]
1226   },
1227   {
1228    "cell_type": "code",
1229    "execution_count": 443,
1230    "metadata": {},
1231    "outputs": [
1232     {
1233      "data": {
1234       "image/png": 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EIgoDEQHCDVEpNbMtZva2md0SoqaIpFfKYWBmecB/khyiMgj4rpkNSLXu0Zg0KbnL2uzZ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\n",
1235       "text/plain": [
1236        "<matplotlib.figure.Figure at 0x7fc85ebd9f28>"
1237       ]
1238      },
1239      "metadata": {},
1240      "output_type": "display_data"
1241     }
1242    ],
1243    "source": [
1244     "plot_trace(trace_tour(long_walks[0]))"
1245    ]
1246   },
1247   {
1248    "cell_type": "code",
1249    "execution_count": 444,
1250    "metadata": {},
1251    "outputs": [
1252     {
1253      "data": {
1254       "image/png": 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AGxoagtRbvXq1T58+3ffu3RukXkyAL1q0yO+77z4/duxYsdtpF/kGLMi0bV8m1KQ3O3fu\nZODAgQC8+uqrXH/99YlrShhmRl1dHUOHDi12K+2mvSa9aTcDBgxonfFV4ZKOosMETKQjUsBEIlLA\nRCJSwEQiUsBEIlLARCJSwEQiUsBEIlLARCJSwEQiUsBEIlLARCJKFDAzu87M3jGzbWY2LVRTIp1F\nkjtcpoDfAN8C/h64zcyGh2pMOoampqYvfJQvSnIEGwPUufuH7t4A/Bdwc5i2pKNouY/0+PHjO8Uk\nNaElCdgAYMdJjz/KfS66K664gocffjhIrQ8//JA77rgj2E3Gjxw5wuzZsxk6dCjvv/9+4nruzrJl\nyxgxYgTPPvtsgA5h06ZNTJ48malTpyauNXHiRFKpFFdddRVmZxx/eO7JZ9jz6RZgCjD3pMffBx4/\nzXbBhmnPnj076LwPgHfp0sXNLHjdUl7KysqC19y6dWuwn3NHQJ5TBiSZVeojYNBJjwcCu0634cyZ\nM1vX0+k06XS6oB3+9Kc/5fLLL+f+++9n0qRJzJgxo6A6J/vrX//KjBkzeO+993jjjTcS1zt8+DBP\nPPEE8+fPZ/ny5Vx88cWJ6jU3N/Pyyy/z4IMP8tBDD3H77bcn7nHjxo088MAD9OjRgxdeeCFxvVQq\nRVlZWeI6pSyTyZDJZM766wqek8PMyoB3gauBj4E1wG3uvvWU7bzQfYiUqnzn5Cj4CObuTWb2b8Br\nZN/LLTg1XCLnug4zq5RIKel0s0qJdEQKmEhECphIRAqYSEQKmEhECphIRAqYSEQKmEhECphIRAqY\nSEQKmEhECphIRB0uYIWMyWnPejFqlnq9GDVLvV6+FDC92EqyZqnXy1eHC5hIR6KAiUTULgMuo+5A\npEjyGXAZPWAi5zKdIopEpICJRNQuATOzKWa2ycyazGx0gjrBbjZhZgvMbLeZbUhS56R6A81slZlt\nMbONZvbDADW7mtlbZlabq5l8Ishs3ZSZrTWzlwPU+sDM1ud6XBOgXh8ze9HMtprZZjP7ZsJ6w3K9\nrc19PJj0Z2Nm9+VezxvM7Fkz69LmxvnMTpp0Ab4G/B2wChhdYI0U8L/AYKACWAcMT9DTlcDXgQ2B\nnmMV8PXcek+yc0YW3N9JdbvnPpYB/wOMCVDzPmAR8HKAWu8DfQO+Vv4DuDu3Xg70Dlg7RXZy3AsT\n1Phq7jl3yT1+Abijre3b5Qjm7u+6ex2QZPLyoDebcPfVwIEE/Zxar97d1+XWDwNbCTBXv7t/nlvt\nSvYFl+iqlJkNBG4A5idsrbUkgc6EzKwXMN7dFwK4e6O7HwpRO+ca4D1333HGLb9cGdDDzMqB7rQx\nozV0rPdgRbvZxNkysyFkj45vBaiVMrNaoB5Y4e5vJyw5B7ifhEE9iQPLzextM7snYa2Lgb1mtjB3\nSjfXzM4L0GOLqcDzSQq4+y7gUWA7sBP41N1XtrV9sICZ2YrcOWnLsjH38cZQuzjN50rubwxm1hNY\nDPwodyRLxN2b3f0fyM79/00zuyRBb5OA3bkjrZHsjKLFWHf/Btmj4r+a2ZUJapUDo4En3H008Dkw\nPUCPmFkFcBPwYsI655M9cxpM9nSxp5l9r63tk9z84Qvc/dpQtdqQ980miiV3yrAYeMbdl4Ws7e6H\nzCwDXAdsKbDMOOAmM7sBOA/oZWb/6e53JOirPvdxj5m9RPZUfnWB5T4Cdrj7n3OPFwOh7px6PfAX\nd9+TsM41wPvuvh/AzJYCY4HnTrdxMU4RC/2t+TYw1MwG567afBdIehUs1G/xFk8BW9z98RDFzKzS\nzPrk1s8j+8N9p9B67v6guw9y94vJfv9WJQmXmXXPHbExsx5ANbApQX+7gR1mNiz3qasp/JfJqW4j\n4elhznbgH82sm2VviHY12ffbpxfqCs0Zrrz8M9n3T0fJ3onlDwXWuY7s1bk6YHrCnp4jewQ8nvum\n3Z2w3jigiezVzVpgLXBdwpojc3XWARuAhwL+TCaQ8CoicNFJz3dj0p9JruYosr9M1wFLgT4Bap4H\n7AF6BfrezciFagPwNFDR1rb6r1IiEXWkq4giHY4CJhKRAiYSkQImEpECJhKRAiYSkQImEpECJhLR\n/wGantOCZJhsswAAAABJRU5ErkJggg==\n",
1255       "text/plain": [
1256        "<matplotlib.figure.Figure at 0x7fc8640290b8>"
1257       ]
1258      },
1259      "metadata": {},
1260      "output_type": "display_data"
1261     }
1262    ],
1263    "source": [
1264     "plot_trace(trace_tour(long_walks[1]))"
1265    ]
1266   },
1267   {
1268    "cell_type": "code",
1269    "execution_count": 445,
1270    "metadata": {},
1271    "outputs": [
1272     {
1273      "data": {
1274       "image/png": 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dRkHbtWuXp1IpT6VSfujQoai1d+/e7RUVFX7PPfd4Y2Nj1NpnrVmzxisrK33+/Pm6vwvE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\n/wDymFXfd/I9VwAAAABJRU5ErkJggg==\n",
1275       "text/plain": [
1276        "<matplotlib.figure.Figure at 0x7fc85eddf7b8>"
1277       ]
1278      },
1279      "metadata": {},
1280      "output_type": "display_data"
1281     }
1282    ],
1283    "source": [
1284     "plot_trace(trace_tour(long_walks[2]))"
1285    ]
1286   },
1287   {
1288    "cell_type": "code",
1289    "execution_count": 446,
1290    "metadata": {},
1291    "outputs": [
1292     {
1293      "data": {
1294       "image/png": 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4TojILcAWEp/1HuoYMudahe7K3eUd+CtaTkv1Fc33DDgTHjRnwoPmTHjQnAkPmjPhQXMm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\n",
1295       "text/plain": [
1296        "<matplotlib.figure.Figure at 0x7fc85ef41048>"
1297       ]
1298      },
1299      "metadata": {},
1300      "output_type": "display_data"
1301     }
1302    ],
1303    "source": [
1304     "plot_trace(trace_tour(long_walks[3]))"
1305    ]
1306   },
1307   {
1308    "cell_type": "code",
1309    "execution_count": 447,
1310    "metadata": {},
1311    "outputs": [
1312     {
1313      "data": {
1314       "image/png": 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TiYTPmDEjWOZXvvIVf/XVV72xsTFI5ukAv+qqq3zatGn+s5/9LGj28ePHfcGCBf7tb387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\n",
1315       "text/plain": [
1316        "<matplotlib.figure.Figure at 0x7fc85ef240f0>"
1317       ]
1318      },
1319      "metadata": {},
1320      "output_type": "display_data"
1321     }
1322    ],
1323    "source": [
1324     "plot_trace(trace_tour(long_walks[4]))"
1325    ]
1326   },
1327   {
1328    "cell_type": "code",
1329    "execution_count": 448,
1330    "metadata": {},
1331    "outputs": [
1332     {
1333      "data": {
1334       "image/png": 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9KCkpyfJs5GToG4giAigMRCRQGIgIoDAQkUBhICKAwkBEAoWBiAAKAxEJFAYiAigMRCRQ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\nEJFAYSAigMJARAKFgYgA8L/NCDjmYn8xcQAAAABJRU5ErkJggg==\n",
1335       "text/plain": [
1336        "<matplotlib.figure.Figure at 0x7fc87c3185c0>"
1337       ]
1338      },
1339      "metadata": {},
1340      "output_type": "display_data"
1341     }
1342    ],
1343    "source": [
1344     "plot_trace(trace_tour(long_walks[5]))"
1345    ]
1346   },
1347   {
1348    "cell_type": "code",
1349    "execution_count": 449,
1350    "metadata": {},
1351    "outputs": [
1352     {
1353      "data": {
1354       "image/png": 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DqnuAD4F+qnorsBf4j9RHCt+uXbsA2L59e8iTmKClVABVXaeqDWembyD+LfGhuHDhgrOs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\n",
1355       "text/plain": [
1356        "<matplotlib.figure.Figure at 0x7fc85ec78198>"
1357       ]
1358      },
1359      "metadata": {},
1360      "output_type": "display_data"
1361     }
1362    ],
1363    "source": [
1364     "plot_trace(trace_tour(long_walks[6]))"
1365    ]
1366   },
1367   {
1368    "cell_type": "code",
1369    "execution_count": 450,
1370    "metadata": {},
1371    "outputs": [
1372     {
1373      "data": {
1374       "image/png": 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k80gSMu7+Z+B/UtTqiPLy8ti4cSMAmzdvTn7C57Vr17J48eKcHe4lxzedcv8IFBQUMHv2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\n",
1375       "text/plain": [
1376        "<matplotlib.figure.Figure at 0x7fc85f006a90>"
1377       ]
1378      },
1379      "metadata": {},
1380      "output_type": "display_data"
1381     }
1382    ],
1383    "source": [
1384     "plot_trace(trace_tour(long_walks[7]))"
1385    ]
1386   },
1387   {
1388    "cell_type": "code",
1389    "execution_count": 451,
1390    "metadata": {},
1391    "outputs": [
1392     {
1393      "data": {
1394       "image/png": 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KW0QkQCpvEZEAqbxFRAKk8hYRCZDKW0QkQCpvEZEA5aS8zewmM2s2syNysT8REWlb1uVt\nZj2As4H12Y8jEob333+fiy++GIAJEyawbNmyhCeSKMybN4/q6moAxo8fT0NDQ8IT/VMuzrz/Dbg5\nB/uJnLsnPUKs3D3vjjkuGzZsYO7cuQAsWrSIlStXJjZLPj7GcR3zX/7yF9577z0AnnrqKT7++ONY\ncr+MrMrbzC4A3nX3mhzNE4k333yTYcOG0bdv36RHiYW7s3DhQgYOHMh5552X9Dgd0sCBAznzzDMB\nOProoxk7dmwiczz66KN0796dn//854nkx62hoYEZM2Zw5JFH8uyzz0aeN3HiREpLS0mn01x22WVU\nVFREnvml7Tk7O9ACzAOWt1pqWn4dCSwBOrVstxbo1sZ+PG5LlixxwEtKStzMHIht+drXvubLli2L\n/Zi3bt3qvXv39rKysliPF/ATTjjBN27cGPsxJ+XPf/6zAz5r1qzYs4877jhPp9NeXl4e++M8ZswY\nb25ujv2Yf/nLX3p5ebmXlZXF/nw2M6+rq4v9mN3dW7pzn041/4ovP8ysHzAfaAAM6AFsBAa5+6b9\nbO97rh0BVFZWUllZ+ZWyvyx3p6qqiqeeeoqmpiYaGxvp3bt3pJkATU1NrFu3jrPPPps//vGPkee1\ndtdddzFlyhRKSkrYuXMnTU1NsRxzY2Mj69ev50c/+hEPPPBA5HnthZmxatUq+vTpE2vu0qVLueqq\nq1i1atXe67BxPM7btm1j06ZNPP/884wYMSLyvNbMjPLycsyMhoYGmpubYzlmgB//+MdcccUVsWRl\nMhkymcze9alTp+Luts+G+2v0r7Kw+8y7axu/H/U3qAP64IMPfNKkST5ixIhY8iZPnuxFRUVeWlrq\ny5cvjyVzjzvuuMMBX7NmjV966aVeVVUVS+4FF1zgqVTKS0tL/YMPPoglsz0A/J133kks/+WXX/bB\ngwfHcva/fft279atmwP+7W9/O/azb8CHDh3qzz33nA8YMMAzmUys+UnhAGfeuSzvNcARbfx+HMeZ\nuM8++8yLi4v3vtS68MILY83fU95xWrNmzd6Xl6lUym+55ZZY85OUdHnH6fHHH/d0Ou1m5mbmCxcu\njDV/T3nnmwOVd85u0nH349x9S672F6qysjLuv/9+AEpKSrjxxhsTnih6PXv25N577wXge9/7HuPH\nj094IonC8OHDmThxIu7O9OnTGTBgQNIj5TXdYRmBCRMmADB69GiGDBmS8DTRKygoYPLkyQBcccUV\n9OvXL+GJJAo9evTYezJy22230alTp4Qnym8qbxGRAKm8RUQCpPIWEQmQyltEJEAqbxGRAKm8RUQC\npPIWEQmQyltEJEAqbxGRAKm8RUQCpPIWEQmQyltEJEAqbxGRAKm8RUQCpPIWEQmQyltEJEAqbxGR\nAKm8RUQCpPIWEQmQyltEJEAqbxGRAGVV3mZWbWYbzOzNluW8XA0mh27btm38/e9/B2DVqlUJT9Ox\nuTvLly8H4O2332bHjh0JT9SxrV27FoB3332XzZs3JzxN+5CLM+//6e6ntiwv5mB/8hXdfPPNzJw5\nE4ATTzyR999/P9mBOrAFCxbQv39/AEaPHr33711yb9euXXznO98Bdpf4D37wg4Qnah9yUd6Wg310\nWJs3b2b69Om89957kWeNHz+esrIyAAYMGMBRRx0Veeb+rF+/njvvvJNt27bFmrtz504ee+wx5s2b\nF3nW4MGDOfzwwwEoLi5m5MiRkWe2N4sXL+b++++PPKegoICRI0eSTqcpLy/nyiuvjDwzBAU52Mf1\nZjYe+Asw2d3jfca2Y3/961/p1asXjY2NbNy4kdGjR0ee2bNnT1avXs2MGTMiz9qfxx57jIkTJ9LY\n2EgqlWLgwIGRZzY1NbF27VqmTZvGli1b6NmzJw899FDkuRdffDG/+tWvuPLKK+nevXvkee3JGWec\nwbJly2hoaODEE0+MPO/cc8/l6aefplOnTlx66aWR54XA3L3tDczmAV9v/SnAgSnAEuBDd3czuxPo\n7u5XH2A/Xl1dvXe9srKSysrK7KZvx84//3xeeOGFRLJPP/10lixZEnvuSSedRE1NTey5AGaGmdHc\n3Bx79oYNG6ioqIg9Nwn19fVUVFTw2Wef0dTUFHv+ww8/zDXXXBN7bpwymQyZTGbv+tSpU3H3fa9w\nuHtOFqAXsLyN3/d80tzc7PPnz/eTTz7ZAX/yySeTHilyTU1NPnfuXP/GN77hgL/yyiuxZa9Zs8Yv\nvfRST6VSfu6558aWm4/q6+v97rvv9s6dO3s6nU56nA6vpTv36dSDnnm3xcyOcvf3Wz6+ETjN3S85\nwLaeTVao3J2lS5dy0kknkU6nkx4nFs3NzSxdupRTTjkFs3h/JLJ27Vo6d+5Mt27dYs3NR5999hl1\ndXWxXDbJZ2a23zPvbMv7fwP9gWZgHTDB3T84wLZ5Wd4iItmIpLwPcQCVt4jIITpQeesOSxGRAKm8\nRUQCpPIWEQmQyltEJEAqbxGRAKm8RUQCpPIWEQmQyltEJEAqbxGRAKm8RUQCpPIWEQmQyltEJEAq\nbxGRAKm8RUQCpPIWEQmQyltEJEAqbxGRAKm8RUQCpPIWEQmQyltEJEAqbxGRAGVd3mY20cxWmlmN\nmd2Ti6FERKRtWZW3mVUCFwD93P07wL25GKqjyGQySY8QOx1zx5dvxwvt85izPfP+IXCPu+8CcPcP\nsx+p42iPD3jUdMwdX74dL7TPY862vPsAQ81siZktNLOBuRhKRETaVnCwDcxsHvD11p8CHPgfLX++\ni7t/18xOA54GjotiUBER+Sdz96/+h82eZ/dlk5da1t8BTnf3j/az7VcPEhHJY+5uX/zcQc+8D+IZ\nYBjwkpn1AQr3V9wHChcRka8m2/J+AnjczGqAHcBl2Y8kIiIHk9VlExERSUasd1ia2clm9pqZvWVm\nr+fLu1Py8UYmM7vJzJrN7IikZ4mamf3MzP5mZkvN7N/NrHPSM0XFzM5r+VpebWa3Jj1P1Mysh5kt\nMLMVLc/fSUnPtEfct8f/DKh291OAamBGzPmxy8cbmcysB3A2sD7pWWLyJ6Cvu/cHaoHbEp4nEmaW\nAn4BnAv0Bf6rmX0r2akitwv47+7+beB7wPXt5ZjjLu9m4PCWj7sAG2POT0I+3sj0b8DNSQ8RF3ef\n7+7NLatLgB5JzhOhQUCtu693953AHGBUwjNFyt3fd/elLR/XA38DKpKdare4y/tG4F4zq2P3WXiH\nPEP5gry6kcnMLgDedfeapGdJyFXAC0kPEZEK4N1W6xtoJ0UWBzM7FugP/DnZSXbL9t0m+2jjpp4p\n7H4pfYO7P2NmY4HHgeG5niFu+XYj00GO98f8/49ph3iLaFtf1+7+XMs2U4Cd7v6bBEaMw/4ey7x4\nx4OZHQb8jt39VZ/0PBDzu03MbKu7d2m1vs3dD2/rz4TuUG5kCp2Z9QPmAw3sfqL3YPelsUHuvinJ\n2aJmZpcD1wJnufuOpOeJgpl9F7jd3c9rWf9XwN39p8lOFi0zKwD+L/CCu9+f9Dx7xH3ZZKOZ/ScA\nMxsGrI45Pwl7bmTiYDcyhc7d/8Pdj3L349z9G+x+WX1KHhT3ecAtwMiOWtwt3gCON7NeZlYE/Avw\nfxKeKQ6PAyvaU3FD/GfeZwD/C0gD24Hr3P2t2AZIgJkVsvvB78/uG5kmu/uiZKeKh5mtAQa6+5ak\nZ4mSmdUCRcCeb8pL3P26BEeKTMs3qvvZfeL3mLt36Le+mtlg4CWght2XiBz4sbu/mOhg6CYdEZEg\n6b9BExEJkMpbRCRAKm8RkQCpvEVEAqTyFhEJkMpbRCRAKm8RkQCpvEVEAvT/AD5x/5P4IpqkAAAA\nAElFTkSuQmCC\n",
1395       "text/plain": [
1396        "<matplotlib.figure.Figure at 0x7fc85efd7208>"
1397       ]
1398      },
1399      "metadata": {},
1400      "output_type": "display_data"
1401     }
1402    ],
1403    "source": [
1404     "plot_trace(trace_tour(long_walks[8]))"
1405    ]
1406   },
1407   {
1408    "cell_type": "code",
1409    "execution_count": 416,
1410    "metadata": {},
1411    "outputs": [
1412     {
1413      "data": {
1414       "text/plain": [
1415        "['RFLRFFRFFFFRLRFRFFRLLFFFFFRRLRRL',\n",
1416        " 'FFFFRFRLRLFRLRLRFRRLLFFRFRLFLRRFLRRL',\n",
1417        " 'RLLRLFFFRFFLLRRLLFRLLRRFLLRRLLFFFFLRFLRF',\n",
1418        " 'FFLRRLFRLFLFFFFLLRFRLFFFFLLRLRRL',\n",
1419        " 'FLFRFLFRFFFLFRLFRLLFFLRRFLRLLFRLRLRRLLFFFRFLFLRLRL',\n",
1420        " 'LRFRLRFLFFFFFRRFLRLRFRLRLFRLFFRRLR',\n",
1421        " 'LRFLFLRLRRFLFFRRFFFLFRFFLRFRFLLRFFRRLLRFFRLRRFFLLRLR',\n",
1422        " 'LFRLFFFRLLRLLFFRRLLRLFFFLRRLLFFL',\n",
1423        " 'FLRFFLFFRLFRLLFRLLFFFRLFRRLFLFFL',\n",
1424        " 'LLRFRLRRLRLFRFFFFRLRFFLRFFRLRRLFRFFL']"
1425       ]
1426      },
1427      "execution_count": 416,
1428      "metadata": {},
1429      "output_type": "execute_result"
1430     }
1431    ],
1432    "source": [
1433     "walks"
1434    ]
1435   },
1436   {
1437    "cell_type": "code",
1438    "execution_count": 452,
1439    "metadata": {},
1440    "outputs": [
1441     {
1442      "data": {
1443       "image/png": 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2WNK1JH91f1tmDqEfEWwFZpvZQUlfA54luWXzZJK/7PZ0qzHcGDbMMoXjPGNmp0g6GnhW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\n8v89qQ80wuYWhQAAAABJRU5ErkJggg==\n",
1444       "text/plain": [
1445        "<matplotlib.figure.Figure at 0x7fc85eaed1d0>"
1446       ]
1447      },
1448      "metadata": {},
1449      "output_type": "display_data"
1450     }
1451    ],
1452    "source": [
1453     "plot_trace(trace_tour('FLFFLRFRLFRRRR'))"
1454    ]
1455   },
1456   {
1457    "cell_type": "code",
1458    "execution_count": 582,
1459    "metadata": {},
1460    "outputs": [
1461     {
1462      "data": {
1463       "text/plain": [
1464        "(408, [8, 16, 20])"
1465       ]
1466      },
1467      "execution_count": 582,
1468      "metadata": {},
1469      "output_type": "execute_result"
1470     }
1471    ],
1472    "source": [
1473     "w = random_walk()\n",
1474     "ms = mistake_positions(w)\n",
1475     "len(ms), returns_to_origin(ms)"
1476    ]
1477   },
1478   {
1479    "cell_type": "code",
1480    "execution_count": 583,
1481    "metadata": {},
1482    "outputs": [
1483     {
1484      "data": {
1485       "image/png": 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n5ua67FetPiVSQs+vmyAIgvAKGtgjFHeMn2qPv2rGH7V0wThhiHOu2TAcKBwN\nloHqF8d61AyE7qLWt46fvbPPwNeG0mCeYKV2v6u1Wa3PW1paZO/1er1qW9TqcDSIO4YJ1oSzxfdA\nXTYVCE+prq52anDR4kjjLO+SJUtk6dzxHu3evbvP2vf111+r1tGpUyef1SGE7d2wYYNH+Z31w/Ll\ny32m47p167wyvkVHR3O9Xi+W19zczAHws2fPijLBeFpUVKSpfVovLeF4f//732sur3///j7r15aW\nFr8YVP1xOWKXBdZBiQgMGRkZ+OWXX3Dq1ClRZjKZMGPGDFy4cMFllLnjx4/j0KFDMseLLl26YOzY\nsbJ0e/fuxbfffisz/pjNZjEsq0BUVBQuu+wyb5sl8s033wCAzCC3e/duLFmyxGd1CAZFT2ebLS0t\nKC4ulsmmTp2KZcuW4b777vNaPwCYOXMmUlJSEBMTIxoaN27ciDfeeAPPPvus2Ibi4mJ89tln+PTT\nT8W12draWsyePVu2FizEWpEaXgVHH0cnoGPHjuHYsWOy+CxTp07FoEGDsHz5clGm1+tx5MgRWd7H\nHnsMdXV1Ltu3du1azJo1S3YvWSwWtLa2yu7hhx56CAcOHHBZnlYSExNRUlKC2tpasX+MRiOuvvpq\n3HPPPcjJyQFgM1Q/9dRTmDFjBsaNGyfq98QTT+DSSy/F4MGDAdgmym+//TaSk5PFdACwbds2xMbG\n4pNPPhFldXV1+Omnn2RG6La2NhgMBplz1mOPPeZ+w5yN+IG6QDN2vwAoQwqEI6+99ppitrJlyxbV\nGYw3AOCbNm3yaXmO2z59zerVqxX9oNZfQjwUNR11Op1CpiWkAAA+ZcoUTemSk5NdptPKrbfe6vPP\nXg0A/ODBgwrZypUrFbI1a9YoZJdeeqlC5ulTZlZWltszdlpjJwiCiDBoYCfCjlAznDpDGqY4UHAf\n+IRoLUOroTaYBlBfo9Y3av2gJgtoPzibygfqAi3F+BxfGIQcH0ODxYoVKxSPoR988AEHIIsQ6KzN\nSUlJsuUGk8nE09PTVdPu3r3bZ3rDx0sxX331VcCMdF9++aWm9mm9PD3LdOXKlarlJSQkeFSeOwSq\nr7Vew4cPV9WRk/G045CYmIiffvoJ3377rSgzGAyIioqSRcIzmUwwm80yA5rFYsEDDzyAN998E6+8\n8kpA9VbDcRsh8OuxY1IP0+pqWyDRl156SWyPyWTCgw8+KEvHGMP58+exYMECmWGsW7duKCgo8Knu\nvjww5J1k5vA3AAAasklEQVR33gEArFixQpStWbMGe/fuxXXXXSd+rkePHsWBAwdw4403ivUfOHAA\nR48exdVXXy0ayQ0GAzZv3ozf/va3Yn+azWZs3LhRU2TPLVu2YMWKFWJfc85hNBphsVgUDklvv/22\nR21+5JFHFG2ur6/HzTff7FF57vDMM89g165dMsNtWVkZTp8+LRpZOeeIj49HXFycrB8SEhIwffp0\nWT/++c9/RkxMDK6//nox3QcffICsrCyZcbSxsRHJyckyx7GGhgbMmTPHvQY4G/EDdYFm7CEHAP6X\nv/wl2GpwzrUbT0+cOOHUwOQY0xsAP3z4sO+VdajDlzP2Rx99VNG+22+/XSFT6y9h5qumo6fG00Aw\nZswYVb3DEQA8OztbIfNXPHZaYycIgogwaGAnVFEL5RsqcB8YCAOBmveuLwkXIzJhQ8146uih6jOc\nTeUDdSFCHrUiCQTIIHT33Xe71OX1119XPI5v2rTJrXqkSzFCmON9+/b5vN+kAOCpqaku073zzjuq\nOjsetzZ37tygGu/OnTvnUT/Mnz/fq3q7devmUb3BZOrUqV61+V//+pemetDOUgyF7SUUnDx5Eq++\n+qos7GtTU5PsKDWr1YoLFy7IjvvinKO2thaZmZmyWXVVVRVycnJkM5b//ve/qKqqcjn7fuaZZ/Dk\nk0/K0nHO8a9//Qt79+4VZadOncLmzZvxwAMPiLKGhgZccskluPfee0WZyWRCXFwcfvzxR0UEQ1/C\nGENubi5OnDjhMh0Amd4ffPABKioqZG3Ozc3FqVOnZOnefPNN6PV6REVFieVI+9gxFG63bt1EWVtb\nG5qbmzFr1iwxgmFTUxPWrFmDmTNnIiMjA4BtRrl69WqsX78e//M//+NRP8TGxuKee+4RdTl37hwy\nMjJk7auurkZWVpbsKaSyshKLFy/G0KFD3a43mDDGMGjQIEybNk2Umc1mVFVVoVevXqLs1VdfBfDr\nZ885x/Lly5GWlqbJW7e9sL3ezrZvgu0sUwuA0Q7/WwigFMARAFe1U4b7P4lE2DNt2jRNhjE1Y6Aa\nzoynagChYzwdNmyYQu8bbrhBIRs7dqxC1r9/f4XsgQceUMh++ukn1b4BwI8dO6aQORpPAfD169e7\nbIsaAHhBQYFHecMVQHmYtbN0jsZTADwxMVFzPdzJuOrtdscDAK4H8A+HX5J8ADcDyAeQA2A7Y2yA\nXRmCIAjCj3hlPOWcH+OclwJwfBy4FsB6zrmZc14G28x9jDd1EZGF43mUkYinZ6FqNVwHcp5EczL3\n8MbL1Bdn6PprV0w2gHLJ+wq7jCAA2NZztaB1QBHc97V+KYYMGQLGmHgJx91Jr7S0NJSWlsry3Xvv\nvYp0ahegbVdMRkYGOnfuLJMJzlbS8kpKShQy4Zg8qUxYt5XKRo0aBUDu5i5EAz1+/LgoE6Jb/uY3\nv1G0ZdasWZrardYP0nXljsKyZcs09Y3ayWK++BF1uRTDGPsCQIZUBJv1dhHn/GNn2VRkTrWVhmAt\nLCxEYWGhK7WIMEcwzrlC63FpwuAo9aJ1xvPPP4/169eLnqeA7Yi0PXv2IDc3V5R99tlnePvtt/Hc\nc8+JspUrV6JHjx64+OKLAdhm19u3b0dUVJTMWJaWloa//e1vLnVROyc1JycHe/bsQbdu3UTv0bq6\nOlgsFkyePFkMbbtv3z5UVlZiwoQJYvtLS0tRWlqKzp07i2F2m5ub0draCp1OJx4FJxi9pZ9DbGws\n1q9fj7Vr14oDj06nQ1tbG06fPi2mMxqNYIwhLi5OHITMZjPq6+uRnZ2NESNGALD9UNTV1eGNN95w\n2Q+RRHFxsey807a2Nuj1eqSnp4vGYbPZjHPnzmH16tWyvLGxseJn5EhRURGKioq0KeFs8d2dC8AO\nSIynABYAeFTyfguAsU7yajIUEJFFMI2nWgHAX375ZYVs/vz5CllaWppHdWg1nnrjeeqO8dQbAPDZ\ns2f7rLyOCHxkPPXlUox0lr4ZwEzGWBxjrB+APADf+7AugiAIwgleDeyMsesYY+UACgB8whj7HAA4\n54cB/BfAYQCfAbjH/gtDEAAiK5Qr4Fsv0HDuG/KG9R6fnBvrbCofqAu0FNMhEZYgHK/MzExVuSv2\n7t3LAcjO9XQHbz0k1a5du3a5rHf06NE+r9fX17Bhw3hNTY1M7zlz5qimveqqqzzqf8KGs8/g3//+\nt2pa7mRcJc9TIihUVVXh9ttvl53Vevz4cVx22WUoLy+XyZYtW4aHH3643fKOHz+OAQMGeLSjwGq1\nIjo6GhkZGeJ5nzqdDrW1tejatatozGppaUFVVRUAIC8vT1Y3Ywz9+/cHYDOMlZWVYciQITh06FC7\ndQtGyt69e4vhYMvLy2EwGBR1OMMxFDNgM95269YNgO0s0srKSpf5LRaLOON2rHvVqlW46667FHpL\n0w0cOBBr165Fenp6e00m2uHgwYOYM2eOLFy18Nk73tt+8zz1xQWasRM+wFvjKaA88xReGE8BbZ6n\n8fHxmoynPXv2VMjUzjz9+uuv3TKeVlRUKGRaPE8B8KeffrqdlhG+gs48JQiCIGhgJwh34SrLPVpl\nBOEuHt1HzqbygbpASzGED9i3b59XxlM4MVoxxjTJHM/hFOSe1uuYt1u3bl4bQa1Wq1heQ0ODW3nV\nlmKio6MV6c6fP+9R/0cSTz31lKJfBg0apJDl5uYqZL169dJ0P3BOSzFEB0DwONXiearGbbfdpirn\nKrMltbNMx40bJ3sfHx8vemC2x8cfO3PelqN26r276PV68XXnzp01e/+qsWLFCtm5nAKLFi3yuMxI\nYfHixT4tr0ePHvjiiy/cykMDOxERxMR4F6h07dq1ak+TyM/PV8jmzp2rkDn+ABgMBly4cMFlvTNm\nzFDUKxx4LEU4IFqaTvgxkcpee+01hUzYESOEIgBsOyqqq6tV2/zjjz8qZI7ce++9MBgMinTSH4+O\nzMKFC2V9c/ToUUVfnzhxQiE7c+aMQlZTU4MrrrjCrfppYCeIEEPYSkgQnkIDO0EQRITh7UEbBBES\nCCFy8/LyxBlvRUUFRo4ciXPnzonpamtrMWDAADHMLwDU19ejT58+2LNnj2K2fOTIEdFxSEDqVCXw\n1VdfYcCAATLZ2bNnPWqLEFIgJiZGXM8XHI8yMzNFJ6qysjIAtjV/YSlKzR1dcDqSpjObzUhKSkJL\nS4soE+qVrucLSyy33HILZs+eLf4/KioKzc3N6NSpk6wuqXMZAHz++ef43e9+J3Nk6tGjB95++21F\nf4USt99+O9atWycLq3v55ZfjtddekzmEPffcc3j88cdl7QNs91lQcWZVDdQF2hVD+AC9Xs/Hjx+v\n2EnQuXNnhSwmJkZ118Hnn38uK1MtDQB+xRVXuEyXkJDAt2/f7lFbRo4c6fUOmNbWVrG8Q4cOuZX3\nyy+/FPNaLBan6a699lpFP8ybN09TH4b6996Zzlu2bHGZrm/fvvz48eMB0ZHTrhgikklISEBxcbHi\nBm9sbFTITCaTqtFQ7eSil156SZGub9++inRpaWmydHq9HpdffrlHbRFmidLyxo4dq5AJIQykMsF4\nKp1JC4eQOxsEHNuXmpoq5hWeGKZNm6ZIp3ZYitrJWAUFBYq8joeLhCI1NTUKvZOTkxXp1qxZI0t3\n6tQp8bMJFjSwE0Q7qBky1bY7+hK1bYSRhnQ5g/A9NLATBEFEGGQ8JTo8gnFx8eLF+Mc//gGg/fNK\n161bpzCM1tfXY/r06QBsRsjKykp8/vnnyM52/6hfwYiZnp4uPh0IBuAePXqI6QSZ9AlCWDKQoiYD\ngOnTp6O4uFg8Qk8wvE6YMEFcchBkW7duFesW9CspKRHbLJw1+8knn4gyIe8PP/wgyoS+Fvbl+wvO\nOW666SbU1NSgS5cuouyOO+7AzTffLEv74IMPori4WNG+5uZmWX8DwB/+8AcMGTJEJpMa4kMGLetu\n/rwQ4kYUomNw9dVXqxrCLly4IEs3d+5czUbIyZMne6TLJZdc4rXxVIpgPG1ubhZl7oYU8PX16aef\netQ3Wtm8ebPTuo1Go5hOp9OppsnPz5eFpzCZTKrpunfvzsvKyvzaFmfAX8ZTxthNjLGDjDELY2y0\nRN6HMaZnjO21Xyu9qYcg/M3mzZtVvyCOBwuvXr1asxHyxIkTHukiuPpLyxMOz5bKhDAIUplgPJUi\nGE+lnqfCLLaiokKh9zPPPKOQTZ06VSHr16+fQjZ79myFzNF4yjnH7373O4/6RivCE5e0zu+/t53O\nKV3fF54gHPU7fPiwLDyFsCV05cqVsnS1tbWyLZGhgrdLMQcAXA/gHyr/O845H60iJwiiHRz3zQPq\nBtVAeqiSN2x44dXAzjk/BgBM/VOnO4EgCCII+NN42pcx9iMAHYAnOOfFfqyLIEIOTz1PBf785z+L\nSwCnT58GAHTt2lWcvet0OgDA4MGDxWWD6upqALa96MKSg2DEjIuLE/MKyyT33HOPuC9fWJaQ7kUX\n0u3cuROjRo0C8KtnaktLi0Ln999/HwcOHJDl/fnnnz3tAk1wznH//ffDZDKJ+/elOjjOO+fOnSt6\n7wpLNq2trbKll7feegtFRUXi8YJCW9ra2vzaFl/hcmBnjH0BQBrfk8FmOFjEOXcWc7QSQG/Oeb19\n7f0jxtgQzrnqVoMlS5aIrwsLC1FYWKhNe4IIUXJyctCvXz+P8i5atAgbNmzA66+/rvif9CxMgWPH\njilkajs1TCaTIuTApk2bFOnU9pi3trZi3759Mpmw00VKW1ubIt0ll1yiSOdL3nrrLaxYsUIhHzdu\nnGxQz8/PB2BzKJKSm5uriA46b9481bq6d+/urboeU1RUhKKiIm2JtRiCNBiKdgAY7cn/QbtiiAgE\n0HbmqTesWrVKsQPG3TNPjx07ppC9++67Ctm6desUMsczTwHw2bNnK2QFBQXaGuQhS5YsUW2fNwDg\nNTU1Ctk333zj03q8AQEKKSD+NDLG0hljUfbXuQDyAJz0YV0E0eHxtwesFDKe2giXfvB2u+N1jLFy\nAAUAPmGMfW7/1yQA+xljPwH4L4C7OecN3qlKEARBaMHbXTEfAfhIRb4BwAZvyiaIcMfReKrX6/HH\nP/5RZoCrq6vDc889Jwb58oRXXnlFXBc/evQoAJshVJjRC8bQ5cuXKwyvakG7Pv74YzQ0yOdhf/nL\nX7B06VKZ7M033xSNlAKbN29WeHYeOXLEo3Zp5fz58wAgs0nodDp06dJFNHoCNkPpmDFjcNlll7Vb\nnmCHWLVqlegDEC5GUwEmbXhQFGCMB1sHgvA1vXv3Rt++ffH111+LMmeP8TExMapx1F1RXl6O3r17\nK+Q9e/bE2bNnxYF9165dGD9+vGoZu3btwqWXXgrANqCp7aH3ln79+uHkSf+txBYXF2PixIma07sa\nbwwGAzIzMxU/bgBw4cIFhdNasGCMgXOuelNREDCC8APl5eWqB3IA8g0L8fHxHh9U3atXL1XDWWVl\npWz9Xdid45gOgMxrUpj179mzR5Fu/fr1mrxt1TxPPT1gXCsTJkzQtMlD8Dx1RXx8POrr61XLCJVB\n3RU0sBMEIcPXBsJwiL0eadDAThAEEWFQ2F6C8BNnz57Ftm3bFHKpTDBeSmUtLS0YN26cGAzMHwjL\nPy+++CJ69uzpMr1er9dU7oEDBxRtDhUbmnBC1tatW8WnEoPBgJycHNGrNmLQsjblzwvkoEREIJdf\nfrlXYW0zMjJ8pota2N7m5mandS9atEhMZ7VaOQD+3nvvuawnNzdXtTxHh6dgcfLkSU1hjsMFtOOg\nRDN2gvAD27dvV8iEAxxcHX13ww03YOPGjT7TRTjDVBq2V3hdUVGBrKwsUc4Yk4UUEGa2Wpyh1MIU\nWyyWkDnqTwgzLKWxsVF2xmukQAM7QQQIrQOcr42X7pbny4E4VAb1jgYZTwmCICIMmrETRIhRWVkJ\nALJ98K2trejZs6foCSlQU1MjM2yaTCYYjUbZsotQnhTBeHry5EnRgCuE7T158qToWCUsXZw5c0am\nj16vx9ChQz1vZIggLI9JPXUjAfI8JYgQ46WXXsIjjzyikKelpaGurk58v3nzZlx77bWay21ubhYH\n/MrKSo8O2payZcsWTJ061asygs2ZM2fQp08f6HQ6MUZ7uECepwQRRjz88MOKXQ4PPfSQIhZ7eXk5\nAPnONovFgtbWVplsz549AOTGU8FgqtPpFJ6i//znP2UyvV6v6mWq1ZMzlBHOfg23Qd0VNLATRBig\nZoQUTguSEhUVpZC7a8B0PGjD3yEBCN9DAztBEESEQQM7QYQBzo6604LUQCggLKdIZQKOsubmZtFr\nU0pTU5Om+kMJx+Usoa2RZuejgZ0gwoDRo0cDsBnMhOtPf/qT6nKMM6Kjo8W8wg6Q1tZW8f/CD8Vt\nt90mqyclJQXx8fEyGQCMGDHCV80LCBUVFejatausHUK0RiGOfaRAu2IIIkwwm82ymaXBYIDVanUZ\nPbGqqgpZWVkwGAwyZ6WoqCjF+jtjDEVFRRg3bpwoa2pqQnx8vCxWO2NMcQB0qPPDDz9gzJgxsn7Y\nv38/Lr74YlgslrDb7tjerhivPhnG2DIAVwMwADgB4E7Ouc7+v4UA5gAwA3iAc66MhkQQhGYcB1JH\nI6crtB6ikZKSIis7XGKQa0XaD/Hx8QACe35sIPC2NdsADOWcjwRQCmAhADDGhgC4GUA+gN8CWMnC\n5RRYgiCIMMergZ1zvp1zLlhavgOQY399DYD1nHMz57wMtkF/jDd1EQThGWoGUkD9vNNIRjAiS3HW\nN+GOLxfJ5gBYZ3+dDWC35H8VdhlBEH7k6NGjyM/PV/2f1ofm9PR0X6oUMgj78dX6obKyUhblMtxx\nObAzxr4AII34z2CLYbyIc/6xPc0iACbO+TpJGkecWkiXLFkivi4sLERhYaErtQiCUOHs2bMAgEOH\nDomyqqoqXHHFFTKZ4KGanJwsyqxWK6Kjo1UPyI4ERowYgYqKCtkh1WVlZZg+fToyMzODqJk2ioqK\nUFRUpCmt17tiGGO3A5gPYArn3GCXLYAtCPxS+/stABZzzktU8tOuGILwEd988w0mTZok2z0j7Iqh\n75kSIVZMOPaN32LFMMamAXgEwDXCoG5nM4CZjLE4xlg/AHkAwj+wBEEQRBjg7Rr7awDiAHxhX7f6\njnN+D+f8MGPsvwAOAzABuIem5QQRHDrCV08t7K5WWSRCDkoEEUEcOXIEQ4YMUf2fNGxvJHHw4EEM\nHz7cp2VGRUWhpqYmpA3JfnNQIggitMjPz8e2bdvQ2NgoczIaOnRoRA7qAPDhhx8CADZu3Cjb8dLa\n2oq4uDiZd63BYEBUVJSsb/R6PaKjo0VnJavVihtuuCGst4PSwE4QEcaVV14ZbBWCwnXXXefT8tz1\n7A0lIn+xiSAIooNBAztBEGFNOC+Z+AtaiiEIIqxJTEwEoM2z1m5w1FRuOC/F0MBOEERY8/jjjyMv\nL088AxYAGhoakJ6eDrPZLMp0Oh3S0tJkMWOam5vRuXNnWcwYvV6PgQMHIi0tLTAN8AMRObAXFRVF\nRFiCSGkHQG0JVSKlLZmZmZg5c2aw1fAJvvhMInKNXWs8hVAnUtoBUFtClUhpS6S0A/BNWyJyYCcI\ngujI0MBOEAQRYYRESIGgKkAQBBGmOAspEPSBnSAIgvAttBRDEAQRYdDAThAEEWHQwE4QBBFhRMzA\nzhh7mjH2M2PsJ8bYFsZYpuR/yxljpYyxfYyxkcHUUwuMsWWMsSN2fT9kjHWW/G+hvS1HGGNXBVNP\nLTDGbmKMHWSMWRhjox3+F25tmcYYO8oY+4Ux9miw9XEHxthbjLEaxth+iSyNMbaNMXaMMbaVMdYl\nmDpqhTGWwxj7ijF2mDF2gDF2v10eVu1hjMUzxkrsY9YBxthiu7wvY+w7ezvWMcbcdyTlnEfEBSBZ\n8vo+AH+3v/4dgE/tr8fCdspT0PV10ZYrAETZX78I4AX76yEAfoLNY7gvgOOwG8BD9QIwCMAAAF8B\nGC2R54dTW2CbBB0H0AdALIB9AAYHWy839J8AYCSA/RLZUgCP2F8/CuDFYOupsS2ZAEbaXycDOAZg\ncDi2B0Ci/W80gO/sY9R/APzeLv87gLvdLTdiZuyc82bJ2yQAQvCHawC8Y09TAqALYywjwOq5Bed8\nO+dc0P87ADn219cAWM85N3POywCUAhgTBBU1wzk/xjkvBeC4LetahFdbxgAo5Zyf5pybAKyHrQ1h\nAee8GEC9g/haAGvtr9cC8G1Acz/BOa/mnO+zv24GcAS270jYtYdzrre/jIdtksMBXAbgQ7t8LYDr\n3S03YgZ2AGCMPcsYOwPgFgBP2sXZAMolySrssnBhDoDP7K/DvS1Swq0tjvqeRWjrq4UenPMawDZY\nAugeZH3chjHWF7Ynke8AZIRbexhjUYyxnwBUA/gCwAkADZKJ3VkAWe6WG1ZBwBhjXwCQzrYZbL9w\nizjnH3POHwfwuH398z4AS6CcKcKeJ6i4aos9zSIAJs75OkkaR8KiLWrZVGRBb0s7hJu+EQ9jLBnA\nBwAe4Jw3h6Ozo30AH2W3o22EbYlSkczdcsNqYOecaz3zax2AT2Ab2M8C6CX5Xw6ASt9q5j6u2sIY\nux02+8AUiTgs2+KEkGxLO5wF0FvyPtT11UINYyyDc15j32xQG2yFtGI3KH4A4F+c8012cdi2h3Ou\nY4ztBFAAIJUxFmUf9D26zyJmKYYxlid5ey2Ao/bXmwHcZk9TANtjTk2A1XMLxtg0AI8AuIZzLj0e\nZjOAmYyxOMZYPwB5AL4Pho4eIp31hltbfgCQxxjrwxiLAzATtjaEEwzKz+AO++vbAWxyzBDCrAFw\nmHP+qkQWVu1hjKULO3cYYwmwbZo4DGAHgN/bk3nWjmBbhX1oXf4AwH7YditsAtBT8r8VsO1o+BmS\nnRmhesFmSDwNYK/9Win530J7W44AuCrYumpoy3WwrU23AqgC8HkYt2UabDswSgEsCLY+bur+Hmwz\nPwOAMwDuBJAGYLu9TV8ASA22nhrbMh6Axf5d/8n+HZkGoGs4tQfAcLvu++xj1yK7vB+AEgC/wLZD\nJtbdsilWDEEQRIQRMUsxBEEQhA0a2AmCICIMGtgJgiAiDBrYCYIgIgwa2AmCICIMGtgJgiAiDBrY\nCYIgIoz/D/EoAGQ0K3jsAAAAAElFTkSuQmCC\n",
1486       "text/plain": [
1487        "<matplotlib.figure.Figure at 0x7fc85ce54208>"
1488       ]
1489      },
1490      "metadata": {},
1491      "output_type": "display_data"
1492     }
1493    ],
1494    "source": [
1495     "plot_trace(trace_tour(w))"
1496    ]
1497   },
1498   {
1499    "cell_type": "code",
1500    "execution_count": 488,
1501    "metadata": {},
1502    "outputs": [],
1503    "source": [
1504     "walks_m = {i: list() for i in range(4)}\n",
1505     "while all(len(w_m) < 10 for w_m in walks_m.values()):\n",
1506     "    w = random_walk()\n",
1507     "    ps = mistake_positions(w)\n",
1508     "    if not ps or ps[0][0] > 30:\n",
1509     "        walks_m[0] += [w[:ps[0][0]]]\n",
1510     "    if len(ps) >= 2\n",
1511     "        \n",
1512     "    if len(w) > 30: \n",
1513     "        walks_m[i] += [w]"
1514    ]
1515   },
1516   {
1517    "cell_type": "code",
1518    "execution_count": 489,
1519    "metadata": {},
1520    "outputs": [
1521     {
1522      "data": {
1523       "text/plain": [
1524        "{0: ['LRLRLRLFRFLFFLRFRRLRLFLLRFLRRLLFFFLRLRLLRLF',\n",
1525        "  'FFRLLFFFFRFLRFRLLRFFRFFFFFFLLRRLRRFFR',\n",
1526        "  'LFRRFLLRFFLFRLRFLRRLLFRRFLFLRRFFLFFLRFFLFFLFLFRRR',\n",
1527        "  'FLFLFFLRRFFFFLFRFFLFRFFLFFRLFRRR',\n",
1528        "  'LLFLLRFFRLLFRFLFRLRFFRFFLFFLRLFRLLFLFF',\n",
1529        "  'RFRRLRLLRRFLFFRRLRFFFLFRRLFLFLRRR',\n",
1530        "  'FFLFFRFLFLRLFFLLFRRFFFRLLFFFRFFRRR',\n",
1531        "  'LRRLFRFLRFFFFRLLRLRFLRFLLRRFRLLRFRLFLFLRRR',\n",
1532        "  'LRLFLRRFLFRRLRFRFLFLRLLFRRFFRLRFLLFL',\n",
1533        "  'RLRRLFLFRRLLFFRFRFLFFLRLFLRLRFLLFRFFFLRRFRFLFFRFLFRLFFRRR'],\n",
1534        " 1: ['RRFLRRLLFLRLRRLFRLFFFRLLFRFLFRRLLLL',\n",
1535        "  'LRLFFLRRFLLRLRRLLRLRFLRLFFLLLFLRRR',\n",
1536        "  'RFRRLFRLRLRRFLLRFLFFLRRFLRRFRRL',\n",
1537        "  'FFFRFLFRLFFLFLLLFLFFLRFFRFFFRRLRRLF',\n",
1538        "  'FLFRFFRLLRFRLLRFFRFLFLFLRFFFLRRLLLF',\n",
1539        "  'FRRLRLLFRFLRFRLRRFRFFFLRFFRLRFFLLFRFLRFFRLFRRLLL',\n",
1540        "  'FFLRLRFLFLRRFFLFFRRRFRLFLFRRLLFRFRLLFFLLF',\n",
1541        "  'FLRRFLRLFFFFRFLFLLLFFRFLFRLLFRRLLL',\n",
1542        "  'RFFFRFLLRFFRFFFRRRFLRLFRFFLRLLFLF',\n",
1543        "  'FFRFLFLLRRLRLFFRLFFLFRLFLRFFLLFFLF'],\n",
1544        " 2: ['FFLRFRFRLFRFFFFLRFRLRFRLFLLLRLFLRLFLLRLR',\n",
1545        "  'FFLFRLLRLRRFFRLFLRFFFFRLFLRFFLLLFRFLFRRLR',\n",
1546        "  'RRLFRRFFFLLRFFLFFLFFLFLRFRLLRFFLFFLFRLLFRF',\n",
1547        "  'FFRFLRLLRRFFRRLFFFFFFLLLFRFLFRFL',\n",
1548        "  'FFRFFFLFLFRLRFRRLRLLFFLLLFLRFLRFLLLL',\n",
1549        "  'FFFFFFFFFFFFFFLLFLFLFRLRFFLRFFRFLFRFLFRRLLRLRLRLFRFLFLLLL',\n",
1550        "  'LFFRFFRFFFFRFRLFFRLFRLFFLLRFRLLFLRFLRRLLFR',\n",
1551        "  'FRFRLRLLFFRFFLRFLRFRFLLFLRLFFLLL',\n",
1552        "  'LRLLLLRFLRRFFLFRFRFFLFLLRRLFRLFRLFLFFFFFFRFRFLFRLFFLRFFLRFRRLLRFFRRLRRL',\n",
1553        "  'FLRFLRLLRLRFRLRLLRFLFFLRLRLFRRRLLFLFFRFLLRLLRFLRLFRFLFRRR']}"
1554       ]
1555      },
1556      "execution_count": 489,
1557      "metadata": {},
1558      "output_type": "execute_result"
1559     }
1560    ],
1561    "source": [
1562     "walks_m"
1563    ]
1564   },
1565   {
1566    "cell_type": "code",
1567    "execution_count": 490,
1568    "metadata": {},
1569    "outputs": [
1570     {
1571      "data": {
1572       "image/png": 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L3H777UC0w4aWlhb27t3LtddeG2mPLoWXl2tnm9mzwHF3/34vzylomFtbW7nkkktYtWoV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\nTwAAAABJRU5ErkJggg==\n",
1573       "text/plain": [
1574        "<matplotlib.figure.Figure at 0x7fc85eae9c88>"
1575       ]
1576      },
1577      "metadata": {},
1578      "output_type": "display_data"
1579     }
1580    ],
1581    "source": [
1582     "plot_trace(trace_tour(walks_m[0][0]))"
1583    ]
1584   },
1585   {
1586    "cell_type": "code",
1587    "execution_count": null,
1588    "metadata": {
1589     "collapsed": true
1590    },
1591    "outputs": [],
1592    "source": []
1593   }
1594  ],
1595  "metadata": {
1596   "kernelspec": {
1597    "display_name": "Python 3",
1598    "language": "python",
1599    "name": "python3"
1600   },
1601   "language_info": {
1602    "codemirror_mode": {
1603     "name": "ipython",
1604     "version": 3
1605    },
1606    "file_extension": ".py",
1607    "mimetype": "text/x-python",
1608    "name": "python",
1609    "nbconvert_exporter": "python",
1610    "pygments_lexer": "ipython3",
1611    "version": "3.5.2+"
1612   }
1613  },
1614  "nbformat": 4,
1615  "nbformat_minor": 2
1616 }