06-tour-shapes/tour-shapes-build-raw-tours.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": 1,
  15    "metadata": {
  16     "collapsed": true
  17    },
  18    "outputs": [],
  19    "source": [
  20     "import collections\n",
  21     "import enum\n",
  22     "import random\n",
  23     "import os\n",
  24     "\n",
  25     "import matplotlib.pyplot as plt\n",
  26     "%matplotlib inline\n"
  27    ]
  28   },
  29   {
  30    "cell_type": "code",
  31    "execution_count": 2,
  32    "metadata": {
  33     "collapsed": true
  34    },
  35    "outputs": [],
  36    "source": [
  37     "class Direction(enum.Enum):\n",
  38     "    UP = 1\n",
  39     "    RIGHT = 2\n",
  40     "    DOWN = 3\n",
  41     "    LEFT = 4\n",
  42     "    \n",
  43     "turn_lefts = {Direction.UP: Direction.LEFT, Direction.LEFT: Direction.DOWN,\n",
  44     "              Direction.DOWN: Direction.RIGHT, Direction.RIGHT: Direction.UP}\n",
  45     "\n",
  46     "turn_rights = {Direction.UP: Direction.RIGHT, Direction.RIGHT: Direction.DOWN,\n",
  47     "               Direction.DOWN: Direction.LEFT, Direction.LEFT: Direction.UP}\n",
  48     "\n",
  49     "def turn_left(d):\n",
  50     "    return turn_lefts[d]\n",
  51     "\n",
  52     "def turn_right(d):\n",
  53     "    return turn_rights[d]\n"
  54    ]
  55   },
  56   {
  57    "cell_type": "code",
  58    "execution_count": 3,
  59    "metadata": {
  60     "collapsed": true
  61    },
  62    "outputs": [],
  63    "source": [
  64     "Step = collections.namedtuple('Step', ['x', 'y', 'dir'])\n",
  65     "Mistake = collections.namedtuple('Mistake', ['i', 'step'])"
  66    ]
  67   },
  68   {
  69    "cell_type": "code",
  70    "execution_count": 4,
  71    "metadata": {
  72     "collapsed": true
  73    },
  74    "outputs": [],
  75    "source": [
  76     "def advance(step, d):\n",
  77     "    if d == Direction.UP:\n",
  78     "        return Step(step.x, step.y+1, d)\n",
  79     "    elif d == Direction.DOWN:\n",
  80     "        return Step(step.x, step.y-1, d)\n",
  81     "    elif d == Direction.LEFT:\n",
  82     "        return Step(step.x-1, step.y, d)\n",
  83     "    elif d == Direction.RIGHT:\n",
  84     "        return Step(step.x+1, step.y, d)"
  85    ]
  86   },
  87   {
  88    "cell_type": "code",
  89    "execution_count": 5,
  90    "metadata": {
  91     "collapsed": true
  92    },
  93    "outputs": [],
  94    "source": [
  95     "def step(s, current):\n",
  96     "    if s == 'F':\n",
  97     "        return advance(current, current.dir)\n",
  98     "    elif s == 'L':\n",
  99     "        return advance(current, turn_left(current.dir))\n",
 100     "    elif s == 'R':\n",
 101     "        return advance(current, turn_right(current.dir))\n",
 102     "    else:\n",
 103     "        raise ValueError"
 104    ]
 105   },
 106   {
 107    "cell_type": "code",
 108    "execution_count": 6,
 109    "metadata": {
 110     "collapsed": true
 111    },
 112    "outputs": [],
 113    "source": [
 114     "def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
 115     "    current = Step(startx, starty, startdir)\n",
 116     "    trace = [current]\n",
 117     "    for s in tour:\n",
 118     "        current = step(s, current)\n",
 119     "        trace += [current]\n",
 120     "    return trace    "
 121    ]
 122   },
 123   {
 124    "cell_type": "code",
 125    "execution_count": 6,
 126    "metadata": {
 127     "collapsed": true
 128    },
 129    "outputs": [],
 130    "source": [
 131     "# def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
 132     "#     current = Step(startx, starty, startdir)\n",
 133     "#     trace = [current]\n",
 134     "#     for s in tour:\n",
 135     "#         if s == 'F':\n",
 136     "#             current = advance(current, current.dir)\n",
 137     "#         elif s == 'L':\n",
 138     "#             current = advance(current, turn_left(current.dir))\n",
 139     "#         elif s == 'R':\n",
 140     "#             current = advance(current, turn_right(current.dir))\n",
 141     "#         trace += [current]\n",
 142     "#     return trace    "
 143    ]
 144   },
 145   {
 146    "cell_type": "code",
 147    "execution_count": 7,
 148    "metadata": {
 149     "collapsed": true
 150    },
 151    "outputs": [],
 152    "source": [
 153     "k = Step(1, 2, 3)"
 154    ]
 155   },
 156   {
 157    "cell_type": "code",
 158    "execution_count": 8,
 159    "metadata": {},
 160    "outputs": [
 161     {
 162      "data": {
 163       "text/plain": [
 164        "Step(x=1, y=2, dir=3)"
 165       ]
 166      },
 167      "execution_count": 8,
 168      "metadata": {},
 169      "output_type": "execute_result"
 170     }
 171    ],
 172    "source": [
 173     "k"
 174    ]
 175   },
 176   {
 177    "cell_type": "code",
 178    "execution_count": 9,
 179    "metadata": {},
 180    "outputs": [
 181     {
 182      "data": {
 183       "text/plain": [
 184        "__main__.Step"
 185       ]
 186      },
 187      "execution_count": 9,
 188      "metadata": {},
 189      "output_type": "execute_result"
 190     }
 191    ],
 192    "source": [
 193     "Step"
 194    ]
 195   },
 196   {
 197    "cell_type": "code",
 198    "execution_count": 10,
 199    "metadata": {},
 200    "outputs": [
 201     {
 202      "data": {
 203       "text/plain": [
 204        "<Direction.UP: 1>"
 205       ]
 206      },
 207      "execution_count": 10,
 208      "metadata": {},
 209      "output_type": "execute_result"
 210     }
 211    ],
 212    "source": [
 213     "d = Direction.UP\n",
 214     "d"
 215    ]
 216   },
 217   {
 218    "cell_type": "code",
 219    "execution_count": 11,
 220    "metadata": {},
 221    "outputs": [
 222     {
 223      "data": {
 224       "text/plain": [
 225        "<Direction.RIGHT: 2>"
 226       ]
 227      },
 228      "execution_count": 11,
 229      "metadata": {},
 230      "output_type": "execute_result"
 231     }
 232    ],
 233    "source": [
 234     "turn_right(d)"
 235    ]
 236   },
 237   {
 238    "cell_type": "code",
 239    "execution_count": 12,
 240    "metadata": {},
 241    "outputs": [
 242     {
 243      "data": {
 244       "text/plain": [
 245        "{<Direction.RIGHT: 2>: <Direction.DOWN: 3>,\n",
 246        " <Direction.UP: 1>: <Direction.RIGHT: 2>,\n",
 247        " <Direction.LEFT: 4>: <Direction.UP: 1>,\n",
 248        " <Direction.DOWN: 3>: <Direction.LEFT: 4>}"
 249       ]
 250      },
 251      "execution_count": 12,
 252      "metadata": {},
 253      "output_type": "execute_result"
 254     }
 255    ],
 256    "source": [
 257     "turn_rights"
 258    ]
 259   },
 260   {
 261    "cell_type": "code",
 262    "execution_count": 13,
 263    "metadata": {},
 264    "outputs": [
 265     {
 266      "data": {
 267       "text/plain": [
 268        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 269        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 270        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 271        " Step(x=2, y=1, dir=<Direction.RIGHT: 2>),\n",
 272        " Step(x=2, y=2, dir=<Direction.UP: 1>)]"
 273       ]
 274      },
 275      "execution_count": 13,
 276      "metadata": {},
 277      "output_type": "execute_result"
 278     }
 279    ],
 280    "source": [
 281     "trace_tour('FLRL')"
 282    ]
 283   },
 284   {
 285    "cell_type": "code",
 286    "execution_count": 14,
 287    "metadata": {},
 288    "outputs": [
 289     {
 290      "data": {
 291       "text/plain": [
 292        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 293        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 294        " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
 295        " Step(x=2, y=1, dir=<Direction.UP: 1>),\n",
 296        " Step(x=3, y=1, dir=<Direction.RIGHT: 2>),\n",
 297        " Step(x=3, y=2, dir=<Direction.UP: 1>),\n",
 298        " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
 299        " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
 300        " Step(x=1, y=1, dir=<Direction.DOWN: 3>),\n",
 301        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
 302        " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
 303       ]
 304      },
 305      "execution_count": 14,
 306      "metadata": {},
 307      "output_type": "execute_result"
 308     }
 309    ],
 310    "source": [
 311     "trace_tour('FFLRLLFLRL')"
 312    ]
 313   },
 314   {
 315    "cell_type": "code",
 316    "execution_count": 15,
 317    "metadata": {},
 318    "outputs": [
 319     {
 320      "data": {
 321       "text/plain": [
 322        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 323        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 324        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 325        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
 326        " Step(x=-1, y=1, dir=<Direction.LEFT: 4>),\n",
 327        " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
 328        " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
 329        " Step(x=-2, y=-1, dir=<Direction.DOWN: 3>),\n",
 330        " Step(x=-2, y=-2, dir=<Direction.DOWN: 3>),\n",
 331        " Step(x=-2, y=-3, dir=<Direction.DOWN: 3>),\n",
 332        " Step(x=-1, y=-3, dir=<Direction.RIGHT: 2>),\n",
 333        " Step(x=0, y=-3, dir=<Direction.RIGHT: 2>),\n",
 334        " Step(x=1, y=-3, dir=<Direction.RIGHT: 2>),\n",
 335        " Step(x=1, y=-2, dir=<Direction.UP: 1>),\n",
 336        " Step(x=1, y=-1, dir=<Direction.UP: 1>),\n",
 337        " Step(x=0, y=-1, dir=<Direction.LEFT: 4>),\n",
 338        " Step(x=0, y=-2, dir=<Direction.DOWN: 3>),\n",
 339        " Step(x=-1, y=-2, dir=<Direction.LEFT: 4>),\n",
 340        " Step(x=-1, y=-1, dir=<Direction.UP: 1>),\n",
 341        " Step(x=-1, y=0, dir=<Direction.UP: 1>),\n",
 342        " Step(x=0, y=0, dir=<Direction.RIGHT: 2>)]"
 343       ]
 344      },
 345      "execution_count": 15,
 346      "metadata": {},
 347      "output_type": "execute_result"
 348     }
 349    ],
 350    "source": [
 351     "trace_tour('FLLFFLFFFLFFLFLLRRFR')"
 352    ]
 353   },
 354   {
 355    "cell_type": "code",
 356    "execution_count": 16,
 357    "metadata": {},
 358    "outputs": [
 359     {
 360      "data": {
 361       "text/plain": [
 362        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 363        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 364        " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
 365        " Step(x=2, y=-1, dir=<Direction.DOWN: 3>),\n",
 366        " Step(x=3, y=-1, dir=<Direction.RIGHT: 2>),\n",
 367        " Step(x=3, y=0, dir=<Direction.UP: 1>),\n",
 368        " Step(x=3, y=1, dir=<Direction.UP: 1>),\n",
 369        " Step(x=4, y=1, dir=<Direction.RIGHT: 2>),\n",
 370        " Step(x=4, y=2, dir=<Direction.UP: 1>),\n",
 371        " Step(x=3, y=2, dir=<Direction.LEFT: 4>),\n",
 372        " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
 373        " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
 374        " Step(x=0, y=2, dir=<Direction.LEFT: 4>),\n",
 375        " Step(x=0, y=3, dir=<Direction.UP: 1>),\n",
 376        " Step(x=0, y=4, dir=<Direction.UP: 1>),\n",
 377        " Step(x=-1, y=4, dir=<Direction.LEFT: 4>),\n",
 378        " Step(x=-1, y=3, dir=<Direction.DOWN: 3>),\n",
 379        " Step(x=-2, y=3, dir=<Direction.LEFT: 4>),\n",
 380        " Step(x=-2, y=2, dir=<Direction.DOWN: 3>),\n",
 381        " Step(x=-1, y=2, dir=<Direction.RIGHT: 2>),\n",
 382        " Step(x=-1, y=1, dir=<Direction.DOWN: 3>),\n",
 383        " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
 384        " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
 385        " Step(x=-1, y=0, dir=<Direction.RIGHT: 2>),\n",
 386        " Step(x=-1, y=-1, dir=<Direction.DOWN: 3>),\n",
 387        " Step(x=0, y=-1, dir=<Direction.RIGHT: 2>),\n",
 388        " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
 389       ]
 390      },
 391      "execution_count": 16,
 392      "metadata": {},
 393      "output_type": "execute_result"
 394     }
 395    ],
 396    "source": [
 397     "trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL')"
 398    ]
 399   },
 400   {
 401    "cell_type": "code",
 402    "execution_count": 17,
 403    "metadata": {
 404     "collapsed": true
 405    },
 406    "outputs": [],
 407    "source": [
 408     "def positions(trace):\n",
 409     "    return [(s.x, s.y) for s in trace]"
 410    ]
 411   },
 412   {
 413    "cell_type": "code",
 414    "execution_count": 18,
 415    "metadata": {},
 416    "outputs": [
 417     {
 418      "data": {
 419       "text/plain": [
 420        "[(0, 0),\n",
 421        " (1, 0),\n",
 422        " (2, 0),\n",
 423        " (2, -1),\n",
 424        " (3, -1),\n",
 425        " (3, 0),\n",
 426        " (3, 1),\n",
 427        " (4, 1),\n",
 428        " (4, 2),\n",
 429        " (3, 2),\n",
 430        " (2, 2),\n",
 431        " (1, 2),\n",
 432        " (0, 2),\n",
 433        " (0, 3),\n",
 434        " (0, 4),\n",
 435        " (-1, 4),\n",
 436        " (-1, 3),\n",
 437        " (-2, 3),\n",
 438        " (-2, 2),\n",
 439        " (-1, 2),\n",
 440        " (-1, 1),\n",
 441        " (-2, 1),\n",
 442        " (-2, 0),\n",
 443        " (-1, 0),\n",
 444        " (-1, -1),\n",
 445        " (0, -1),\n",
 446        " (0, 0)]"
 447       ]
 448      },
 449      "execution_count": 18,
 450      "metadata": {},
 451      "output_type": "execute_result"
 452     }
 453    ],
 454    "source": [
 455     "positions(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 456    ]
 457   },
 458   {
 459    "cell_type": "code",
 460    "execution_count": 19,
 461    "metadata": {
 462     "collapsed": true
 463    },
 464    "outputs": [],
 465    "source": [
 466     "def valid(trace):\n",
 467     "    return (trace[-1].x == 0 \n",
 468     "            and trace[-1].y == 0 \n",
 469     "            and len(set(positions(trace))) + 1 == len(trace))"
 470    ]
 471   },
 472   {
 473    "cell_type": "code",
 474    "execution_count": 20,
 475    "metadata": {},
 476    "outputs": [
 477     {
 478      "data": {
 479       "text/plain": [
 480        "True"
 481       ]
 482      },
 483      "execution_count": 20,
 484      "metadata": {},
 485      "output_type": "execute_result"
 486     }
 487    ],
 488    "source": [
 489     "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 490    ]
 491   },
 492   {
 493    "cell_type": "code",
 494    "execution_count": 21,
 495    "metadata": {},
 496    "outputs": [
 497     {
 498      "data": {
 499       "text/plain": [
 500        "False"
 501       ]
 502      },
 503      "execution_count": 21,
 504      "metadata": {},
 505      "output_type": "execute_result"
 506     }
 507    ],
 508    "source": [
 509     "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLLFF'))"
 510    ]
 511   },
 512   {
 513    "cell_type": "code",
 514    "execution_count": 22,
 515    "metadata": {},
 516    "outputs": [
 517     {
 518      "data": {
 519       "text/plain": [
 520        "False"
 521       ]
 522      },
 523      "execution_count": 22,
 524      "metadata": {},
 525      "output_type": "execute_result"
 526     }
 527    ],
 528    "source": [
 529     "valid(trace_tour('FFLLLFRR'))"
 530    ]
 531   },
 532   {
 533    "cell_type": "code",
 534    "execution_count": 23,
 535    "metadata": {},
 536    "outputs": [
 537     {
 538      "data": {
 539       "text/plain": [
 540        "False"
 541       ]
 542      },
 543      "execution_count": 23,
 544      "metadata": {},
 545      "output_type": "execute_result"
 546     }
 547    ],
 548    "source": [
 549     "valid(trace_tour('F'))"
 550    ]
 551   },
 552   {
 553    "cell_type": "code",
 554    "execution_count": 24,
 555    "metadata": {},
 556    "outputs": [
 557     {
 558      "data": {
 559       "text/plain": [
 560        "True"
 561       ]
 562      },
 563      "execution_count": 24,
 564      "metadata": {},
 565      "output_type": "execute_result"
 566     }
 567    ],
 568    "source": [
 569     "valid(trace_tour('LLLL'))"
 570    ]
 571   },
 572   {
 573    "cell_type": "code",
 574    "execution_count": 25,
 575    "metadata": {
 576     "collapsed": true
 577    },
 578    "outputs": [],
 579    "source": [
 580     "def chunks(items, n=2):\n",
 581     "    return [items[i:i+n] for i in range(len(items) - n + 1)]"
 582    ]
 583   },
 584   {
 585    "cell_type": "code",
 586    "execution_count": 26,
 587    "metadata": {},
 588    "outputs": [
 589     {
 590      "data": {
 591       "text/plain": [
 592        "['abcdefg',\n",
 593        " 'bcdefgh',\n",
 594        " 'cdefghi',\n",
 595        " 'defghij',\n",
 596        " 'efghijk',\n",
 597        " 'fghijkl',\n",
 598        " 'ghijklm',\n",
 599        " 'hijklmn',\n",
 600        " 'ijklmno',\n",
 601        " 'jklmnop',\n",
 602        " 'klmnopq',\n",
 603        " 'lmnopqr',\n",
 604        " 'mnopqrs',\n",
 605        " 'nopqrst',\n",
 606        " 'opqrstu',\n",
 607        " 'pqrstuv',\n",
 608        " 'qrstuvw',\n",
 609        " 'rstuvwx',\n",
 610        " 'stuvwxy',\n",
 611        " 'tuvwxyz']"
 612       ]
 613      },
 614      "execution_count": 26,
 615      "metadata": {},
 616      "output_type": "execute_result"
 617     }
 618    ],
 619    "source": [
 620     "import string\n",
 621     "chunks(string.ascii_lowercase, 7)"
 622    ]
 623   },
 624   {
 625    "cell_type": "markdown",
 626    "metadata": {},
 627    "source": [
 628     "Using the [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula)"
 629    ]
 630   },
 631   {
 632    "cell_type": "code",
 633    "execution_count": 27,
 634    "metadata": {
 635     "collapsed": true
 636    },
 637    "outputs": [],
 638    "source": [
 639     "def shoelace(trace):\n",
 640     "    return abs(sum(s.x * t.y - t.x * s.y for s, t in chunks(trace, 2))) // 2"
 641    ]
 642   },
 643   {
 644    "cell_type": "code",
 645    "execution_count": 28,
 646    "metadata": {},
 647    "outputs": [
 648     {
 649      "data": {
 650       "text/plain": [
 651        "4"
 652       ]
 653      },
 654      "execution_count": 28,
 655      "metadata": {},
 656      "output_type": "execute_result"
 657     }
 658    ],
 659    "source": [
 660     "shoelace(trace_tour('FFLRLLFLRL'))"
 661    ]
 662   },
 663   {
 664    "cell_type": "code",
 665    "execution_count": 29,
 666    "metadata": {},
 667    "outputs": [
 668     {
 669      "data": {
 670       "text/plain": [
 671        "9"
 672       ]
 673      },
 674      "execution_count": 29,
 675      "metadata": {},
 676      "output_type": "execute_result"
 677     }
 678    ],
 679    "source": [
 680     "shoelace(trace_tour('FLLFFLFFFLFFLFLLRRFR'))"
 681    ]
 682   },
 683   {
 684    "cell_type": "code",
 685    "execution_count": 30,
 686    "metadata": {},
 687    "outputs": [
 688     {
 689      "data": {
 690       "text/plain": [
 691        "15"
 692       ]
 693      },
 694      "execution_count": 30,
 695      "metadata": {},
 696      "output_type": "execute_result"
 697     }
 698    ],
 699    "source": [
 700     "shoelace(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 701    ]
 702   },
 703   {
 704    "cell_type": "code",
 705    "execution_count": 31,
 706    "metadata": {
 707     "collapsed": true
 708    },
 709    "outputs": [],
 710    "source": [
 711     "def valid_prefix(tour):\n",
 712     "    current = Step(0, 0, Direction.RIGHT)\n",
 713     "    prefix = []\n",
 714     "    posns = []\n",
 715     "    for s in tour:\n",
 716     "        current = step(s, current)\n",
 717     "        prefix += [s]\n",
 718     "        if (current.x, current.y) in posns:\n",
 719     "            return ''\n",
 720     "        elif current.x == 0 and current.y == 0: \n",
 721     "            return ''.join(prefix)\n",
 722     "        posns += [(current.x, current.y)]\n",
 723     "    if current.x == 0 and current.y == 0:\n",
 724     "        return ''.join(prefix)\n",
 725     "    else:\n",
 726     "        return ''"
 727    ]
 728   },
 729   {
 730    "cell_type": "code",
 731    "execution_count": 32,
 732    "metadata": {
 733     "collapsed": true
 734    },
 735    "outputs": [],
 736    "source": [
 737     "def mistake_positions(trace, debug=False):\n",
 738     "    mistakes = []\n",
 739     "    current = trace[0]\n",
 740     "    posns = [(0, 0)]\n",
 741     "    for i, current in enumerate(trace[1:]):\n",
 742     "        if (current.x, current.y) in posns:\n",
 743     "            if debug: print(i, current)\n",
 744     "            mistakes += [Mistake(i+1, current)]\n",
 745     "        posns += [(current.x, current.y)]\n",
 746     "    if (current.x, current.y) == (0, 0):\n",
 747     "        return mistakes[:-1]\n",
 748     "    else:\n",
 749     "        return mistakes + [Mistake(len(trace)+1, current)]"
 750    ]
 751   },
 752   {
 753    "cell_type": "code",
 754    "execution_count": 33,
 755    "metadata": {
 756     "collapsed": true
 757    },
 758    "outputs": [],
 759    "source": [
 760     "def returns_to_origin(mistake_positions):\n",
 761     "    return [i for i, m in mistake_positions\n",
 762     "           if (m.x, m.y) == (0, 0)]"
 763    ]
 764   },
 765   {
 766    "cell_type": "code",
 767    "execution_count": 34,
 768    "metadata": {
 769     "collapsed": true
 770    },
 771    "outputs": [],
 772    "source": [
 773     "sample_tours = ['FFLRLLFLRL', 'FLLFFLFFFLFFLFLLRRFR', 'FFRLLFRLLFFFRFLLRLLRRLLRLL']"
 774    ]
 775   },
 776   {
 777    "cell_type": "code",
 778    "execution_count": 35,
 779    "metadata": {},
 780    "outputs": [
 781     {
 782      "data": {
 783       "text/plain": [
 784        "'FFLRLLFLRL'"
 785       ]
 786      },
 787      "execution_count": 35,
 788      "metadata": {},
 789      "output_type": "execute_result"
 790     }
 791    ],
 792    "source": [
 793     "valid_prefix(sample_tours[0])"
 794    ]
 795   },
 796   {
 797    "cell_type": "code",
 798    "execution_count": 36,
 799    "metadata": {
 800     "scrolled": true
 801    },
 802    "outputs": [
 803     {
 804      "data": {
 805       "text/plain": [
 806        "True"
 807       ]
 808      },
 809      "execution_count": 36,
 810      "metadata": {},
 811      "output_type": "execute_result"
 812     }
 813    ],
 814    "source": [
 815     "all(valid_prefix(t) == t for t in sample_tours)"
 816    ]
 817   },
 818   {
 819    "cell_type": "code",
 820    "execution_count": 37,
 821    "metadata": {},
 822    "outputs": [
 823     {
 824      "data": {
 825       "text/plain": [
 826        "True"
 827       ]
 828      },
 829      "execution_count": 37,
 830      "metadata": {},
 831      "output_type": "execute_result"
 832     }
 833    ],
 834    "source": [
 835     "valid_prefix(sample_tours[0] + 'FLLLL') == sample_tours[0]"
 836    ]
 837   },
 838   {
 839    "cell_type": "code",
 840    "execution_count": 38,
 841    "metadata": {},
 842    "outputs": [
 843     {
 844      "data": {
 845       "text/plain": [
 846        "[Mistake(i=10, step=Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
 847        " Mistake(i=13, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
 848       ]
 849      },
 850      "execution_count": 38,
 851      "metadata": {},
 852      "output_type": "execute_result"
 853     }
 854    ],
 855    "source": [
 856     "mistake_positions(trace_tour(sample_tours[0] + 'F'))"
 857    ]
 858   },
 859   {
 860    "cell_type": "code",
 861    "execution_count": 39,
 862    "metadata": {},
 863    "outputs": [
 864     {
 865      "data": {
 866       "text/plain": [
 867        "[Mistake(i=10, step=Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
 868        " Mistake(i=13, step=Step(x=1, y=0, dir=<Direction.UP: 1>)),\n",
 869        " Mistake(i=14, step=Step(x=0, y=0, dir=<Direction.LEFT: 4>)),\n",
 870        " Mistake(i=15, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>)),\n",
 871        " Mistake(i=17, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
 872       ]
 873      },
 874      "execution_count": 39,
 875      "metadata": {},
 876      "output_type": "execute_result"
 877     }
 878    ],
 879    "source": [
 880     "mistake_positions(trace_tour(sample_tours[0] + 'FLLLL'))"
 881    ]
 882   },
 883   {
 884    "cell_type": "code",
 885    "execution_count": 40,
 886    "metadata": {},
 887    "outputs": [
 888     {
 889      "data": {
 890       "text/plain": [
 891        "'FFLRLLFLRL'"
 892       ]
 893      },
 894      "execution_count": 40,
 895      "metadata": {},
 896      "output_type": "execute_result"
 897     }
 898    ],
 899    "source": [
 900     "(sample_tours[0] + 'FLLLL')[:10]"
 901    ]
 902   },
 903   {
 904    "cell_type": "code",
 905    "execution_count": 41,
 906    "metadata": {
 907     "collapsed": true
 908    },
 909    "outputs": [],
 910    "source": [
 911     "def random_walk(steps=1000):\n",
 912     "    return ''.join(random.choice('FFLR') for _ in range(steps))"
 913    ]
 914   },
 915   {
 916    "cell_type": "code",
 917    "execution_count": 42,
 918    "metadata": {},
 919    "outputs": [
 920     {
 921      "data": {
 922       "text/plain": [
 923        "''"
 924       ]
 925      },
 926      "execution_count": 42,
 927      "metadata": {},
 928      "output_type": "execute_result"
 929     }
 930    ],
 931    "source": [
 932     "valid_prefix(random_walk(1000))"
 933    ]
 934   },
 935   {
 936    "cell_type": "code",
 937    "execution_count": 45,
 938    "metadata": {},
 939    "outputs": [
 940     {
 941      "data": {
 942       "text/plain": [
 943        "'FFRRFR'"
 944       ]
 945      },
 946      "execution_count": 45,
 947      "metadata": {},
 948      "output_type": "execute_result"
 949     }
 950    ],
 951    "source": [
 952     "valid_prefix(random_walk(1000))"
 953    ]
 954   },
 955   {
 956    "cell_type": "code",
 957    "execution_count": 46,
 958    "metadata": {
 959     "collapsed": true,
 960     "scrolled": true
 961    },
 962    "outputs": [],
 963    "source": [
 964     "walks = []\n",
 965     "while len(walks) < 10:\n",
 966     "    w = valid_prefix(random_walk())\n",
 967     "    if len(w) > 30: walks += [w]"
 968    ]
 969   },
 970   {
 971    "cell_type": "code",
 972    "execution_count": 47,
 973    "metadata": {},
 974    "outputs": [
 975     {
 976      "data": {
 977       "text/plain": [
 978        "['RLFFLRFFFFRRLFFFRFFFFRFFLFFFRFRF',\n",
 979        " 'FFFFFLLFFRRLFFFFLLFFRLRFFLFFLRLL',\n",
 980        " 'LRLRLFFFFLLRLRLRFLFFFRLFLFFFLRLL',\n",
 981        " 'FLFFFFLFRLFFFFRLRFLLFFFFFFLRFLFLFLRFRFFRFFFFLRFFFLFRLRFLLFFFFRLFLFFR',\n",
 982        " 'LLFRLRFFLLRFRFLFFFLRLFFLFRFFFLFFRFFLFFFFLLFFFRFRFFLFRF',\n",
 983        " 'FLLFLFFFRLFFLLRFFFFLRFLFFLFFFFLRRF',\n",
 984        " 'FFLFRLLFFRFFFLRLFRLFLFFRLFFFLFFFRFRLRLFFLRRFFLLRLRFLFFLFFRFLFLLRRFFFRL',\n",
 985        " 'RFFFFFLLRLFFFRLFLRFLLFRFFFFFFFLLFFFFRLLR',\n",
 986        " 'LLFFFRLLFFFRFLLFRFFLLRFFLRLFLRRFLL',\n",
 987        " 'FLLRFLRFFRRFLFFRRLFFFFFFRFFRFFRL']"
 988       ]
 989      },
 990      "execution_count": 47,
 991      "metadata": {},
 992      "output_type": "execute_result"
 993     }
 994    ],
 995    "source": [
 996     "walks"
 997    ]
 998   },
 999   {
1000    "cell_type": "code",
1001    "execution_count": 48,
1002    "metadata": {},
1003    "outputs": [
1004     {
1005      "data": {
1006       "text/plain": [
1007        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
1008        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
1009        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
1010        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
1011        " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
1012       ]
1013      },
1014      "execution_count": 48,
1015      "metadata": {},
1016      "output_type": "execute_result"
1017     }
1018    ],
1019    "source": [
1020     "trace_tour('FLLL')"
1021    ]
1022   },
1023   {
1024    "cell_type": "code",
1025    "execution_count": 49,
1026    "metadata": {},
1027    "outputs": [
1028     {
1029      "data": {
1030       "text/plain": [
1031        "(-1, 3)"
1032       ]
1033      },
1034      "execution_count": 49,
1035      "metadata": {},
1036      "output_type": "execute_result"
1037     },
1038     {
1039      "data": {
1040       "image/png": 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aZghIUsMMAUlqmCEgSQ3rFAJJPpzkn5McTXLeceo2J9mb5IdJru3SpiSpP11nAnuA/wz8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\n",
1041       "text/plain": [
1042        "<matplotlib.figure.Figure at 0x7f03fdf356d8>"
1043       ]
1044      },
1045      "metadata": {},
1046      "output_type": "display_data"
1047     }
1048    ],
1049    "source": [
1050     "import matplotlib.pyplot as plt\n",
1051     "%matplotlib inline\n",
1052     "plt.axis('on')\n",
1053     "plt.arrow(0, 0, 0.8, 0, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
1054     "plt.arrow(0.2, 0, 0, 1, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
1055     "plt.xlim([-1, 2])\n",
1056     "plt.ylim([-1, 3])"
1057    ]
1058   },
1059   {
1060    "cell_type": "code",
1061    "execution_count": 50,
1062    "metadata": {
1063     "collapsed": true
1064    },
1065    "outputs": [],
1066    "source": [
1067     "def bounds(trace):\n",
1068     "    return (max(s.x for s in trace),\n",
1069     "            max(s.y for s in trace),\n",
1070     "            min(s.x for s in trace),\n",
1071     "            min(s.y for s in trace))"
1072    ]
1073   },
1074   {
1075    "cell_type": "code",
1076    "execution_count": 51,
1077    "metadata": {},
1078    "outputs": [
1079     {
1080      "data": {
1081       "text/plain": [
1082        "(0, 2, -13, -13)"
1083       ]
1084      },
1085      "execution_count": 51,
1086      "metadata": {},
1087      "output_type": "execute_result"
1088     }
1089    ],
1090    "source": [
1091     "bounds(trace_tour('RFRFFLRFLFFRRFFRRRRLLLRRRRRRFRLFRFFRFFRRFRLRRFLLFRLLFRFLFLFRFRLLFRLFRFLRRLLFRRRFRRRRLLFLFRFRRFFRRLLLRLRRFRLRRFFRRFLFRRLLRRFFRFRRRRRFLLLLLRRFFFLLFFFRRLFLFFLRRRFRFLLFFRRLLRFLLRRF'))"
1092    ]
1093   },
1094   {
1095    "cell_type": "code",
1096    "execution_count": 52,
1097    "metadata": {
1098     "collapsed": true
1099    },
1100    "outputs": [],
1101    "source": [
1102     "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
1103     "           Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
1104    ]
1105   },
1106   {
1107    "cell_type": "code",
1108    "execution_count": 53,
1109    "metadata": {
1110     "collapsed": true
1111    },
1112    "outputs": [],
1113    "source": [
1114     "def plot_trace(trace, colour='k', highlight_start=True,\n",
1115     "               xybounds=None, fig=None, subplot_details=None, filename=None):\n",
1116     "    plt.axis('on')\n",
1117     "    plt.axes().set_aspect('equal')\n",
1118     "        \n",
1119     "    if highlight_start:\n",
1120     "        plt.axes().add_patch(plt.Circle((trace[0].x, trace[0].y), 0.2, color=colour))\n",
1121     "        \n",
1122     "    for s, t in chunks(trace, 2):\n",
1123     "        w, h = plot_wh[t.dir]\n",
1124     "        plt.arrow(s.x, s.y, w, h, head_width=0.1, head_length=0.1, fc=colour, ec=colour, length_includes_head=True)\n",
1125     "    xh, yh, xl, yl = bounds(trace)\n",
1126     "    if xybounds is not None:    \n",
1127     "        bxh, byh, bxl, byl = xybounds\n",
1128     "        plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
1129     "        plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
1130     "    else:\n",
1131     "        plt.xlim([xl-1, xh+1])\n",
1132     "        plt.ylim([yl-1, yh+1])\n",
1133     "    if filename:\n",
1134     "        plt.savefig(filename)"
1135    ]
1136   },
1137   {
1138    "cell_type": "code",
1139    "execution_count": 53,
1140    "metadata": {
1141     "collapsed": true
1142    },
1143    "outputs": [],
1144    "source": [
1145     "# def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None):\n",
1146     "#     plt.ioff()\n",
1147     "#     if fig is None:\n",
1148     "#         fig = plt.figure()\n",
1149     "#         ax = fig.gca()\n",
1150     "#     if subplot_details is not None:\n",
1151     "#         ax = fig.add_subplot(*subplot_details)\n",
1152     "#     plt.axis('on')\n",
1153     "# #     plt.axes().set_aspect('equal')\n",
1154     "#     ax.set_aspect('equal')\n",
1155     "#     for s, t in chunks(trace, 2):\n",
1156     "#         w, h = plot_wh[t.dir]\n",
1157     "#         ax.arrow(s.x, s.y, w, h, head_width=0.1, head_length=0.1, fc=colour, ec=colour, length_includes_head=True)\n",
1158     "#     xh, yh, xl, yl = bounds(trace)\n",
1159     "#     if xybounds is not None:    \n",
1160     "#         bxh, byh, bxl, byl = xybounds\n",
1161     "#         ax.set_xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
1162     "#         ax.set_ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
1163     "#     else:\n",
1164     "#         ax.set_xlim([xl-1, xh+1])\n",
1165     "#         ax.set_ylim([yl-1, yh+1])\n",
1166     "#     plt.close(fig)\n",
1167     "#     return fig"
1168    ]
1169   },
1170   {
1171    "cell_type": "code",
1172    "execution_count": 54,
1173    "metadata": {
1174     "collapsed": true
1175    },
1176    "outputs": [],
1177    "source": [
1178     "def pqr(p, q, r):\n",
1179     "    return '{}:{};{}'.format(p, q, r)"
1180    ]
1181   },
1182   {
1183    "cell_type": "code",
1184    "execution_count": 55,
1185    "metadata": {},
1186    "outputs": [
1187     {
1188      "data": {
1189       "text/plain": [
1190        "'1:2;3'"
1191       ]
1192      },
1193      "execution_count": 55,
1194      "metadata": {},
1195      "output_type": "execute_result"
1196     }
1197    ],
1198    "source": [
1199     "pqrt = (1, 2, 3)\n",
1200     "pqr(*pqrt)"
1201    ]
1202   },
1203   {
1204    "cell_type": "code",
1205    "execution_count": 56,
1206    "metadata": {},
1207    "outputs": [
1208     {
1209      "data": {
1210       "image/png": 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kP1LxyGazsUcYkVKbFzRzMckrBu6+2d37wsMXgIb8RyoepfafXmrzgmYuJkleM/gnYGOC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\n",
1211       "text/plain": [
1212        "<matplotlib.figure.Figure at 0x7f03fdc55b70>"
1213       ]
1214      },
1215      "metadata": {},
1216      "output_type": "display_data"
1217     }
1218    ],
1219    "source": [
1220     "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'))"
1221    ]
1222   },
1223   {
1224    "cell_type": "code",
1225    "execution_count": 57,
1226    "metadata": {},
1227    "outputs": [
1228     {
1229      "data": {
1230       "image/png": 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mVpXUYCKSX7muDH4DjHX3I4HVwA25j1Q4MplM7BH6pdjmBc1cSHKKgbsvcPeO8PRFoCb3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\nAABJRU5ErkJggg==\n",
1231       "text/plain": [
1232        "<matplotlib.figure.Figure at 0x7f03fdcc74a8>"
1233       ]
1234      },
1235      "metadata": {},
1236      "output_type": "display_data"
1237     }
1238    ],
1239    "source": [
1240     "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'), colour='g')"
1241    ]
1242   },
1243   {
1244    "cell_type": "code",
1245    "execution_count": 58,
1246    "metadata": {},
1247    "outputs": [
1248     {
1249      "data": {
1250       "image/png": 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+ACSCwAeARJQU+LbPsv2Y7c22f2t7QAftmmyvsf2s7V+U0icA4NQ4Ik79w/Y3JL0WEXNt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\nRU5ErkJggg==\n",
1251       "text/plain": [
1252        "<matplotlib.figure.Figure at 0x7f03fdb35b00>"
1253       ]
1254      },
1255      "metadata": {},
1256      "output_type": "display_data"
1257     }
1258    ],
1259    "source": [
1260     "plot_trace(trace_tour('FFFLLFFL'))"
1261    ]
1262   },
1263   {
1264    "cell_type": "code",
1265    "execution_count": 59,
1266    "metadata": {
1267     "scrolled": true
1268    },
1269    "outputs": [
1270     {
1271      "data": {
1272       "text/plain": [
1273        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
1274        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
1275        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
1276        " Step(x=1, y=2, dir=<Direction.UP: 1>),\n",
1277        " Step(x=1, y=3, dir=<Direction.UP: 1>),\n",
1278        " Step(x=1, y=4, dir=<Direction.UP: 1>),\n",
1279        " Step(x=1, y=5, dir=<Direction.UP: 1>),\n",
1280        " Step(x=0, y=5, dir=<Direction.LEFT: 4>),\n",
1281        " Step(x=-1, y=5, dir=<Direction.LEFT: 4>),\n",
1282        " Step(x=-1, y=6, dir=<Direction.UP: 1>),\n",
1283        " Step(x=-2, y=6, dir=<Direction.LEFT: 4>),\n",
1284        " Step(x=-3, y=6, dir=<Direction.LEFT: 4>),\n",
1285        " Step(x=-4, y=6, dir=<Direction.LEFT: 4>),\n",
1286        " Step(x=-5, y=6, dir=<Direction.LEFT: 4>),\n",
1287        " Step(x=-6, y=6, dir=<Direction.LEFT: 4>),\n",
1288        " Step(x=-6, y=7, dir=<Direction.UP: 1>),\n",
1289        " Step(x=-7, y=7, dir=<Direction.LEFT: 4>),\n",
1290        " Step(x=-7, y=8, dir=<Direction.UP: 1>),\n",
1291        " Step(x=-7, y=9, dir=<Direction.UP: 1>),\n",
1292        " Step(x=-8, y=9, dir=<Direction.LEFT: 4>),\n",
1293        " Step(x=-8, y=8, dir=<Direction.DOWN: 3>),\n",
1294        " Step(x=-8, y=7, dir=<Direction.DOWN: 3>),\n",
1295        " Step(x=-8, y=6, dir=<Direction.DOWN: 3>),\n",
1296        " Step(x=-8, y=5, dir=<Direction.DOWN: 3>),\n",
1297        " Step(x=-8, y=4, dir=<Direction.DOWN: 3>),\n",
1298        " Step(x=-8, y=3, dir=<Direction.DOWN: 3>),\n",
1299        " Step(x=-8, y=2, dir=<Direction.DOWN: 3>),\n",
1300        " Step(x=-7, y=2, dir=<Direction.RIGHT: 2>),\n",
1301        " Step(x=-7, y=1, dir=<Direction.DOWN: 3>),\n",
1302        " Step(x=-7, y=0, dir=<Direction.DOWN: 3>),\n",
1303        " Step(x=-6, y=0, dir=<Direction.RIGHT: 2>),\n",
1304        " Step(x=-5, y=0, dir=<Direction.RIGHT: 2>),\n",
1305        " Step(x=-5, y=1, dir=<Direction.UP: 1>),\n",
1306        " Step(x=-5, y=2, dir=<Direction.UP: 1>),\n",
1307        " Step(x=-6, y=2, dir=<Direction.LEFT: 4>),\n",
1308        " Step(x=-6, y=3, dir=<Direction.UP: 1>),\n",
1309        " Step(x=-6, y=4, dir=<Direction.UP: 1>),\n",
1310        " Step(x=-5, y=4, dir=<Direction.RIGHT: 2>),\n",
1311        " Step(x=-4, y=4, dir=<Direction.RIGHT: 2>),\n",
1312        " Step(x=-3, y=4, dir=<Direction.RIGHT: 2>),\n",
1313        " Step(x=-3, y=3, dir=<Direction.DOWN: 3>),\n",
1314        " Step(x=-3, y=2, dir=<Direction.DOWN: 3>),\n",
1315        " Step(x=-3, y=1, dir=<Direction.DOWN: 3>),\n",
1316        " Step(x=-3, y=0, dir=<Direction.DOWN: 3>),\n",
1317        " Step(x=-3, y=-1, dir=<Direction.DOWN: 3>),\n",
1318        " Step(x=-2, y=-1, dir=<Direction.RIGHT: 2>),\n",
1319        " Step(x=-2, y=-2, dir=<Direction.DOWN: 3>),\n",
1320        " Step(x=-2, y=-3, dir=<Direction.DOWN: 3>),\n",
1321        " Step(x=-2, y=-4, dir=<Direction.DOWN: 3>),\n",
1322        " Step(x=-2, y=-5, dir=<Direction.DOWN: 3>),\n",
1323        " Step(x=-1, y=-5, dir=<Direction.RIGHT: 2>),\n",
1324        " Step(x=0, y=-5, dir=<Direction.RIGHT: 2>),\n",
1325        " Step(x=0, y=-6, dir=<Direction.DOWN: 3>),\n",
1326        " Step(x=1, y=-6, dir=<Direction.RIGHT: 2>),\n",
1327        " Step(x=1, y=-7, dir=<Direction.DOWN: 3>),\n",
1328        " Step(x=1, y=-8, dir=<Direction.DOWN: 3>),\n",
1329        " Step(x=2, y=-8, dir=<Direction.RIGHT: 2>),\n",
1330        " Step(x=2, y=-7, dir=<Direction.UP: 1>),\n",
1331        " Step(x=2, y=-6, dir=<Direction.UP: 1>),\n",
1332        " Step(x=2, y=-5, dir=<Direction.UP: 1>),\n",
1333        " Step(x=2, y=-4, dir=<Direction.UP: 1>),\n",
1334        " Step(x=2, y=-3, dir=<Direction.UP: 1>),\n",
1335        " Step(x=3, y=-3, dir=<Direction.RIGHT: 2>),\n",
1336        " Step(x=3, y=-2, dir=<Direction.UP: 1>),\n",
1337        " Step(x=3, y=-1, dir=<Direction.UP: 1>),\n",
1338        " Step(x=2, y=-1, dir=<Direction.LEFT: 4>),\n",
1339        " Step(x=1, y=-1, dir=<Direction.LEFT: 4>),\n",
1340        " Step(x=0, y=-1, dir=<Direction.LEFT: 4>),\n",
1341        " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
1342       ]
1343      },
1344      "execution_count": 59,
1345      "metadata": {},
1346      "output_type": "execute_result"
1347     }
1348    ],
1349    "source": [
1350     "trace_tour(walks[3])"
1351    ]
1352   },
1353   {
1354    "cell_type": "code",
1355    "execution_count": 60,
1356    "metadata": {},
1357    "outputs": [
1358     {
1359      "data": {
1360       "image/png": "iVBORw0KGgoAAAANSUhEUgAAALwAAAEACAYAAAAJNhwRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nVxR48cr/AwOlW67H9WljAAAAAElFTkSuQmCC\n",
1361       "text/plain": [
1362        "<matplotlib.figure.Figure at 0x7f03fda79780>"
1363       ]
1364      },
1365      "metadata": {},
1366      "output_type": "display_data"
1367     }
1368    ],
1369    "source": [
1370     "plot_trace(trace_tour(walks[3]))"
1371    ]
1372   },
1373   {
1374    "cell_type": "code",
1375    "execution_count": 61,
1376    "metadata": {},
1377    "outputs": [
1378     {
1379      "data": {
1380       "text/plain": [
1381        "10"
1382       ]
1383      },
1384      "execution_count": 61,
1385      "metadata": {},
1386      "output_type": "execute_result"
1387     }
1388    ],
1389    "source": [
1390     "long_walks = [w for w in walks if len(w) >= 30]\n",
1391     "len(long_walks)"
1392    ]
1393   },
1394   {
1395    "cell_type": "code",
1396    "execution_count": 62,
1397    "metadata": {},
1398    "outputs": [
1399     {
1400      "data": {
1401       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAADkCAYAAABXPKW7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nirCFtp8KBQAAAABJRU5ErkJggg==\n",
1402       "text/plain": [
1403        "<matplotlib.figure.Figure at 0x7f03fdbb2710>"
1404       ]
1405      },
1406      "metadata": {},
1407      "output_type": "display_data"
1408     }
1409    ],
1410    "source": [
1411     "plot_trace(trace_tour(long_walks[0]))"
1412    ]
1413   },
1414   {
1415    "cell_type": "code",
1416    "execution_count": 63,
1417    "metadata": {},
1418    "outputs": [
1419     {
1420      "data": {
1421       "text/plain": [
1422        "['RLFFLRFFFFRRLFFFRFFFFRFFLFFFRFRF',\n",
1423        " 'FFFFFLLFFRRLFFFFLLFFRLRFFLFFLRLL',\n",
1424        " 'LRLRLFFFFLLRLRLRFLFFFRLFLFFFLRLL',\n",
1425        " 'FLFFFFLFRLFFFFRLRFLLFFFFFFLRFLFLFLRFRFFRFFFFLRFFFLFRLRFLLFFFFRLFLFFR',\n",
1426        " 'LLFRLRFFLLRFRFLFFFLRLFFLFRFFFLFFRFFLFFFFLLFFFRFRFFLFRF',\n",
1427        " 'FLLFLFFFRLFFLLRFFFFLRFLFFLFFFFLRRF',\n",
1428        " 'FFLFRLLFFRFFFLRLFRLFLFFRLFFFLFFFRFRLRLFFLRRFFLLRLRFLFFLFFRFLFLLRRFFFRL',\n",
1429        " 'RFFFFFLLRLFFFRLFLRFLLFRFFFFFFFLLFFFFRLLR',\n",
1430        " 'LLFFFRLLFFFRFLLFRFFLLRFFLRLFLRRFLL',\n",
1431        " 'FLLRFLRFFRRFLFFRRLFFFFFFRFFRFFRL']"
1432       ]
1433      },
1434      "execution_count": 63,
1435      "metadata": {},
1436      "output_type": "execute_result"
1437     }
1438    ],
1439    "source": [
1440     "walks"
1441    ]
1442   },
1443   {
1444    "cell_type": "code",
1445    "execution_count": 64,
1446    "metadata": {},
1447    "outputs": [
1448     {
1449      "data": {
1450       "image/png": 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2WNK1JH91f1tmDqEfEWwFZpvZQUlfA54luWXzZJK/7PZ0qzHcGDbMMoXjPGNmp0g6GnhW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\n8v89qQ80wuYWhQAAAABJRU5ErkJggg==\n",
1451       "text/plain": [
1452        "<matplotlib.figure.Figure at 0x7f03fd986160>"
1453       ]
1454      },
1455      "metadata": {},
1456      "output_type": "display_data"
1457     }
1458    ],
1459    "source": [
1460     "plot_trace(trace_tour('FLFFLRFRLFRRRR'))"
1461    ]
1462   },
1463   {
1464    "cell_type": "code",
1465    "execution_count": 65,
1466    "metadata": {},
1467    "outputs": [
1468     {
1469      "data": {
1470       "text/plain": [
1471        "(313, [])"
1472       ]
1473      },
1474      "execution_count": 65,
1475      "metadata": {},
1476      "output_type": "execute_result"
1477     }
1478    ],
1479    "source": [
1480     "w = random_walk()\n",
1481     "ms = mistake_positions(trace_tour(w))\n",
1482     "len(ms), returns_to_origin(ms)"
1483    ]
1484   },
1485   {
1486    "cell_type": "code",
1487    "execution_count": 66,
1488    "metadata": {},
1489    "outputs": [
1490     {
1491      "data": {
1492       "image/png": 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NznnIthXxQ1b+eL/88kuUl5fLlTLOOZqammRfnHMUFBRgzZo1qmwJyu/q1KlTqvvdunUr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\nQREEYVr+H+clU6giyaiIAAAAAElFTkSuQmCC\n",
1493       "text/plain": [
1494        "<matplotlib.figure.Figure at 0x7f03fd8c0898>"
1495       ]
1496      },
1497      "metadata": {},
1498      "output_type": "display_data"
1499     }
1500    ],
1501    "source": [
1502     "plot_trace(trace_tour(w))"
1503    ]
1504   },
1505   {
1506    "cell_type": "code",
1507    "execution_count": 67,
1508    "metadata": {
1509     "collapsed": true
1510    },
1511    "outputs": [],
1512    "source": [
1513     "def trim_loop(tour, random_mistake=False):\n",
1514     "    trace = trace_tour(tour)\n",
1515     "    mistakes = mistake_positions(trace)\n",
1516     "    if random_mistake:\n",
1517     "        end_mistake_index = random.randrange(len(mistakes))\n",
1518     "    else:\n",
1519     "        end_mistake_index = 0\n",
1520     "#     print('end_mistake_index {} pointing to trace position {}; {} mistakes and {} in trace; {}'.format(end_mistake_index, mistakes[end_mistake_index].i, len(mistakes), len(trace), mistakes))\n",
1521     "    # while this mistake extends to the next step in the trace...\n",
1522     "    while (mistakes[end_mistake_index].i + 1 < len(trace) and \n",
1523     "           end_mistake_index + 1 < len(mistakes) and\n",
1524     "           mistakes[end_mistake_index].i + 1 == \n",
1525     "           mistakes[end_mistake_index + 1].i):\n",
1526     "#         print('end_mistake_index {} pointing to trace position {}; {} mistakes and {} in trace'.format(end_mistake_index, mistakes[end_mistake_index].i, len(mistakes), len(trace), mistakes))\n",
1527     "        # push this mistake finish point later\n",
1528     "        end_mistake_index += 1\n",
1529     "    mistake = mistakes[end_mistake_index]\n",
1530     "    \n",
1531     "    # find the first location that mentions where this mistake ends (which the point where the loop starts)\n",
1532     "    mistake_loop_start = max(i for i, loc in enumerate(trace[:mistake.i])\n",
1533     "                             if (loc.x, loc.y) == (mistake.step.x, mistake.step.y))\n",
1534     "#     print('Dealing with mistake from', mistake_loop_start, 'to', mistake.i, ', trace has len', len(trace))\n",
1535     "    \n",
1536     "    # direction before entering the loop\n",
1537     "    direction_before = trace[mistake_loop_start].dir\n",
1538     "    \n",
1539     "    # find the new instruction to turn from heading before the loop to heading after the loop\n",
1540     "    new_instruction = 'F'\n",
1541     "    if (mistake.i + 1) < len(trace):\n",
1542     "        if turn_left(direction_before) == trace[mistake.i + 1].dir:\n",
1543     "            new_instruction = 'L'\n",
1544     "        if turn_right(direction_before) == trace[mistake.i + 1].dir:\n",
1545     "            new_instruction = 'R'\n",
1546     "#     if (mistake.i + 1) < len(trace):\n",
1547     "#         print('turning from', direction_before, 'to', trace[mistake.i + 1].dir, 'with', new_instruction )\n",
1548     "#     else:\n",
1549     "#         print('turning from', direction_before, 'to BEYOND END', 'with', new_instruction )\n",
1550     "    return tour[:mistake_loop_start] + new_instruction + tour[mistake.i+1:]\n",
1551     "#     return mistake, mistake_loop_start, trace[mistake_loop_start-2:mistake_loop_start+8]"
1552    ]
1553   },
1554   {
1555    "cell_type": "code",
1556    "execution_count": 68,
1557    "metadata": {},
1558    "outputs": [
1559     {
1560      "data": {
1561       "text/plain": [
1562        "'RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF'"
1563       ]
1564      },
1565      "execution_count": 68,
1566      "metadata": {},
1567      "output_type": "execute_result"
1568     }
1569    ],
1570    "source": [
1571     "w = 'RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF'\n",
1572     "w"
1573    ]
1574   },
1575   {
1576    "cell_type": "code",
1577    "execution_count": 69,
1578    "metadata": {},
1579    "outputs": [
1580     {
1581      "data": {
1582       "image/png": 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1583       "text/plain": [
1584        "<matplotlib.figure.Figure at 0x7f03fd29a710>"
1585       ]
1586      },
1587      "metadata": {},
1588      "output_type": "display_data"
1589     }
1590    ],
1591    "source": [
1592     "w_short = w[:100]\n",
1593     "plot_trace(trace_tour(w_short))"
1594    ]
1595   },
1596   {
1597    "cell_type": "code",
1598    "execution_count": 70,
1599    "metadata": {},
1600    "outputs": [
1601     {
1602      "name": "stdout",
1603      "output_type": "stream",
1604      "text": [
1605       "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n",
1606       "RFFRRFFFRFFRFLLRFLFFFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n"
1607      ]
1608     },
1609     {
1610      "data": {
1611       "image/png": 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1612       "text/plain": [
1613        "<matplotlib.figure.Figure at 0x7f03fd244b70>"
1614       ]
1615      },
1616      "metadata": {},
1617      "output_type": "display_data"
1618     }
1619    ],
1620    "source": [
1621     "trimmed = trim_loop(w_short)\n",
1622     "print('{}\\n{}'.format(w_short, trimmed))\n",
1623     "plot_trace(trace_tour(trimmed))"
1624    ]
1625   },
1626   {
1627    "cell_type": "code",
1628    "execution_count": 71,
1629    "metadata": {},
1630    "outputs": [
1631     {
1632      "name": "stdout",
1633      "output_type": "stream",
1634      "text": [
1635       "RFFRRFFFRFFRFLLRFLFFFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n",
1636       "RFFRRFFFRFFRFLLRFLFFLLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n"
1637      ]
1638     },
1639     {
1640      "data": {
1641       "image/png": 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kBnQDtgATW/l3X4t4TWJmzpyp+fn5vhZ3X3LJJUm1Mw0YMMDXnC+99NK0tF8BumDBAs/z\nLS8vV0D37dvn6/ESZuuWiOQArwMvq+qbrR33+OOPN98PY9etTHLy5EkqKio8L+6ORCLNzb7XXXcd\nL730Euecc05CY48cOUJRURGHDh2iqqqqeZF5ojZs2MCCBQsoLy9nxowZCY9bvXo1kyZNIjc3l+PH\njyc8bs+ePTzxxBO8+uqrnH/++Z7mCtFdswBKSkqa9wM9m9N33UpYIslt6wa8BDzdxjG+frqYxPht\n3VLV5quH1z01W7Z9+blC+1VRUaGAjhs3ztd4QH/3u995Hhdv+9q4caPvuhpG65aIfAkoBsaKyJ9E\nZKuIjE/2vCY8eXl5AHTq1MnTuPhVOScnJ9T2q379+gH+2q+SEW/7iv+ZKkk/fVXVjYC3dndjTKts\nRY8xjrFQGuMYC6UxjrFQGuMYC6UxjrFQGuMYC6UxjrFQGuMYC2UHsXTpUoDmbQS8qKmpAaC2tjbQ\nOblo27ZtAKxatSrNM2md7SXSQcR3+Jo3bx4XXHBBwuOmTZvWfH/+/Pnk5+cnPPbee+8FouunvbSM\nnTp1igceeICpU6dSXFzseR+RZMTnWVpaGlpNzxJZIBvEDVuQnlL33HNP2tqgkrn52Q+koaFB+/Xr\np08++aTnsfH9T5YvX+557Mcff6ydOnXSDz74wPNY1cQXpFsoO4j4N/mKFSs8jbvrrrt01qxZ2tjY\n6LnmxIkT9Re/+IXncXV1dfrkk08qoGPGjPE8Pr7Rjt/vKXx2idx1110K6G233ea7rlooM8fEiRMV\n0JqamnRPJWF+Q3nixAkF9Gtf+5rvun5C+dFHHymg77//vu+6GkbrlnHD0KFDAejatWuaZ5J63bp1\nA/D0u3MQ4o3RfhqkvbBQGuMYC6UxjrFQGuMYC6UxjrFQGuMYC6UxjrFQGuOYQEIpIuNFZJeIfCgi\njwRxTmMyVRDv+5oFPA9cAwwD/lNELkr2vMZkqiCulJcBH6nqXlVtAF4BJgZwXtOBVVRUANGNiaIr\n0MIR30bg5ZdfDq2mV0G0bp0L7Gvx8X6iQTXtRFNTE7W1tc3L18IQ390rKysLVfX1DuubNm3imWee\nSfj4srIynnvuOSDawuVl7JYtW3jzzVa3yQlUEKE802fzjD/6bIOf1BERevbsSX19veftBx588EFW\nrFjBrl3h7fNbWFhI3759GT9+vOd+yvimPitXrvS9pd2OHTuYOnWq53Hnnnsu2dmJbQiQtg1+gMuB\nFS0+ng48cobjfK2sN4kh1srkp09w1KhRvtugkoHPLpHHHnvMV+tWdXW1vvrqq766RA4fPqxLlizR\nSCTiaVxLhNgl8kfgfBEZJCKdgFuBtwI4r/Fg8uTJAIwbNy7NM0m9Rx99FIBhw4Z5Gte9e3duueUW\nXzXz8/O58cYbE75KJiOIDX4aRWQKsIroC0cLVXVn0jMznvTv3x+I7oDV0cV/943vvtXRBPIVVNUV\nwIVBnMuYTGcreoxxjIXSGMdYKI1xjIXSGMdYKI1xjIXSGMdYKI1xjIXSGMdYKDNcY2MjmzdvBuDA\ngQOh1Y1vSLR27Vqampo8jdUkWr3eeOMNAJ566inf50i1jr8mK0P4/UbNysqioKCAw4cPk5eXF/Cs\nWhev1aVLF26++eaEx1VWVrJhwwbA32OO1z3vvPM8jw2LhbKDqK+vp3PnztTU1HgKl4hw2WWXsWbN\nGnr16pXCGf69vn37MnPmTEpKSpqvXl4NHz7c85j4gv2bbrrJV80w2NPXDuLZZ5/ls88+Y+PGjZ7H\nVlRUpGXD2O9973ueWwWbmpqYM2cOAC+88ILnmvFmapcX7lsoO4j4Bq4dvXVLRJqbkx9++OE0zyY1\nLJQdRPwpq5+31Whv4u9UEObvwGGyUBrjGAulMY6xUBrjGAulMY6xUBrjGAulMY6xUBrjmKRCKSJP\nichOEdkmIr8RkR5BTcyYTJXslXIVMExVLwY+Ah5NfkrGZLakQqmq76hqvO9mE1CY/JRMmCKRSHPr\n1scff5zm2XjT2NhIfX29pzGLFi0C4KGHHkrFlAIR5KrcO4lug2fSwG/rVk5ODiNHjmTnzp0MGDAg\n4Fml1qxZs5g1axZ9+/ZNeEwkEgFg0qRJqZpW0toMpYisBvq3/Cuim6vMUNWlsWNmAA2quvhs57Jd\nt1LnyJEj5ObmcuTIEU/fpAAFBQVs376dLl26pGh2wYu3fUH0sXsxevRoXztueeV31y1JposbQERu\nB/4LGKuqdWc5TpOtZVoXX4i+du1azz/sLr/8cjZv3hzq5q1BOHHiBCIS6r6ayRARVLXNjoFkX30d\nD3wHuOFsgTSpF/8dKZOefXTv3r3dBNKLZF99fQ7oBqwWka0i4r3r1ATC68arxl1JvdCjqhcENRFj\nTJT9eDXGMRZKYxxjoTTGMRZKYxxjoTTGMRZKYxxjoTTGMRZKQ0NDQ7qnYFqwUHYwZWVlno6PRCJs\n3boVgA8//DAVUzIeubuhgvGkR4/omz58/vOf9zW+d+/eDB48OMgpGZ+S7hJJuJB1iaRUfX09N954\nI8uXL6egoIA+ffokPLZz587Mnz+fyy+/PIUzNIl2iVgoO5j6+no6deqU7mmYM7BQGuOYUPopjTHB\ns1Aa4xgLpTGOsVAa4xgLpTGOsVAa4xgLpTGOCSSUIvKwiDSJSOLLSIwxZ5R0KEWkELga2Jv8dM7M\nz7tMt9e6mfRYM7FuIoK4Uv4UmBbAeVqVSV+4THqsmVg3Ecm+Q/r1wD5VfS+g+RiT8ZLZ4Oe7wGPA\nuNP+zRiTBN8L0kVkOPAOUEs0jIXAAeAyVT18huNtNbrJeKF2iYjIx8AlqnoskBMak6GC/H9KxZ6+\nGpO00PopjTGJaVcrekTkfhHZJSLvicjsEOuGujhCRJ4SkZ0isk1EfiMiPVJcb3zs8/qhiDySylqx\neoUiskZE3o99Lb+d6pqn1c+Kbd34Vog1e4rIa7Gv619EZFRrx7abUIrIlcD1wHBV/SIwJ6S6KV8c\ncQargGGqejHwEfBoqgqJSBbwPHANMAz4TxG5KFX1YiLAg6r6D8C/APeFULOlB4D3Q6wHMBdYrqpf\nAEYCO1s7sN2EErgHmK2qEQBVrQypbsoXR5xOVd9R1abYh5uIvrKdKpcBH6nqXlVtAF4BJqawHqp6\nSFW3xe6fJPoNem4qa8bFfsheC/w8jHqxmt2B0aq6CEBVI6pa3drx7SmUQ4F/E5FNIrJWRP451QUd\nWRxxJ/DbFJ7/XGBfi4/3E1JAAETkPOBiYHNIJeM/ZMN8MWUIUCkii2JPm38mIl1aO9ip931tY6FC\nDtBLVS8XkUuBXxN9sKmsmbLFEWepO0NVl8aOmQE0qOrioOqeaSpn+LtQvmFFpBvwOvBA7IqZ6noT\ngHJV3Rb7dSis/y3IAS4B7lPVLSLyDDAdKGntYGeo6rjW/k1EvgUsiR33x9gLL31V9UgqasYWR5wH\nbBeR+OKId0XkjIsjgqrbov7tRJ9mjU22Vhv2A0UtPi4EDqa4JiKSQzSQL6vqm6muF/Ml4AYRuRbo\nAnQXkZdUdXKK6+4n+oxrS+zj14FWX1BrT09f/we4CkBEhgK5yQbybFR1h6oOUNUhqjqY6Cf2H4MI\nZFtEZDzwHeAGVa1Lcbk/AueLyCAR6QTcCoTxquSLwPuqOjeEWgCo6mOqWqSqQ4g+zjUhBBJVLQf2\nxb5vIfp93OoLTU5dKduwCHhRRN4D6oCUfzJPE+biiOeATsDq6EWaTap6byoKqWqjiEwh+opvFrBQ\nVVt9ZTAIIvIloBh4T0T+RPRz+5iqrkhl3TT7NvBLEckFyoA7WjvQFg8Y45j29PTVmIxgoTTGMRZK\nYxxjoTTGMRZKYxxjoTTGMRZKYxxjoTTGMf8PuSvpL7lBRvYAAAAASUVORK5CYII=\n",
1642       "text/plain": [
1643        "<matplotlib.figure.Figure at 0x7f03fd00c9b0>"
1644       ]
1645      },
1646      "metadata": {},
1647      "output_type": "display_data"
1648     }
1649    ],
1650    "source": [
1651     "trimmed2 = trim_loop(trimmed)\n",
1652     "print('{}\\n{}'.format(trimmed, trimmed2))\n",
1653     "plot_trace(trace_tour(trimmed2))"
1654    ]
1655   },
1656   {
1657    "cell_type": "code",
1658    "execution_count": 72,
1659    "metadata": {},
1660    "outputs": [
1661     {
1662      "data": {
1663       "text/plain": [
1664        "[Mistake(i=104, step=Step(x=-4, y=6, dir=<Direction.DOWN: 3>)),\n",
1665        " Mistake(i=105, step=Step(x=-5, y=6, dir=<Direction.LEFT: 4>)),\n",
1666        " Mistake(i=106, step=Step(x=-5, y=7, dir=<Direction.UP: 1>)),\n",
1667        " Mistake(i=107, step=Step(x=-5, y=8, dir=<Direction.UP: 1>)),\n",
1668        " Mistake(i=108, step=Step(x=-5, y=9, dir=<Direction.UP: 1>)),\n",
1669        " Mistake(i=115, step=Step(x=-5, y=12, dir=<Direction.LEFT: 4>)),\n",
1670        " Mistake(i=116, step=Step(x=-5, y=11, dir=<Direction.DOWN: 3>)),\n",
1671        " Mistake(i=127, step=Step(x=2, y=11, dir=<Direction.LEFT: 4>)),\n",
1672        " Mistake(i=130, step=Step(x=3, y=11, dir=<Direction.UP: 1>)),\n",
1673        " Mistake(i=132, step=Step(x=3, y=11, dir=<Direction.UP: 1>))]"
1674       ]
1675      },
1676      "execution_count": 72,
1677      "metadata": {},
1678      "output_type": "execute_result"
1679     }
1680    ],
1681    "source": [
1682     "mistake_positions(trace_tour(w[:130]))[-10:]"
1683    ]
1684   },
1685   {
1686    "cell_type": "code",
1687    "execution_count": 73,
1688    "metadata": {},
1689    "outputs": [
1690     {
1691      "name": "stdout",
1692      "output_type": "stream",
1693      "text": [
1694       "Step(x=40, y=36, dir=<Direction.UP: 1>)\n"
1695      ]
1696     },
1697     {
1698      "data": {
1699       "image/png": 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4BuzPuLRMdHS0Ko21u+j1enndOp1OtUsMQEC/aDqdzqUt3PqaEhISwtJ+rkXS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\nRK5CYII=\n",
1700       "text/plain": [
1701        "<matplotlib.figure.Figure at 0x7f03fcecd470>"
1702       ]
1703      },
1704      "metadata": {},
1705      "output_type": "display_data"
1706     }
1707    ],
1708    "source": [
1709     "w_tour_start = w #[:250]\n",
1710     "print(trace_tour(w_tour_start)[-1])\n",
1711     "plot_trace(trace_tour(w_tour_start))"
1712    ]
1713   },
1714   {
1715    "cell_type": "code",
1716    "execution_count": 74,
1717    "metadata": {},
1718    "outputs": [
1719     {
1720      "name": "stdout",
1721      "output_type": "stream",
1722      "text": [
1723       "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF\n",
1724       "RFFRRFFFRFLRFRFLLRFLLRLRRLFRLRRFFLLRLLRRFRFLRLFFLFLRRLRRLRLFLLRRFFLRLLFFFFFRRFFLFRLFFRLLRRFLFFFLRFLRRLRFLFLFFRLLFFRRFFLRLFRFFRLFFLRRFLRFLRRLFRRLFFFFRLFLFFLRFFLFRFLRRFFFFFLFRLRRFRLLRLLFRFLFFFRLFRFLFLRLRFFFFFLFFRFFFFLRFLFRFLRLRLFFLRRFFFRLLFRLFLRRFLRLLRLFFRFLRRLFLLRFLFFRFLFRLRFFFFFLRLLFRFLLRRFLRRFLRLRFLRRLFFFRFLRRLF\n",
1725       "Step(x=40, y=36, dir=<Direction.UP: 1>)\n"
1726      ]
1727     },
1728     {
1729      "data": {
1730       "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
1731       "text/plain": [
1732        "<matplotlib.figure.Figure at 0x7f03fd292eb8>"
1733       ]
1734      },
1735      "metadata": {},
1736      "output_type": "display_data"
1737     }
1738    ],
1739    "source": [
1740     "w_tour = w_tour_start\n",
1741     "w_trace = trace_tour(w_tour)\n",
1742     "mks = mistake_positions(w_trace)\n",
1743     "while len(mks) > 1:\n",
1744     "#     print(len(mks))\n",
1745     "    w_tour = trim_loop(w_tour)\n",
1746     "    w_trace = trace_tour(w_tour)\n",
1747     "    mks = mistake_positions(w_trace)\n",
1748     "print('{}\\n{}\\n{}'.format(w_tour_start, w_tour, trace_tour(w_tour)[-1]))\n",
1749     "plot_trace(trace_tour(w_tour))"
1750    ]
1751   },
1752   {
1753    "cell_type": "code",
1754    "execution_count": 75,
1755    "metadata": {
1756     "collapsed": true
1757    },
1758    "outputs": [],
1759    "source": [
1760     "def trim_all_loops(tour, mistake_reduction_attempt_limit=10):\n",
1761     "    trace = trace_tour(tour)\n",
1762     "    mistake_limit = 1\n",
1763     "    if trace[-1].x == 0 and trace[-1].y == 0:\n",
1764     "        mistake_limit = 0\n",
1765     "    mistakes = mistake_positions(trace)\n",
1766     "    \n",
1767     "    old_mistake_count = len(mistakes)\n",
1768     "    mistake_reduction_tries = 0\n",
1769     "    \n",
1770     "    while len(mistakes) > mistake_limit and mistake_reduction_tries < mistake_reduction_attempt_limit:\n",
1771     "        tour = trim_loop(tour)\n",
1772     "        trace = trace_tour(tour)\n",
1773     "        mistakes = mistake_positions(trace)\n",
1774     "        if len(mistakes) < old_mistake_count:\n",
1775     "            old_mistake_count = len(mistakes)\n",
1776     "            mistake_reduction_tries = 0\n",
1777     "        else:\n",
1778     "            mistake_reduction_tries += 1\n",
1779     "    if mistake_reduction_tries >= mistake_reduction_attempt_limit:\n",
1780     "        return ''\n",
1781     "    else:\n",
1782     "        return tour"
1783    ]
1784   },
1785   {
1786    "cell_type": "code",
1787    "execution_count": 76,
1788    "metadata": {},
1789    "outputs": [
1790     {
1791      "data": {
1792       "text/plain": [
1793        "'RFFRRFFFRFLRFRFLLRFLLRLRRLFRLRRFFLLRLLRRFRFLRLFFLFLRRLRRLRLFLLRRFFLRLLFFFFFRRFFLFRLFFRLLRRFLFFFLRFLRRLRFLFLFFRLLFFRRFFLRLFRFFRLFFLRRFLRFLRRLFRRLFFFFRLFLFFLRFFLFRFLRRFFFFFLFRLRRFRLLRLLFRFLFFFRLFRFLFLRLRFFFFFLFFRFFFFLRFLFRFLRLRLFFLRRFFFRLLFRLFLRRFLRLLRLFFRFLRRLFLLRFLFFRFLFRLRFFFFFLRLLFRFLLRRFLRRFLRLRFLRRLFFFRFLRRLF'"
1794       ]
1795      },
1796      "execution_count": 76,
1797      "metadata": {},
1798      "output_type": "execute_result"
1799     }
1800    ],
1801    "source": [
1802     "w_trimmed = trim_all_loops(w)\n",
1803     "w_trimmed"
1804    ]
1805   },
1806   {
1807    "cell_type": "code",
1808    "execution_count": 77,
1809    "metadata": {},
1810    "outputs": [
1811     {
1812      "data": {
1813       "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
1814       "text/plain": [
1815        "<matplotlib.figure.Figure at 0x7f03fcfd4358>"
1816       ]
1817      },
1818      "metadata": {},
1819      "output_type": "display_data"
1820     }
1821    ],
1822    "source": [
1823     "plot_trace(trace_tour(trim_all_loops(w)))"
1824    ]
1825   },
1826   {
1827    "cell_type": "code",
1828    "execution_count": 78,
1829    "metadata": {
1830     "collapsed": true
1831    },
1832    "outputs": [],
1833    "source": [
1834     "def reverse_tour(tour):\n",
1835     "    def swap(tour_step):\n",
1836     "        if tour_step == 'R':\n",
1837     "            return 'L'\n",
1838     "        elif tour_step == 'L':\n",
1839     "            return 'R'\n",
1840     "        else:\n",
1841     "            return tour_step\n",
1842     "        \n",
1843     "    return ''.join(swap(s) for s in reversed(tour))"
1844    ]
1845   },
1846   {
1847    "cell_type": "code",
1848    "execution_count": 79,
1849    "metadata": {},
1850    "outputs": [
1851     {
1852      "data": {
1853       "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
1854       "text/plain": [
1855        "<matplotlib.figure.Figure at 0x7f03fd7e2940>"
1856       ]
1857      },
1858      "metadata": {},
1859      "output_type": "display_data"
1860     }
1861    ],
1862    "source": [
1863     "plot_trace(trace_tour(w_trimmed))"
1864    ]
1865   },
1866   {
1867    "cell_type": "code",
1868    "execution_count": 80,
1869    "metadata": {},
1870    "outputs": [
1871     {
1872      "data": {
1873       "image/png": 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ZmUHGpTOGE4saVopgjOGFF15g9OjRAFxwwQUJ1ii9UcNKIc4991wuuuiiRKuhoH2slECd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\ngjJMbcJZvAAAAABJRU5ErkJggg==\n",
1874       "text/plain": [
1875        "<matplotlib.figure.Figure at 0x7f03fcf89198>"
1876       ]
1877      },
1878      "metadata": {},
1879      "output_type": "display_data"
1880     }
1881    ],
1882    "source": [
1883     "plot_trace(trace_tour(reverse_tour(w_trimmed)))"
1884    ]
1885   },
1886   {
1887    "cell_type": "code",
1888    "execution_count": 81,
1889    "metadata": {},
1890    "outputs": [
1891     {
1892      "data": {
1893       "image/png": 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QN910kywvL5enPvlEyaioUH+1liJUrAb7c+aEJysWCdV4YvpqN1ecefPmyRQv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\nH6uGZnvGhXMvAAAAAElFTkSuQmCC\n",
1894       "text/plain": [
1895        "<matplotlib.figure.Figure at 0x7f03fdaa1ef0>"
1896       ]
1897      },
1898      "metadata": {},
1899      "output_type": "display_data"
1900     }
1901    ],
1902    "source": [
1903     "w1 = random_walk()\n",
1904     "w2 = random_walk()\n",
1905     "plot_trace(trace_tour(w1))\n",
1906     "w1bounds = bounds(trace_tour(w1))\n",
1907     "plot_trace(trace_tour(w2), colour='r', xybounds=w1bounds)"
1908    ]
1909   },
1910   {
1911    "cell_type": "code",
1912    "execution_count": 82,
1913    "metadata": {},
1914    "outputs": [
1915     {
1916      "name": "stdout",
1917      "output_type": "stream",
1918      "text": [
1919       "w1 = 'RLFFFLFFLRFLFLRFFFFFFLLFFFLFLFLFFLLLFFFFFRFFLRFLFFLFFFFLLFLLRFFFFLRLFRRLLFLRFLFLLFFLFFRFFFFLRFLLRFFLRFFRFRLFRFRFFLFLRFRLLFRLFFLLLFFFRFLFFLFLLRFRFLFRRFRFLLFRFFFFLFFFRLFFFFRFRFRFLFFRFFFLFRFFRRLRFRFFLFFFRRFLFFRRRFLFFLRFFLLFFLFRFFRFRRFFRRLLLFFFFFFFRFLFLFLLFRFFFLFFFRRFFLFFRRFFLRFRLRFFFRFRLFRLFRRFLLLFLRFLFRFFRLFLFRFFFFLFRLFFRRFFRFRFFFFFFLFLRLFFFFRLRFFRLFFLFFFLRFFFFLRFFRFFRFRFFRFFRRRFFRFLRLLLFLFFFLFRFFRLFRLLFLFLFLLRFLFLFLFLFFRFFRRLLFRRLRLFFFFLRLRRRFFRFFRRFFRLLFFLLLLFLLLLFFRLFFRRRRFFRRRRLFFLFFFRLLRLFRLRFLFRFRRFLLLFFFFFLFFRRRFRLRLFRLLLRFLFFFFFFFFRRFFFFRLRRFFRLFFRLFFLLLFFLFFFFFLFFLFRRRFLFLFFFFLFLFLLLRFRFLFRLFLFFLRFLLFLRLLLFLFRRLFFRLFLRLFFRFLFLFFFRFRFRFFRFFRRFFRFRFFFFFRRFFLFFRFLRFFFLFFFFRFRLFRFFRRFFFFLFFFFLRFRFFLLLRLRRLLFFLRLLFFFRFFFFFFLFRFFFLRFRLRFFLLFFRLRFFFFRRFRFFLRFRFRFLFFFRFFFFRLFLRLFFLRLFFFFFRLFLRFFRLLFFRLFRFFFLRLRFLFLFFFLFFFFLFLRRFFRLLFFLFFLFRLFFFRLFRFRFFLFFLFLLFRLLFFRFLFLFFFFLFLRFRFRLFRRFLLRRRRFFRFLFRFFLLFRRRFRLRRLRFFLRLFLLFLLFFFRLLFLRFRLFLRFLRFFRLLRLRRFFFLLFFLLFLFRFLLLRFRRLFLLLRRFFFRFFFF\n",
1920       "w2 = 'LFLFFFFFFRFFFRRLLFFFFLFFFLFFLFFLLFFFLFLLFFRFRRLFFRLLLRFRLRLRRFFFFLRFLFLLLLRRFFRFLFFFFRFFFLLLRFRFFFLFRRFRLFFLLFLRFFFRFRLFFLFFFRLFFFRFFFRFRFRFFRFRRRLFRFRRFFRFRLRLFLFFFRLFRLRFLRFFFLFFRRFFRLLLLFRFFRFLRFFRFLLLRRFLFFFLLRLLFFFFLRFLLLLFRRFLRFFFLFFFLFRLLFRRLLLLFRLRRLRLFFFRFFFFFLRRFFLFFRFLRFLLFFFLFRLLLFRRRFFLLLLRFFLFFFRLRRFFFFLLRFFLFRFLRFRFLLFFRRLLFFRLRFFFRLFLRFLLFRLLLRRRFRFRRFFFRFFFFFLRFFRLFFLFFRRRRLFFRFRLFFRLRLFFLRFFRLLFFRFFLLRRLRRLRLLFLLFRRFLFFLLFFFLFFRFRFLFRFLFFFFLFLRRFLRLRLFLFRFFLFLFFFFLRLLFRFLLRFLRRFFFLRFFLLRFFRRFLFFRFRFFFFFFFFLFLRLFLFFFFLLRFRFLFFLRFFRFFFLLFRLFLRLFFLRFFLLLFFRFLFFRFFFFLRRFRLFFFLFLLLLFFFFLRFFRFFFRFRLRRLRFFRFFLLFLFRFFFRRFFFFFFFRFRLFFFLFRFFFFFFRFRLRFFLLLFFLRFRLLLLLLRFFFFLFFLFFLFRLFRLFFFLLFFFFRRRFRFRFLFLFFRLFFFLLRRFFFFLLFFFFFRRFFLRFLFFFFFLLFFFRFFLFLRFRFFFLFFFFRLRRFFRRFLRFLLLRRLRFLLFFRRLFFFFLFFRFFLRLLRRRLLLFFFLLFFLFFFFFFFRFFLLFFLRLFFFRFLFFFLLFRRFLRRFLLRFFLRFFFLFFFFLRFRRFRLLFFFFFFFFFLFFFFFRFRFLLLFFLRLFLFRLLFLFFRFFRRFLFFRRRFLFLLLFRFLFLFFFFLLLLLFFFRFFFLRFRLRFFLFFLFFFRFFRLFLFRFRFLFF\n"
1921      ]
1922     }
1923    ],
1924    "source": [
1925     "print(\"w1 = '{}\".format(w1))\n",
1926     "print(\"w2 = '{}\".format(w2))"
1927    ]
1928   },
1929   {
1930    "cell_type": "code",
1931    "execution_count": 83,
1932    "metadata": {
1933     "collapsed": true
1934    },
1935    "outputs": [],
1936    "source": [
1937     "def wander_near(locus, current, limit=10):\n",
1938     "    valid_proposal = False\n",
1939     "    while not valid_proposal:\n",
1940     "        s = random.choice('FFFRL')\n",
1941     "        if s == 'F':\n",
1942     "            proposed = advance(current, current.dir)\n",
1943     "        elif s == 'L':\n",
1944     "            proposed = advance(current, turn_left(current.dir))\n",
1945     "        elif s == 'R':\n",
1946     "            proposed = advance(current, turn_right(current.dir))\n",
1947     "        if abs(proposed.x - locus.x) < limit and abs(proposed.y - locus.y) < limit:\n",
1948     "            valid_proposal = True\n",
1949     "#     print('At {} going to {} by step {} to {}'.format(current, locus, s, proposed))\n",
1950     "    return s, proposed"
1951    ]
1952   },
1953   {
1954    "cell_type": "code",
1955    "execution_count": 84,
1956    "metadata": {
1957     "collapsed": true
1958    },
1959    "outputs": [],
1960    "source": [
1961     "def seek(goal, current):\n",
1962     "    dx = current.x - goal.x\n",
1963     "    dy = current.y - goal.y\n",
1964     "\n",
1965     "    if dx < 0 and abs(dx) > abs(dy): # to the left\n",
1966     "        side = 'left'\n",
1967     "        if current.dir == Direction.RIGHT:\n",
1968     "            s = 'F'\n",
1969     "        elif current.dir == Direction.UP:\n",
1970     "            s = 'R'\n",
1971     "        else:\n",
1972     "            s = 'L'\n",
1973     "    elif dx > 0 and abs(dx) > abs(dy): # to the right\n",
1974     "        side = 'right'\n",
1975     "        if current.dir == Direction.LEFT:\n",
1976     "            s = 'F'\n",
1977     "        elif current.dir == Direction.UP:\n",
1978     "            s = 'L'\n",
1979     "        else:\n",
1980     "            s = 'R'\n",
1981     "    elif dy > 0 and abs(dx) <= abs(dy): # above\n",
1982     "        side = 'above'\n",
1983     "        if current.dir == Direction.DOWN:\n",
1984     "            s = 'F'\n",
1985     "        elif current.dir == Direction.RIGHT:\n",
1986     "            s = 'R'\n",
1987     "        else:\n",
1988     "            s = 'L'\n",
1989     "    else: # below\n",
1990     "        side = 'below'\n",
1991     "        if current.dir == Direction.UP:\n",
1992     "            s = 'F'\n",
1993     "        elif current.dir == Direction.LEFT:\n",
1994     "            s = 'R'\n",
1995     "        else:\n",
1996     "            s = 'L'\n",
1997     "    if s == 'F':\n",
1998     "        proposed = advance(current, current.dir)\n",
1999     "    elif s == 'L':\n",
2000     "        proposed = advance(current, turn_left(current.dir))\n",
2001     "    elif s == 'R':\n",
2002     "        proposed = advance(current, turn_right(current.dir))\n",
2003     "        \n",
2004     "#     print('At {} going to {}, currently {},  by step {} to {}'.format(current, goal, side, s, proposed))\n",
2005     "\n",
2006     "    return s, proposed"
2007    ]
2008   },
2009   {
2010    "cell_type": "code",
2011    "execution_count": 85,
2012    "metadata": {
2013     "collapsed": true
2014    },
2015    "outputs": [],
2016    "source": [
2017     "def guided_walk(loci, locus_limit=5, wander_limit=10, seek_step_limit=20, return_anyway=False):\n",
2018     "    trail = ''\n",
2019     "    current = Step(0, 0, Direction.RIGHT)    \n",
2020     "    l = 0\n",
2021     "    finished = False\n",
2022     "    while not finished:\n",
2023     "        if abs(current.x - loci[l].x) < locus_limit and abs(current.y - loci[l].y) < locus_limit:\n",
2024     "            l += 1\n",
2025     "            if l == len(loci) - 1:\n",
2026     "                finished = True\n",
2027     "        s, proposed = wander_near(loci[l], current, limit=wander_limit)\n",
2028     "        trail += s\n",
2029     "        current = proposed\n",
2030     "#     print('!! Finished loci')\n",
2031     "    seek_steps = 0\n",
2032     "    while not (current.x == loci[l].x and current.y == loci[l].y) and seek_steps < seek_step_limit:\n",
2033     "#         error = max(abs(current.x - loci[l].x), abs(current.y - loci[l].y))\n",
2034     "#         s, proposed = wander_near(loci[l], current, limit=error+1)\n",
2035     "        s, proposed = seek(loci[l], current)\n",
2036     "        trail += s\n",
2037     "        current = proposed\n",
2038     "        seek_steps += 1\n",
2039     "    if seek_steps >= seek_step_limit and not return_anyway:\n",
2040     "        return ''\n",
2041     "    else:\n",
2042     "        return trail"
2043    ]
2044   },
2045   {
2046    "cell_type": "code",
2047    "execution_count": 86,
2048    "metadata": {},
2049    "outputs": [
2050     {
2051      "data": {
2052       "image/png": 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FIBNJl6SFQEV+muMwZFu3buWGG25QGDKRAEKHIVsFPOHufxk9LykEWfRehSETqYDQYcgs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\nEKlyKgREqpwKAZEqp0JApMr9P8nYgJi0MFyGAAAAAElFTkSuQmCC\n",
2053       "text/plain": [
2054        "<matplotlib.figure.Figure at 0x7f03fdaa1f98>"
2055       ]
2056      },
2057      "metadata": {},
2058      "output_type": "display_data"
2059     }
2060    ],
2061    "source": [
2062     "def square_tour(a=80):\n",
2063     "    \"a is width of square\"\n",
2064     "    return ('F' * a + 'L') * 4\n",
2065     "\n",
2066     "plot_trace(trace_tour(square_tour()))"
2067    ]
2068   },
2069   {
2070    "cell_type": "code",
2071    "execution_count": 87,
2072    "metadata": {},
2073    "outputs": [
2074     {
2075      "data": {
2076       "image/png": 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k6yMEKDzGmzHGPSUtKopIo4g8KSJxEXlbRG4WkWYReU5E+kXkuIg0rvT+6urqghdbGGPc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\nybOEYIzJ+/+3mLJIMXCXRQAAAABJRU5ErkJggg==\n",
2077       "text/plain": [
2078        "<matplotlib.figure.Figure at 0x7f03fcf938d0>"
2079       ]
2080      },
2081      "metadata": {},
2082      "output_type": "display_data"
2083     }
2084    ],
2085    "source": [
2086     "def cross_tour(a=50, b=40):\n",
2087     "    \"a is width of cross arm, b is length of cross arm\"\n",
2088     "    return ('F' *  a + 'L' + 'F' * b + 'R' + 'F' * b + 'L') * 4\n",
2089     "\n",
2090     "plot_trace(trace_tour(cross_tour()))"
2091    ]
2092   },
2093   {
2094    "cell_type": "code",
2095    "execution_count": 88,
2096    "metadata": {},
2097    "outputs": [
2098     {
2099      "data": {
2100       "image/png": 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Ukpa9WWhgqFF+bEHHGFQ509PTzM7Out0MR2hgqJGOMahqqqVkbyYaGJRySDgcrno7c7PQ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\n",
2101       "text/plain": [
2102        "<matplotlib.figure.Figure at 0x7f03fda6aeb8>"
2103       ]
2104      },
2105      "metadata": {},
2106      "output_type": "display_data"
2107     }
2108    ],
2109    "source": [
2110     "def quincunx_tour(a=60, b=30, c=50):\n",
2111     "    \"a is length of indent, b is indent/outdent distance, c is outdent outer length\"\n",
2112     "    return ('F' * a + 'R' + 'F' * b + 'L' + 'F' * c + 'L' + 'F' * c + 'L' + 'F' * b + 'R') * 4\n",
2113     "plot_trace(trace_tour(quincunx_tour()))"
2114    ]
2115   },
2116   {
2117    "cell_type": "code",
2118    "execution_count": 89,
2119    "metadata": {},
2120    "outputs": [
2121     {
2122      "data": {
2123       "image/png": 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iqnu92C4RrS2vFgeNIrZGYOlMl0rkA15dAoiH2yKiAvHqDEABvCYiCuC/VPWpbDM+8cQT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\nWKIAAAAASUVORK5CYII=\n",
2124       "text/plain": [
2125        "<matplotlib.figure.Figure at 0x7f03fc91f7f0>"
2126       ]
2127      },
2128      "metadata": {},
2129      "output_type": "display_data"
2130     }
2131    ],
2132    "source": [
2133     "plot_trace(trace_tour(('F' * 10 + 'R' + 'F' * 5 + 'L' + 'F' * 10 + 'L' + 'F' * 10 + 'L' + 'F' * 5 + 'R') * 4))"
2134    ]
2135   },
2136   {
2137    "cell_type": "code",
2138    "execution_count": 90,
2139    "metadata": {},
2140    "outputs": [
2141     {
2142      "data": {
2143       "image/png": 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ZZ57hwIED7Nu3r84N3FRGpzCGuczMTFJSUjx/7Pv27aN79+6WU6lgVv6cyBEj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\nVBW0UCqlVBW0UCqlVBX+P0VFnoIKajtRAAAAAElFTkSuQmCC\n",
2144       "text/plain": [
2145        "<matplotlib.figure.Figure at 0x7f03fd7f34e0>"
2146       ]
2147      },
2148      "metadata": {},
2149      "output_type": "display_data"
2150     }
2151    ],
2152    "source": [
2153     "heart_points = [Step(60, 50, Direction.UP), Step(50, 90, Direction.UP),\n",
2154     "                Step(20, 70, Direction.UP), \n",
2155     "                Step(-40, 90, Direction.UP), Step(-60, 80, Direction.UP), \n",
2156     "                Step(0, 0, Direction.RIGHT)]\n",
2157     "\n",
2158     "heart_tour = ''\n",
2159     "current = Step(0, 0, Direction.RIGHT)\n",
2160     "\n",
2161     "for hp in heart_points:\n",
2162     "    while not (current.x == hp.x and current.y == hp.y):\n",
2163     "        s, proposed = seek(hp, current)\n",
2164     "        heart_tour += s\n",
2165     "        current = proposed\n",
2166     "\n",
2167     "plot_trace(trace_tour(heart_tour))\n",
2168     "\n",
2169     "def heart_tour_func(): return heart_tour"
2170    ]
2171   },
2172   {
2173    "cell_type": "code",
2174    "execution_count": 91,
2175    "metadata": {},
2176    "outputs": [
2177     {
2178      "data": {
2179       "text/plain": [
2180        "'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'"
2181       ]
2182      },
2183      "execution_count": 91,
2184      "metadata": {},
2185      "output_type": "execute_result"
2186     }
2187    ],
2188    "source": [
2189     "# lc = trace_tour(('F' * 50 + 'L') * 4)\n",
2190     "# lc = trace_tour(('F' * 50 + 'L' + 'F' * 20 + 'R' + 'F' * 20 + 'L') * 4)\n",
2191     "# lc = trace_tour(('F' * 60 + 'R' + 'F' * 30 + 'L' + 'F' * 60 + 'L' + 'F' * 60 + 'L' + 'F' * 30 + 'R') * 4)\n",
2192     "lc = trace_tour(heart_tour)\n",
2193     "rw = guided_walk(lc, wander_limit=8)\n",
2194     "rw"
2195    ]
2196   },
2197   {
2198    "cell_type": "code",
2199    "execution_count": 92,
2200    "metadata": {},
2201    "outputs": [
2202     {
2203      "data": {
2204       "image/png": 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Nm9mxYwdnzpypvTPuJKevNrx8gk6YMEGT7qGhoV4dK/GclJSUGp+sc+fOdblI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\nZiANwzAiYAbSMAwjAmYgDcMwIvB/2ZiakzGZzHoAAAAASUVORK5CYII=\n",
2205       "text/plain": [
2206        "<matplotlib.figure.Figure at 0x7f03fd0eab00>"
2207       ]
2208      },
2209      "metadata": {},
2210      "output_type": "display_data"
2211     }
2212    ],
2213    "source": [
2214     "plot_trace(trace_tour(rw))"
2215    ]
2216   },
2217   {
2218    "cell_type": "code",
2219    "execution_count": 93,
2220    "metadata": {},
2221    "outputs": [
2222     {
2223      "data": {
2224       "image/png": 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LWi2pR9JvJJ3ejj5G2dOlkl6tH5v1kr7R5n7ultQraeMQNSvrx2iDpHnt7GekfUlaIGlX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\nmaU4RMws5f8Az4SYkuCKQGwAAAAASUVORK5CYII=\n",
2225       "text/plain": [
2226        "<matplotlib.figure.Figure at 0x7f03fc90abe0>"
2227       ]
2228      },
2229      "metadata": {},
2230      "output_type": "display_data"
2231     }
2232    ],
2233    "source": [
2234     "rw_trimmed = trim_all_loops(rw)\n",
2235     "plot_trace(trace_tour(rw_trimmed))"
2236    ]
2237   },
2238   {
2239    "cell_type": "code",
2240    "execution_count": 94,
2241    "metadata": {},
2242    "outputs": [
2243     {
2244      "data": {
2245       "text/plain": [
2246        "4"
2247       ]
2248      },
2249      "execution_count": 94,
2250      "metadata": {},
2251      "output_type": "execute_result"
2252     }
2253    ],
2254    "source": [
2255     "len(rw_trimmed)"
2256    ]
2257   },
2258   {
2259    "cell_type": "code",
2260    "execution_count": 95,
2261    "metadata": {},
2262    "outputs": [
2263     {
2264      "data": {
2265       "text/plain": [
2266        "(250,\n",
2267        " 92,\n",
2268        " 'LFLRRFFFFRFRFRLLFFFFLFFFFLFLRFFRFRLLFRFLRFFLFFFLFRLRFFLFLFRLFRFFFFRFLFFFFFLFFFLRRLFFFFLLRFRL')"
2269       ]
2270      },
2271      "execution_count": 95,
2272      "metadata": {},
2273      "output_type": "execute_result"
2274     },
2275     {
2276      "data": {
2277       "image/png": 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hk4tOP/10AL75zW9muJLco6ARkeAUNCISnIJGRIJT0IhIcAoaEQlOQSMiwaUcNGZ2vJk9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\nBPf/AaHHidH8UAAMAAAAAElFTkSuQmCC\n",
2278       "text/plain": [
2279        "<matplotlib.figure.Figure at 0x7f03fcf7c438>"
2280       ]
2281      },
2282      "metadata": {},
2283      "output_type": "display_data"
2284     }
2285    ],
2286    "source": [
2287     "lc = trace_tour(square_tour(a=10))\n",
2288     "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
2289     "rw_trimmed = trim_all_loops(rw)\n",
2290     "plot_trace(trace_tour(rw_trimmed))\n",
2291     "len(rw), len(rw_trimmed), rw_trimmed"
2292    ]
2293   },
2294   {
2295    "cell_type": "code",
2296    "execution_count": 96,
2297    "metadata": {
2298     "collapsed": true
2299    },
2300    "outputs": [],
2301    "source": [
2302     "# success_count = 0\n",
2303     "# while success_count <= 20:\n",
2304     "#     lc = trace_tour(square_tour(a=10))\n",
2305     "#     rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
2306     "#     if rw:\n",
2307     "#         rw_trimmed = trim_all_loops(rw)\n",
2308     "#         if len(rw_trimmed) > 10:\n",
2309     "#             with open('small-squares.txt', 'a') as f:\n",
2310     "#                 f.write(rw_trimmed + '\\n')\n",
2311     "#                 success_count += 1"
2312    ]
2313   },
2314   {
2315    "cell_type": "code",
2316    "execution_count": 97,
2317    "metadata": {
2318     "collapsed": true
2319    },
2320    "outputs": [],
2321    "source": [
2322     "# success_count = 0\n",
2323     "# while success_count <= 20:\n",
2324     "#     lc = trace_tour(square_tour())\n",
2325     "#     rw = guided_walk(lc)\n",
2326     "#     if rw:\n",
2327     "#         rw_trimmed = trim_all_loops(rw)\n",
2328     "#         if len(rw_trimmed) > 10:\n",
2329     "#             with open('large-squares.txt', 'a') as f:\n",
2330     "#                 f.write(rw_trimmed + '\\n')\n",
2331     "#                 success_count += 1"
2332    ]
2333   },
2334   {
2335    "cell_type": "code",
2336    "execution_count": 98,
2337    "metadata": {
2338     "collapsed": true
2339    },
2340    "outputs": [],
2341    "source": [
2342     "# success_count = 0\n",
2343     "# while success_count <= 20:\n",
2344     "#     lc = trace_tour(cross_tour())\n",
2345     "#     rw = guided_walk(lc)\n",
2346     "#     if rw:\n",
2347     "#         rw_trimmed = trim_all_loops(rw)\n",
2348     "#         if len(rw_trimmed) > 10:\n",
2349     "#             with open('cross.txt', 'a') as f:\n",
2350     "#                 f.write(rw_trimmed + '\\n')\n",
2351     "#                 success_count += 1"
2352    ]
2353   },
2354   {
2355    "cell_type": "code",
2356    "execution_count": 99,
2357    "metadata": {
2358     "collapsed": true
2359    },
2360    "outputs": [],
2361    "source": [
2362     "# success_count = 0\n",
2363     "# while success_count <= 20:\n",
2364     "#     lc = trace_tour(quincunx_tour())\n",
2365     "#     rw = guided_walk(lc)\n",
2366     "#     if rw:\n",
2367     "#         rw_trimmed = trim_all_loops(rw)\n",
2368     "#         if len(rw_trimmed) > 10:\n",
2369     "#             with open('quincunx.txt', 'a') as f:\n",
2370     "#                 f.write(rw_trimmed + '\\n')\n",
2371     "#                 success_count += 1"
2372    ]
2373   },
2374   {
2375    "cell_type": "code",
2376    "execution_count": 100,
2377    "metadata": {},
2378    "outputs": [
2379     {
2380      "data": {
2381       "image/png": 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hk4tOP/10AL75zW9muJLco6ARkeAUNCISnIJGRIJT0IhIcAoaEQlOQSMiwaUcNGZ2vJk9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\nBPf/AaHHidH8UAAMAAAAAElFTkSuQmCC\n",
2382       "text/plain": [
2383        "<matplotlib.figure.Figure at 0x7f03fd7d8a20>"
2384       ]
2385      },
2386      "metadata": {},
2387      "output_type": "display_data"
2388     }
2389    ],
2390    "source": [
2391     "plot_trace(trace_tour(rw_trimmed), filename='test.png')"
2392    ]
2393   },
2394   {
2395    "cell_type": "code",
2396    "execution_count": 101,
2397    "metadata": {
2398     "collapsed": true
2399    },
2400    "outputs": [],
2401    "source": [
2402     "# patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
2403     "# tours_filename = 'tours.txt'\n",
2404     "\n",
2405     "# try:\n",
2406     "#     os.remove(tours_filename)\n",
2407     "# except OSError:\n",
2408     "#     pass\n",
2409     "\n",
2410     "# success_count = 0\n",
2411     "# while success_count < 100:\n",
2412     "#     lc = trace_tour(random.choice(patterns)())\n",
2413     "#     rw = guided_walk(lc)\n",
2414     "#     if rw:\n",
2415     "#         rw_trimmed = trim_all_loops(rw)\n",
2416     "#         if len(rw_trimmed) > 10:\n",
2417     "#             with open(tours_filename, 'a') as f:\n",
2418     "#                 f.write(rw_trimmed + '\\n')\n",
2419     "#                 success_count += 1"
2420    ]
2421   },
2422   {
2423    "cell_type": "code",
2424    "execution_count": 102,
2425    "metadata": {},
2426    "outputs": [
2427     {
2428      "name": "stdout",
2429      "output_type": "stream",
2430      "text": [
2431       "Found mistakes: 1867\n"
2432      ]
2433     },
2434     {
2435      "data": {
2436       "text/plain": [
2437        "(5242,\n",
2438        " 1244,\n",
2439        " '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')"
2440       ]
2441      },
2442      "execution_count": 102,
2443      "metadata": {},
2444      "output_type": "execute_result"
2445     },
2446     {
2447      "data": {
2448       "image/png": 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PldVqpWfPnqSnpzN27Fhuv/125yYyv0X7iuq9JMGYl1YogkWHDh28zrbWqVMn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\nvEYZDIVC4TXKYCgUCq9RBkOhUHjN/wcaO9HUZ2T8GQAAAABJRU5ErkJggg==\n",
2449       "text/plain": [
2450        "<matplotlib.figure.Figure at 0x7f03fdb72e48>"
2451       ]
2452      },
2453      "metadata": {},
2454      "output_type": "display_data"
2455     }
2456    ],
2457    "source": [
2458     "lc = trace_tour(cross_tour())\n",
2459     "rw = guided_walk(lc)\n",
2460     "print('Found mistakes:', len(mistake_positions(trace_tour(rw))))\n",
2461     "rw_trimmed = trim_all_loops(rw)\n",
2462     "plot_trace(trace_tour(rw_trimmed))\n",
2463     "len(rw), len(rw_trimmed), rw_trimmed"
2464    ]
2465   },
2466   {
2467    "cell_type": "code",
2468    "execution_count": 103,
2469    "metadata": {},
2470    "outputs": [
2471     {
2472      "data": {
2473       "image/png": 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GBry9veHk5IQ9e/ZAq9Xi4sWL+PTTT9GmTRs8/vjj2LRpE1xcXNClSxckJSVBJpNBoVBA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\nG1NhmJiY+I2pMExMTPzm/wGejUjhDTUtvQAAAABJRU5ErkJggg==\n",
2474       "text/plain": [
2475        "<matplotlib.figure.Figure at 0x7f03fdba0cf8>"
2476       ]
2477      },
2478      "metadata": {},
2479      "output_type": "display_data"
2480     }
2481    ],
2482    "source": [
2483     "plot_trace(trace_tour(rw))"
2484    ]
2485   },
2486   {
2487    "cell_type": "code",
2488    "execution_count": 104,
2489    "metadata": {},
2490    "outputs": [
2491     {
2492      "data": {
2493       "image/png": 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PldVqpWfPnqSnpzN27Fhuv/125yYyv0X7iuq9JMGYl1YogkWHDh28zrbWqVMn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\nvEYZDIVC4TXKYCgUCq9RBkOhUHjN/wcaO9HUZ2T8GQAAAABJRU5ErkJggg==\n",
2494       "text/plain": [
2495        "<matplotlib.figure.Figure at 0x7f03fd5f98d0>"
2496       ]
2497      },
2498      "metadata": {},
2499      "output_type": "display_data"
2500     }
2501    ],
2502    "source": [
2503     "plot_trace(trace_tour(trim_all_loops(rw)))"
2504    ]
2505   },
2506   {
2507    "cell_type": "code",
2508    "execution_count": 105,
2509    "metadata": {
2510     "scrolled": true
2511    },
2512    "outputs": [
2513     {
2514      "name": "stdout",
2515      "output_type": "stream",
2516      "text": [
2517       "[Mistake(i=8, step=Step(x=0, y=0, dir=<Direction.RIGHT: 2>)), Mistake(i=30, step=Step(x=0, y=-8, dir=<Direction.LEFT: 4>)), Mistake(i=31, step=Step(x=-1, y=-8, dir=<Direction.LEFT: 4>))]\n"
2518      ]
2519     },
2520     {
2521      "data": {
2522       "text/plain": [
2523        "'RFFRLFFLRFRFLLFFFFLLFFFFFLRRFRFFFFFFLFFFFFLFFRLLFFFLRRRFFFFRRLFFFFFLFFRFRFFRFRLRLRFFFFFFFRFFRFRRFRFFFFRFFFFLLLFRRRFFFRFFFRFFFFRFFFLLFFFLFFFFLRFRLFFLFFLFRRLFFFFRRFFRFLLLFFFRFLFFFRLFLFRFFFLLRLRLFRFFFRRFFLFFLLRLLFFFFFFRLFFFRLLLFFFRLLFRFFFFRFRFFRFLFFFLFFLFFFFRLFLLRRFFFFFFRLLFFLFFFLFFFRFLFRFFLLRFRRFLFRLLFLFFLLFRFLFLFRFFFFLLFFFFFFFFRLLLFLFLFFRFLFFFLFFFLLRFFFFFLFFFFFFFFRFFFRLLLLLFFFLFFFFLFFLRFFRFLFFFFRRRFRLLRRFLRRLFFFFRFFFFFFFRRFFFFFLLLRFFRFFFFRFFFFLRRFFFFFFFLLFFFLFRRLLFFRFRFFFRRFFFRFFFRRFRFFFFFFFFLLFLRRLLRFFFRLFRFFLLFLLFFFLRRRFFFFFFFLFLLFLLRLLLLLFFFFFFFLFLLLRLFFLLFFFRFFLRFFRLFFFFRLLFRLFLLRLFFFFFLFFLLFFRFLRFRFLFLFRFFFFFRFRRRRFRFFFFFFRRFLFLLFLFFFFLFRFRFFFFFFFFFFFRFFLLRFLFLFLFFFFRFFLFFFRFFFRFFFRFLFFFLLLRFLRRFFLFLRRRFFFFFFFRFFFFRFFFFFFRLFFFLRLLFLRRLFFFFFLFFFRFFRFRFFLRFFRFFRFRRLRFFLFFFFFFLLFLFFRLFRLLFRRRFFRFRFFRFLFFLFFFFRRRRFFFFFFRLFLRRRFRFFFFLFFFLLRFFRFFFFLLFFFFFFFFLFFFFFFFFFFFFFFRFFRFFRFFFLLFFFFLFFRRFRFLFFFRFRLFRLFFRRFFFLLFLFLRFFFLRLLFLFFFFLRRFFRFFRFLLRRFFFFFFFFRRLFRRFRFFFFFLRFFFLLFFFFRRLFFFLLLLFFLLLLRFLRRFRLFFFFRFRRFFFFLRRFFFFLFRFLFFFRLFRLFFLRFFLFLFFFLRLFRFFFFFFFFRFRFRRLRFFRFFLFLFFLFFFFFLRFFFFLFFFRRFRRFFLFFFLLLFRFFLFFFRFRLFFFLFFFRRRFFFRFFRFLFLFLFFLRLFRFFFFFFLLLFFFRFFRLRLLRLRRLLLLFFFLFRFFLLFLFFRFFFFLFFLFFRFFRFRRRFFLFLRRRFFRFFRFFFLFRRFLLLLRFLFFFLFFFFFLFFFLLRRFFRRFFFRFFFFFFFRRFFRLFFFFFFFLFRLLRRFFFRFLFFLLFFRRFFLFLRFLFFRFLFFRRFRLLFRLRRLLFFFRLFLRRLFLRLFFFFFFFRFLFFLFFFFLRFFFFLRFFLFLFFFFFFRLLFFFLRFFRRLFFFLLFLRFLFFFFFFLFFLFRRRLRRLFLFFFLFFFRLFRFRFRRRRFRFLFFLLLFRLFFRLRFFRRLFFFFRFRFFLRRFRFFLFLRRLFFRRFFFFFFRFLRFFFFFFRFFLFFRFFFLFFFRLRFFFFFFFFRFFFFFFFLFFLFFFLFRFRLFRFRRLFLLFFLFFFFFFFFFFLRFFFLRLRFLFFFFFFFFFLFFRLRFLLRFFFFFFLFFFLRLFRRFLFFFFFFLFRRRLLLFRLLFLFFLFRFRLFLRFFFRFLFLFRFFFRFFFFFFFFFFFRFLRRRFFRRRFFFRRFFFFFRRFRLFFLFFFFRLFFFLRLRFRFLLFFFLLFRFRFFFLFLFFFRFRFFRFFFRFFFFFRFFFLFFFFFLRLRRFFRRLRFRRFFFLRRFRFRFLLFRFRRFFFFFFFFRRFFFFFFFRRLRFFRFLFRFFFFFLFRFLLLFFRFLFFFFLFFLFLFRRLLRFFFFLRFFRFLFFLFLFFFLFRFFLLFRRRFFLLFFRRFFFFLLFFFLFFFFFLFLRLRRFLRFFFFLLFRFRLFLRFLFLFLRRFFRFRFFFFFFLFFFFLFRFRLFRLFFFLFFFFFLRLRRRFFFFLFRFFRFFRFFFFRFFLFFLFFFFFRFFRFLFFFLFRFFRRRFLFLFRFFRLRFLLLFFRFRLFFFFLFLLFLFRFFLFFRFRFFFLFFFLFFFRRLRFLRRFRLFFFRRRFLLFFFLLRRFFFRFFFFFRFFFRFFFFFFFRFRFLFFFFLRRRFFFRFRFLRFRLLFFFFRFLFRFFLFRFFFFRFLRRFLRRLLFRLRFLRRRLLFFFFRFRRFRLLLFFLLLFRFFFRRFFRLRFFRFFFFRLLLRRFRLLLLFFFFRRFRFFFRFRLLFRRFFFFRFFFFFFFFRRFFLFFLFRLFFLFFRRFRRFRRFLFRFRFRLRFLLFLFFRFFLFFLFFLLFFFRFFFFLFRRFRFFFFFFRFFFFRFFLFFFLLFFFFFRLRRFFRFRFLRLLFFFLFFRLLFFFFFFFFFLLFFFFFRFRRRRRFFFFRLRFRRFRLFFFFLFRFFFFFFRFRFFRFRFFFLLFFFRFFFRFFFLFRFLFFFLFFRFFFLLRRFFFLRFFLFFFRFFFFFFFRRFFFFFLLFFLFFFFFRFLRFLFRLFFFRFFFLLFFFFFRFFFRFFFLLFFFLFFFRFFFFRFFFRFFFFFFFFLLRFFRFFFFRRFRLFRRLFFFFLFLLFLFFFFFFFFFFFRFLLFFRFLFFLLFRFFLFFFFFFFLLFRFFFFFRFLFFLLRLFFRFFLFLFLFLFFRRLRFFRFRFLFFLFFLFFLLLRFRFRFRFRFRFFRFFFFFFLFLFRRFFFFFFRFLFFFFLFFFRLLFRFFRLRLLFFFRFLFRRLFFRFRRFFRLLFFFLFLLLFLRFFFLFFFFRFFRFFFLRRFFFFRFFRRFFRFFFLFFRFFFLLFFLLRFFFFFFFLFFFFFFFLLLLFFLFFFFFFFFFRLFRLFFFLFFFRRFLLLRRRFRFRFLFFFFFLFLRLFFLFFLLFLFFFFLFLLLRFFFFFRFFRRRFFFFFFFRLFFRRFFLFFFFFFLRFRFRFRFFFFFLFFFFFLFLFRRFFRFFLRFFLFRFFFRRFFFLFLFFLLLRFLFRFRRFFFRFFRFLFFFLFFRLFFLFLLFFFRFRLRLFRRLRFFFRLLRFRFFFFFRFFFLRRFLFFFRFLLFFLLFFRFFFFFFFFFRRFRRFFFRFFFFRFFFLFRFLFFFFRFFFFRLLRRFFRFRFLLFFLFFLFLRRLFFFRLLFFLFRFFFFFRRFLRFRFRFRLFFFRFRFFRLFFLRRFLLLFLFFRFFFFRLFLLFFLFRFLFLLFFFRFRFFFFRFFRFRFFFLRRLFRFFFRLLLFFFFFFLFLRFLFFFLFLLLLFFRFFFRRFRLFLRFFFLFFFFFFFFLFRFFLFLFFFFFFFLFFLFRRFFFRRFFFFFFFFFFLLLRFLLFFFLLFFFFLRRRLRFLFFFFRRRFFFFRFFLFFFFFRFFFFRLLLFFFFFFLFFLLLRLFRFFLLFFFFFLFLFRLFFFRFFRRFFFLRFRRRRLLFFFFFRLFFFLRFLRLLFFLFLFFFFFFFLFFLLLLLFLLRLLFLLRLRFFFRRLRFFFFRRFRRFRFFFFRLFFFFFFFFFFFRFLLFFLFFFLFFRFRFRRFFRFFRFFLLFFLFFFLFFFLFFFLFRRLRLFFFLFRFFRFRRFFLLFFLFLFFFFLFFRFFFFFFLRLRFFRFFRFLLFRLLFFFFFLFFFFFFRFFFFRFRFRFFFFFFFFFFRFLFFRFLFFFFLFFFLFLFFRFRFFFFFFRFFLFLRFRFLLFLFFLFRFFFRRLFRLLLFLFFRRLRFFRFLFRRFFFFFFFLRLLFFFLFFFRLLFLFLLLRRRLFFRFFFLLLFLFFFFFFFFFFFLLFFFLLRFFLLFFFLFFLFRLRFFFFRFRFRFFFRRFFFRFFRRLFFLFFFFRFLFRFLFFLFFFFLFLRFFFFRFRFFFFRFRFFFFFFRRLRFRFLFLFLFFLFFFFFFFFFRFLFFFFFFFFRRRRLRFFFLLFFLFLFFLFLRLLFFFRLFRRFFFFFFFRFFRFRLFFFLRFRFFRRRFFFRLLLFFFFRFFRRRLFRFFFFFLLFFFLFFLRFFFLRFFRRLFFRFRFRLFFFFRFFLFFFLFLFFRRFFLFLFLRFFFRLFFFFLLFFFLRFFFFFRRFFLLFFFRRFLRRFLFFLFFFFLFFFFRRFFFFRFRRFFFFFLFFFLFRLFLFFFFFFFFFFFFLFRFFRFLLLRLFFLFRFFFRFRFLFFFLFFFRFLFFFLRLFFLFFLFLFFFFLFLFLFRFFFFRFRFFFRFLLFLFFFFFFFFLFFLFFFRFRFFRFFFLFRLLFFLRFFFFFRFRFFFFFFFFRFFFFFFFFRFFFFFFFFFRRLFLLFFFFFFFRRLRFFLFFFFFLFLFFRFFLFFRRLLLLLLFLLFFFFFFRFRFLRRFFRFLFFRRFRLRRFFRLLFFFLRFFFFFFFRFFLFLFFFLFLLFRFFRLLFFRFFFFLLFFFFFFFFFLFLFFFFFFLLRRFRFFLFFFFFFRFRLFFFFFFLRRFFRFFRLFFFFFFFRRLRFFFFRFLFRRLRFFFFFFFFRFRRFRRRFRLFLFFFRRFRFFLLLFLFLFFRRFFFRRRLFFLFFLFFRFRFRFFFFLLFLFRFRFLLFFFFFLFRFLFFLFFFFFLFLFRFFRLFFLRRFRFFFFRFFFFRLFFFRLFRFRRRFFFLRFRFFLLFFFLLRRLFLRFLRRFRFFRFLFFFLFRRFRFRRFFFFFFFLLFLFFFFLLLRFRRFFFLRFFFFFRFLFFLFLFFFFFLRRRFFFFFRFLFRLFLLRLFFLFFFFFRRFFFLFRFFRRFFFFRRFFFFRFRRFRRRFFFFFRFRRLFFFFRRFFRFRFLFFLFLFLFRLLFFLLFRLFFFRLLLFLFRLRFFLFFRLFFFLRRRRFFFFRFFRFFFLFFLFFFFFFFFLRRRFFFFFFFRLFLLLFFLLLFFFFFFFFFFFLFLLFFRFFFRFFFFFFLRFFFLFFLLFLFFRLRLFLFFFLFFFLFRRLLLFRFFRLRRFLFFLRFFFFFFLRLLFLFFRLLLFFRFRRFFFFRRRFRFFFFFRRRRFRLLLFFFFRFLLFFRRRRFLLFFLFFLFFFFLLLFFFFRFFFRFFFFFRFRRFRFFRFLLFLFFFLFFLLRLFLFFFLFLFRLRFRLFRFLLFLFFFRRFRRRRRLFFFLRFLLRRRFFFFFLFRFLFFFFLRFFRLFLFFFRFRFFFRFFFRFFFFFFFFFLRFFFLFLRFRFFLLFFRFLFFFFFFFFFFFFLFFFLFRLFLFRFRLFFRFFFFFFRLFFFFLRL'"
2524       ]
2525      },
2526      "execution_count": 105,
2527      "metadata": {},
2528      "output_type": "execute_result"
2529     }
2530    ],
2531    "source": [
2532     "w_tour = rw\n",
2533     "w_trace = trace_tour(w_tour)\n",
2534     "mks = mistake_positions(w_trace)\n",
2535     "print(mks[:3])\n",
2536     "trim_loop(w_tour)"
2537    ]
2538   },
2539   {
2540    "cell_type": "code",
2541    "execution_count": 106,
2542    "metadata": {
2543     "scrolled": true
2544    },
2545    "outputs": [
2546     {
2547      "name": "stdout",
2548      "output_type": "stream",
2549      "text": [
2550       "1867\n",
2551       "1863\n",
2552       "1860\n",
2553       "1859\n",
2554       "1850\n",
2555       "1843\n",
2556       "1837\n",
2557       "1833\n",
2558       "1831\n",
2559       "1829\n",
2560       "1821\n",
2561       "1816\n",
2562       "1814\n",
2563       "1799\n",
2564       "1793\n",
2565       "1788\n",
2566       "1784\n",
2567       "1778\n",
2568       "1777\n",
2569       "1772\n",
2570       "1764\n",
2571       "1760\n",
2572       "1758\n",
2573       "1755\n",
2574       "1752\n",
2575       "1748\n",
2576       "1736\n",
2577       "1731\n",
2578       "1726\n",
2579       "1717\n",
2580       "1705\n",
2581       "1700\n",
2582       "1695\n",
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2602       "1596\n",
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2643       "1442\n",
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2646       "1432\n",
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2650       "1405\n",
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2652       "1393\n",
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2700       "1136\n",
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2706       "1111\n",
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2725       "1019\n",
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2727       "1009\n",
2728       "1008\n",
2729       "1004\n",
2730       "1000\n",
2731       "990\n",
2732       "986\n",
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2734       "982\n",
2735       "980\n",
2736       "974\n",
2737       "966\n",
2738       "960\n",
2739       "959\n",
2740       "957\n",
2741       "956\n",
2742       "954\n",
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2749       "933\n",
2750       "930\n",
2751       "928\n",
2752       "922\n",
2753       "910\n",
2754       "903\n",
2755       "888\n",
2756       "883\n",
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2758       "874\n",
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2760       "857\n",
2761       "849\n",
2762       "847\n",
2763       "836\n",
2764       "833\n",
2765       "818\n",
2766       "808\n",
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2768       "801\n",
2769       "800\n",
2770       "789\n",
2771       "783\n",
2772       "768\n",
2773       "766\n",
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2775       "754\n",
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2778       "734\n",
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2780       "706\n",
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2794       "633\n",
2795       "616\n",
2796       "603\n",
2797       "601\n",
2798       "594\n",
2799       "593\n",
2800       "592\n",
2801       "586\n",
2802       "582\n",
2803       "573\n",
2804       "571\n",
2805       "562\n",
2806       "550\n",
2807       "548\n",
2808       "545\n",
2809       "537\n",
2810       "530\n",
2811       "519\n",
2812       "517\n",
2813       "513\n",
2814       "509\n",
2815       "508\n",
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2817       "497\n",
2818       "476\n",
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2820       "465\n",
2821       "459\n",
2822       "448\n",
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2824       "435\n",
2825       "428\n",
2826       "421\n",
2827       "413\n",
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2862       "199\n",
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2864       "180\n",
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2868       "149\n",
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2870       "141\n",
2871       "139\n",
2872       "132\n",
2873       "128\n",
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2876       "102\n",
2877       "97\n",
2878       "89\n",
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2880       "65\n",
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2885       "37\n",
2886       "33\n",
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2889       "20\n",
2890       "17\n",
2891       "14\n",
2892       "12\n",
2893       "8\n",
2894       "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF\n",
2895       "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\n",
2896       "Step(x=0, y=0, dir=<Direction.LEFT: 4>)\n"
2897      ]
2898     },
2899     {
2900      "data": {
2901       "image/png": 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PldVqpWfPnqSnpzN27Fhuv/125yYyv0X7iuq9JMGYl1YogkWHDh28zrbWqVMn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\nvEYZDIVC4TXKYCgUCq9RBkOhUHjN/wcaO9HUZ2T8GQAAAABJRU5ErkJggg==\n",
2902       "text/plain": [
2903        "<matplotlib.figure.Figure at 0x7f03fdaa1860>"
2904       ]
2905      },
2906      "metadata": {},
2907      "output_type": "display_data"
2908     }
2909    ],
2910    "source": [
2911     "w_tour = rw\n",
2912     "w_trace = trace_tour(w_tour)\n",
2913     "mks = mistake_positions(w_trace)\n",
2914     "while len(mks) > 3:\n",
2915     "    print(len(mks))\n",
2916     "    w_tour = trim_loop(w_tour)\n",
2917     "    w_trace = trace_tour(w_tour)\n",
2918     "    mks = mistake_positions(w_trace)\n",
2919     "print('{}\\n{}\\n{}'.format(w_tour_start, w_tour, trace_tour(w_tour)[-1]))\n",
2920     "plot_trace(trace_tour(w_tour))"
2921    ]
2922   },
2923   {
2924    "cell_type": "code",
2925    "execution_count": 107,
2926    "metadata": {},
2927    "outputs": [
2928     {
2929      "data": {
2930       "text/plain": [
2931        "[]"
2932       ]
2933      },
2934      "execution_count": 107,
2935      "metadata": {},
2936      "output_type": "execute_result"
2937     }
2938    ],
2939    "source": [
2940     "mks"
2941    ]
2942   },
2943   {
2944    "cell_type": "code",
2945    "execution_count": 108,
2946    "metadata": {},
2947    "outputs": [
2948     {
2949      "ename": "IndexError",
2950      "evalue": "list index out of range",
2951      "output_type": "error",
2952      "traceback": [
2953       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
2954       "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
2955       "\u001b[0;32m<ipython-input-108-982d2ade068b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtrim_loop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw_tour\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
2956       "\u001b[0;32m<ipython-input-67-102a8e4a5818>\u001b[0m in \u001b[0;36mtrim_loop\u001b[0;34m(tour, random_mistake)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;31m#     print('end_mistake_index {} pointing to trace position {}; {} mistakes and {} in trace; {}'.format(end_mistake_index, mistakes[end_mistake_index].i, len(mistakes), len(trace), mistakes))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m     \u001b[0;31m# while this mistake extends to the next step in the trace...\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m     while (mistakes[end_mistake_index].i + 1 < len(trace) and \n\u001b[0m\u001b[1;32m     11\u001b[0m            \u001b[0mend_mistake_index\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmistakes\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m            \u001b[0mmistakes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mend_mistake_index\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m==\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
2957       "\u001b[0;31mIndexError\u001b[0m: list index out of range"
2958      ]
2959     }
2960    ],
2961    "source": [
2962     "trim_loop(w_tour)"
2963    ]
2964   },
2965   {
2966    "cell_type": "code",
2967    "execution_count": 109,
2968    "metadata": {},
2969    "outputs": [
2970     {
2971      "data": {
2972       "image/png": 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JLrGspqZGt2nTRi9evNgo/vDhwxGfV9Dc7cSJE8b7h1jo1Y+Pj+fkyZOOWna9lJOT841Z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\nED4khS+ED0nhC+FD/x8fErW+FPwE4wAAAABJRU5ErkJggg==\n",
2973       "text/plain": [
2974        "<matplotlib.figure.Figure at 0x7f03fd0eab38>"
2975       ]
2976      },
2977      "metadata": {},
2978      "output_type": "display_data"
2979     }
2980    ],
2981    "source": [
2982     "lc = trace_tour(square_tour(a=10))\n",
2983     "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
2984     "plot_trace(trace_tour(rw))"
2985    ]
2986   },
2987   {
2988    "cell_type": "code",
2989    "execution_count": 110,
2990    "metadata": {},
2991    "outputs": [
2992     {
2993      "data": {
2994       "text/plain": [
2995        "(292,\n",
2996        " 10,\n",
2997        " 'RFLLFFLFLL',\n",
2998        " [Step(x=-1, y=0, dir=<Direction.DOWN: 3>),\n",
2999        "  Step(x=0, y=0, dir=<Direction.RIGHT: 2>)])"
3000       ]
3001      },
3002      "execution_count": 110,
3003      "metadata": {},
3004      "output_type": "execute_result"
3005     },
3006     {
3007      "data": {
3008       "image/png": 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XwMXArjyPX0Pu5BrAx4FnEpp7ObChF3nPAy6Org8FXu3muSg5c5/t2dz95+7+wYfczwBj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\n",
3009       "text/plain": [
3010        "<matplotlib.figure.Figure at 0x7f03fd712198>"
3011       ]
3012      },
3013      "metadata": {},
3014      "output_type": "display_data"
3015     }
3016    ],
3017    "source": [
3018     "rw_trimmed = trim_all_loops(rw)\n",
3019     "plot_trace(trace_tour(rw_trimmed))\n",
3020     "len(rw), len(rw_trimmed), rw_trimmed, trace_tour(rw_trimmed)[-2:]"
3021    ]
3022   },
3023   {
3024    "cell_type": "code",
3025    "execution_count": 111,
3026    "metadata": {},
3027    "outputs": [
3028     {
3029      "data": {
3030       "text/plain": [
3031        "(1, Step(x=0, y=0, dir=<Direction.RIGHT: 2>))"
3032       ]
3033      },
3034      "execution_count": 111,
3035      "metadata": {},
3036      "output_type": "execute_result"
3037     },
3038     {
3039      "data": {
3040       "image/png": 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AX3nllUROAN+V559/PnDvixcvBpKb61TYEnDHHXcAH8/2RSWbQOTDYHFvBe19xowZANx4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\noOEAAAAASUVORK5CYII=\n",
3041       "text/plain": [
3042        "<matplotlib.figure.Figure at 0x7f03fd6c24a8>"
3043       ]
3044      },
3045      "metadata": {},
3046      "output_type": "display_data"
3047     }
3048    ],
3049    "source": [
3050     "rw_trimmed = rw\n",
3051     "mks = len(mistake_positions(trace_tour(rw_trimmed)))\n",
3052     "while mks >= 4:\n",
3053     "    rw_trimmed = trim_loop(rw_trimmed, random_mistake=True)\n",
3054     "    mks = len(mistake_positions(trace_tour(rw_trimmed)))\n",
3055     "    \n",
3056     "# rw_trimmed = trim_all_loops(rw)\n",
3057     "plot_trace(trace_tour(rw_trimmed))\n",
3058     "mks, trace_tour(rw_trimmed)[-1]"
3059    ]
3060   },
3061   {
3062    "cell_type": "code",
3063    "execution_count": 112,
3064    "metadata": {
3065     "collapsed": true
3066    },
3067    "outputs": [],
3068    "source": [
3069     "def trim_some_mistakes(tour, mistake_limit):\n",
3070     "    trimmed_tour = rw\n",
3071     "    mistake_count = len(mistake_positions(trace_tour(trimmed_tour)))\n",
3072     "    while len(mistake_positions(trace_tour(trimmed_tour))) > mistake_limit:\n",
3073     "        trimmed_tour = trim_loop(trimmed_tour, random_mistake=True)\n",
3074     "    return trimmed_tour"
3075    ]
3076   },
3077   {
3078    "cell_type": "code",
3079    "execution_count": 113,
3080    "metadata": {},
3081    "outputs": [
3082     {
3083      "data": {
3084       "text/plain": [
3085        "(3, Step(x=0, y=0, dir=<Direction.RIGHT: 2>))"
3086       ]
3087      },
3088      "execution_count": 113,
3089      "metadata": {},
3090      "output_type": "execute_result"
3091     },
3092     {
3093      "data": {
3094       "image/png": 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il+/KoG+Z2Rtm1mxm/25mZ4eamEgo+e7JnwcucfepQCtwV/5TOjPt2bOH6667DoAJEyao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\n",
3095       "text/plain": [
3096        "<matplotlib.figure.Figure at 0x7f03fdb2d6d8>"
3097       ]
3098      },
3099      "metadata": {},
3100      "output_type": "display_data"
3101     }
3102    ],
3103    "source": [
3104     "rw_trimmed = trim_some_mistakes(rw, 4)\n",
3105     "\n",
3106     "plot_trace(trace_tour(rw_trimmed))\n",
3107     "len(mistake_positions(trace_tour(rw_trimmed))), trace_tour(rw_trimmed)[-1]"
3108    ]
3109   },
3110   {
3111    "cell_type": "code",
3112    "execution_count": 114,
3113    "metadata": {
3114     "collapsed": true
3115    },
3116    "outputs": [],
3117    "source": [
3118     "# patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
3119     "# tours_filename = 'tours-with-mistakes.txt'\n",
3120     "\n",
3121     "# try:\n",
3122     "#     os.remove(tours_filename)\n",
3123     "# except OSError:\n",
3124     "#     pass\n",
3125     "\n",
3126     "# success_count = 0\n",
3127     "# while success_count < 100:\n",
3128     "#     lc = trace_tour(random.choice(patterns)())\n",
3129     "#     rw = guided_walk(lc)\n",
3130     "#     if rw:\n",
3131     "#         rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
3132     "#         if len(rw_trimmed) > 10:\n",
3133     "#             with open(tours_filename, 'a') as f:\n",
3134     "#                 f.write(rw_trimmed + '\\n')\n",
3135     "#                 success_count += 1"
3136    ]
3137   },
3138   {
3139    "cell_type": "code",
3140    "execution_count": 115,
3141    "metadata": {},
3142    "outputs": [
3143     {
3144      "data": {
3145       "image/png": 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ffzFhwgSuuuoqjEYjb731FgkJCbzzzjscOXKEjIyMOpaCFixYAMBbb72lypy2AqAt1bq7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\nEPGGH0ccYxDxhh9HHGMQ/w87It8NbHAcAQAAAABJRU5ErkJggg==\n",
3146       "text/plain": [
3147        "<matplotlib.figure.Figure at 0x7f03fd276ac8>"
3148       ]
3149      },
3150      "metadata": {},
3151      "output_type": "display_data"
3152     }
3153    ],
3154    "source": [
3155     "lc = trace_tour(square_tour())\n",
3156     "rw = guided_walk(lc, seek_step_limit=0, return_anyway=True)\n",
3157     "plot_trace(trace_tour(rw))"
3158    ]
3159   },
3160   {
3161    "cell_type": "code",
3162    "execution_count": 116,
3163    "metadata": {},
3164    "outputs": [
3165     {
3166      "data": {
3167       "image/png": 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hLSISIYW3iEiEFN4iIhFSeIuIREjhLSISIYW3iEiEFN4iIhFSeIuIREjhLSISoUyHMZSZ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\niEiEFN4iIhFSeIuIREjhLSISof8HrbA0eP/SgKEAAAAASUVORK5CYII=\n",
3168       "text/plain": [
3169        "<matplotlib.figure.Figure at 0x7f03fc718f28>"
3170       ]
3171      },
3172      "metadata": {},
3173      "output_type": "display_data"
3174     }
3175    ],
3176    "source": [
3177     "rw_trimmed = trim_some_mistakes(rw, 1)\n",
3178     "plot_trace(trace_tour(rw_trimmed))"
3179    ]
3180   },
3181   {
3182    "cell_type": "code",
3183    "execution_count": 117,
3184    "metadata": {},
3185    "outputs": [
3186     {
3187      "data": {
3188       "text/plain": [
3189        "[Mistake(i=32, step=Step(x=10, y=4, dir=<Direction.RIGHT: 2>))]"
3190       ]
3191      },
3192      "execution_count": 117,
3193      "metadata": {},
3194      "output_type": "execute_result"
3195     }
3196    ],
3197    "source": [
3198     "mistake_positions(trace_tour(rw_trimmed))"
3199    ]
3200   },
3201   {
3202    "cell_type": "code",
3203    "execution_count": null,
3204    "metadata": {
3205     "collapsed": true
3206    },
3207    "outputs": [],
3208    "source": [
3209     "# patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
3210     "# tours_filename = 'tours-open.txt'\n",
3211     "\n",
3212     "# try:\n",
3213     "#     os.remove(tours_filename)\n",
3214     "# except OSError:\n",
3215     "#     pass\n",
3216     "\n",
3217     "# success_count = 0\n",
3218     "# while success_count < 100:\n",
3219     "#     lc = trace_tour(random.choice(patterns)())\n",
3220     "#     rw = guided_walk(lc, seek_step_limit=0, return_anyway=True)\n",
3221     "#     if rw:\n",
3222     "#         rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
3223     "#         if len(rw_trimmed) > 10:\n",
3224     "#             with open(tours_filename, 'a') as f:\n",
3225     "#                 f.write(rw_trimmed + '\\n')\n",
3226     "#                 success_count += 1"
3227    ]
3228   },
3229   {
3230    "cell_type": "code",
3231    "execution_count": 119,
3232    "metadata": {
3233     "collapsed": true
3234    },
3235    "outputs": [],
3236    "source": [
3237     "tours_filename = 'tours-random-walk.txt'\n",
3238     "\n",
3239     "try:\n",
3240     "    os.remove(tours_filename)\n",
3241     "except OSError:\n",
3242     "    pass\n",
3243     "\n",
3244     "success_count = 0\n",
3245     "while success_count < 200:\n",
3246     "    rw = random_walk()\n",
3247     "    if rw:\n",
3248     "        if random.choice([True, False]):\n",
3249     "            rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
3250     "        else:\n",
3251     "            rw_trimmed = trim_all_loops(rw)\n",
3252     "        if len(rw_trimmed) > 10:\n",
3253     "            with open(tours_filename, 'a') as f:\n",
3254     "                f.write(rw_trimmed + '\\n')\n",
3255     "                success_count += 1"
3256    ]
3257   },
3258   {
3259    "cell_type": "code",
3260    "execution_count": null,
3261    "metadata": {
3262     "collapsed": true
3263    },
3264    "outputs": [],
3265    "source": []
3266   }
3267  ],
3268  "metadata": {
3269   "kernelspec": {
3270    "display_name": "Python 3",
3271    "language": "python",
3272    "name": "python3"
3273   },
3274   "language_info": {
3275    "codemirror_mode": {
3276     "name": "ipython",
3277     "version": 3
3278    },
3279    "file_extension": ".py",
3280    "mimetype": "text/x-python",
3281    "name": "python",
3282    "nbconvert_exporter": "python",
3283    "pygments_lexer": "ipython3",
3284    "version": "3.5.2+"
3285   }
3286  },
3287  "nbformat": 4,
3288  "nbformat_minor": 2
3289 }