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

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "markdown",
   5    "metadata": {},
   6    "source": [
   7     "Given a sequence of {F|L|R}, each of which is \"move forward one step\", \"turn left, then move forward one step\", \"turn right, then move forward one step\":\n",
   8     "1. which tours are closed?\n",
   9     "2. what is the area enclosed by the tour?"
  10    ]
  11   },
  12   {
  13    "cell_type": "code",
  14    "execution_count": 2,
  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": 3,
  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": 4,
  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": 5,
  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": 6,
  90    "metadata": {
  91     "collapsed": true
  92    },
  93    "outputs": [],
  94    "source": [
  95     "def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
  96     "    current = Step(startx, starty, startdir)\n",
  97     "    trace = [current]\n",
  98     "    for s in tour:\n",
  99     "        if s == 'F':\n",
 100     "            current = advance(current, current.dir)\n",
 101     "        elif s == 'L':\n",
 102     "            current = advance(current, turn_left(current.dir))\n",
 103     "        elif s == 'R':\n",
 104     "            current = advance(current, turn_right(current.dir))\n",
 105     "        trace += [current]\n",
 106     "    return trace    "
 107    ]
 108   },
 109   {
 110    "cell_type": "code",
 111    "execution_count": 7,
 112    "metadata": {
 113     "collapsed": true
 114    },
 115    "outputs": [],
 116    "source": [
 117     "k = Step(1, 2, 3)"
 118    ]
 119   },
 120   {
 121    "cell_type": "code",
 122    "execution_count": 8,
 123    "metadata": {},
 124    "outputs": [
 125     {
 126      "data": {
 127       "text/plain": [
 128        "Step(x=1, y=2, dir=3)"
 129       ]
 130      },
 131      "execution_count": 8,
 132      "metadata": {},
 133      "output_type": "execute_result"
 134     }
 135    ],
 136    "source": [
 137     "k"
 138    ]
 139   },
 140   {
 141    "cell_type": "code",
 142    "execution_count": 9,
 143    "metadata": {},
 144    "outputs": [
 145     {
 146      "data": {
 147       "text/plain": [
 148        "__main__.Step"
 149       ]
 150      },
 151      "execution_count": 9,
 152      "metadata": {},
 153      "output_type": "execute_result"
 154     }
 155    ],
 156    "source": [
 157     "Step"
 158    ]
 159   },
 160   {
 161    "cell_type": "code",
 162    "execution_count": 10,
 163    "metadata": {},
 164    "outputs": [
 165     {
 166      "data": {
 167       "text/plain": [
 168        "<Direction.UP: 1>"
 169       ]
 170      },
 171      "execution_count": 10,
 172      "metadata": {},
 173      "output_type": "execute_result"
 174     }
 175    ],
 176    "source": [
 177     "d = Direction.UP\n",
 178     "d"
 179    ]
 180   },
 181   {
 182    "cell_type": "code",
 183    "execution_count": 11,
 184    "metadata": {},
 185    "outputs": [
 186     {
 187      "data": {
 188       "text/plain": [
 189        "<Direction.RIGHT: 2>"
 190       ]
 191      },
 192      "execution_count": 11,
 193      "metadata": {},
 194      "output_type": "execute_result"
 195     }
 196    ],
 197    "source": [
 198     "turn_right(d)"
 199    ]
 200   },
 201   {
 202    "cell_type": "code",
 203    "execution_count": 12,
 204    "metadata": {},
 205    "outputs": [
 206     {
 207      "data": {
 208       "text/plain": [
 209        "{<Direction.RIGHT: 2>: <Direction.DOWN: 3>,\n",
 210        " <Direction.UP: 1>: <Direction.RIGHT: 2>,\n",
 211        " <Direction.DOWN: 3>: <Direction.LEFT: 4>,\n",
 212        " <Direction.LEFT: 4>: <Direction.UP: 1>}"
 213       ]
 214      },
 215      "execution_count": 12,
 216      "metadata": {},
 217      "output_type": "execute_result"
 218     }
 219    ],
 220    "source": [
 221     "turn_rights"
 222    ]
 223   },
 224   {
 225    "cell_type": "code",
 226    "execution_count": 13,
 227    "metadata": {},
 228    "outputs": [
 229     {
 230      "data": {
 231       "text/plain": [
 232        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 233        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 234        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 235        " Step(x=2, y=1, dir=<Direction.RIGHT: 2>),\n",
 236        " Step(x=2, y=2, dir=<Direction.UP: 1>)]"
 237       ]
 238      },
 239      "execution_count": 13,
 240      "metadata": {},
 241      "output_type": "execute_result"
 242     }
 243    ],
 244    "source": [
 245     "trace_tour('FLRL')"
 246    ]
 247   },
 248   {
 249    "cell_type": "code",
 250    "execution_count": 14,
 251    "metadata": {},
 252    "outputs": [
 253     {
 254      "data": {
 255       "text/plain": [
 256        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 257        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 258        " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
 259        " Step(x=2, y=1, dir=<Direction.UP: 1>),\n",
 260        " Step(x=3, y=1, dir=<Direction.RIGHT: 2>),\n",
 261        " Step(x=3, y=2, dir=<Direction.UP: 1>),\n",
 262        " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
 263        " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
 264        " Step(x=1, y=1, dir=<Direction.DOWN: 3>),\n",
 265        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
 266        " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
 267       ]
 268      },
 269      "execution_count": 14,
 270      "metadata": {},
 271      "output_type": "execute_result"
 272     }
 273    ],
 274    "source": [
 275     "trace_tour('FFLRLLFLRL')"
 276    ]
 277   },
 278   {
 279    "cell_type": "code",
 280    "execution_count": 15,
 281    "metadata": {},
 282    "outputs": [
 283     {
 284      "data": {
 285       "text/plain": [
 286        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 287        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 288        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 289        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
 290        " Step(x=-1, y=1, dir=<Direction.LEFT: 4>),\n",
 291        " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
 292        " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
 293        " Step(x=-2, y=-1, dir=<Direction.DOWN: 3>),\n",
 294        " Step(x=-2, y=-2, dir=<Direction.DOWN: 3>),\n",
 295        " Step(x=-2, y=-3, dir=<Direction.DOWN: 3>),\n",
 296        " Step(x=-1, y=-3, dir=<Direction.RIGHT: 2>),\n",
 297        " Step(x=0, y=-3, dir=<Direction.RIGHT: 2>),\n",
 298        " Step(x=1, y=-3, dir=<Direction.RIGHT: 2>),\n",
 299        " Step(x=1, y=-2, dir=<Direction.UP: 1>),\n",
 300        " Step(x=1, y=-1, dir=<Direction.UP: 1>),\n",
 301        " Step(x=0, y=-1, dir=<Direction.LEFT: 4>),\n",
 302        " Step(x=0, y=-2, dir=<Direction.DOWN: 3>),\n",
 303        " Step(x=-1, y=-2, dir=<Direction.LEFT: 4>),\n",
 304        " Step(x=-1, y=-1, dir=<Direction.UP: 1>),\n",
 305        " Step(x=-1, y=0, dir=<Direction.UP: 1>),\n",
 306        " Step(x=0, y=0, dir=<Direction.RIGHT: 2>)]"
 307       ]
 308      },
 309      "execution_count": 15,
 310      "metadata": {},
 311      "output_type": "execute_result"
 312     }
 313    ],
 314    "source": [
 315     "trace_tour('FLLFFLFFFLFFLFLLRRFR')"
 316    ]
 317   },
 318   {
 319    "cell_type": "code",
 320    "execution_count": 16,
 321    "metadata": {},
 322    "outputs": [
 323     {
 324      "data": {
 325       "text/plain": [
 326        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 327        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 328        " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
 329        " Step(x=2, y=-1, dir=<Direction.DOWN: 3>),\n",
 330        " Step(x=3, y=-1, dir=<Direction.RIGHT: 2>),\n",
 331        " Step(x=3, y=0, dir=<Direction.UP: 1>),\n",
 332        " Step(x=3, y=1, dir=<Direction.UP: 1>),\n",
 333        " Step(x=4, y=1, dir=<Direction.RIGHT: 2>),\n",
 334        " Step(x=4, y=2, dir=<Direction.UP: 1>),\n",
 335        " Step(x=3, y=2, dir=<Direction.LEFT: 4>),\n",
 336        " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
 337        " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
 338        " Step(x=0, y=2, dir=<Direction.LEFT: 4>),\n",
 339        " Step(x=0, y=3, dir=<Direction.UP: 1>),\n",
 340        " Step(x=0, y=4, dir=<Direction.UP: 1>),\n",
 341        " Step(x=-1, y=4, dir=<Direction.LEFT: 4>),\n",
 342        " Step(x=-1, y=3, dir=<Direction.DOWN: 3>),\n",
 343        " Step(x=-2, y=3, dir=<Direction.LEFT: 4>),\n",
 344        " Step(x=-2, y=2, dir=<Direction.DOWN: 3>),\n",
 345        " Step(x=-1, y=2, dir=<Direction.RIGHT: 2>),\n",
 346        " Step(x=-1, y=1, dir=<Direction.DOWN: 3>),\n",
 347        " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
 348        " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
 349        " Step(x=-1, y=0, dir=<Direction.RIGHT: 2>),\n",
 350        " Step(x=-1, y=-1, dir=<Direction.DOWN: 3>),\n",
 351        " Step(x=0, y=-1, dir=<Direction.RIGHT: 2>),\n",
 352        " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
 353       ]
 354      },
 355      "execution_count": 16,
 356      "metadata": {},
 357      "output_type": "execute_result"
 358     }
 359    ],
 360    "source": [
 361     "trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL')"
 362    ]
 363   },
 364   {
 365    "cell_type": "code",
 366    "execution_count": 17,
 367    "metadata": {
 368     "collapsed": true
 369    },
 370    "outputs": [],
 371    "source": [
 372     "def positions(trace):\n",
 373     "    return [(s.x, s.y) for s in trace]"
 374    ]
 375   },
 376   {
 377    "cell_type": "code",
 378    "execution_count": 18,
 379    "metadata": {},
 380    "outputs": [
 381     {
 382      "data": {
 383       "text/plain": [
 384        "[(0, 0),\n",
 385        " (1, 0),\n",
 386        " (2, 0),\n",
 387        " (2, -1),\n",
 388        " (3, -1),\n",
 389        " (3, 0),\n",
 390        " (3, 1),\n",
 391        " (4, 1),\n",
 392        " (4, 2),\n",
 393        " (3, 2),\n",
 394        " (2, 2),\n",
 395        " (1, 2),\n",
 396        " (0, 2),\n",
 397        " (0, 3),\n",
 398        " (0, 4),\n",
 399        " (-1, 4),\n",
 400        " (-1, 3),\n",
 401        " (-2, 3),\n",
 402        " (-2, 2),\n",
 403        " (-1, 2),\n",
 404        " (-1, 1),\n",
 405        " (-2, 1),\n",
 406        " (-2, 0),\n",
 407        " (-1, 0),\n",
 408        " (-1, -1),\n",
 409        " (0, -1),\n",
 410        " (0, 0)]"
 411       ]
 412      },
 413      "execution_count": 18,
 414      "metadata": {},
 415      "output_type": "execute_result"
 416     }
 417    ],
 418    "source": [
 419     "positions(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 420    ]
 421   },
 422   {
 423    "cell_type": "code",
 424    "execution_count": 19,
 425    "metadata": {
 426     "collapsed": true
 427    },
 428    "outputs": [],
 429    "source": [
 430     "def valid(trace):\n",
 431     "    return (trace[-1].x == 0 \n",
 432     "            and trace[-1].y == 0 \n",
 433     "            and len(set(positions(trace))) + 1 == len(trace))"
 434    ]
 435   },
 436   {
 437    "cell_type": "code",
 438    "execution_count": 20,
 439    "metadata": {},
 440    "outputs": [
 441     {
 442      "data": {
 443       "text/plain": [
 444        "True"
 445       ]
 446      },
 447      "execution_count": 20,
 448      "metadata": {},
 449      "output_type": "execute_result"
 450     }
 451    ],
 452    "source": [
 453     "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 454    ]
 455   },
 456   {
 457    "cell_type": "code",
 458    "execution_count": 21,
 459    "metadata": {},
 460    "outputs": [
 461     {
 462      "data": {
 463       "text/plain": [
 464        "False"
 465       ]
 466      },
 467      "execution_count": 21,
 468      "metadata": {},
 469      "output_type": "execute_result"
 470     }
 471    ],
 472    "source": [
 473     "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLLFF'))"
 474    ]
 475   },
 476   {
 477    "cell_type": "code",
 478    "execution_count": 22,
 479    "metadata": {},
 480    "outputs": [
 481     {
 482      "data": {
 483       "text/plain": [
 484        "False"
 485       ]
 486      },
 487      "execution_count": 22,
 488      "metadata": {},
 489      "output_type": "execute_result"
 490     }
 491    ],
 492    "source": [
 493     "valid(trace_tour('FFLLLFRR'))"
 494    ]
 495   },
 496   {
 497    "cell_type": "code",
 498    "execution_count": 23,
 499    "metadata": {},
 500    "outputs": [
 501     {
 502      "data": {
 503       "text/plain": [
 504        "False"
 505       ]
 506      },
 507      "execution_count": 23,
 508      "metadata": {},
 509      "output_type": "execute_result"
 510     }
 511    ],
 512    "source": [
 513     "valid(trace_tour('F'))"
 514    ]
 515   },
 516   {
 517    "cell_type": "code",
 518    "execution_count": 24,
 519    "metadata": {},
 520    "outputs": [
 521     {
 522      "data": {
 523       "text/plain": [
 524        "True"
 525       ]
 526      },
 527      "execution_count": 24,
 528      "metadata": {},
 529      "output_type": "execute_result"
 530     }
 531    ],
 532    "source": [
 533     "valid(trace_tour('LLLL'))"
 534    ]
 535   },
 536   {
 537    "cell_type": "code",
 538    "execution_count": 25,
 539    "metadata": {
 540     "collapsed": true
 541    },
 542    "outputs": [],
 543    "source": [
 544     "def chunks(items, n=2):\n",
 545     "    return [items[i:i+n] for i in range(len(items) - n + 1)]"
 546    ]
 547   },
 548   {
 549    "cell_type": "code",
 550    "execution_count": 26,
 551    "metadata": {},
 552    "outputs": [
 553     {
 554      "data": {
 555       "text/plain": [
 556        "['abcdefg',\n",
 557        " 'bcdefgh',\n",
 558        " 'cdefghi',\n",
 559        " 'defghij',\n",
 560        " 'efghijk',\n",
 561        " 'fghijkl',\n",
 562        " 'ghijklm',\n",
 563        " 'hijklmn',\n",
 564        " 'ijklmno',\n",
 565        " 'jklmnop',\n",
 566        " 'klmnopq',\n",
 567        " 'lmnopqr',\n",
 568        " 'mnopqrs',\n",
 569        " 'nopqrst',\n",
 570        " 'opqrstu',\n",
 571        " 'pqrstuv',\n",
 572        " 'qrstuvw',\n",
 573        " 'rstuvwx',\n",
 574        " 'stuvwxy',\n",
 575        " 'tuvwxyz']"
 576       ]
 577      },
 578      "execution_count": 26,
 579      "metadata": {},
 580      "output_type": "execute_result"
 581     }
 582    ],
 583    "source": [
 584     "import string\n",
 585     "chunks(string.ascii_lowercase, 7)"
 586    ]
 587   },
 588   {
 589    "cell_type": "markdown",
 590    "metadata": {},
 591    "source": [
 592     "Using the [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula)"
 593    ]
 594   },
 595   {
 596    "cell_type": "code",
 597    "execution_count": 27,
 598    "metadata": {
 599     "collapsed": true
 600    },
 601    "outputs": [],
 602    "source": [
 603     "def shoelace(trace):\n",
 604     "    return abs(sum(s.x * t.y - t.x * s.y for s, t in chunks(trace, 2))) // 2"
 605    ]
 606   },
 607   {
 608    "cell_type": "code",
 609    "execution_count": 28,
 610    "metadata": {},
 611    "outputs": [
 612     {
 613      "data": {
 614       "text/plain": [
 615        "4"
 616       ]
 617      },
 618      "execution_count": 28,
 619      "metadata": {},
 620      "output_type": "execute_result"
 621     }
 622    ],
 623    "source": [
 624     "shoelace(trace_tour('FFLRLLFLRL'))"
 625    ]
 626   },
 627   {
 628    "cell_type": "code",
 629    "execution_count": 29,
 630    "metadata": {},
 631    "outputs": [
 632     {
 633      "data": {
 634       "text/plain": [
 635        "9"
 636       ]
 637      },
 638      "execution_count": 29,
 639      "metadata": {},
 640      "output_type": "execute_result"
 641     }
 642    ],
 643    "source": [
 644     "shoelace(trace_tour('FLLFFLFFFLFFLFLLRRFR'))"
 645    ]
 646   },
 647   {
 648    "cell_type": "code",
 649    "execution_count": 30,
 650    "metadata": {},
 651    "outputs": [
 652     {
 653      "data": {
 654       "text/plain": [
 655        "15"
 656       ]
 657      },
 658      "execution_count": 30,
 659      "metadata": {},
 660      "output_type": "execute_result"
 661     }
 662    ],
 663    "source": [
 664     "shoelace(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 665    ]
 666   },
 667   {
 668    "cell_type": "code",
 669    "execution_count": 31,
 670    "metadata": {
 671     "collapsed": true
 672    },
 673    "outputs": [],
 674    "source": [
 675     "def step(s, current):\n",
 676     "    if s == 'F':\n",
 677     "        return advance(current, current.dir)\n",
 678     "    elif s == 'L':\n",
 679     "        return advance(current, turn_left(current.dir))\n",
 680     "    elif s == 'R':\n",
 681     "        return advance(current, turn_right(current.dir))\n",
 682     "    else:\n",
 683     "        raise ValueError"
 684    ]
 685   },
 686   {
 687    "cell_type": "code",
 688    "execution_count": 32,
 689    "metadata": {
 690     "collapsed": true
 691    },
 692    "outputs": [],
 693    "source": [
 694     "def valid_prefix(tour):\n",
 695     "    current = Step(0, 0, Direction.RIGHT)\n",
 696     "    prefix = []\n",
 697     "    posns = []\n",
 698     "    for s in tour:\n",
 699     "        current = step(s, current)\n",
 700     "        prefix += [s]\n",
 701     "        if (current.x, current.y) in posns:\n",
 702     "            return ''\n",
 703     "        elif current.x == 0 and current.y == 0: \n",
 704     "            return ''.join(prefix)\n",
 705     "        posns += [(current.x, current.y)]\n",
 706     "    if current.x == 0 and current.y == 0:\n",
 707     "        return ''.join(prefix)\n",
 708     "    else:\n",
 709     "        return ''"
 710    ]
 711   },
 712   {
 713    "cell_type": "code",
 714    "execution_count": 33,
 715    "metadata": {
 716     "collapsed": true
 717    },
 718    "outputs": [],
 719    "source": [
 720     "def mistake_positions(trace, debug=False):\n",
 721     "    mistakes = []\n",
 722     "    current = trace[0]\n",
 723     "    posns = [(0, 0)]\n",
 724     "    for i, current in enumerate(trace[1:]):\n",
 725     "        if (current.x, current.y) in posns:\n",
 726     "            if debug: print(i, current)\n",
 727     "            mistakes += [Mistake(i+1, current)]\n",
 728     "        posns += [(current.x, current.y)]\n",
 729     "    if (current.x, current.y) == (0, 0):\n",
 730     "        return mistakes[:-1]\n",
 731     "    else:\n",
 732     "        return mistakes + [Mistake(len(trace)+1, current)]"
 733    ]
 734   },
 735   {
 736    "cell_type": "code",
 737    "execution_count": 34,
 738    "metadata": {
 739     "collapsed": true
 740    },
 741    "outputs": [],
 742    "source": [
 743     "def returns_to_origin(mistake_positions):\n",
 744     "    return [i for i, m in mistake_positions\n",
 745     "           if (m.x, m.y) == (0, 0)]"
 746    ]
 747   },
 748   {
 749    "cell_type": "code",
 750    "execution_count": 35,
 751    "metadata": {
 752     "collapsed": true
 753    },
 754    "outputs": [],
 755    "source": [
 756     "sample_tours = ['FFLRLLFLRL', 'FLLFFLFFFLFFLFLLRRFR', 'FFRLLFRLLFFFRFLLRLLRRLLRLL']"
 757    ]
 758   },
 759   {
 760    "cell_type": "code",
 761    "execution_count": 36,
 762    "metadata": {},
 763    "outputs": [
 764     {
 765      "data": {
 766       "text/plain": [
 767        "'FFLRLLFLRL'"
 768       ]
 769      },
 770      "execution_count": 36,
 771      "metadata": {},
 772      "output_type": "execute_result"
 773     }
 774    ],
 775    "source": [
 776     "valid_prefix(sample_tours[0])"
 777    ]
 778   },
 779   {
 780    "cell_type": "code",
 781    "execution_count": 37,
 782    "metadata": {
 783     "scrolled": true
 784    },
 785    "outputs": [
 786     {
 787      "data": {
 788       "text/plain": [
 789        "True"
 790       ]
 791      },
 792      "execution_count": 37,
 793      "metadata": {},
 794      "output_type": "execute_result"
 795     }
 796    ],
 797    "source": [
 798     "all(valid_prefix(t) == t for t in sample_tours)"
 799    ]
 800   },
 801   {
 802    "cell_type": "code",
 803    "execution_count": 38,
 804    "metadata": {},
 805    "outputs": [
 806     {
 807      "data": {
 808       "text/plain": [
 809        "True"
 810       ]
 811      },
 812      "execution_count": 38,
 813      "metadata": {},
 814      "output_type": "execute_result"
 815     }
 816    ],
 817    "source": [
 818     "valid_prefix(sample_tours[0] + 'FLLLL') == sample_tours[0]"
 819    ]
 820   },
 821   {
 822    "cell_type": "code",
 823    "execution_count": 39,
 824    "metadata": {},
 825    "outputs": [
 826     {
 827      "data": {
 828       "text/plain": [
 829        "[Mistake(i=10, step=Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
 830        " Mistake(i=13, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
 831       ]
 832      },
 833      "execution_count": 39,
 834      "metadata": {},
 835      "output_type": "execute_result"
 836     }
 837    ],
 838    "source": [
 839     "mistake_positions(trace_tour(sample_tours[0] + 'F'))"
 840    ]
 841   },
 842   {
 843    "cell_type": "code",
 844    "execution_count": 40,
 845    "metadata": {},
 846    "outputs": [
 847     {
 848      "data": {
 849       "text/plain": [
 850        "[Mistake(i=10, step=Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
 851        " Mistake(i=13, step=Step(x=1, y=0, dir=<Direction.UP: 1>)),\n",
 852        " Mistake(i=14, step=Step(x=0, y=0, dir=<Direction.LEFT: 4>)),\n",
 853        " Mistake(i=15, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>)),\n",
 854        " Mistake(i=17, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
 855       ]
 856      },
 857      "execution_count": 40,
 858      "metadata": {},
 859      "output_type": "execute_result"
 860     }
 861    ],
 862    "source": [
 863     "mistake_positions(trace_tour(sample_tours[0] + 'FLLLL'))"
 864    ]
 865   },
 866   {
 867    "cell_type": "code",
 868    "execution_count": 41,
 869    "metadata": {},
 870    "outputs": [
 871     {
 872      "data": {
 873       "text/plain": [
 874        "'FFLRLLFLRL'"
 875       ]
 876      },
 877      "execution_count": 41,
 878      "metadata": {},
 879      "output_type": "execute_result"
 880     }
 881    ],
 882    "source": [
 883     "(sample_tours[0] + 'FLLLL')[:10]"
 884    ]
 885   },
 886   {
 887    "cell_type": "code",
 888    "execution_count": 42,
 889    "metadata": {
 890     "collapsed": true
 891    },
 892    "outputs": [],
 893    "source": [
 894     "def random_walk(steps=1000):\n",
 895     "    return ''.join(random.choice('FFLR') for _ in range(steps))"
 896    ]
 897   },
 898   {
 899    "cell_type": "code",
 900    "execution_count": 43,
 901    "metadata": {},
 902    "outputs": [
 903     {
 904      "data": {
 905       "text/plain": [
 906        "''"
 907       ]
 908      },
 909      "execution_count": 43,
 910      "metadata": {},
 911      "output_type": "execute_result"
 912     }
 913    ],
 914    "source": [
 915     "valid_prefix(random_walk(1000))"
 916    ]
 917   },
 918   {
 919    "cell_type": "code",
 920    "execution_count": 44,
 921    "metadata": {},
 922    "outputs": [
 923     {
 924      "data": {
 925       "text/plain": [
 926        "''"
 927       ]
 928      },
 929      "execution_count": 44,
 930      "metadata": {},
 931      "output_type": "execute_result"
 932     }
 933    ],
 934    "source": [
 935     "valid_prefix(random_walk(1000))"
 936    ]
 937   },
 938   {
 939    "cell_type": "code",
 940    "execution_count": 45,
 941    "metadata": {
 942     "collapsed": true,
 943     "scrolled": true
 944    },
 945    "outputs": [],
 946    "source": [
 947     "walks = []\n",
 948     "while len(walks) < 10:\n",
 949     "    w = valid_prefix(random_walk())\n",
 950     "    if len(w) > 30: walks += [w]"
 951    ]
 952   },
 953   {
 954    "cell_type": "code",
 955    "execution_count": 46,
 956    "metadata": {},
 957    "outputs": [
 958     {
 959      "data": {
 960       "text/plain": [
 961        "['FFFFRFFLRLRRFFFFFFFLRFFFFRFFFRFFFFFLFR',\n",
 962        " 'RFLFFFLFFFFLFRFRFLRFLLFRLFFFFFFLFFFFFLFRFL',\n",
 963        " 'FFRFLFFRFFFLRFRFFFFFRFFFLFRFRFLF',\n",
 964        " 'FFRLFLFFFLRRLLFLRFFFFFLFLRFFLFFL',\n",
 965        " 'FFFFFRFFFFRFLFRFRFFFLFFFFRFFRFFF',\n",
 966        " 'RRLFFLRRLFLFRRFLFLFRFLLFFFFFFLRFFFFL',\n",
 967        " 'LFFFRRLLRFLFLLRFFFRLFFFLFFRFFLFLFFFLRFRLRFLFLL',\n",
 968        " 'FRFLFLRFLRFLFLLRFRFFFFLLFRFFLFFF',\n",
 969        " 'RFFFRLRFFRFFFFLLFFFRFRFFFFFFRFRFLFFRLF',\n",
 970        " 'LLFRFRLFFFFLFLFFFRFFLFFFLLRRFLFLRF']"
 971       ]
 972      },
 973      "execution_count": 46,
 974      "metadata": {},
 975      "output_type": "execute_result"
 976     }
 977    ],
 978    "source": [
 979     "walks"
 980    ]
 981   },
 982   {
 983    "cell_type": "code",
 984    "execution_count": 47,
 985    "metadata": {},
 986    "outputs": [
 987     {
 988      "data": {
 989       "text/plain": [
 990        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 991        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 992        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 993        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
 994        " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
 995       ]
 996      },
 997      "execution_count": 47,
 998      "metadata": {},
 999      "output_type": "execute_result"
1000     }
1001    ],
1002    "source": [
1003     "trace_tour('FLLL')"
1004    ]
1005   },
1006   {
1007    "cell_type": "code",
1008    "execution_count": 48,
1009    "metadata": {},
1010    "outputs": [
1011     {
1012      "data": {
1013       "text/plain": [
1014        "(-1, 3)"
1015       ]
1016      },
1017      "execution_count": 48,
1018      "metadata": {},
1019      "output_type": "execute_result"
1020     },
1021     {
1022      "data": {
1023       "image/png": 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aZghIUsMMAUlqmCEgSQ3rFAJJPpzkn5McTXLeceo2J9mb5IdJru3SpiSpP11nAnuA/wz8\n/VwFSdYANwHvB34PuDzJOzq2uyINh8NJd+EV5fhWttU8vtU8tq46hUBV/aCq9gHH+5b7C4B9VfWj\nqjoC3AFs6dLuSrXaH4iOb2VbzeNbzWPraimuCZwB7J9x+yej+yRJE7b2RAVJvgWcPvMuoID/UVX3\nzKONcbOEml/3JEmvpFR1fz5O8m3gz6vqsTH7NgFTVbV5dPs6oKrqhjG1hoMkLUJVHW9Zfk4nnAks\nwFwdeAR4a5INwM+Ay4DLxxUudhCSpMXp+hbRDyXZD2wCtie5b3T/m5NsB6iqo8CfAfcD/xe4o6qe\n6NZtSVIfelkOkiStTBP9xPBq/7BZktcnuT/JD5L8XZJT56g7muSxJDuT3LXU/VyoE52PJCcluSPJ\nviQPJTlrEv1crHmM74okPx+ds8eS/Okk+rkYSW5JciDJ7uPUfGl07nYl2biU/evqRONLclGSQzPO\n3eeWuo+LleTMJA8meTzJniRXz1G3sPNXVRP7Ad4OnAM8CJw3R80a4F+ADcA6YBfwjkn2ewHjuwH4\n76Pta4G/nKPu2Un3dQFjOuH5AD4NfHm0/VGmlwAn3vcex3cF8KVJ93WR4/v3wEZg9xz7LwXuHW1f\nCPzjpPvc8/guAu6edD8XObY3ARtH268BfjDmsbng8zfRmUCt/g+bbQFuHW3fCnxojrqVdEF8Pudj\n5ri3Ae9dwv51Nd/H20o6Z8dU1XeBXx2nZAtw26h2B3BqktOPU7+szGN8sHLP3TNVtWu0/WvgCV7+\nmasFn7+V8B/IreQPm72xqg7A9AkEfnuOuvVJHk7yvSTLPeDmcz6O1dT0GwMOJTltabrX2Xwfb380\nmm7fmeTMpenakpg9/p+ycv7e5mvTaOn13iTvmnRnFiPJ2UzPeHbM2rXg89fnW0THWu0fNjvO+Bay\n1nhWVT2T5HeAB5Psrqon++xnj+ZzPmbXZEzNcjWf8d0N3F5VR5JcxfSsZyXNdo5nWf+99eBRYENV\nPZ/kUuAu4G0T7tOCJHkN0zPsa0YzgpfsHvMrxz1/r3gIVNUfdjzET4CZFxbPBJ7ueMzeHG98owtU\np1fVgSRvAn4+xzGeGf37ZJIhcC6wXENgPudjP/AW4OkkrwJeW1UnmqIvFycc36yxfI3paz+rxU+Y\nPncvWlZ/b13NfNKsqvuSfDnJaVV1cJL9mq8ka5kOgK9X1TfHlCz4/C2n5aATftgsyUlMf9js7qXr\nVid3Ax8fbV8BvOykJXndaFwkeQPw74DHl6qDizCf83EP0+MF+AjTF/5XihOObxToL9rC8j5f44S5\n/97uBj4Gxz7tf+jFJc0VZM7xzVwfT3IB02+TXxEBMPLXwONVdeMc+xd+/iZ8tftDTL9qfIHpTxPf\nN7r/zcD2GXWbmb4Svg+4btJX6RcwvtOA/zPq+7eA143uPx+4ebT9B8BuYCfwT8DHJ93veYzrZecD\nuB74T6Pt9cCdo/3/CJw96T73PL4vAP88OmcPAG+bdJ8XMLbbmX5leBj4MfAJ4CrgUzNqbmL6HVL/\nxBzv2luuPycaH/DfZpy77wEXTrrPCxjbu4GjTL9jbSfw2Oix2un8+WExSWrYcloOkiQtMUNAkhpm\nCEhSwwwBSWqYISBJDTMEJKlhhoAkNcwQkKSG/X+XpHhUiY9RnAAAAABJRU5ErkJggg==\n",
1024       "text/plain": [
1025        "<matplotlib.figure.Figure at 0x7f1034b579e8>"
1026       ]
1027      },
1028      "metadata": {},
1029      "output_type": "display_data"
1030     }
1031    ],
1032    "source": [
1033     "import matplotlib.pyplot as plt\n",
1034     "%matplotlib inline\n",
1035     "plt.axis('on')\n",
1036     "plt.arrow(0, 0, 0.8, 0, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
1037     "plt.arrow(0.2, 0, 0, 1, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
1038     "plt.xlim([-1, 2])\n",
1039     "plt.ylim([-1, 3])"
1040    ]
1041   },
1042   {
1043    "cell_type": "code",
1044    "execution_count": 49,
1045    "metadata": {
1046     "collapsed": true
1047    },
1048    "outputs": [],
1049    "source": [
1050     "def bounds(trace):\n",
1051     "    return (max(s.x for s in trace),\n",
1052     "            max(s.y for s in trace),\n",
1053     "            min(s.x for s in trace),\n",
1054     "            min(s.y for s in trace))"
1055    ]
1056   },
1057   {
1058    "cell_type": "code",
1059    "execution_count": 50,
1060    "metadata": {},
1061    "outputs": [
1062     {
1063      "data": {
1064       "text/plain": [
1065        "(0, 2, -13, -13)"
1066       ]
1067      },
1068      "execution_count": 50,
1069      "metadata": {},
1070      "output_type": "execute_result"
1071     }
1072    ],
1073    "source": [
1074     "bounds(trace_tour('RFRFFLRFLFFRRFFRRRRLLLRRRRRRFRLFRFFRFFRRFRLRRFLLFRLLFRFLFLFRFRLLFRLFRFLRRLLFRRRFRRRRLLFLFRFRRFFRRLLLRLRRFRLRRFFRRFLFRRLLRRFFRFRRRRRFLLLLLRRFFFLLFFFRRLFLFFLRRRFRFLLFFRRLLRFLLRRF'))"
1075    ]
1076   },
1077   {
1078    "cell_type": "code",
1079    "execution_count": 51,
1080    "metadata": {
1081     "collapsed": true
1082    },
1083    "outputs": [],
1084    "source": [
1085     "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
1086     "           Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
1087    ]
1088   },
1089   {
1090    "cell_type": "code",
1091    "execution_count": 52,
1092    "metadata": {
1093     "collapsed": true
1094    },
1095    "outputs": [],
1096    "source": [
1097     "def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None, filename=None):\n",
1098     "    plt.axis('on')\n",
1099     "    plt.axes().set_aspect('equal')\n",
1100     "    for s, t in chunks(trace, 2):\n",
1101     "        w, h = plot_wh[t.dir]\n",
1102     "        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",
1103     "    xh, yh, xl, yl = bounds(trace)\n",
1104     "    if xybounds is not None:    \n",
1105     "        bxh, byh, bxl, byl = xybounds\n",
1106     "        plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
1107     "        plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
1108     "    else:\n",
1109     "        plt.xlim([xl-1, xh+1])\n",
1110     "        plt.ylim([yl-1, yh+1])\n",
1111     "    if filename:\n",
1112     "        plt.savefig(filename)"
1113    ]
1114   },
1115   {
1116    "cell_type": "code",
1117    "execution_count": 53,
1118    "metadata": {
1119     "collapsed": true
1120    },
1121    "outputs": [],
1122    "source": [
1123     "# def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None):\n",
1124     "#     plt.ioff()\n",
1125     "#     if fig is None:\n",
1126     "#         fig = plt.figure()\n",
1127     "#         ax = fig.gca()\n",
1128     "#     if subplot_details is not None:\n",
1129     "#         ax = fig.add_subplot(*subplot_details)\n",
1130     "#     plt.axis('on')\n",
1131     "# #     plt.axes().set_aspect('equal')\n",
1132     "#     ax.set_aspect('equal')\n",
1133     "#     for s, t in chunks(trace, 2):\n",
1134     "#         w, h = plot_wh[t.dir]\n",
1135     "#         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",
1136     "#     xh, yh, xl, yl = bounds(trace)\n",
1137     "#     if xybounds is not None:    \n",
1138     "#         bxh, byh, bxl, byl = xybounds\n",
1139     "#         ax.set_xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
1140     "#         ax.set_ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
1141     "#     else:\n",
1142     "#         ax.set_xlim([xl-1, xh+1])\n",
1143     "#         ax.set_ylim([yl-1, yh+1])\n",
1144     "#     plt.close(fig)\n",
1145     "#     return fig"
1146    ]
1147   },
1148   {
1149    "cell_type": "code",
1150    "execution_count": 54,
1151    "metadata": {
1152     "collapsed": true
1153    },
1154    "outputs": [],
1155    "source": [
1156     "def pqr(p, q, r):\n",
1157     "    return '{}:{};{}'.format(p, q, r)"
1158    ]
1159   },
1160   {
1161    "cell_type": "code",
1162    "execution_count": 55,
1163    "metadata": {},
1164    "outputs": [
1165     {
1166      "data": {
1167       "text/plain": [
1168        "'1:2;3'"
1169       ]
1170      },
1171      "execution_count": 55,
1172      "metadata": {},
1173      "output_type": "execute_result"
1174     }
1175    ],
1176    "source": [
1177     "pqrt = (1, 2, 3)\n",
1178     "pqr(*pqrt)"
1179    ]
1180   },
1181   {
1182    "cell_type": "code",
1183    "execution_count": 56,
1184    "metadata": {},
1185    "outputs": [
1186     {
1187      "data": {
1188       "image/png": 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kP1LxyGazsUcYkVKbFzRzMckrBu6+2d37wsMXgIb8RyoepfafXmrzgmYuJkleM/gnYGOC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\n",
1189       "text/plain": [
1190        "<matplotlib.figure.Figure at 0x7f10348a6358>"
1191       ]
1192      },
1193      "metadata": {},
1194      "output_type": "display_data"
1195     }
1196    ],
1197    "source": [
1198     "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'))"
1199    ]
1200   },
1201   {
1202    "cell_type": "code",
1203    "execution_count": 57,
1204    "metadata": {},
1205    "outputs": [
1206     {
1207      "data": {
1208       "image/png": 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mVpXUYCKSX7muDH4DjHX3I4HVwA25j1Q4MplM7BH6pdjmBc1cSHKKgbsvcPeO8PRFoCb3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\nAABJRU5ErkJggg==\n",
1209       "text/plain": [
1210        "<matplotlib.figure.Figure at 0x7f10347d76a0>"
1211       ]
1212      },
1213      "metadata": {},
1214      "output_type": "display_data"
1215     }
1216    ],
1217    "source": [
1218     "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'), colour='g')"
1219    ]
1220   },
1221   {
1222    "cell_type": "code",
1223    "execution_count": 58,
1224    "metadata": {},
1225    "outputs": [
1226     {
1227      "data": {
1228       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAADqCAYAAAChr/4gAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
1229       "text/plain": [
1230        "<matplotlib.figure.Figure at 0x7f1034735828>"
1231       ]
1232      },
1233      "metadata": {},
1234      "output_type": "display_data"
1235     }
1236    ],
1237    "source": [
1238     "plot_trace(trace_tour('FFFLLFFL'))"
1239    ]
1240   },
1241   {
1242    "cell_type": "code",
1243    "execution_count": 59,
1244    "metadata": {},
1245    "outputs": [
1246     {
1247      "data": {
1248       "text/plain": [
1249        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
1250        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
1251        " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
1252        " Step(x=2, y=-1, dir=<Direction.DOWN: 3>),\n",
1253        " Step(x=3, y=-1, dir=<Direction.RIGHT: 2>),\n",
1254        " Step(x=4, y=-1, dir=<Direction.RIGHT: 2>),\n",
1255        " Step(x=4, y=0, dir=<Direction.UP: 1>),\n",
1256        " Step(x=4, y=1, dir=<Direction.UP: 1>),\n",
1257        " Step(x=4, y=2, dir=<Direction.UP: 1>),\n",
1258        " Step(x=4, y=3, dir=<Direction.UP: 1>),\n",
1259        " Step(x=3, y=3, dir=<Direction.LEFT: 4>),\n",
1260        " Step(x=3, y=4, dir=<Direction.UP: 1>),\n",
1261        " Step(x=4, y=4, dir=<Direction.RIGHT: 2>),\n",
1262        " Step(x=4, y=5, dir=<Direction.UP: 1>),\n",
1263        " Step(x=3, y=5, dir=<Direction.LEFT: 4>),\n",
1264        " Step(x=2, y=5, dir=<Direction.LEFT: 4>),\n",
1265        " Step(x=2, y=4, dir=<Direction.DOWN: 3>),\n",
1266        " Step(x=1, y=4, dir=<Direction.LEFT: 4>),\n",
1267        " Step(x=0, y=4, dir=<Direction.LEFT: 4>),\n",
1268        " Step(x=-1, y=4, dir=<Direction.LEFT: 4>),\n",
1269        " Step(x=-2, y=4, dir=<Direction.LEFT: 4>),\n",
1270        " Step(x=-3, y=4, dir=<Direction.LEFT: 4>),\n",
1271        " Step(x=-4, y=4, dir=<Direction.LEFT: 4>),\n",
1272        " Step(x=-4, y=3, dir=<Direction.DOWN: 3>),\n",
1273        " Step(x=-4, y=2, dir=<Direction.DOWN: 3>),\n",
1274        " Step(x=-3, y=2, dir=<Direction.RIGHT: 2>),\n",
1275        " Step(x=-3, y=1, dir=<Direction.DOWN: 3>),\n",
1276        " Step(x=-3, y=0, dir=<Direction.DOWN: 3>),\n",
1277        " Step(x=-3, y=-1, dir=<Direction.DOWN: 3>),\n",
1278        " Step(x=-2, y=-1, dir=<Direction.RIGHT: 2>),\n",
1279        " Step(x=-1, y=-1, dir=<Direction.RIGHT: 2>),\n",
1280        " Step(x=0, y=-1, dir=<Direction.RIGHT: 2>),\n",
1281        " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
1282       ]
1283      },
1284      "execution_count": 59,
1285      "metadata": {},
1286      "output_type": "execute_result"
1287     }
1288    ],
1289    "source": [
1290     "trace_tour(walks[3])"
1291    ]
1292   },
1293   {
1294    "cell_type": "code",
1295    "execution_count": 60,
1296    "metadata": {},
1297    "outputs": [
1298     {
1299      "data": {
1300       "image/png": 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DLgDu6nT/X4H6LvbzEL333nteXl7uEydOTLuVILS2tvp3vvMdB2LfqqqqvLq62keOHJlI\nvd69e3tNTY3PmDEj7ac5NkOGDPFMJpNozfZs6TKfolgXtavV7L2rHevq6jpuZ7NZstlsBOXTNWDA\nANra2hgwYEDarQTh4Ycf5rHHHkusnllXf77xaWlp4brrrmPKlCmJ1k3CzlDp06cPbW1tlJeXx1In\nn8+Tz+e/WFP7ugEnAPM73f8P4Pou9ksgy9MBeC6XS7uNbq9QKPjAgQMd8GHDhvn27dtjq3XBBRd4\nLpfzzZs3x1Zjp9bWVj/99NN95syZfuONN3qor4Vnn33We/fu7b179/b7778/sbrsYQYXRcCVA6uA\nw4BewKvAMV3sl9DhJk8BF43nn3/+H97SrVixIu2WIpfL5YINuLFjx3b87oYPH55Y3T0FXNEfMrh7\nGzAJWAC8Bjzi7iuKHVd6nlGjRnHfffcBsGDBAo466qiUO5Ivor6+vuP2gw8+mGInn4niHBzuPh/Q\nX6MUpaKigtGjRwN0/CvdR21tLf3796exsZGjjy6NK8X0TQYRCZYCTkSCpYATkWAp4EQkWAo4EQmW\nAk5EgqWAE5FgKeBEJFgKOBEJlgJORIKlgBORYCngRCRYCjgRCZYCTkSCpYATkWAp4EQkWAo4EQmW\nAk5EglVUwJnZhWb2VzNrM7PhUTUlIhKFYmdwy4HzgP+OoJduae7cuQA888wzrFu3LuVupJStW7eO\nZ555Bvjs70biVVTAufvf3H0lXS/+HLxCocD48eMBWLJkCQ888EDKHUkpe+CBB1iyZAkA48ePp1Ao\npNxR+HQOrgiVlZVMmjSJXr16kclkmDhxYmy1brnlFk444QReeuml2Gp0dsUVVzB69GiWLVuWSL3z\nzz+fCy+8kNWrVydSLw0TJ04kk8nQq1cvJk+eTGVlZSx1NmzYwDHHHENdXR1btmyJpUZnq1ev5sgj\nj2TWrFk710AuGfZ5DZnZQqBf54fYsbjrT9x9bvs+LwBT3H3pHsbxUjv4KGzcuJF+/fqxbdu2ROpl\nMhkGDhzIqlWrEqm33377UVtbyxtvvBF7rbKyMsrLyykUCiX3QonKNddcQ319fSLHV1VVBex4Xpua\nmmKvV11dTUtLC3379mX9+vWx19vJzHD3Lt9Ffu66qO4e2QKVdXV1Hbez2SzZbDaqoVNz4IEH8uST\nT5LL5WKts3TpUsrLywEYOnQoBxxwQOz1KisrqaysZNiwYVRXVydSL5PJMHXq1FhrpWn69Ols2LCB\nFSviWxv9ww8/ZO3atZSXl3PIIYdw2GGHxRo4q1at6pgpDh06lDvuuCO2WgD5fJ58Pr9X+37uDG6v\nBtkxg7vO3f+8h32CnMEl5eGHH2bx4sXccMMNHHzwwbHXmz17Nh999BHXXnstNTU1sdfL5XLU1NTw\nwx/+kEwmE3u9kH3yySdMmjSJCRMmMGbMGMziPUX+wQcfMGXKFC6//HJGjRoVa62u7GkGV1TAmdm/\nALOBg4CPgVfd/czd7KuAE5HIxRZwX7AJBZyIRG5PAadPUUUkWAo4EQmWAk5EgqWAE5FgKeBEJFgK\nOBEJlgJORIKlgBORYCngRCRYCjgRCZYCTkSCpYATkWAp4EQkWAo4EQmWAk5EgqWAE5FgKeBEJFgK\nOBEJlgJORIJVVMCZ2W1mtsLMXjWzJ8ws3rXsRES+gGJncAuAIe4+FFgJ3FB8S9HY23UTu6uQjy/k\nYwMdX5KKCjh3f9bdt7ff/RMwqPiWolFKT3IcQj6+kI8NdHxJivIc3L8B/xXheCIiRan4vB3MbCHQ\nr/NDgAM/cfe57fv8BCi4+0OxdCkisg+KXvjZzC4F/h04xd1b9rCfVn0WkVjsbuHnz53B7YmZnQFM\nBf55T+G2pwZEROJS1AzOzFYCvYCP2h/6k7tfEUVjIiLFKvotqohIqeoR32Qws+vMbLuZHZh2L1EJ\n9SJrMzvDzN4wszfN7Pq0+4mSmQ0ys+fN7HUzW25mV6XdU9TMrMzMlprZ02n3Aj0g4MxsEHAa8G7a\nvUSsZC+y3ldmVgb8GhgDDAEmmNnR6XYVqW3Aj9z9WOBE4MrAjg/gauD1tJvYKfiAA34J/DjtJqJW\nyhdZF2EEsNLd33X3AvAIMC7lniLj7o3u/mr77U+BFcDAdLuKTvtk4izgt2n3slPQAWdm5wBr3H15\n2r3ELJSLrAcCazrdX0tAAdCZmQ0GhgIN6XYSqZ2TiZI5sV/UZSKlYA8XIv8ncCMwepefdRs98CLr\nrn4/JfNiiYqZ7Q88DlzdPpPr9szsbOADd3/VzLKUyGut2wecu4/u6nEzOw4YDPzFzIwdb+H+bGYj\n3P3DBFvcZ7s7tp3aL7I+CzglmY5itxY4tNP9QcB7KfUSCzOrYEe43e/uv0+7nwidBJxrZmcBGaCP\nmf3O3S9Js6kec5mImb0NDHf3TWn3EoX2i6xnsuMi648+b//uwMzKgb8BpwLvA/8DTHD3Fak2FiEz\n+x2wwd1/lHYvcTGzk4Ep7n5u2r0EfQ5uF06JTJsjMhvYH1jY/rH8HWk3VCx3bwMmseMT4teARwIL\nt5OAi4FTzGxZ++/tjLT7ClmPmcGJSM/Tk2ZwItLDKOBEJFgKOBEJlgJORIKlgBORYCngRCRYCjgR\nCZYCTkSC9X9HKanR5sBgvwAAAABJRU5ErkJggg==\n",
1301       "text/plain": [
1302        "<matplotlib.figure.Figure at 0x7f10347d5630>"
1303       ]
1304      },
1305      "metadata": {},
1306      "output_type": "display_data"
1307     }
1308    ],
1309    "source": [
1310     "plot_trace(trace_tour(walks[3]))"
1311    ]
1312   },
1313   {
1314    "cell_type": "code",
1315    "execution_count": 61,
1316    "metadata": {},
1317    "outputs": [
1318     {
1319      "data": {
1320       "text/plain": [
1321        "10"
1322       ]
1323      },
1324      "execution_count": 61,
1325      "metadata": {},
1326      "output_type": "execute_result"
1327     }
1328    ],
1329    "source": [
1330     "long_walks = [w for w in walks if len(w) >= 30]\n",
1331     "len(long_walks)"
1332    ]
1333   },
1334   {
1335    "cell_type": "code",
1336    "execution_count": 62,
1337    "metadata": {},
1338    "outputs": [
1339     {
1340      "data": {
1341       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAADTCAYAAABOQ5KuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
1342       "text/plain": [
1343        "<matplotlib.figure.Figure at 0x7f1034735710>"
1344       ]
1345      },
1346      "metadata": {},
1347      "output_type": "display_data"
1348     }
1349    ],
1350    "source": [
1351     "plot_trace(trace_tour(long_walks[0]))"
1352    ]
1353   },
1354   {
1355    "cell_type": "code",
1356    "execution_count": 63,
1357    "metadata": {},
1358    "outputs": [
1359     {
1360      "data": {
1361       "text/plain": [
1362        "['FFFFRFFLRLRRFFFFFFFLRFFFFRFFFRFFFFFLFR',\n",
1363        " 'RFLFFFLFFFFLFRFRFLRFLLFRLFFFFFFLFFFFFLFRFL',\n",
1364        " 'FFRFLFFRFFFLRFRFFFFFRFFFLFRFRFLF',\n",
1365        " 'FFRLFLFFFLRRLLFLRFFFFFLFLRFFLFFL',\n",
1366        " 'FFFFFRFFFFRFLFRFRFFFLFFFFRFFRFFF',\n",
1367        " 'RRLFFLRRLFLFRRFLFLFRFLLFFFFFFLRFFFFL',\n",
1368        " 'LFFFRRLLRFLFLLRFFFRLFFFLFFRFFLFLFFFLRFRLRFLFLL',\n",
1369        " 'FRFLFLRFLRFLFLLRFRFFFFLLFRFFLFFF',\n",
1370        " 'RFFFRLRFFRFFFFLLFFFRFRFFFFFFRFRFLFFRLF',\n",
1371        " 'LLFRFRLFFFFLFLFFFRFFLFFFLLRRFLFLRF']"
1372       ]
1373      },
1374      "execution_count": 63,
1375      "metadata": {},
1376      "output_type": "execute_result"
1377     }
1378    ],
1379    "source": [
1380     "walks"
1381    ]
1382   },
1383   {
1384    "cell_type": "code",
1385    "execution_count": 64,
1386    "metadata": {},
1387    "outputs": [
1388     {
1389      "data": {
1390       "image/png": 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2WNK1JH91f1tmDqEfEWwFZpvZQUlfA54luWXzZJK/7PZ0qzHcGDbMMoXjPGNmp0g6GnhW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\n8v89qQ80wuYWhQAAAABJRU5ErkJggg==\n",
1391       "text/plain": [
1392        "<matplotlib.figure.Figure at 0x7f10345119b0>"
1393       ]
1394      },
1395      "metadata": {},
1396      "output_type": "display_data"
1397     }
1398    ],
1399    "source": [
1400     "plot_trace(trace_tour('FLFFLRFRLFRRRR'))"
1401    ]
1402   },
1403   {
1404    "cell_type": "code",
1405    "execution_count": 66,
1406    "metadata": {},
1407    "outputs": [
1408     {
1409      "data": {
1410       "text/plain": [
1411        "(383, [])"
1412       ]
1413      },
1414      "execution_count": 66,
1415      "metadata": {},
1416      "output_type": "execute_result"
1417     }
1418    ],
1419    "source": [
1420     "w = random_walk()\n",
1421     "ms = mistake_positions(trace_tour(w))\n",
1422     "len(ms), returns_to_origin(ms)"
1423    ]
1424   },
1425   {
1426    "cell_type": "code",
1427    "execution_count": 67,
1428    "metadata": {},
1429    "outputs": [
1430     {
1431      "data": {
1432       "image/png": 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YpX2bzYaLLmJ9dH/xi1/g2LFj2Lt3ryhrb2/HiBEj4HA4/Aqp4Q8lJSWmGLOV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\n+wAAAABJRU5ErkJggg==\n",
1433       "text/plain": [
1434        "<matplotlib.figure.Figure at 0x7f10345996a0>"
1435       ]
1436      },
1437      "metadata": {},
1438      "output_type": "display_data"
1439     }
1440    ],
1441    "source": [
1442     "plot_trace(trace_tour(w))"
1443    ]
1444   },
1445   {
1446    "cell_type": "code",
1447    "execution_count": 68,
1448    "metadata": {
1449     "collapsed": true
1450    },
1451    "outputs": [],
1452    "source": [
1453     "def trim_loop(tour, random_mistake=False):\n",
1454     "    trace = trace_tour(tour)\n",
1455     "    mistakes = mistake_positions(trace)\n",
1456     "    if random_mistake:\n",
1457     "        end_mistake_index = random.randrange(len(mistakes))\n",
1458     "    else:\n",
1459     "        end_mistake_index = 0\n",
1460     "#     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",
1461     "    # while this mistake extends to the next step in the trace...\n",
1462     "    while (mistakes[end_mistake_index].i + 1 < len(trace) and \n",
1463     "           end_mistake_index + 1 < len(mistakes) and\n",
1464     "           mistakes[end_mistake_index].i + 1 == \n",
1465     "           mistakes[end_mistake_index + 1].i):\n",
1466     "#         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",
1467     "        # push this mistake finish point later\n",
1468     "        end_mistake_index += 1\n",
1469     "    mistake = mistakes[end_mistake_index]\n",
1470     "    \n",
1471     "    # find the first location that mentions where this mistake ends (which the point where the loop starts)\n",
1472     "    mistake_loop_start = max(i for i, loc in enumerate(trace[:mistake.i])\n",
1473     "                             if (loc.x, loc.y) == (mistake.step.x, mistake.step.y))\n",
1474     "#     print('Dealing with mistake from', mistake_loop_start, 'to', mistake.i, ', trace has len', len(trace))\n",
1475     "    \n",
1476     "    # direction before entering the loop\n",
1477     "    direction_before = trace[mistake_loop_start].dir\n",
1478     "    \n",
1479     "    # find the new instruction to turn from heading before the loop to heading after the loop\n",
1480     "    new_instruction = 'F'\n",
1481     "    if (mistake.i + 1) < len(trace):\n",
1482     "        if turn_left(direction_before) == trace[mistake.i + 1].dir:\n",
1483     "            new_instruction = 'L'\n",
1484     "        if turn_right(direction_before) == trace[mistake.i + 1].dir:\n",
1485     "            new_instruction = 'R'\n",
1486     "#     if (mistake.i + 1) < len(trace):\n",
1487     "#         print('turning from', direction_before, 'to', trace[mistake.i + 1].dir, 'with', new_instruction )\n",
1488     "#     else:\n",
1489     "#         print('turning from', direction_before, 'to BEYOND END', 'with', new_instruction )\n",
1490     "    return tour[:mistake_loop_start] + new_instruction + tour[mistake.i+1:]\n",
1491     "#     return mistake, mistake_loop_start, trace[mistake_loop_start-2:mistake_loop_start+8]"
1492    ]
1493   },
1494   {
1495    "cell_type": "code",
1496    "execution_count": 69,
1497    "metadata": {},
1498    "outputs": [
1499     {
1500      "data": {
1501       "text/plain": [
1502        "'RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF'"
1503       ]
1504      },
1505      "execution_count": 69,
1506      "metadata": {},
1507      "output_type": "execute_result"
1508     }
1509    ],
1510    "source": [
1511     "w = 'RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF'\n",
1512     "w"
1513    ]
1514   },
1515   {
1516    "cell_type": "code",
1517    "execution_count": 70,
1518    "metadata": {},
1519    "outputs": [
1520     {
1521      "data": {
1522       "image/png": 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iIm2AD0RkharuCGDbxpizSHpPrKr7VXVL7PpxYDtwXrLbNd5s2rQJ8NZNlCxtsCRJw+th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\nrC2Hf85MaAAAAABJRU5ErkJggg==\n",
1523       "text/plain": [
1524        "<matplotlib.figure.Figure at 0x7f1033e45b38>"
1525       ]
1526      },
1527      "metadata": {},
1528      "output_type": "display_data"
1529     }
1530    ],
1531    "source": [
1532     "w_short = w[:100]\n",
1533     "plot_trace(trace_tour(w_short))"
1534    ]
1535   },
1536   {
1537    "cell_type": "code",
1538    "execution_count": 71,
1539    "metadata": {},
1540    "outputs": [
1541     {
1542      "name": "stdout",
1543      "output_type": "stream",
1544      "text": [
1545       "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n",
1546       "RFFRRFFFRFFRFLLRFLFFFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n"
1547      ]
1548     },
1549     {
1550      "data": {
1551       "image/png": 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1552       "text/plain": [
1553        "<matplotlib.figure.Figure at 0x7f1033e457f0>"
1554       ]
1555      },
1556      "metadata": {},
1557      "output_type": "display_data"
1558     }
1559    ],
1560    "source": [
1561     "trimmed = trim_loop(w_short)\n",
1562     "print('{}\\n{}'.format(w_short, trimmed))\n",
1563     "plot_trace(trace_tour(trimmed))"
1564    ]
1565   },
1566   {
1567    "cell_type": "code",
1568    "execution_count": 72,
1569    "metadata": {},
1570    "outputs": [
1571     {
1572      "name": "stdout",
1573      "output_type": "stream",
1574      "text": [
1575       "RFFRRFFFRFFRFLLRFLFFFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n",
1576       "RFFRRFFFRFFRFLLRFLFFLLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n"
1577      ]
1578     },
1579     {
1580      "data": {
1581       "image/png": 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kBnQDtgATW/l3X4t4TWJmzpyp+fn5vhZ3X3LJJUm1Mw0YMMDXnC+99NK0tF8BumDBAs/z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\n",
1582       "text/plain": [
1583        "<matplotlib.figure.Figure at 0x7f1033c33940>"
1584       ]
1585      },
1586      "metadata": {},
1587      "output_type": "display_data"
1588     }
1589    ],
1590    "source": [
1591     "trimmed2 = trim_loop(trimmed)\n",
1592     "print('{}\\n{}'.format(trimmed, trimmed2))\n",
1593     "plot_trace(trace_tour(trimmed2))"
1594    ]
1595   },
1596   {
1597    "cell_type": "code",
1598    "execution_count": 73,
1599    "metadata": {},
1600    "outputs": [
1601     {
1602      "data": {
1603       "text/plain": [
1604        "[Mistake(i=104, step=Step(x=-4, y=6, dir=<Direction.DOWN: 3>)),\n",
1605        " Mistake(i=105, step=Step(x=-5, y=6, dir=<Direction.LEFT: 4>)),\n",
1606        " Mistake(i=106, step=Step(x=-5, y=7, dir=<Direction.UP: 1>)),\n",
1607        " Mistake(i=107, step=Step(x=-5, y=8, dir=<Direction.UP: 1>)),\n",
1608        " Mistake(i=108, step=Step(x=-5, y=9, dir=<Direction.UP: 1>)),\n",
1609        " Mistake(i=115, step=Step(x=-5, y=12, dir=<Direction.LEFT: 4>)),\n",
1610        " Mistake(i=116, step=Step(x=-5, y=11, dir=<Direction.DOWN: 3>)),\n",
1611        " Mistake(i=127, step=Step(x=2, y=11, dir=<Direction.LEFT: 4>)),\n",
1612        " Mistake(i=130, step=Step(x=3, y=11, dir=<Direction.UP: 1>)),\n",
1613        " Mistake(i=132, step=Step(x=3, y=11, dir=<Direction.UP: 1>))]"
1614       ]
1615      },
1616      "execution_count": 73,
1617      "metadata": {},
1618      "output_type": "execute_result"
1619     }
1620    ],
1621    "source": [
1622     "mistake_positions(trace_tour(w[:130]))[-10:]"
1623    ]
1624   },
1625   {
1626    "cell_type": "code",
1627    "execution_count": 74,
1628    "metadata": {},
1629    "outputs": [
1630     {
1631      "name": "stdout",
1632      "output_type": "stream",
1633      "text": [
1634       "Step(x=40, y=36, dir=<Direction.UP: 1>)\n"
1635      ]
1636     },
1637     {
1638      "data": {
1639       "image/png": 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4BuzPuLRMdHS0Ko21u+j1enndOp1OtUsMQEC/aDqdzqUt3PqaEhISwtJ+rkXS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\nRK5CYII=\n",
1640       "text/plain": [
1641        "<matplotlib.figure.Figure at 0x7f1033a7d6a0>"
1642       ]
1643      },
1644      "metadata": {},
1645      "output_type": "display_data"
1646     }
1647    ],
1648    "source": [
1649     "w_tour_start = w #[:250]\n",
1650     "print(trace_tour(w_tour_start)[-1])\n",
1651     "plot_trace(trace_tour(w_tour_start))"
1652    ]
1653   },
1654   {
1655    "cell_type": "code",
1656    "execution_count": 75,
1657    "metadata": {},
1658    "outputs": [
1659     {
1660      "name": "stdout",
1661      "output_type": "stream",
1662      "text": [
1663       "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF\n",
1664       "RFFRRFFFRFLRFRFLLRFLLRLRRLFRLRRFFLLRLLRRFRFLRLFFLFLRRLRRLRLFLLRRFFLRLLFFFFFRRFFLFRLFFRLLRRFLFFFLRFLRRLRFLFLFFRLLFFRRFFLRLFRFFRLFFLRRFLRFLRRLFRRLFFFFRLFLFFLRFFLFRFLRRFFFFFLFRLRRFRLLRLLFRFLFFFRLFRFLFLRLRFFFFFLFFRFFFFLRFLFRFLRLRLFFLRRFFFRLLFRLFLRRFLRLLRLFFRFLRRLFLLRFLFFRFLFRLRFFFFFLRLLFRFLLRRFLRRFLRLRFLRRLFFFRFLRRLF\n",
1665       "Step(x=40, y=36, dir=<Direction.UP: 1>)\n"
1666      ]
1667     },
1668     {
1669      "data": {
1670       "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
1671       "text/plain": [
1672        "<matplotlib.figure.Figure at 0x7f1033a7dfd0>"
1673       ]
1674      },
1675      "metadata": {},
1676      "output_type": "display_data"
1677     }
1678    ],
1679    "source": [
1680     "w_tour = w_tour_start\n",
1681     "w_trace = trace_tour(w_tour)\n",
1682     "mks = mistake_positions(w_trace)\n",
1683     "while len(mks) > 1:\n",
1684     "#     print(len(mks))\n",
1685     "    w_tour = trim_loop(w_tour)\n",
1686     "    w_trace = trace_tour(w_tour)\n",
1687     "    mks = mistake_positions(w_trace)\n",
1688     "print('{}\\n{}\\n{}'.format(w_tour_start, w_tour, trace_tour(w_tour)[-1]))\n",
1689     "plot_trace(trace_tour(w_tour))"
1690    ]
1691   },
1692   {
1693    "cell_type": "code",
1694    "execution_count": 76,
1695    "metadata": {
1696     "collapsed": true
1697    },
1698    "outputs": [],
1699    "source": [
1700     "def trim_all_loops(tour, mistake_reduction_attempt_limit=10):\n",
1701     "    trace = trace_tour(tour)\n",
1702     "    mistake_limit = 1\n",
1703     "    if trace[-1].x == 0 and trace[-1].y == 0:\n",
1704     "        mistake_limit = 0\n",
1705     "    mistakes = mistake_positions(trace)\n",
1706     "    \n",
1707     "    old_mistake_count = len(mistakes)\n",
1708     "    mistake_reduction_tries = 0\n",
1709     "    \n",
1710     "    while len(mistakes) > mistake_limit and mistake_reduction_tries < mistake_reduction_attempt_limit:\n",
1711     "        tour = trim_loop(tour)\n",
1712     "        trace = trace_tour(tour)\n",
1713     "        mistakes = mistake_positions(trace)\n",
1714     "        if len(mistakes) < old_mistake_count:\n",
1715     "            old_mistake_count = len(mistakes)\n",
1716     "            mistake_reduction_tries = 0\n",
1717     "        else:\n",
1718     "            mistake_reduction_tries += 1\n",
1719     "    if mistake_reduction_tries >= mistake_reduction_attempt_limit:\n",
1720     "        return ''\n",
1721     "    else:\n",
1722     "        return tour"
1723    ]
1724   },
1725   {
1726    "cell_type": "code",
1727    "execution_count": 77,
1728    "metadata": {},
1729    "outputs": [
1730     {
1731      "data": {
1732       "text/plain": [
1733        "'RFFRRFFFRFLRFRFLLRFLLRLRRLFRLRRFFLLRLLRRFRFLRLFFLFLRRLRRLRLFLLRRFFLRLLFFFFFRRFFLFRLFFRLLRRFLFFFLRFLRRLRFLFLFFRLLFFRRFFLRLFRFFRLFFLRRFLRFLRRLFRRLFFFFRLFLFFLRFFLFRFLRRFFFFFLFRLRRFRLLRLLFRFLFFFRLFRFLFLRLRFFFFFLFFRFFFFLRFLFRFLRLRLFFLRRFFFRLLFRLFLRRFLRLLRLFFRFLRRLFLLRFLFFRFLFRLRFFFFFLRLLFRFLLRRFLRRFLRLRFLRRLFFFRFLRRLF'"
1734       ]
1735      },
1736      "execution_count": 77,
1737      "metadata": {},
1738      "output_type": "execute_result"
1739     }
1740    ],
1741    "source": [
1742     "w_trimmed = trim_all_loops(w)\n",
1743     "w_trimmed"
1744    ]
1745   },
1746   {
1747    "cell_type": "code",
1748    "execution_count": 78,
1749    "metadata": {},
1750    "outputs": [
1751     {
1752      "data": {
1753       "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
1754       "text/plain": [
1755        "<matplotlib.figure.Figure at 0x7f1033a3d908>"
1756       ]
1757      },
1758      "metadata": {},
1759      "output_type": "display_data"
1760     }
1761    ],
1762    "source": [
1763     "plot_trace(trace_tour(trim_all_loops(w)))"
1764    ]
1765   },
1766   {
1767    "cell_type": "code",
1768    "execution_count": 79,
1769    "metadata": {
1770     "collapsed": true
1771    },
1772    "outputs": [],
1773    "source": [
1774     "def reverse_tour(tour):\n",
1775     "    def swap(tour_step):\n",
1776     "        if tour_step == 'R':\n",
1777     "            return 'L'\n",
1778     "        elif tour_step == 'L':\n",
1779     "            return 'R'\n",
1780     "        else:\n",
1781     "            return tour_step\n",
1782     "        \n",
1783     "    return ''.join(swap(s) for s in reversed(tour))"
1784    ]
1785   },
1786   {
1787    "cell_type": "code",
1788    "execution_count": 80,
1789    "metadata": {},
1790    "outputs": [
1791     {
1792      "data": {
1793       "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
1794       "text/plain": [
1795        "<matplotlib.figure.Figure at 0x7f1033accef0>"
1796       ]
1797      },
1798      "metadata": {},
1799      "output_type": "display_data"
1800     }
1801    ],
1802    "source": [
1803     "plot_trace(trace_tour(w_trimmed))"
1804    ]
1805   },
1806   {
1807    "cell_type": "code",
1808    "execution_count": 81,
1809    "metadata": {},
1810    "outputs": [
1811     {
1812      "data": {
1813       "image/png": 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ZmUHGpTOGE4saVopgjOGFF15g9OjRAFxwwQUJ1ii9UcNKIc4991wuuuiiRKuhoH2slECd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\ngjJMbcJZvAAAAABJRU5ErkJggg==\n",
1814       "text/plain": [
1815        "<matplotlib.figure.Figure at 0x7f1033cf2eb8>"
1816       ]
1817      },
1818      "metadata": {},
1819      "output_type": "display_data"
1820     }
1821    ],
1822    "source": [
1823     "plot_trace(trace_tour(reverse_tour(w_trimmed)))"
1824    ]
1825   },
1826   {
1827    "cell_type": "code",
1828    "execution_count": 82,
1829    "metadata": {},
1830    "outputs": [
1831     {
1832      "data": {
1833       "image/png": 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Mst8dQoCICPk8MNB0zC8khA1R2NOfmzpVToO7/V+1ijWxAwOBxYvluOYWW7XWPYmTEH1I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\nkAKBF/H/E7cUOhxnMSgAAAAASUVORK5CYII=\n",
1834       "text/plain": [
1835        "<matplotlib.figure.Figure at 0x7f103452c198>"
1836       ]
1837      },
1838      "metadata": {},
1839      "output_type": "display_data"
1840     }
1841    ],
1842    "source": [
1843     "w1 = random_walk()\n",
1844     "w2 = random_walk()\n",
1845     "plot_trace(trace_tour(w1))\n",
1846     "w1bounds = bounds(trace_tour(w1))\n",
1847     "plot_trace(trace_tour(w2), colour='r', xybounds=w1bounds)"
1848    ]
1849   },
1850   {
1851    "cell_type": "code",
1852    "execution_count": 83,
1853    "metadata": {},
1854    "outputs": [
1855     {
1856      "name": "stdout",
1857      "output_type": "stream",
1858      "text": [
1859       "w1 = 'FRRFRRFFLFRRRLFFFLRFFFRLRFRRFLFLFFFFLRLFFFFFFLRRFLRLLFLLRFLFLLFFFLRLLFRFFFLFLFFRRLFRFRFFFRLFFFFRFFFRFFLRFRRRRFLLFFFRFFLLFLFLRFLFFLFFFRFLRLFRFLFFLLFFFLFFFFLFFFFFLRFFRRRFFLFRFFRFRRRRLLRFFFRFFRFRRFRLLRLLRFRFFLFLFRFRRLFLFLFLFFFFFLLLRRRFRFFRLLRRLRFLFLLLFFFLLFLLFLRFRLRLFFFRLLFLFRFRFRRLFRLFFLFFFFLFFFFRRRLFFFRLLLLFFRFRLRFFFFRFFRFFLLLFFFLRFRLFFFRFFFFRLLFFLRRFFLFRFFFFFFFFRLRLFFLFFLLFFLRFLRFFFFFFFFFLFFFLFRRRRFRFLLLRRFFRFRLFRFLFFFLLRFLLFLFRFLFFRFFFFFRLFRLLRRFFLRRFFFFFFRRFFFFFFRFFLRFFFLFLRRFLLLFFRFLFFFFFLFLLLRFRLFFFLFRFLRLLFRFRFFLFLFLRLFLFFFFFFFFFRFRLFRRRLFLRFLFFFFLLLLFFLFFFFFFFLLFLLLRRRLFLLLRLLFFFFFLFFFFRFFFLLRLRRLFFRFRLLRRFFFFFLFRFFRFLLFFFLRRRFFLLRLLFFFLLRFLFFLFRFFFRLRFFLRFLFFRFFRFFLFRRFFRFRLFLFRRRFRFFRFFFFFRFFFLRRFRFFRRFFFRFRFLFRLRLFLRLFFRFFFFFRRFRFLFFRLFRRFLFFLFRFLFLLLFLRFLLFLFRRRRFFRFFRFFFRLFFFLFRFRLRRFFFLRFRFFLFRRRFFRFFFFRFLRFFRFRFRRFFLFLFLRLFLFLFLLFLFFRFFFFFFFLFRFFLRLFRRLFFRRRFFRFRFRRLRLFFRFFRRFFFRFRFRLLRLFFLLLRFFRRFRFRFRFLLFFFFFLFFLFFFLLFFFFFLRFLFFFFLFRRFFFLFLFLLFFLFFFFFFFRFFLLFFLLLLFFRFFLL\n",
1860       "w2 = 'FLFFFRLRLFFFLRLRRFFFFFFLFFFFLRFFFFRLFLFFLLRFLRLLFLFRLRRFFLFFRRLLRFRLRRLRRLRFFFFFRLFLRLFFFFLFFFFFRRLFFLFRFRFLFFRRLFFLRLLFRFFRFRFFLLFLRFRRFLFFRRFFFLRLFFRLLFFFFFFFRFFRFFFFRFRFLRFFLFLFLFLFRRRRFFFRFRRFFFFRFFLFFLRLFLFFFRLFFFRRLFFFFFLFRFRFFFFRRFRRFRLFRFFLRRRFFFLFLFFRRRFFFFRFFFFFLRLLLFRFLFLRFRLLFFFRFRLRLFRFFLLFFLFFRLFLLLFRRFRLFRFLLRRRFFLFLLFRFFFFFLLLRRLFLLRLLFFFFRRFLFFFLFFLLFFFRFRFFFRFFRFRLFFFLFLRRRLRFLLLRFLLFFRRFRFRFRFFFFLFLFLFFFFFRFFLLLRRFLLLRFRFFFFFFFLLFLFLFLFFLRFLFRLLFFFFRLFRFFLLFFLFLLRFRRLFFRFFRFFRFFLLLFFFFLLLFRRLFRFLLRLRFLLFLRFRFFFFLFLFLRFFLLLLLRRRLFRFFFLFRFRLLFRFFLRFFLFFFFFLRFRFFFFRLFLFRLRRRFLRFFFFLFRRRRFRFFLLRRFRFFRFFFLLRFFFLFLLLFRFLRLRFLRFFRFRFLRRFRFLLRFFLLRLRFFFRLFFFRFLRRRLRRFFLRFLLLLFFFLFRLRLRLLLRFFLFRRFRRLRFRFRLLLFRFFLFLFFLFLFLFFRLRFRFFLLLLRFFLFRFLFLRRRRRFFFFFLFRFRFLLRFRFLFFFFFLRLFLFLFFRLFFFLRRFLRFLFFFFRLFRFLLRFFRFFRFLRFFLLFFRLLRFFLLRRRLFLLFFFLLFFFRRLLRFLFFLLLLFFFFRFFRFRFRLFFFRLRFRLFFFRLLRFFFFFFFFFRLLFFFRRFFRFRFRRFRLFRLLRFRRLRFRFRFFFLFFFFRRFFFLRFRLFRFFFRFRFFLFFFRLLFRRRRFRLFFFFFRFFL\n"
1861      ]
1862     }
1863    ],
1864    "source": [
1865     "print(\"w1 = '{}\".format(w1))\n",
1866     "print(\"w2 = '{}\".format(w2))"
1867    ]
1868   },
1869   {
1870    "cell_type": "code",
1871    "execution_count": 84,
1872    "metadata": {
1873     "collapsed": true
1874    },
1875    "outputs": [],
1876    "source": [
1877     "def wander_near(locus, current, limit=10):\n",
1878     "    valid_proposal = False\n",
1879     "    while not valid_proposal:\n",
1880     "        s = random.choice('FFFRL')\n",
1881     "        if s == 'F':\n",
1882     "            proposed = advance(current, current.dir)\n",
1883     "        elif s == 'L':\n",
1884     "            proposed = advance(current, turn_left(current.dir))\n",
1885     "        elif s == 'R':\n",
1886     "            proposed = advance(current, turn_right(current.dir))\n",
1887     "        if abs(proposed.x - locus.x) < limit and abs(proposed.y - locus.y) < limit:\n",
1888     "            valid_proposal = True\n",
1889     "#     print('At {} going to {} by step {} to {}'.format(current, locus, s, proposed))\n",
1890     "    return s, proposed"
1891    ]
1892   },
1893   {
1894    "cell_type": "code",
1895    "execution_count": 85,
1896    "metadata": {
1897     "collapsed": true
1898    },
1899    "outputs": [],
1900    "source": [
1901     "def seek(goal, current):\n",
1902     "    dx = current.x - goal.x\n",
1903     "    dy = current.y - goal.y\n",
1904     "\n",
1905     "    if dx < 0 and abs(dx) > abs(dy): # to the left\n",
1906     "        side = 'left'\n",
1907     "        if current.dir == Direction.RIGHT:\n",
1908     "            s = 'F'\n",
1909     "        elif current.dir == Direction.UP:\n",
1910     "            s = 'R'\n",
1911     "        else:\n",
1912     "            s = 'L'\n",
1913     "    elif dx > 0 and abs(dx) > abs(dy): # to the right\n",
1914     "        side = 'right'\n",
1915     "        if current.dir == Direction.LEFT:\n",
1916     "            s = 'F'\n",
1917     "        elif current.dir == Direction.UP:\n",
1918     "            s = 'L'\n",
1919     "        else:\n",
1920     "            s = 'R'\n",
1921     "    elif dy > 0 and abs(dx) <= abs(dy): # above\n",
1922     "        side = 'above'\n",
1923     "        if current.dir == Direction.DOWN:\n",
1924     "            s = 'F'\n",
1925     "        elif current.dir == Direction.RIGHT:\n",
1926     "            s = 'R'\n",
1927     "        else:\n",
1928     "            s = 'L'\n",
1929     "    else: # below\n",
1930     "        side = 'below'\n",
1931     "        if current.dir == Direction.UP:\n",
1932     "            s = 'F'\n",
1933     "        elif current.dir == Direction.LEFT:\n",
1934     "            s = 'R'\n",
1935     "        else:\n",
1936     "            s = 'L'\n",
1937     "    if s == 'F':\n",
1938     "        proposed = advance(current, current.dir)\n",
1939     "    elif s == 'L':\n",
1940     "        proposed = advance(current, turn_left(current.dir))\n",
1941     "    elif s == 'R':\n",
1942     "        proposed = advance(current, turn_right(current.dir))\n",
1943     "        \n",
1944     "#     print('At {} going to {}, currently {},  by step {} to {}'.format(current, goal, side, s, proposed))\n",
1945     "\n",
1946     "    return s, proposed"
1947    ]
1948   },
1949   {
1950    "cell_type": "code",
1951    "execution_count": 124,
1952    "metadata": {
1953     "collapsed": true
1954    },
1955    "outputs": [],
1956    "source": [
1957     "def guided_walk(loci, locus_limit=5, wander_limit=10, seek_step_limit=20, return_anyway=False):\n",
1958     "    trail = ''\n",
1959     "    current = Step(0, 0, Direction.RIGHT)    \n",
1960     "    l = 0\n",
1961     "    finished = False\n",
1962     "    while not finished:\n",
1963     "        if abs(current.x - loci[l].x) < locus_limit and abs(current.y - loci[l].y) < locus_limit:\n",
1964     "            l += 1\n",
1965     "            if l == len(loci) - 1:\n",
1966     "                finished = True\n",
1967     "        s, proposed = wander_near(loci[l], current, limit=wander_limit)\n",
1968     "        trail += s\n",
1969     "        current = proposed\n",
1970     "#     print('!! Finished loci')\n",
1971     "    seek_steps = 0\n",
1972     "    while not (current.x == loci[l].x and current.y == loci[l].y) and seek_steps < seek_step_limit:\n",
1973     "#         error = max(abs(current.x - loci[l].x), abs(current.y - loci[l].y))\n",
1974     "#         s, proposed = wander_near(loci[l], current, limit=error+1)\n",
1975     "        s, proposed = seek(loci[l], current)\n",
1976     "        trail += s\n",
1977     "        current = proposed\n",
1978     "        seek_steps += 1\n",
1979     "    if seek_steps >= seek_step_limit and not return_anyway:\n",
1980     "        return ''\n",
1981     "    else:\n",
1982     "        return trail"
1983    ]
1984   },
1985   {
1986    "cell_type": "code",
1987    "execution_count": 87,
1988    "metadata": {},
1989    "outputs": [
1990     {
1991      "data": {
1992       "image/png": 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FIBNJl6SFQEV+muMwZFu3buWGG25QGDKRAEKHIVsFPOHufxk9LykEWfRehSETqYDQYcgs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\nEKlyKgREqpwKAZEqp0JApMr9P8nYgJi0MFyGAAAAAElFTkSuQmCC\n",
1993       "text/plain": [
1994        "<matplotlib.figure.Figure at 0x7f10342c3b00>"
1995       ]
1996      },
1997      "metadata": {},
1998      "output_type": "display_data"
1999     }
2000    ],
2001    "source": [
2002     "def square_tour(a=80):\n",
2003     "    \"a is width of square\"\n",
2004     "    return ('F' * a + 'L') * 4\n",
2005     "\n",
2006     "plot_trace(trace_tour(square_tour()))"
2007    ]
2008   },
2009   {
2010    "cell_type": "code",
2011    "execution_count": 88,
2012    "metadata": {},
2013    "outputs": [
2014     {
2015      "data": {
2016       "image/png": 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k6yMEKDzGmzHGPSUtKopIo4g8KSJxEXlbRG4WkWYReU5E+kXkuIg0rvT+6urqghdbGGPc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\nybOEYIzJ+/+3mLJIMXCXRQAAAABJRU5ErkJggg==\n",
2017       "text/plain": [
2018        "<matplotlib.figure.Figure at 0x7f10345c7fd0>"
2019       ]
2020      },
2021      "metadata": {},
2022      "output_type": "display_data"
2023     }
2024    ],
2025    "source": [
2026     "def cross_tour(a=50, b=40):\n",
2027     "    \"a is width of cross arm, b is length of cross arm\"\n",
2028     "    return ('F' *  a + 'L' + 'F' * b + 'R' + 'F' * b + 'L') * 4\n",
2029     "\n",
2030     "plot_trace(trace_tour(cross_tour()))"
2031    ]
2032   },
2033   {
2034    "cell_type": "code",
2035    "execution_count": 90,
2036    "metadata": {},
2037    "outputs": [
2038     {
2039      "data": {
2040       "image/png": 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Ukpa9WWhgqFF+bEHHGFQ509PTzM7Out0MR2hgqJGOMahqqqVkbyYaGJRySDgcrno7c7PQ\nwKCUQ5aWlpibm3O7GY7QwFAjHWNQ1czPz5NOp91uhiM0MFwiHWNQ5egYg1KqRDgcZvfu3W43wxEa\nGJRyyMLCQtPkYqhGA0ON8ocQOsagykmn09tmGgQNDDXKBwQdY1DlBAIBt5vgGA0MNdKAoKoJhUI6\nxrDT6OlKVU0qlWJ0dNTtZjhCA0ON9JJoVc3q6qrbTXCMU1PUhUTkuyIyIiJPi8j1ItInIiesKep+\nKiKV58RSqsl1dXXR2upItkTXOdVj+BLwkDHmSuCPgGfIJYN92Jqi7hRwl0PrUsqTgsEgAwMDbjfD\nEU7MXdkNvNYY8w0AY8y6MSZFbhKaB61iDwK32V2XF+gYgypnZmZG08cXOAhMicg3ROQJEfmaiHQA\nMWNMAsAYMwFsi1CqYwyqnO1yDQM4kz6+FXgl8D5jzK9E5H5yhxE1f4PuueeejcdenaJOewqqmt7e\nXrq6utxuRlmFU9RV48QUdTHg/xpjDlrP/4RcYDgEHDPGJEQkDjxijUEUv78ppqhbXV0lEAjoFHWq\nrLe97W089thjJBIJt5tSk7pOUWcdLpwXkSPWovwUdceBO61lOkWd2va2U/p4p86tfAD4poi0AS8A\n7wZagO+IyHvIzW/59grv97zC6xg0OKitbKf9wqkp6n4D/IstXrrRifq9YDv90VV9hMNhPV250zTD\nOIhyVyaTYX193e1mOEIDQ430XglVzczMjKaP32n0XglVjaZ2U0qV6OvrY3Bw0O1mOEIDg1IOWVlZ\nIZVKud0MR2hgqJGOMahqUqmUpo/fqXSMQZXj9/vdboJjNDAo5ZC+vj5N7aaU2mxxcVHTx+80mj5e\nVbO4uLhtbr3WwFAjTR+vqtH08TuQBgRVjaaP34H0dKWqRtPH70B6SbSqRtPHK6VKdHV10dLS4nYz\nHKGBQSmHBINBYrGY281whAaGS6RjDKqc2dlZvY5hp9IxBlVOJpNxuwmOcSwwiIjPmlfiuPV8v4ic\ntqao+5aINPXcXdpTUNV4PX38pXCyx/BBYLjg+ReAe60p6uaAv3RwXUp5js/no7Oz0+1mOMKpSW13\nA28C/mvB4tcD37cePwi81Yl1uU17DqqcmZmZpplTohqnegz3Ax/Fmn1KRCLArDEmf+H4KLDLoXW5\nQq9jUNVspx8N28f9IvJnQMIY86SIHMsvtv4VKvuN0inq1HYQDofp7+93uxllNXqKuv8EvAtYB9qB\nbuAfgTcCcWNMVkRuAO42xty6xfubYoq6lZUVgsGgTlGnynrrW9/Ko48+yvT0tNtNqUm9p6j7pDFm\nrzV35TuAU8aYdwGP8PLsU00/RZ3eK6GqmZ6eZmZmxu1mOKKe1zF8AviwiPweCANfr+O66k7HGFQ1\n2ym1m6PXFhhjfg783Hr8InC9k/Ur5WXhcFjTxyulNlteXtb08TuNjjGoajR9/A6mYwyqHJ2iTilV\nIhKJcNlll7ndDEdoYFDKIRcvXmRiYsLtZjhCA0ONNH28qiadTm+bW681MNRI08erarbTdQwaGGqk\nAUFV09vbq+njdxo9Xamq0fTxO5BeEq2q0fTxSqkSnZ2dmj5eKbVZe3u7po/fqXSMQZWj6eN3MB1j\nUOVks9nqhZqEBoYaaU9BVdPT06NZopVSm7W0tOi8EjuV9hxUOZo+fgfS6xhUNdvpR8N2YBCR3SJy\nSkSGReS3IvIBa3mfiJywpqj7qYiE7DfXPdvpj67qIxwOE4lE3G6GI5zoMawDHzbGXAX8MfA+EbmC\nXDLYh60p6k4BdzmwLtdoT0FVk8lkts1+4kT6+AljzJPW4wVgBNgNvIXc1HRY/99md11u0nslVDUz\nMzPbJn28o1miRWQ/cC1wGogZYxKQCx4iMlDufel0moWFhXwdGGPIZrObLi/NZDK0trZuTPiSfz1/\n7tgYg4hsvD//vKh9NdVd+Dxf99ra2qb1KFWstTX3dUomkxv7qM/nK+lFbPVafp8sfp5XWL5c3fn9\nslrdQNUZsxwLDCLSBXwP+KAxZkFEau5TbZdzv2pnu/nmmzl16lRTXBZdLQWd7SnqAESkFfjfwI+N\nMV+ylo0Ax4wxCRGJA48YY67c4r0GYHR0dNvky1PKy2644QYuXLjA6Oho/aaos/wdMJwPCpbjwJ3W\n46pT1G2XQRulvC6RSFTNG+HE6crXAP8OeL2I/FpEnhCRW4AvADeJyLPAjcDnKzbEp5dUKNUIHR0d\nBIPBimVsjzEYY34BlLsJ/cZLqMduU5RSNYjFYhhjGBkZKVvGMz/TOtKvVGOkUimmpqYqlvFMYNhO\nt6wq5WVzc3NMTk5WLOOZwKA9BqUao729vepdoBoYlNphotEoe/bsqVhGA4NSO8zU1BTj4+MVy3gm\nMKyvr7vdBKV2hHQ6zdzcXMUyngkM2yXttlJeFwqFqt4r4ZnAoJRqjJ6enuYJDDrGoFRjJJNJzp07\nV7GMZwKDjjEo1Rirq6uk0+mKZTwTGHSMQanGiEQiVe9k9kxg0HsllGqMQCBQNQeKZwKDjjEo1RgT\nExO88MILFct4JjBkMhm3m6DUjpDNZqt+3zwTGDQfg1KNMTg4yIEDByqW8cy3UQ8llGqMWu5kdjRL\ntFLK+8bGxnjxxRcrlvFMj0HzMSjVGH6/fyPVfTl1DwwicouIPCMivxeRj5dtiI4xKNUQ8XicgwcP\nVixT12+jiPiAvwVuBq4G3mlNX1dCr2NQqjGWl5ddv/LxOuCMMeasMWYN+Da5qetKaGBQqjEakj6+\nisuA8wXPR61lpQ3RQ4kS+WCZn3Kv8LHTz7d73epl7e3t9U8fX8VW5yC3/CvpH28zPX3rnJtuuokT\nJ0643QzPiMfjABXTx9c7MIwCewue7wbGtip433330d3dzbFjxzh27Fidm9Uczp8/z8DAy3MB5yfl\nLX5eGES2er3weaFKZbd6z6XWXdg+t+p+1atexalTp0pe34mGhoYYGhpiZGSE+fn5imUdmbuybOUi\nLcCzwBuAceBx4J3GmJGCMgZyX4Ldu3fXrS3NRkRIJBJEo1G3m9LUDh8+zHPPPac90gKHDh3auFei\n3NyVde0xGGMyIvJ+4AS58YyvFwaFQtp1LqWfiX2Dg4OsrKy43QxPyaePX1hYKFum7lc+GmN+Ahyt\nVk6/BKoeWltbaWtrc7sZnhKNRslmszpFXbPSq0HtSyaTVW8x3mk0fXyT01O49unt/KVqSR/vmZuo\nNLVbKR0wsy8ej+sYQ5F8luhKE9t65idJvwSl9PDKvmw2q73RIk01r4T2GEppN9i+ZDLJ+fPnqxfc\nQRKJRPOkj19bW3O7CZ6jwdK+1tZW/RyLrK2tVb2JSscYPEwPr+yLRqM6xlAkEomwtLTEhQsXypbx\nTI9BqXpYWloilUq53QxPaar08aqUXsdg3+zsLMlk0u1meIqmj29y1dJvqeoCgQDt7e1uN8NTakkf\n75k9T8cYSukYg30DAwMsLS253QxPicfjZDKZiglhPdNjUKU0MNg3OzvLxMSE283wlOJb9beigcHD\nNDDYt7CwUDX3wE4zPj7ePGMMOtBWSu+VsK+7u5tQKOR2MzyltbXV/fTxtdIvgaqH3t7ejVRmKmdw\ncNDd9PGXQrvNqh6SySQvvfSS283wlOXl5aoDshoYPEwPr+xbXl7WKx+LJBKJqvePeCYw6KFEKf1M\n7AuHw5o3s0gt6eNt7Xki8tciMiIiT4rI90Wkp+C1u0TkjPX6G6vVpT2GUvqZ2NfZ2Ulvb6/bzfCU\neDzOgQMHKpax+5N0ArjaGHMtcAa4C0BErgL+HLgSuBX4ilQ5caq5B0rpZ2JfIpHg+eefd7sZnjI/\nP8/09HTFMrYCgzHmYWNM/kD4NLl5IwDeDHzbGLNujHmJXNC4rlJdejxdSnsM9i0vL+vl9kVquX/E\nyYPY9wAPWY+Lp6a7QJmp6fL017GUfib2DQ4O6nwlRfLp4yupeq+EiJwEYoWLyE0z9yljzI+sMp8C\n1owx3yooU6ziz59+CUppj8G+1tZW/H6/283wlGg0ijGG4eHhsmWqBgZjzE2VXheRO4A3Aa8vWDwK\n7Cl4XnZqurx7771Xp6grooHBPk0f/7L8FHVPP/101RwVtqaoE5FbgHuBf2WMmS5YfhXwTeB6cocQ\nJ4HDZouV5aeoO3fuHHv27Cl+eccSEZLJ5Ka5K9Wlu/LKK3nmmWc0yBZoxBR1DwB+4KR1KHDaGPNe\nY8ywiHwHGAbWgPduFRQK6W3XpXRntk/Tx5cKhUJEIpGKZyZsBQZjzOEKr30O+Nwl1GWnKduSjrvY\nZ4zR9PFFQqEQAwMDFQODZy6t0x5DKT3NZp+mjy+VTCY1fXwz02Bpn8/n00vLi6yurjZP+nj945XS\nwyv7YrGYjjEUiUQipNNpxsbKnyj0zLdRj6dVPSwvL2sGpyKBQKDqBU6eCQyqlF4mbt/MzIymjy8y\nMTFRMREseCgw6MhxKU0fb18gEKh6i/FOU8uZGs/sefolKKU9Bvs0fXypWCzG+vp6c6SP14E2VQ+a\nPn5r1Qb7PRMY7A4+Dg0NOdMQD63LGLMtt6uR62p0+vhm+AzHxsaq5qjwTP99fHycTCaDz+dDRBAR\n1tfXaWlpwRiDz+djbW2N1tbWjQkzstnsRtnjx49z+PDhjQCTzWbx+Xwb781kMhtly9Xd0tJS8v78\n4/z7AI4fP86RI0f+4LozmczG63lbrdfn8zE0NNSwm8q247q6u7vx+/2MjY2V/bwL/7bF+836+vqm\nfbJwHyx+3Rizad/I76d/SN0isun7kK8v/35jDD/60Y829vnC/Sa/D5b7LkHuGpmKF9DlV+LWP3K3\nY+u/Lf4tLi6au+++2zTKdlzX+9//ftf/jl78d9tttxnAmDLfS08cSpRr3KX8u/vuuxsWzBq1ro6O\nDrf/NE3vgQce2Jb7ht11/eAHP6j4udm67doJ+duulVKNZ8rcdu16YFBKeY8nDiWUUt6igUEpVWJb\nBAYR+YiIZEUkXLDsb6wJb54UkWsdWIdjk+vUuL5bROQZEfm9iHzciToL6t4tIqdEZFhEfisiH7CW\n94nICRF5VkR+KiKOTRMtIj4ReUJEjlvP94vIaWtd3xIRR06di0hIRL5r/S2eFpHr67VdIvIhEfmd\niDwlIt8UEb+T2yUiXxeRhIg8VbCs7LY4us83agS1Xv/IJZr9CfAiELaW3Qr8H+vx9eRSztldz42A\nz3r8eeBz1uOrgF+TuyZkP/Ac1tiNjXX5rHr2AW3Ak8AVDn5mceBa63EX8CxwBfAF4GPW8o8Dn3dw\nnR8C/idw3Hr+D8Dbrcf/Bfgrh9bz34B3W49bgVA9tgvYBbwA+Au25w4ntwv4E+Ba4KmCZVtui9P7\nvCN/dDf/Ad8FrikKDF8F/k1BmREg5uA6bwP+h/X4E8DHC177MXC9zfpvAH5c8HzTOurwGf6jFfie\nyX9OVvB4xqH6d5NLCHysIDBMFgTaG4CfOLCebuD5LZY7vl1WYDgL9FkB6DhwE5B0crvI/TgUBobi\nbRmxHju6zzf1oYSI/GvgvDHmt0UvXfKEN5fI1uQ6NSiuc9SBOrckIvvJ/SqdJrcjJQCMMROAUymq\n7wc+Su7iGkQkAsyal2cxGyX3RbPrIDAlIt+wDlu+JiId1GG7jDFj5DKknyP3N08BTwBzddiuQtGi\nbcnP2OvofuiZS6LLqTDhzaeBT5KL0iVv22JZ1fOyjZpcpwb1qLN0JSJdwPeADxpjFupxTYmI/BmQ\nMMY8KSLH8osp3UYn1t0KvBJ4nzHmVyJyP7neVj22qxd4C7lf9BS5nuutWxRt1PUAju4zng8MpsyE\nNyLyz8gd0/9Gchej7waeEJHr+AMmvKm0roJ13oEDk+vUYBTY63Cdm1iDYt8jd0j0Q2txQkRixpiE\niMTJdYvteg3wZhF5E9BOrrv/n4GQiPisX1entm+UXA/yV9bz75MLDPXYrhuBF4wxMwAi8gPgXwK9\nddiuQuW2xdH9sGkPJYwxvzPGxI0xB40xB8h9MP/cGJMkd7z3FwAicgO57l3CzvokN7nOx4A3G2MK\nkwgeB95hjUgfAC4HHrezLuD/AZeLyD4R8QPvsNbjpL8Dho0xXypYdhy403p8B/DD4jddKmPMJ40x\ne40xB8khgmMMAAAA+ElEQVRtxyljzLuAR4C3O7yuBHBeRI5Yi94APE0dtovcIcQNIhK0fpjy63J6\nu4p7V4XbcmdB/c7u83YHYbzyj9wIcbjg+d+SG9n/DfBKB+o/Q26w6Qnr31cKXrvLWtcI8EaHtucW\ncmcLzgCfcPizeg2QIXe249fW9twChIGHrfWeBHodXu+f8vLg4wHgn4DfkxvJb3NoHX9ELrA+Cfwv\ncmcl6rJdwN3W3/wp4EFyZ5Ac2y7g78n96q+QC0TvJjfYueW2OLnP6yXRSqkSTXsooZSqHw0MSqkS\nGhiUUiU0MCilSmhgUEqV0MCglCqhgUEpVUIDg1KqxP8Hcqx+SW6w/jsAAAAASUVORK5CYII=\n",
2041       "text/plain": [
2042        "<matplotlib.figure.Figure at 0x7f10346c3cf8>"
2043       ]
2044      },
2045      "metadata": {},
2046      "output_type": "display_data"
2047     }
2048    ],
2049    "source": [
2050     "def quincunx_tour(a=60, b=30, c=50):\n",
2051     "    \"a is length of indent, b is indent/outdent distance, c is outdent outer length\"\n",
2052     "    return ('F' * a + 'R' + 'F' * b + 'L' + 'F' * c + 'L' + 'F' * c + 'L' + 'F' * b + 'R') * 4\n",
2053     "plot_trace(trace_tour(quincunx_tour()))"
2054    ]
2055   },
2056   {
2057    "cell_type": "code",
2058    "execution_count": 91,
2059    "metadata": {},
2060    "outputs": [
2061     {
2062      "data": {
2063       "image/png": 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iqnu92C4RrS2vFgeNIrZGYOlMl0rkA15dAoiH2yKiAvHqDEABvCYiCuC/VPWpbDM+8cQT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\nWKIAAAAASUVORK5CYII=\n",
2064       "text/plain": [
2065        "<matplotlib.figure.Figure at 0x7f10346ee208>"
2066       ]
2067      },
2068      "metadata": {},
2069      "output_type": "display_data"
2070     }
2071    ],
2072    "source": [
2073     "plot_trace(trace_tour(('F' * 10 + 'R' + 'F' * 5 + 'L' + 'F' * 10 + 'L' + 'F' * 10 + 'L' + 'F' * 5 + 'R') * 4))"
2074    ]
2075   },
2076   {
2077    "cell_type": "code",
2078    "execution_count": 92,
2079    "metadata": {},
2080    "outputs": [
2081     {
2082      "data": {
2083       "image/png": 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ZZ57hwIED7Nu3r84N3FRGpzCGuczMTFJSUjx/7Pv27aN79+6WU6lgVv6cyBEj\nRvDxxx9bTBMcdNQ7zCUnJ1NWVgY4X+yioiLLiVQoSE5OZsOGDbZjhBwdzAkTvXr1QkSYMWOG7Sgq\niJw7d67CwE1ycrLlRKFJu95hoKCggOPHj3PttddSVFSkx56Ux9GjR0lISGD//v1ERESQmJhYJ9eT\nvByd612HNG3alK5du3paDSLCuHHjLKdSNmVmZtKuXTsSEhIA6Nq1K507d9YiWUNV/tZEpK2IrBOR\nvSKyR0Qect0eJyJrRGS/iHwkIk38H1ddyQcffOD5IPp3333Xchpl06hRozh8+DAAt9xyi+U0oa/K\nrreItAJaGWOyRCQW2AGMBX4O5BtjnheRmUCcMWZWJY/XrneA5ebm0r59e+1u1UHuwzB9+vTh/Pnz\nehimCj7rehtjjhljslyXzwH7gLY4i+Uy192WAdrXCxJNmjgb9926daNLly784Q9/sJxIBUpcXBzd\nunXj/Pnz/PSnP7UdJ2xU6/QgEekIJAGfAi2NMXngLKYiEu/zdKpGGjdu7GlJiAiZmZmWE6lA2r59\nO3379rUdI6x43R9zdbuXAw+7Wpbapg8R69atQ0RITU21HUX5wcaNG4mIiPAM5tWvX99yovDjVYtS\nRCJxFsk3jDHuUYI8EWlpjMlzHcc8frnHp6WleS6npKSQkpJS48Cqer744gvmzJnD/v37Wbt2re04\nyg8WLFhAWVkZo0ePplOnTvTs2dN2pKCVkZFBRkZGtR/n1XmUIvI6cNIY89tyt80HThlj5utgTvB7\n8cUXefDBB3nhhReIjY3lV7/6le1IqpZyc3NZvnw5y5YtY9euXTpwUwM+m+stItcDmcAenN1tAzwJ\nbAPeAtoBh4BJxpiCSh6vhTII7Nq1i6SkJM/1FStWMGHCBIuJVG2Vn7s9evRoVq9ebTFNaPLZXG9j\nzGYg4jI/vrG6wZQdvXr1qjDAc/DgQcuJlC/MmTNHP9I4APTkujrqt7/9rS7+G4K+/PLLCnO3u3Tp\nYjlR3aCrB9VBBw8eZPXq1bz00ku6+G+I2bZtG4Dng+b0XMnA0EUx6rDhw4ezfv16UlJS6NGjB4sW\nLbIdSV3G9u3bmT17Nv/4xz84cOCADtz4iC7cq6q0YcMGRowYQWlpKQA5OTkkJiZaTqUqU37g5sYb\nb9RTvXxEF+5VVRo6dCglJSWA8w+mpKSkwoCPCi79+/f3dL1VYOlgjvLo2rUrDoeDu+66y3YUBVy4\ncKHCwM35Wnu2AAALJUlEQVTw4cMtJ6q7tOutAPj+++8pKCigffv2AHoMLAgUFBQQFxfHoUOHcDgc\nJCQkaEvfx3ThXlUtjRo1ol27dp7rIsKtt95qMVHdlZmZSatWrYiLiwOgXbt2tGnTRoukRVooVQXr\n16+nY8eOOBwOVq1aZTtOnTRu3Djy8vJwOBy6Un2Q0K63qtT+/fvp3r07WVlZREZG0qNHD13818/y\n8/M5fPgww4cP59SpU3r4IwC0661qpXnz5gAkJSXRs2dP5s2bZzlR+GvevDlJSUmcOnWKqVOn2o6j\nytHTg1SlmjVrVuFUoS1btlhOVDds2rSJ66+/3nYMdQltUSqvrF69GhFh1KhRtqOElU2bNlU4BSgm\nJsZyIlUZbVGqKu3atYtnn32W7OxsPvzwQ9txwspLL70EwMSJE2nXrh19+vSxnEhVRgdzlNeef/55\nZs6cydy5c2ncuDEPPvig7Ugh69ChQ7zxxhssX76crKwsHbixRKcwKp+78Ubn8qOzZ88GoGPHjnqu\nZQ116NDBc/mmm26ymER5Q49RKq/16dMHY4yn9fPdd99ZThTaZs2ahTGGDz74wHYUVQUtlKrG7r33\nXkRET4r20ldffVVh4KZbt26WEylvaddb1cihQ4f45JNPmD9/Pu+++27VD1Ds2rULgKVLlxIdHc2U\nKVMsJ1Le0sEcVSuDBg3is88+Y8CAAVx33XUsXrzYdqSgs23bNmbNmsXBgwfJycnRgZsgogv3qoDI\nyMggNTWV4uJiwHncMiEhwXKq4FJ+MYvhw4fzySefWEyjytNCqQJORDh06BBt27b1XFfO30PPnj3Z\ns2eP7SjqEjrXWwWU+59h+/btcTgc3H333ZYT2VVUVFRh4CY1NdVyIlUb2qJUPnPhwgXOnz9PfHw8\n0dHRXLhwwXYkay5evEh0dDQnTpwAnHPntYUdfLRFqQIuJibGs+pQYWEhIsLo0aMtpwqsDRs20Lx5\nc6KjowHnikDNmzfXIhnitFAqn8vIyODqq68mOjq6zp1MPWXKFPLz84mNjeW2226zHUf5iHa9ld/s\n2rWLpKQktm7dSlRUFL179w7bxX9PnDjBN998w/jx4zl27JieAhQidK63sq5169YADB48GHAuqvH4\n44/bjOQ3LVq08FyeNGmSxSTKH7RQKr9p0aJFhcV/w/0zqdesWcNPfvIT2zGUH4RnP0gFpeXLlyMi\nYbNaztatWyucAhQbG2s5kfIXbVGqgMjOzmbevHns3LmTjz76yHYcn3BP15w2bRpt2rTxHGJQ4UcH\nc1RApaWlMWfOHGbPnk3Tpk159NFHbUeqtoMHD7JkyRJWrVqli+6GOJ3CqILSjh076Nevn+f6+++/\nH3Kfw1P+nMhRo0bx/vvvW0yjakNPOFdBqW/fvhUW/z1+/LjlRDXz8MMPY4zRIllHaKFUVs2YMQMR\nYfz48bajXFFOTk6FgZuePXtaTqQCSQdzlDW5ubls3ryZp59+mpUrV9qOc0X79u0DID09nejoaMaM\nGWM5kQokPUaprEtKSmLXrl307NmTfv36sXTpUtuRPLZu3cpjjz1Gbm4uubm5OnATZnQwR4WM9evX\nM3r0aAoLCwHIz8/nqquuspzKqfzAzY033sjatWstplG+poVShSQR4eTJk55CaXvVHRGhc+fOfP31\n11ZzKP/QUW8Vctz/UJs3b47D4eD++++3kqO0tLTCwM3NN99sJYcKHrVqUYrITcCfcRbcV40x8yu5\nj7YoldeKioooLi4mNjaWuLg4Tp06ZSWHiHD27FlEhIYNG1pv2Sr/8HuLUkQcwIvASOAaYKqIdK/p\n9pQCqFevHg0bNgTg9OnTAV38NyMjg7i4OE9RbNiwIbGxsVokVa263gOAr4wxB40xxUA6MNY3sVRd\nt2HDBn70ox/RpEmTgC3+O2PGDAoKCoiPj2fy5Mlhu3amqr7anEfZBsgtd/0wzuJZqYyMDFJSUmqx\nO/tC/TmEUv7k5GSys7P59NNPGTx4MOvXr8cYQ1ZWFr179/6X+zscDoqKioiMjHR3p3A4HFy8eJGo\nqCjPbeWXfXNz/6ysrAzw72yhUHoNLifUn0NN8temUFbWH6n0YGRaWponnPsrFNXFPxDb2rVrBzg/\nDzsQJk6c6Nfth+JrcKlQfg4ZGRmkpaVVO39t+haHgfblrrcFjlR2R3ewmgRUdVubNm08LUFjDM88\n80yF677+Wr58ue2nrPzI3VBLS0sjLS3N68fVplB+DnQRkQ4iUg+YArxXi+0ppVRQ8sXpQf/BP08P\nmlfJffTcIKVU0AqKmTlKKRXq9PwHpZSqghZKpZSqQkAKpYg8KCJfisgeEZlX7vbfichXIrJPRFID\nkaWmROQxESkTkavK3bbQlT9LRJJs5rsSEXne9TvOEpEVItK43M9C4jUQkZtcf0MHRGSm7TzeEJG2\nIrJORPa6/vYfct0eJyJrRGS/iHwkIk1sZ70SEXGIyBci8p7rekcR+dSV//+JSFCvaysiTUTkbdff\neLaIDKz2a+DPUy1cxz9TgDVApOt6c9f3HsBOnOdydgS+xnXMNNi+cJ769CHwD+Aq122jgNWuywOB\nT23nvEL+GwGH6/I84DnX5R+FwmuA8x/610AHIArIArrbzuVF7lZAkutyLLAf6A7MB55w3T4TmGc7\naxXP4xHgTeA91/W/AJNcl18G7rGdsYr8/xf4uetyJNCkuq9BIFqU97pClAAYY066bh8LpBtjSowx\n3wJfcYWZPZb9O/D4JbeNBV4HMMZ8BjQRkZaBDuYNY8zHxpgy19VPcRZ+gDGExmsQktNljTHHjDFZ\nrsvngH04f/djgWWuuy0DxtlJWDURaQuMBpaUu3k4sMJ1eRkQtJ/jISKNgBuMMUsBXH/rZ6jmaxCI\nQtkVSHY11deLSF/X7ZdOgfzOdVtQEZFbgVxjzJ5LfhQS+SvxC8D9iVih8hwqmy4bjDkvS0Q6Akk4\n/1G1NMbkgbOYAvH2klXJ3UgwACLSDDhd7h/vYSDBUjZvdAJOishS1+GDV0SkAdV8DXxybEFE1gLl\nW1OC8xc727WPpsaYQSLSH3jbFd7rKZD+VkX+J4GfVPawSm6zdq7VFZ7DU8aYv7nu8xRQbIz5f+Xu\nc6lgPF8sVHJWSkRigeXAw8aYc6FybrGI3AzkGWOyRCTFfTP/+noE8/OJBPoA9xtjtovIvwOzqGZm\nnxRKY0xlhQQAEfk18FfX/T4XkVLXfyWvp0D62+Xyi0hPnMfudolzFYW2wBciMgBn/nbl7m4tP1z5\nNQAQkTtxdqHKT5oOqudwBUHzt1JdroGO5cAbxph3XTfniUhLY0yeiLQCgvUze68HxojIaCAGaIRz\n/dkmIuJwtSqD/bU4jLNHuN11fQXOQlmt1yAQXe+VwAgAEekK1DPG5OOc7jhZROqJSCLQBdgWgDxe\nM8b83RjTyhjTyRiTiPOX3tsYcxxn/p8BiMggoMDdlA82rhlUTwBjjDEXy/3oPWBKML8GLqE8XfY1\nYK8x5j/K3fYeMMN1+U7g3UsfFAyMMU8aY9obYzrh/J2vM8ZMB9YDk1x3C9r8AK73ZK6r9oCzFmVT\n3dcgACNOUcAbwB5gOzC03M9+h3M0cx+Qant0zIvnkoNr1Nt1/UVX/l1AH9v5rpD7K+Ag8IXra1Go\nvQbATThHjb8CZtnO42Xm64FSnKP0O12/+5uAq4CPXc9nLc5DU9bzVvFchvLPUe9E4DPgAM4R8Cjb\n+arI3gvnP9ssnL3bJtV9DXQKo1JKVUFn5iilVBW0UCqlVBW0UCqlVBW0UCqlVBW0UCqlVBW0UCql\nVBW0UCqlVBW0UCqlVBX+P0VFnoIKajtRAAAAAElFTkSuQmCC\n",
2084       "text/plain": [
2085        "<matplotlib.figure.Figure at 0x7f10341de518>"
2086       ]
2087      },
2088      "metadata": {},
2089      "output_type": "display_data"
2090     }
2091    ],
2092    "source": [
2093     "heart_points = [Step(60, 50, Direction.UP), Step(50, 90, Direction.UP),\n",
2094     "                Step(20, 70, Direction.UP), \n",
2095     "                Step(-40, 90, Direction.UP), Step(-60, 80, Direction.UP), \n",
2096     "                Step(0, 0, Direction.RIGHT)]\n",
2097     "\n",
2098     "heart_tour = ''\n",
2099     "current = Step(0, 0, Direction.RIGHT)\n",
2100     "\n",
2101     "for hp in heart_points:\n",
2102     "    while not (current.x == hp.x and current.y == hp.y):\n",
2103     "        s, proposed = seek(hp, current)\n",
2104     "        heart_tour += s\n",
2105     "        current = proposed\n",
2106     "\n",
2107     "plot_trace(trace_tour(heart_tour))\n",
2108     "\n",
2109     "def heart_tour_func(): return heart_tour"
2110    ]
2111   },
2112   {
2113    "cell_type": "code",
2114    "execution_count": 93,
2115    "metadata": {},
2116    "outputs": [
2117     {
2118      "data": {
2119       "text/plain": [
2120        "'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'"
2121       ]
2122      },
2123      "execution_count": 93,
2124      "metadata": {},
2125      "output_type": "execute_result"
2126     }
2127    ],
2128    "source": [
2129     "# lc = trace_tour(('F' * 50 + 'L') * 4)\n",
2130     "# lc = trace_tour(('F' * 50 + 'L' + 'F' * 20 + 'R' + 'F' * 20 + 'L') * 4)\n",
2131     "# lc = trace_tour(('F' * 60 + 'R' + 'F' * 30 + 'L' + 'F' * 60 + 'L' + 'F' * 60 + 'L' + 'F' * 30 + 'R') * 4)\n",
2132     "lc = trace_tour(heart_tour)\n",
2133     "rw = guided_walk(lc, wander_limit=8)\n",
2134     "rw"
2135    ]
2136   },
2137   {
2138    "cell_type": "code",
2139    "execution_count": 94,
2140    "metadata": {},
2141    "outputs": [
2142     {
2143      "data": {
2144       "image/png": 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A0caxrWrln376qZnmb8/UHZPJ1KxszZGYM6NirZUxY8aM9r1anEBrsircR1M3E1s0vv/a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\n0guCoKWIpBcEQUvxN5buseIr1WPNAAAAAElFTkSuQmCC\n",
2145       "text/plain": [
2146        "<matplotlib.figure.Figure at 0x7f10339959b0>"
2147       ]
2148      },
2149      "metadata": {},
2150      "output_type": "display_data"
2151     }
2152    ],
2153    "source": [
2154     "plot_trace(trace_tour(rw))"
2155    ]
2156   },
2157   {
2158    "cell_type": "code",
2159    "execution_count": 95,
2160    "metadata": {},
2161    "outputs": [
2162     {
2163      "data": {
2164       "image/png": 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Yq8MIqGAurxlufLl8HTNmDNHR0Z76wClTpgQ6rG65J2Vxx/Kd73wH0MtwKw36JOleLGsw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\nUimleqBJUimleqBJUimlevD/A80VXGG6+r+KAAAAAElFTkSuQmCC\n",
2165       "text/plain": [
2166        "<matplotlib.figure.Figure at 0x7f103350d470>"
2167       ]
2168      },
2169      "metadata": {},
2170      "output_type": "display_data"
2171     }
2172    ],
2173    "source": [
2174     "rw_trimmed = trim_all_loops(rw)\n",
2175     "plot_trace(trace_tour(rw_trimmed))"
2176    ]
2177   },
2178   {
2179    "cell_type": "code",
2180    "execution_count": 96,
2181    "metadata": {},
2182    "outputs": [
2183     {
2184      "data": {
2185       "text/plain": [
2186        "764"
2187       ]
2188      },
2189      "execution_count": 96,
2190      "metadata": {},
2191      "output_type": "execute_result"
2192     }
2193    ],
2194    "source": [
2195     "len(rw_trimmed)"
2196    ]
2197   },
2198   {
2199    "cell_type": "code",
2200    "execution_count": 97,
2201    "metadata": {},
2202    "outputs": [
2203     {
2204      "data": {
2205       "text/plain": [
2206        "(284, 22, 'FFRRLLRRFFFFFRFFFRFFRL')"
2207       ]
2208      },
2209      "execution_count": 97,
2210      "metadata": {},
2211      "output_type": "execute_result"
2212     },
2213     {
2214      "data": {
2215       "image/png": 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HP/xh7CidMpmMnn76ad18882xo3zMSy+9pGuvvVYfffRR7CidkrCf33///aqoqJAklZeX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\n",
2216       "text/plain": [
2217        "<matplotlib.figure.Figure at 0x7f10346f29b0>"
2218       ]
2219      },
2220      "metadata": {},
2221      "output_type": "display_data"
2222     }
2223    ],
2224    "source": [
2225     "lc = trace_tour(square_tour(a=10))\n",
2226     "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
2227     "rw_trimmed = trim_all_loops(rw)\n",
2228     "plot_trace(trace_tour(rw_trimmed))\n",
2229     "len(rw), len(rw_trimmed), rw_trimmed"
2230    ]
2231   },
2232   {
2233    "cell_type": "code",
2234    "execution_count": 98,
2235    "metadata": {
2236     "collapsed": true
2237    },
2238    "outputs": [],
2239    "source": [
2240     "# success_count = 0\n",
2241     "# while success_count <= 20:\n",
2242     "#     lc = trace_tour(square_tour(a=10))\n",
2243     "#     rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
2244     "#     if rw:\n",
2245     "#         rw_trimmed = trim_all_loops(rw)\n",
2246     "#         if len(rw_trimmed) > 10:\n",
2247     "#             with open('small-squares.txt', 'a') as f:\n",
2248     "#                 f.write(rw_trimmed + '\\n')\n",
2249     "#                 success_count += 1"
2250    ]
2251   },
2252   {
2253    "cell_type": "code",
2254    "execution_count": 99,
2255    "metadata": {
2256     "collapsed": true
2257    },
2258    "outputs": [],
2259    "source": [
2260     "# success_count = 0\n",
2261     "# while success_count <= 20:\n",
2262     "#     lc = trace_tour(square_tour())\n",
2263     "#     rw = guided_walk(lc)\n",
2264     "#     if rw:\n",
2265     "#         rw_trimmed = trim_all_loops(rw)\n",
2266     "#         if len(rw_trimmed) > 10:\n",
2267     "#             with open('large-squares.txt', 'a') as f:\n",
2268     "#                 f.write(rw_trimmed + '\\n')\n",
2269     "#                 success_count += 1"
2270    ]
2271   },
2272   {
2273    "cell_type": "code",
2274    "execution_count": 100,
2275    "metadata": {
2276     "collapsed": true
2277    },
2278    "outputs": [],
2279    "source": [
2280     "# success_count = 0\n",
2281     "# while success_count <= 20:\n",
2282     "#     lc = trace_tour(cross_tour())\n",
2283     "#     rw = guided_walk(lc)\n",
2284     "#     if rw:\n",
2285     "#         rw_trimmed = trim_all_loops(rw)\n",
2286     "#         if len(rw_trimmed) > 10:\n",
2287     "#             with open('cross.txt', 'a') as f:\n",
2288     "#                 f.write(rw_trimmed + '\\n')\n",
2289     "#                 success_count += 1"
2290    ]
2291   },
2292   {
2293    "cell_type": "code",
2294    "execution_count": 101,
2295    "metadata": {
2296     "collapsed": true
2297    },
2298    "outputs": [],
2299    "source": [
2300     "# success_count = 0\n",
2301     "# while success_count <= 20:\n",
2302     "#     lc = trace_tour(quincunx_tour())\n",
2303     "#     rw = guided_walk(lc)\n",
2304     "#     if rw:\n",
2305     "#         rw_trimmed = trim_all_loops(rw)\n",
2306     "#         if len(rw_trimmed) > 10:\n",
2307     "#             with open('quincunx.txt', 'a') as f:\n",
2308     "#                 f.write(rw_trimmed + '\\n')\n",
2309     "#                 success_count += 1"
2310    ]
2311   },
2312   {
2313    "cell_type": "code",
2314    "execution_count": 102,
2315    "metadata": {},
2316    "outputs": [
2317     {
2318      "data": {
2319       "image/png": 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HP/xh7CidMpmMnn76ad18882xo3zMSy+9pGuvvVYfffRR7CidkrCf33///aqoqJAklZeX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\n",
2320       "text/plain": [
2321        "<matplotlib.figure.Figure at 0x7f10342e2390>"
2322       ]
2323      },
2324      "metadata": {},
2325      "output_type": "display_data"
2326     }
2327    ],
2328    "source": [
2329     "plot_trace(trace_tour(rw_trimmed), filename='test.png')"
2330    ]
2331   },
2332   {
2333    "cell_type": "code",
2334    "execution_count": 103,
2335    "metadata": {
2336     "collapsed": true
2337    },
2338    "outputs": [],
2339    "source": [
2340     "# patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
2341     "# tours_filename = 'tours.txt'\n",
2342     "\n",
2343     "# try:\n",
2344     "#     os.remove(tours_filename)\n",
2345     "# except OSError:\n",
2346     "#     pass\n",
2347     "\n",
2348     "# success_count = 0\n",
2349     "# while success_count < 100:\n",
2350     "#     lc = trace_tour(random.choice(patterns)())\n",
2351     "#     rw = guided_walk(lc)\n",
2352     "#     if rw:\n",
2353     "#         rw_trimmed = trim_all_loops(rw)\n",
2354     "#         if len(rw_trimmed) > 10:\n",
2355     "#             with open(tours_filename, 'a') as f:\n",
2356     "#                 f.write(rw_trimmed + '\\n')\n",
2357     "#                 success_count += 1"
2358    ]
2359   },
2360   {
2361    "cell_type": "code",
2362    "execution_count": 104,
2363    "metadata": {},
2364    "outputs": [
2365     {
2366      "name": "stdout",
2367      "output_type": "stream",
2368      "text": [
2369       "Found mistakes: 1916\n"
2370      ]
2371     },
2372     {
2373      "data": {
2374       "text/plain": [
2375        "(5540, 14, 'LFFFFLLRLFFLRL')"
2376       ]
2377      },
2378      "execution_count": 104,
2379      "metadata": {},
2380      "output_type": "execute_result"
2381     },
2382     {
2383      "data": {
2384       "image/png": 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23wCPFrOWvH0uBe7p4L44FRgFrCpw+9nAb5PtU4ClneWox46g7t6Yd/EbQLad3c4CFrn7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\nx0SoEAAAAABJRU5ErkJggg==\n",
2385       "text/plain": [
2386        "<matplotlib.figure.Figure at 0x7f1033d81390>"
2387       ]
2388      },
2389      "metadata": {},
2390      "output_type": "display_data"
2391     }
2392    ],
2393    "source": [
2394     "lc = trace_tour(cross_tour())\n",
2395     "rw = guided_walk(lc)\n",
2396     "print('Found mistakes:', len(mistake_positions(trace_tour(rw))))\n",
2397     "rw_trimmed = trim_all_loops(rw)\n",
2398     "plot_trace(trace_tour(rw_trimmed))\n",
2399     "len(rw), len(rw_trimmed), rw_trimmed"
2400    ]
2401   },
2402   {
2403    "cell_type": "code",
2404    "execution_count": 105,
2405    "metadata": {},
2406    "outputs": [
2407     {
2408      "data": {
2409       "image/png": 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GjEBoaCjefPNNvk9wr1gVioqKUFBQgClTpsBgMMDNzQ1OTk6SZ/nyyy/j1q1b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\nQmCC\n",
2410       "text/plain": [
2411        "<matplotlib.figure.Figure at 0x7f103402bef0>"
2412       ]
2413      },
2414      "metadata": {},
2415      "output_type": "display_data"
2416     }
2417    ],
2418    "source": [
2419     "plot_trace(trace_tour(rw))"
2420    ]
2421   },
2422   {
2423    "cell_type": "code",
2424    "execution_count": 106,
2425    "metadata": {},
2426    "outputs": [
2427     {
2428      "data": {
2429       "image/png": 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23wCPFrOWvH0uBe7p4L44FRgFrCpw+9nAb5PtU4ClneWox46g7t6Yd/EbQLad3c4CFrn7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\nx0SoEAAAAABJRU5ErkJggg==\n",
2430       "text/plain": [
2431        "<matplotlib.figure.Figure at 0x7f1034757358>"
2432       ]
2433      },
2434      "metadata": {},
2435      "output_type": "display_data"
2436     }
2437    ],
2438    "source": [
2439     "plot_trace(trace_tour(trim_all_loops(rw)))"
2440    ]
2441   },
2442   {
2443    "cell_type": "code",
2444    "execution_count": 108,
2445    "metadata": {
2446     "scrolled": true
2447    },
2448    "outputs": [
2449     {
2450      "name": "stdout",
2451      "output_type": "stream",
2452      "text": [
2453       "[Mistake(i=9, step=Step(x=0, y=5, dir=<Direction.RIGHT: 2>)), Mistake(i=29, step=Step(x=5, y=6, dir=<Direction.DOWN: 3>)), Mistake(i=33, step=Step(x=5, y=2, dir=<Direction.DOWN: 3>))]\n"
2454      ]
2455     },
2456     {
2457      "data": {
2458       "text/plain": [
2459        "'LFFFFRFFRFFLFFLFFFLFFRRFRFFFFFFFFFFFRFRLRRLLRFFFFRFLFFLLFLRFFFFFLFFFFFLFFLFRLFRFRLFFFFLLFFFFLFFFRLFRRFFFLFFFFFFFFFLFLRFFFRLRLLFRRFLLFFFLFFFFFRLFFFRRLFFFLLFFLRLFLFLRFRFFFFLFFFRRFFLLLFLLLRLFFFFFLLFFFFFFLFFLRLLFFFRRLFLLLFRRFLFLLFFRFFLFFRFFFFFFFFFFFFFRFRRRRRFFRRRFFFLRRFLRFFFLLFFLRFLFLFFFLFFFLFLFRFFFFFRLFFFFFLFFLFFRRRRFLFFFFFFFFFFFFLFFFFLFRFLLLFFRRFFLLFFLFFLFFFFFFRRFFRLFLLFFFFFFLFFLLFFRFRRLLFRFFRRFLRLFLLFFFRFRFFFFFFFFFFFFFFFFRFFFFRFLFFFFFFFRFFLFFFFRRFFFLLFRFFFRRFFFFRRFFFFFFLLFLFFFFLRRLLFRFFLRFRFLFFFFRRRFFFRRFFRRRRRRFLRRFRFRFRFLFFFFLLLLFFLRRRFFFFFFRFFRFFLLFFFRFFRRFFFLFFFFFLFLFFFFLFLLFFFFFRFFLLFFFLFRFFLLRLFFFFFFLFFLRRLFFRFFFLLFLFFFRRFRRFRFFRFFRFRRRFFRFFFRFRRLRFFFFLFLFFFRFFFFFFFFRFFRFFFRLFRFRFRRRRFRFLRFFFLRLRFRFLFFFFFFLRRFFLLFFFLFLFFFFRFRFRFFLFFRRFFFFFRLRFFFFFRFFFFRFFFFFRFFLLFFRFFLRRLFLFLFFFFFFFFFFFLFFFFFRFFLRLFLLFFFRFRFFFRFFRFFRFLFFLRFFRRLRRFFLLRRLFFFLFFFFFFFRRRLRFFLFRFFRLFRFFRFFFFFLFFFFLFFFFLFFFRRFRFRFLFLFRFFLFFLRFRFFFFRFFFFLFLFFFRRRLFLFFLFRFRFFLFLFFLFLFLLFFFFFFLFFFRFFFLFFRFFFFRFFFLLFLFFRFRFFRFRFFFFFFFFLLLFFLFFFLFFFFFLFRRFFFFLFFFFRRRFRFRFFLLFRFLFRLFLLLRFFLFFLFFFFFRRLFFLFFFFRRFFFLFRFRRRRFRLFLFRFFFLFLRFFFFLFLFLRFFLFRFRFRFLFLFLFRFLRFFRFRLFFFRFLLFFRRFFFFFFFRLFLLFLFFFLFRLRRFFFFLFFLLRFFLFRRRFLFLLFFFFFFLFFLLLFFFFFFLLRRFRFFFRRFLLFFFLLFFFFFRFRRLFFFFLRRLRRFFLRRFFFLFLFFFFLRLFLLRFFRFRFRFRFFLLRRLRLRFRFFFFFFFFFFFFFFFRFFLFRRFFRFFFLRLLLRRFFLFRFRRLFRFRFFRFFFRLFFFRRLFRFFFFRFFFRFFFFFRFFFRLLFFRLFRFFFRFRRRRFFFRRLLFFLFFFFFFFFRFFFRFFFLFFLFFFFFFFFLFLFFRFFFFFFRFFRFFFFLLLLFFFFLLLFRFLFRFRFFFRFFFLRFFRRLFFLFLLRFFRRRLLRFRFRFLFFFFLRRLRRLLFFFFFFRFFRRRFFLFFFFFLFFFFLRFFRLFFFLFFLFLFFLFFFLFFFLLLFFFFLFFFFFLRFFFRLFFFFLFLRRRRFFRFFFLRRLFFFRFLFFLFFFFFLRRFRLFLFLLFRLFRLFLFRFRFRLLFFRFLRFFRFFLRRLRFFFLRFRFFFFFLFFRLRFFFRFRFLRFRFLFFFRRRRRLFFFFFLFFFRFLFFFLFRFFFFFFFRFLFLFLLLRRFFFFFFFFRLFLRFRFFLLLFFFLFLFFRFLFFFRRFFRLFFRLFRFRFFLRFRFFFFFFFFRFFFRLFFRFFFLFLRFFFFLFFLFFFRFFFRFFFLFLLLLFLFFFLFLFFRFLLFLFFLFRFFFFLFFFRFFFFFFFFFFFFLLFFFFFFRLLFRRRFFFFLRFFFFRFFFFRFLFRLFFRFFFLFLFRFRLFFFRRLFRFLRFFFFFFFFRLFRFFFFFRRFRFRRFLFRFRFFFLFFFFFLRRLFLRFRRFRFFRFRRFFFFFFFLFRFFFRFRRLRRFFFFFFRLLLLFRFLLFFLFFLFFFFFFFFFFFFFFFFFLFFLRFFLRFFLFRFLRRLFLFFFLFFRFLRFFFFLRFFRFFFFFFFFRFRFFFRRFFFLLFFFFFFLRFFRRFRFLFFLFLFFLFLFRFLFFFLRFFRFLLFLFRFRFFFFLLFFFFFFFFLFRRRRFFFFFFFFRFFLFFRRFRRFLFFRRFFRRFFFRRFRFRFFFFFRFFFFFRRFFRRFFLFFLFRFLRRRFFFLLFFFFFFFFFLLLFRFFFFRRFLFLFFLRRFFFFRFFLRRFLFRFFFFRLLFLLFFFFRFRFFRFLFLRFLRFLFRFLFFRRRLFFRLFLRLFRFFRFFLFLFRFFFFRFFFFFFFRFFLFRLFLLRLFFFFFFRFFFRFFFFRFFRFFFRFFRLRFFFRLFRRRRRFFRRRRRFFRLRFFRFFLRLFFLRFRRFFRFFFFRFFFFFRFFFFRFFFFFRFRFLLFRFFFFFRFLLFRFRFRFRLFFRRRRRRFFFRRFFFLLFRFRFFRRLFFLLFFFFLFFLRRRFFFFRLLFRFFRFLRRRFRLFFLLFRFFFRFFFFFRFFFFRFFRFRFFFFFFRFLFLFFFFFRRFLLFFFFFLFFLFFFLFFFLRLFFLFFFFFFFLFRFLLFLFFLFFRFFFLFFLLRLFFRFFRFRLFRFFRFFRLRFFLLFRLFFFFRFFLFFLFRRFRFFFLFFLRFRLFFLFLRFFLFLFFFFLFFFLFFFFFFFFFLFFFFFLFFFFRLRFFFFFFFFFFRRFFFFFRRRRFFLLFFLRFFFFRFFFFRFFFFLFFFRFFFFFFRLFFLFFRFFRFRFFLLRFLFLFLFFLFLFFLFLRFFFFRRRFFFRFFLFLRFLFFRRFLFLFLLFFFFRLLLLLRLRRFFRRFFLRLFFRLLFRRLFFRFLLFFFLRLFFFFFFFFFLFRLFRLFLFFFFFRLRLRFFFRFRFFFRFFFFFFRFRFFFLFLFLLRRFRFLRFRFLFRRFRLFFFFFLFLFFFFFFFFLFRFFFFFFRRFFRLFFRFLLFLRFFFFLFRFFFLFFLFLFLFFFRRFRFFLRFLFRLFFFRFFFLFFFFFFRFLFFLFFRFRFFRFFFFFFFFFFFFRFFFFFFRRRFFFRFFFFRFFFLLRFFRLRFRFFLFFFRFFLFLFFFFLLRFFRRRFRLLRRLFFFLFLLFRFFFFRFFFFRFLFFLLFFFLFFFFLFFFFLFLLFRFLFFLRLFFFFLRFRLFRFFRFFFRLFFFRFLFFLLRFRRFFFFFFFFFFFFFFFFRRFLLFFLLRLFFFFFFFFFFFFFFLRFRRFFFRRFLLRFFFRFFLFLFRLRFFFFFRFFRFFFRLRRFFFFFRRRRRLFLLFFLLFFRRFRFFFFFLFFFFLFLFFRFFLFFFFLRLLFFFLFLFFFLLFLFLFFLRRRFFFFFRLFFFRLFFFFRFRFFFFRFFLFLLFLFRRFFRRRFFFLFRFFFRFFFFFFFFRRLFFFFFFRFLLFFFFRLFFFLFFLFFRLFFLFRFFFLFFFFLLFFFRFRLRFRFFRFLFFFLLLRFFFRFFFFFFFFLRLLFRRFLRFRRRLLRFRFFLLRFFLFLLRFFFFFLLFRRRRRRFFFFFRFFRRFLFFFFFRLFFFLFLFFLFLLFFLFFRFFRRRFFLRRRFLFFRFFFFFLFFLLFFRFRRRFFRFRRFRFRFFLRFRFFRRFRFFFRFFLFRFLRFFLFFRLRFFFFFFLRFFFFRLLLFLFLFLFLLFFLRFFRFFRFFLFFFRFFRRRFRLFLFFFLFFLFFFLFFFFFLLRLFFLFLFFFFFFFFLLFFFRRFFLRLFFFLLFLLFFFFLFFFRFFFFLFRFFRFRFRFRLLFFFLLFFFLRRFFRFRFLFLFFFLLRRRRFRRLLLRLFLFFLFFFLFFFFFFFFFLRRRFFFFRFFFRRLFFFFFFFLRFLRLFLFFFFFLFFLFFRFRRFFRRLFFFLFFFFFRLRFFLFRFFFRFFRRRRRLFFFRFFRFRRRLFFFFLFFLLFFRRRRLFLFRRFRRLFFFRFFFLLFRLLLRLFFFRFFRFFFLRRFFFFFFFFFRRRLFFFFLRFFFRRFFFFFRLFFFFRRRLFFFFRRFRLFFFFFFRLLLRLLFFFFFRFLLFFRFFFFRFRFFFLFRFFFFFFFRRRLFFLRFRLFFFFFFFFLFFFFLFRFLRLRFLFFFFFFFFFLFFLLFFFFLFLFFFFFLFFFFLFLFFFLLFFRRFFFRFFFRFFFFRLRFFLFFFFFLRFLLLFRRLLRFFFFFFFFFRFLLLFRLFFFLFRFFRFRFFFFFFFRFLLLFFFFFFLFFFFFRFRLFFFRFLRLFLFLLRFFLRFFFRFFRFFFLRFFLFFLFLFFFFRFFFFFFFFFRFLRRFFFFRRLFRFFFFFRRFRLLFFRRRLLFFRLFFFLLFFFFRFFFFFFRRFRFFLRFFRFFFFFFFFFFFFFFFFRRFLFFFRRFRFFLLFFLRLFLFFFRFFFFRFFRLFFFFFFLFFLFFRLRFFFFRFFFRRLFFFFLLFLRFFLFFFFFFFFFFFRRFRFLFLFRRFFLLFFRFRFFFFLRLRFLLRLLFRFLFRRFLFFRFRFFFRFFFFLFFFRFFRRFFFLFFFFLFFRFLLLFRRLFLRLLLFLFFLLFFFFFFRRFFLLFLLRFRFRFFRFFFFFRFFRRFLFLRFLFFRLFFFLRRRRRFFFRRFFRLFFFRFRLFRFRFLRFRLRFRRFRLFFFLFRFFLRLRFFFRFFFRFFFFFFFFRFLFFFFRFFFFRFFFFLFRRFLFFFFRLLFFFFFLFLFFFRFRFLRLRRFRFLLFLFFFRRLFRFRLFFFLFRFRFLFFFFFFRRFLRRLRLFLLFFFFFFRRFRFFRLFFRFLFFLFFRFFFLFFLFFLFRFRFFFFLLRRRRFFFFFFFFLFFFFFFFFFLFLFRRFFFFRFRFFFFRFFRRFRFFFFLLLRLFFFRFFFFFFRFRLFFFLFFFFFFFFFFLRFFFRRRFRRFRFRFFFFLFLFFLRFLFFLFLFFFLFLFFFLFFFFFLFFFFFRFFFFLLRFFRFFFRFRFLLLFFFLFFFFLFFFFLRRFRFFLRLLFFFRFFFFLLLLRFFFRFFFFFFFFFFFRFRLLFFLFLFRLFFFFFFFFFFFLFFFFFFFFFFFFLRFFFFLFLFFLFLFFRRFRLRFFFFFFFLFLFFRFLRFFFFFRFRFFLLFRLFRFFRRFRLLFFRFLRFFFFRRFRFLFFLFFLFLRFFRFFRRFLLLLFLRFFFFLFFRRFRLFFFFLRFFLFFLFFLFRLFFLFRFFLFFFFLFFFFRRFLFRFFFFRFFFLFLLLRFFFFFFRFFFLLFRFFRRFRFLFFLFFRFLFFFFRFFLRFRFFRFFFLRRFLFFFLRFFLRRFLFRLFFRFFFFRLRLLLRLFFFFFFFFFLFLFFFFRFFFLLFFFFFRFRFFFFFFFLFFLRFFRFRRRLFFLLLRFRFFFLFFFLFRLRFLLFLFFFLFFLRFLFFFLFFLLFLLFRFRFLRLFFLFFFRFFFLLLFRFFFFFFFRLFFLFFLFLFFRLFFFFFRRLRLFFLRL'"
2460       ]
2461      },
2462      "execution_count": 108,
2463      "metadata": {},
2464      "output_type": "execute_result"
2465     }
2466    ],
2467    "source": [
2468     "w_tour = rw\n",
2469     "w_trace = trace_tour(w_tour)\n",
2470     "mks = mistake_positions(w_trace)\n",
2471     "print(mks[:3])\n",
2472     "trim_loop(w_tour)"
2473    ]
2474   },
2475   {
2476    "cell_type": "code",
2477    "execution_count": 109,
2478    "metadata": {
2479     "scrolled": true
2480    },
2481    "outputs": [
2482     {
2483      "name": "stdout",
2484      "output_type": "stream",
2485      "text": [
2486       "1916\n",
2487       "1912\n",
2488       "1909\n",
2489       "1903\n",
2490       "1900\n",
2491       "1896\n",
2492       "1894\n",
2493       "1892\n",
2494       "1883\n",
2495       "1881\n",
2496       "1878\n",
2497       "1872\n",
2498       "1860\n",
2499       "1855\n",
2500       "1854\n",
2501       "1849\n",
2502       "1846\n",
2503       "1845\n",
2504       "1839\n",
2505       "1835\n",
2506       "1833\n",
2507       "1828\n",
2508       "1825\n",
2509       "1821\n",
2510       "1819\n",
2511       "1810\n",
2512       "1800\n",
2513       "1793\n",
2514       "1784\n",
2515       "1783\n",
2516       "1763\n",
2517       "1737\n",
2518       "1735\n",
2519       "1729\n",
2520       "1719\n",
2521       "1716\n",
2522       "1713\n",
2523       "1707\n",
2524       "1697\n",
2525       "1696\n",
2526       "1695\n",
2527       "1694\n",
2528       "1689\n",
2529       "1687\n",
2530       "1673\n",
2531       "1669\n",
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2533       "1628\n",
2534       "1621\n",
2535       "1617\n",
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2537       "1600\n",
2538       "1599\n",
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2540       "1595\n",
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2586       "1300\n",
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2590       "1288\n",
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2600       "1253\n",
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2602       "1231\n",
2603       "1227\n",
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2609       "1173\n",
2610       "1168\n",
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2640       "1019\n",
2641       "1018\n",
2642       "1011\n",
2643       "1008\n",
2644       "1004\n",
2645       "1000\n",
2646       "998\n",
2647       "997\n",
2648       "990\n",
2649       "985\n",
2650       "981\n",
2651       "975\n",
2652       "971\n",
2653       "963\n",
2654       "962\n",
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2657       "952\n",
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2659       "948\n",
2660       "939\n",
2661       "936\n",
2662       "933\n",
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2665       "920\n",
2666       "918\n",
2667       "905\n",
2668       "903\n",
2669       "898\n",
2670       "897\n",
2671       "893\n",
2672       "884\n",
2673       "878\n",
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2675       "870\n",
2676       "850\n",
2677       "842\n",
2678       "834\n",
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2680       "820\n",
2681       "816\n",
2682       "806\n",
2683       "802\n",
2684       "795\n",
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2686       "773\n",
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2688       "759\n",
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2690       "744\n",
2691       "731\n",
2692       "728\n",
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2695       "719\n",
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2697       "707\n",
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2700       "685\n",
2701       "681\n",
2702       "678\n",
2703       "675\n",
2704       "674\n",
2705       "666\n",
2706       "661\n",
2707       "655\n",
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2709       "645\n",
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2711       "638\n",
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2714       "628\n",
2715       "623\n",
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2720       "600\n",
2721       "595\n",
2722       "586\n",
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2725       "577\n",
2726       "573\n",
2727       "568\n",
2728       "562\n",
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2730       "557\n",
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2733       "542\n",
2734       "540\n",
2735       "532\n",
2736       "520\n",
2737       "512\n",
2738       "500\n",
2739       "494\n",
2740       "491\n",
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2742       "486\n",
2743       "485\n",
2744       "481\n",
2745       "477\n",
2746       "471\n",
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2749       "425\n",
2750       "423\n",
2751       "419\n",
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2754       "400\n",
2755       "398\n",
2756       "390\n",
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2758       "381\n",
2759       "371\n",
2760       "369\n",
2761       "367\n",
2762       "363\n",
2763       "362\n",
2764       "358\n",
2765       "357\n",
2766       "340\n",
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2768       "330\n",
2769       "326\n",
2770       "320\n",
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2773       "307\n",
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2777       "288\n",
2778       "284\n",
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2780       "266\n",
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2800       "154\n",
2801       "151\n",
2802       "145\n",
2803       "143\n",
2804       "115\n",
2805       "101\n",
2806       "95\n",
2807       "92\n",
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2809       "85\n",
2810       "79\n",
2811       "75\n",
2812       "72\n",
2813       "68\n",
2814       "65\n",
2815       "63\n",
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2817       "57\n",
2818       "55\n",
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2820       "43\n",
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2822       "39\n",
2823       "38\n",
2824       "29\n",
2825       "28\n",
2826       "24\n",
2827       "22\n",
2828       "20\n",
2829       "14\n",
2830       "10\n",
2831       "9\n",
2832       "8\n",
2833       "6\n",
2834       "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF\n",
2835       "LFFFFRFFRFLRFFFFLFFFRLFFLFLRFRFFFFLFFFRRFLLFFRFFLFFRFFFFFFFFFFFFFRFRFLFFRFFFLFFFLFLFRFFFFFRLFRFFFFFFFFFLFFFFFFLFRLFFFLRLRFFRFLFFRFFFLFFLRFFFRLFLFFFFFRFLRFFFLRLRFFRLRRFFLLRRLFFFLFFFFFLFFLFRFFRLFRFFRFFFFFLFFRLFFLRFRFFFFRFFFFLFLRFFLFRFRFLLFRFFFLRFRFFLLFRFLFRRFLFFLFFFFFRRLFLRFFFFFFFLFRRLFLLRFFFFFFFRLLFFRLFRFFFRFFFFRRLLFFLFFFFFFFFRFFFRFFFLFFLFFFFFFFFFRFFFLFFFFFLFFFFFFFFRLFLRFRFLRFFFFRLLFFRFFFFFFFFFFFFFFFFLFFLRFFLRFFLFRFLRFLRFFFFFRFFFFFLFFLRFFLFRFFRFLFLRFLRFLFRFRRLFLRLFRFFRFFLFLFRFFFFRFFFLFRFLRFFFFLRLFLFRFLLFRFFRFFFFRRLLFLRFFFFFRFFLFFFRFLFLFFFFFRRFLLFRLRLFFLFFFFFFFFRRLFFFFRFFFFFLRFRLFFFLFFFFFFFFFLFFFFFLFFFFRLRFFFFFFFFFFRFFFFFRFFFFLFFFRFFFFFFRLFFRFLFFLFLRFFFLFFRFFLFLRFLFFRRFLRFFRFFLFRLFRLFLFFFFFRLRLFRFFFFFFFLFRFFLFFFFFFRFFFFFFFFLRFLLRFLFFFFFRRLFFFFFFRFFLFLFRFFFFFLRFFLRFRLFFRFFLFRRFFFLFFFRFFFRFLFFFLFFFFFLFFFRRLFFFFFFLFRRLFFFLFFFFFRLRFFLFRFFLRFFFFRFLLFFRFFFFRFRFFFLFLFFFFFFLFFFFLFRLRLLRFFFFFFFFFRRFFFFFLFFFRFFLLFFFFRFFFFLFLRFFRFFFFFFFFFFFFFFFFRRFLRLRLFLFFFRFFFFRLRFLLRRFLFLRFLFFRLFFFFFFLFLFFFFRFFFFRFFFFLFRRFLFFFFRLLFFFFFLFLFFFRFRFRLFLFFFRRLFRFRLFFFLFRFRFLRLFFFFLFRLFFRFLFFFFFFFFFFLLFRLFRFFFRFFFFFFRFRLFFFLFFFFFFFFFFFFFFFFRRFFLFFFLFFFRRLFFRFLFFFLFFFLRFFLRRFLFRLRRFFFLLFFFFFRFRFFFFFFFLFRFFFLFRRFLFFLRFLFFFLFFRLFFFFFFRRLRLFFLRL\n",
2836       "Step(x=0, y=0, dir=<Direction.RIGHT: 2>)\n"
2837      ]
2838     },
2839     {
2840      "data": {
2841       "image/png": 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d+BSY4WMdPnPkyBHOnDkTbDE0Gp+Ij4+v02OWq+1FZGSkz34v6sLrHoaIJACX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\nDI1G4zH/D8E8vVutsQ6KAAAAAElFTkSuQmCC\n",
2842       "text/plain": [
2843        "<matplotlib.figure.Figure at 0x7f10540d85c0>"
2844       ]
2845      },
2846      "metadata": {},
2847      "output_type": "display_data"
2848     }
2849    ],
2850    "source": [
2851     "w_tour = rw\n",
2852     "w_trace = trace_tour(w_tour)\n",
2853     "mks = mistake_positions(w_trace)\n",
2854     "while len(mks) > 3:\n",
2855     "    print(len(mks))\n",
2856     "    w_tour = trim_loop(w_tour)\n",
2857     "    w_trace = trace_tour(w_tour)\n",
2858     "    mks = mistake_positions(w_trace)\n",
2859     "print('{}\\n{}\\n{}'.format(w_tour_start, w_tour, trace_tour(w_tour)[-1]))\n",
2860     "plot_trace(trace_tour(w_tour))"
2861    ]
2862   },
2863   {
2864    "cell_type": "code",
2865    "execution_count": 110,
2866    "metadata": {},
2867    "outputs": [
2868     {
2869      "data": {
2870       "text/plain": [
2871        "[Mistake(i=1219, step=Step(x=0, y=5, dir=<Direction.DOWN: 3>))]"
2872       ]
2873      },
2874      "execution_count": 110,
2875      "metadata": {},
2876      "output_type": "execute_result"
2877     }
2878    ],
2879    "source": [
2880     "mks"
2881    ]
2882   },
2883   {
2884    "cell_type": "code",
2885    "execution_count": 111,
2886    "metadata": {},
2887    "outputs": [
2888     {
2889      "data": {
2890       "text/plain": [
2891        "'LFFFFLLRLFFLRL'"
2892       ]
2893      },
2894      "execution_count": 111,
2895      "metadata": {},
2896      "output_type": "execute_result"
2897     }
2898    ],
2899    "source": [
2900     "trim_loop(w_tour)"
2901    ]
2902   },
2903   {
2904    "cell_type": "code",
2905    "execution_count": 112,
2906    "metadata": {},
2907    "outputs": [
2908     {
2909      "data": {
2910       "image/png": 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mrKXbR44caTx2VFSU0ccsay7I1KlTjca95ZZbgMY3lmAIu8IXQjhPCl8IF5LCF8KFpPCF\ncCEpfCFcSApfCBeSwhfChcKm8PPz8wH497//bRRvre9uQmvNsWPHjOOrq6uBxhZck1bWjIwMAN56\n6y3jfTjFatk17dUP5LiEG6vpaOnSpUbxCxYsACA5Odk21uPxNLdgW/NI/LHmDeTk5NhENgr0uJeX\nf/fWFu1k2vXW1g3Dlt3S0tKA2xcHDx4c8hbKltvTTz9t9Fyd5PP5dHx8fMC5r1q1KtSpB+zIkSMh\n/5139BYI/LTshs0knX79+pGens7f//53266tQ4cOsWnTJqZNm8bRo0dtx964cSP19fVMnjzZ6N07\nJSWFyy67jH379nHq1CkGDx5smw/A8OHDbcd2mlKKXbt28bvf/a757kT+pKSk8OSTTzJp0qQOyC64\nBg0axPr161m4cKHta6agoIAtW7YwcuTI5glh/tTU1ACNa+ufOHGCIUOG+I0/dOgQZ511FldddZXt\nir9er7f55h7Dhw/niiuu8Bufn59PRkYGb775pm3epoxuqNGuHSilnd5HOFBKsXjxYu67775QpyIi\nQGVlJb169eKZZ55h/vz5juxDKYVu5YYaYfMZXwg3saYEh+qeDFL4QriQFL4QLiSFL4QLSeEL4UJS\n+EK4kBS+EC4khR9E1qqvQoQ7Kfwg2Lp1K2DWAy4iQ3FxMR988AGmzWdZWVlkZWUZxWqt+eCDD9qT\nXruFTctuJBs7diwJCQk89NBDoU5F+LF//37OPffcUKfxLSb3bXCCFH4QdO3alYqKCtsebRFaL730\nUvN/J06c6Dd2586d7N69m9tuu81oZebU1FQSEhK46qqrbFfZ1Vrz+uuvc+edd3LxxRebP4Egkl79\nIJFe/fCXnp7OhAkTqKurMyrmSCe9+kJA823W3FD0dqTwhXAhKXwhXEgKXwgXksIXwoWk8IVwISl8\nIVxICj8IvF4v8M0S4UKEu4huNVu3bh1//OMfmT17Nt27d/cb6/P5KCoqYsOGDcyaNct27Pr6ejZt\n2oTWmgkTJviNtdaw//LLL82TFyKEIrZzr6ysjP79+wd93PbIyspi3LhxoU5DtOLDDz9kypQpFBQU\nMGjQoFCn47hO2blnrXu+efNm45t7lJSUsHv3buP4HTt2cOzYMeN4Kfrw9uGHH1JXV8eOHTtCnUrI\nRewZ/9ChQyQmJhpPmxRi+/btXHTRRa55zXTKM74Qou2k8IVwISl8IVxICl8IF5LCF8KF2tXAo5Q6\nAFQAPqBea31lMJISQjirvZ17PiBJa10ejGSEEB2jvZf6KghjtElmZiYAeXl5odi9EBGtvWd8DXyk\nlNLAQq31a0HIycjhw4cB2Lt3LyNHjrSNLysrY/bs2ezZs8c2dv/+/QwZMoS+fftSVVVlFH/zzTez\nf/9+2+aQgoICvF4vU6ZMYfv27UZjAyxfvpw77rjDNj7SffXVV/zkJz/h1KlTfuN8Ph/5+flMmjSJ\n3bt3245rHUfRqF2de0qpgVrrYqVUf2A98KjWeuN3YvTcuXObv09KSiIpKanN+7Tk5+czcuRIfD4f\nSp22Oelbbr75ZlJTU9u939aMGjXK6E3FcsEFFwTcOtrZO868Xm/AS5SPGTOG3Nxc4/jp06ezdOnS\nQFOLCGlpaaSlpTV/P3/+/FY794LWsquUmgtUaq0XfOfnYdGy27VrVzweD5WVlfTo0cNvrDXNNjo6\n2mhsj8cT0MqtgcbPmDGDpUuXdvrCb2hoICYmBjB7k3P6uEc6R1p2lVLdlVI9mr6OB/4PCNvZDzNn\nzgSwLXpoLHjToofAl2sONN7uBg2dhXW2Hz16tFG808e9M2vPZ/wBwHtNn++7AEu01uuCk5YQwklt\nLnytdQEg81CFiEDuuIYUQnyLFL4QLiSFL4QLSeEL4UJS+EK4UMQW/nvvvQfwrU6lzuqtt94C4MSJ\nEyHORHQWEVv4iYmJAPTr188o3m7d/XB25513ApH9HEz179+fs88+O9RpdHoRW/iXXnop0NjzbmL1\n6tUAlJSUOJaTU+Li4oDO33lWV1dHaWkpH3/8cahT6fQitvBNJua01LVrV4CwuwmH+Ib1OxLOi9jC\nD9T48eMB9/S9RzLTXn3RdlIFQriQFL4QLiSFL4QLSeEL4UJS+EK4kBS+EC4UsYVfX18PNK622tmZ\nrPQrRCDCqvA9Hg/Lly+nsrLSNu6JJ54AYMWKFQHtIz09vc35hcrKlSsBWLVqlVG81pr169dTUFBg\nFO/xePjPf/4TUW8wWmvWrl3bvMy6CJDW2tGtcRf2vF6vjo6O1jSu1W+8ff3110bjT506NeCxf//7\n3xuN7bTbbrst4Nyd3BISEvSpU6ccea49e/YMKJeYmBi9Z88eR3KJdE21d9q6DNry2q0xXV47MzOT\nyy+/nJ49e7Jw4ULOPPPMVmOrqqp45513Alpy2mrxffrpp5k9e7bf2Pr6esaMGQOEx1r2I0aMoKCg\ngOeff56pU6faxtfX15OamsrAgQO54oorbONrampYtmwZN998MwMHDvQb++c//5nk5GRHbvBx8uRJ\nEhISAPsbYGitSU5O5rnnniMlJYVp06YFNZfOwN/y2mFzxvf5fBrQkydPNoovLCzUpmNrrfXgwYMD\niqfpjBIOhg8fHja5bN68WQO6rq7OkfEDPe6ATklJcSSXSIefM37YfMa3zsi9evVyZPz4+PiAH2NN\n/RXfsM7ITs4U7OyzEMNB2BS+EKLjSOEL4UJS+EK4kBS+EC4khS+EC0nhC+FCYVP41j3pv/76a6P4\n4uJioLHpw0QkL01tPVfxbdZ8jfz8/BBnEnnac5vsoMrOzgZg48aNPP3005x77rl+463+9UsuuYTH\nH3/cdunp48ePA41FZNed1vIxs2fP5oYbbrCNVUqxbNkyLrvsMs455xzbeK/XyyuvvMKcOXPo1q2b\n39iamhoAdu7cydixY41yj2Qej4eBAwcyatQov3HWa+bZZ59l06ZNfhdSraioICcnhylTpvDf//6X\nBx980HZxT5/PR2FhIZ9//jkzZsywzdvr9ZKenk6XLl247rrrbOOHDRvGhAkTbOMc0VpnT7A2Auzc\nc3KLiYnRDQ0NRvk88cQTjve7BxIfFRVllLfT1q1bp2NjY3VRUZEj4zv9Ggi3bcWKFY4cR+tY6kjp\n3Hvqqaeor6+3fUMpLCwEICMjw/QNiPr6eo4dO2aUz/PPP8+uXbs4fvy40fg+n4/Nmzcb5a61pqSk\nxDj3mTNnhs304/Xr1+PxeNi+fXvQx275se3gwYO2xyU7O5vKyko2b95MQ0OD7e/HuiNRZmam8Ymr\nuLiY/fv3G8fv2LGDEydO2MZt2bIFgFdeeSXox9GI6RNq60aAfdcLFy40ig20V3/OnDkBxYeTmTNn\nhk3uu3fvdjQXcG6ORE5OTtgcR60bn+vKlSsdHV+H+xlfCNFxpPCFcCEpfCFcSApfCBeSwhfChaTw\nhXAhKXwhXChsCt/qpf/000+N4jMyMgD7RRk7g7Vr1wLf9KZ3Vrqp0copmzdvBmhu/nKzsOnVtybn\nrFmzhuHDh/uNPXDgQPPX1157rW2ffsv4SHT22WdTXl5OVVUVffr0Cfr4r7/+Os8++6xtXMvjGBMT\nYxvf0NAAwPnnn091dXVA41udnHZiY2PxeDwAdOni/+Vs5TN06FCioqKIimr9vGfFXnDBBUb3Gzhw\n4ABDhw6lR48enDp1ym+s1+vl0KFDtmM6qrXOnmBtBNAp9etf/9rRvui//OUv7eiDCp0HHnjAsY6z\ngoKCkPeru3W7/PLLdW1trSO/V60jqHPvueeeM35DycvLA8zfuDweD08++WSIn2Hb1NXVOTZ2dHQ0\nANOmTTM6jta6/u+8805A8SaxtbW1zXl5vV6j3ynAm2++aTT+X//6VwC2bt1qetICoLq62ja2oaHB\nKOeWuW/ZssV2hqBTwqrwA2FyqdmeeLcYMmQIAJMnTzaKf/DBBwG46667jOLtLr9balkE/i7DLdbv\nNC4uzmj8G2+8EWicym3CetOymzYNjW+gJjlbQv16jNjCF0K0nRS+EC4khS+EC0nhC+FC7Sp8pdRN\nSqndSqm9SqlfByspIYSz2lz4Sqko4B/AjcBYYLpSanSwEhNCOKc9Z/wrgX1a64Na63pgGWD2b0JC\niJBqT+GfBbTsOyxq+lmHWLFiBWDW2+/z+YzX6weoqqqisrLSOL60tLT5vgBOsBaJLC8vd2wfpgLN\nISUlBTC7r4FJa2xLGzduBL45PnbKysoCGr9TM+00Ok1X053AwhbfzwRePE2cdsKaNWtC3nLZchs4\ncKAuKytz5LlOmzZNA7qurs6R8dvyfL1er9HYU6ZM0Uop7fF4bGO9Xm+H/K5M3X///VopZRwfbvDT\nstueSTpFQGKL788GjpwucN68ec1fJyUlkZSU1I7dNrrllltYtGgRGzZssI394osvqK6uZvLkybYT\nKACWLl3KhAkTGDJkiNGy1osXL6a4uJg1a9Zw3333GeUfCKujLTY2NuhjW2fL+Ph4pk2b5je2sLCQ\nTz75BGicMXjbbbfZjh8bG4vW2qhTreXsw9mzZ/uN1VrzxhtvADBhwgSjiV2fffaZ8dUBwHvvvYfW\nmuPHj3PGGWcYPy5U0tLSSEtLMwtu7R3BbgOigf3AUCAW2AaMOU1cx7y9hRigFy9e7MjYTi6vXVpa\n2jxhxMT777+vAV1aWmoUf9dddwWUOwGelQGdkpJiHB+I/v37a0D7fD5HxncaTkzS0Vp7gUeBdcBO\nYJnWOret44nQ6NevHwBXXHGFUbx1WyvrcU5w4sqmLazbYJlOEY4k7ZqPr7VOBfzf4EwIEXakc08I\nF5LCF8KFpPCFcCEpfCFcSApfCBeSwg8ik5Vk26LlfeMjTVtyD7T9uaamJuB9uJ0UfhBkZmYCsGjR\noqCPXVxczKpVqwCM5htkZmby5ZdfGo9vjW2irq6ONWvWGMcDpKamAmZ98taioiaFr7Xm+eefB8yO\ne21tLW+//bZR5ybA4cOHOXLktI2onUNrnT3B2nBB515dXZ1OSEjQycnJRvH5+fkhn1vQ3q2qqsro\nuf7iF7/QiYmJxt1v3bp1C/lza7mNGjXKKO9whEO9+qJJbGwsFRUVzUtV23n11VcBePnll2373ffu\n3cvjjz/Otm3bjO4As379emJjY7nuuuuMVn392c9+xpo1a+jVqxc7duzwG1tRUcHMmTPJzs4mNTWV\nO+64w3b84uJiCgsLjbrf6urqmi/b7Z6r1pp//etfzJ8/n3/+859MmjTJb/yJEydISUnh7rvvJiEh\nwTaX3NxccnJyePjhh21jI1Jr7wjB2nDBGV/rwHr1t23bpsF8tp2TvfrWjLjbb7/dKD4lJUUDRrPt\ntG5br35cXFxA8U716kc6nOjVF23Xq1cvIDx60q2rgkGDBhnF9+jRA3B2Xfhhw4Y5NrZoJIUvhAtJ\n4QvhQlL4QriQFL4QLiSFL4QLSeEL4UJS+EHQ0NAAwL59+xwZf/v27Y6M2xZW27DpUtg5OTmO5WIt\nzpmXl+fYPjor6dwLgqysLADef/9929VeS0pKWL58OQDJycm2Y2dmZjYX/t133217r/YPPviAwYMH\nM2bMmG/db741y5YtAxo71ezyKSkp4cUXXwTgwgsv5PHHH7e9N/3+/fuBxl5903X6jh49yqxZs2xX\nY7bG3rJli9G4ooXWOnuCteGCzj2fz6evvvrqkPeVh+t2zz33GB/Lxx57LODxc3NzHfztRi78dO5J\n4Xcwn8+nH3jgAQ3otWvX2sZXV1fr7Oxs4/G/+OKL5oIw8cILL2hAX3PNNbaxPp9P/+1vf9OAzsrK\nMs4pULm5ubqiosKx8d3CX+Grxv/vnKY7kTi6j0hTUFDAiBEjcOq4KKWIiYnB4/EYx7/11lvMmDHD\nNvbDDz/klltucSx3ETxKKbTWp50dJX/cE8KFpPCFcCEpfCFcSApfCBeSwhfChaTwhXAhKXwhXEgK\nv5Ox/n3d6mMPtnfffReA9PR0R8YXHUN69UNIKUX37t3p3bu337i4uDi6devGzp07GTx4cEDjm8bP\nnDmTmTNn2q7M6/P5AMjIyOD66683zkWEF+ncCwGfz8dNN93E+vXrjR/Tp08fysvLjWLj4+ONbxwR\n6NgAI0e1vpRAAAACyUlEQVSOZO/evUbLd4vQ8de5J4UfQg0NDXTpYnbRpbXG6/Uaxzc0NBAdHW20\nnj003mnGbqadiCxS+EK4kPTqCyG+RQpfCBeSwhfChaTwhXAhKXwhXEgKP4jS0tJCnUKHcMvzhM77\nXKXwg6izvki+yy3PEzrvc5XCF8KFpPCFcKEO6dxzdAdCiFaFrGVXCBF+5FJfCBeSwhfChTqk8JVS\nc5VSRUqprU3bTR2x346ilLpJKbVbKbVXKfXrUOfjJKXUAaVUtlIqSyn1VajzCSalVLJSqkQpldPi\nZ32UUuuUUnuUUh8ppRJCmWOwdOQZf4HW+tKmLbUD9+sopVQU8A/gRmAsMF0pNTq0WTnKByRprS/R\nWl8Z6mSCbBGNv8eWfgN8rLUeBXwCPNXhWTmgIwvfbEWIyHMlsE9rfVBrXQ8sAyaHOCcnKTrpR0St\n9Ubgu0sRTQbeaPr6DeD2Dk3KIR35C3xEKbVNKfV6Z7lcanIWcKjF90VNP+usNPCRUmqLUurHoU6m\nA5yptS4B0FoXA/1DnE9QBG2xTaXUemBAyx/R+CL5HfBP4A9aa62U+hOwAHggWPsOsdNdyXTmfyO9\nRmtdrJTqD6xXSuU2nSlFBAla4Wutf2AY+hqwOlj7DQNFQGKL788GjoQoF8c1nfXQWpcqpd6j8aNO\nZy78EqXUAK11iVJqIPB1qBMKho76q/7AFt9OBXZ0xH47yBbgHKXUUKVULHAPsCrEOTlCKdVdKdWj\n6et44P/oXL9LaLyCa3kVtwqY3fT1fcD7HZ2QEzpqXf3nlVLjaPyL8AHgoQ7ar+O01l6l1KPAOhrf\nSJO11rkhTsspA4D3mtqwuwBLtNbrQpxT0CillgJJQF+lVCEwF3gO+I9Sag5QCEwLXYbBIy27QrhQ\np/xnGSGEf1L4QriQFL4QLiSFL4QLSeEL4UJS+EK4kBS+EC4khS+EC/0/n19mD39ci/YAAAAASUVO\nRK5CYII=\n",
2911       "text/plain": [
2912        "<matplotlib.figure.Figure at 0x7f1033a4ae10>"
2913       ]
2914      },
2915      "metadata": {},
2916      "output_type": "display_data"
2917     }
2918    ],
2919    "source": [
2920     "lc = trace_tour(square_tour(a=10))\n",
2921     "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
2922     "plot_trace(trace_tour(rw))"
2923    ]
2924   },
2925   {
2926    "cell_type": "code",
2927    "execution_count": 113,
2928    "metadata": {},
2929    "outputs": [
2930     {
2931      "data": {
2932       "text/plain": [
2933        "(326,\n",
2934        " 80,\n",
2935        " 'RFLLRFFLFRFFLFFFRFLFRFFLRLLFLRRFFFFFLFFFFFLFRFRLFLRFFRLLFFLFFFRFFFRFFLFFRLFLRLFF',\n",
2936        " [Step(x=-1, y=0, dir=<Direction.RIGHT: 2>),\n",
2937        "  Step(x=0, y=0, dir=<Direction.RIGHT: 2>)])"
2938       ]
2939      },
2940      "execution_count": 113,
2941      "metadata": {},
2942      "output_type": "execute_result"
2943     },
2944     {
2945      "data": {
2946       "image/png": 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QVFTkbSHka4GALwcUpzRfBUVBQQGAXxf2IeqvoaEBAPD+++97XEn68VVQcCEfOpfYL5Kc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\nRU5ErkJggg==\n",
2947       "text/plain": [
2948        "<matplotlib.figure.Figure at 0x7f10345d82e8>"
2949       ]
2950      },
2951      "metadata": {},
2952      "output_type": "display_data"
2953     }
2954    ],
2955    "source": [
2956     "rw_trimmed = trim_all_loops(rw)\n",
2957     "plot_trace(trace_tour(rw_trimmed))\n",
2958     "len(rw), len(rw_trimmed), rw_trimmed, trace_tour(rw_trimmed)[-2:]"
2959    ]
2960   },
2961   {
2962    "cell_type": "code",
2963    "execution_count": 114,
2964    "metadata": {},
2965    "outputs": [
2966     {
2967      "data": {
2968       "text/plain": [
2969        "(1, Step(x=0, y=0, dir=<Direction.RIGHT: 2>))"
2970       ]
2971      },
2972      "execution_count": 114,
2973      "metadata": {},
2974      "output_type": "execute_result"
2975     },
2976     {
2977      "data": {
2978       "image/png": 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IQAw+kYF8FfyO6+OfPHnS40qI0puvmp6PHj0KAJg1a5altt3S0lLMnz8fr7zyCrv+fOD4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\n",
2979       "text/plain": [
2980        "<matplotlib.figure.Figure at 0x7f1033d95908>"
2981       ]
2982      },
2983      "metadata": {},
2984      "output_type": "display_data"
2985     }
2986    ],
2987    "source": [
2988     "rw_trimmed = rw\n",
2989     "mks = len(mistake_positions(trace_tour(rw_trimmed)))\n",
2990     "while mks >= 4:\n",
2991     "    rw_trimmed = trim_loop(rw_trimmed, random_mistake=True)\n",
2992     "    mks = len(mistake_positions(trace_tour(rw_trimmed)))\n",
2993     "    \n",
2994     "# rw_trimmed = trim_all_loops(rw)\n",
2995     "plot_trace(trace_tour(rw_trimmed))\n",
2996     "mks, trace_tour(rw_trimmed)[-1]"
2997    ]
2998   },
2999   {
3000    "cell_type": "code",
3001    "execution_count": 132,
3002    "metadata": {
3003     "collapsed": true
3004    },
3005    "outputs": [],
3006    "source": [
3007     "def trim_some_mistakes(tour, mistake_limit):\n",
3008     "    trimmed_tour = rw\n",
3009     "    mistake_count = len(mistake_positions(trace_tour(trimmed_tour)))\n",
3010     "    while len(mistake_positions(trace_tour(trimmed_tour))) > mistake_limit:\n",
3011     "        trimmed_tour = trim_loop(trimmed_tour, random_mistake=True)\n",
3012     "    return trimmed_tour"
3013    ]
3014   },
3015   {
3016    "cell_type": "code",
3017    "execution_count": 116,
3018    "metadata": {},
3019    "outputs": [
3020     {
3021      "data": {
3022       "text/plain": [
3023        "(3, Step(x=0, y=0, dir=<Direction.RIGHT: 2>))"
3024       ]
3025      },
3026      "execution_count": 116,
3027      "metadata": {},
3028      "output_type": "execute_result"
3029     },
3030     {
3031      "data": {
3032       "image/png": 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TToq8xsw466yzACgqKkr4b5w9OTVhraqqit27d5Ofn590KZKwKVOm8NlnnzF06FDOOeec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\ni19zoDMAAAAASUVORK5CYII=\n",
3033       "text/plain": [
3034        "<matplotlib.figure.Figure at 0x7f1034745a20>"
3035       ]
3036      },
3037      "metadata": {},
3038      "output_type": "display_data"
3039     }
3040    ],
3041    "source": [
3042     "rw_trimmed = trim_some_mistakes(rw, 4)\n",
3043     "\n",
3044     "plot_trace(trace_tour(rw_trimmed))\n",
3045     "len(mistake_positions(trace_tour(rw_trimmed))), trace_tour(rw_trimmed)[-1]"
3046    ]
3047   },
3048   {
3049    "cell_type": "code",
3050    "execution_count": 117,
3051    "metadata": {
3052     "collapsed": true
3053    },
3054    "outputs": [],
3055    "source": [
3056     "# patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
3057     "# tours_filename = 'tours-with-mistakes.txt'\n",
3058     "\n",
3059     "# try:\n",
3060     "#     os.remove(tours_filename)\n",
3061     "# except OSError:\n",
3062     "#     pass\n",
3063     "\n",
3064     "# success_count = 0\n",
3065     "# while success_count < 100:\n",
3066     "#     lc = trace_tour(random.choice(patterns)())\n",
3067     "#     rw = guided_walk(lc)\n",
3068     "#     if rw:\n",
3069     "#         rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
3070     "#         if len(rw_trimmed) > 10:\n",
3071     "#             with open(tours_filename, 'a') as f:\n",
3072     "#                 f.write(rw_trimmed + '\\n')\n",
3073     "#                 success_count += 1"
3074    ]
3075   },
3076   {
3077    "cell_type": "code",
3078    "execution_count": 138,
3079    "metadata": {},
3080    "outputs": [
3081     {
3082      "data": {
3083       "image/png": 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pbQWEhISQn5/PokWLuP322xk2bBiHDx+mQ4cOHDhwAIAlS5ZgNpspKSmRdvzX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\nA8MAAAAASUVORK5CYII=\n",
3084       "text/plain": [
3085        "<matplotlib.figure.Figure at 0x7f10348f8470>"
3086       ]
3087      },
3088      "metadata": {},
3089      "output_type": "display_data"
3090     }
3091    ],
3092    "source": [
3093     "lc = trace_tour(square_tour())\n",
3094     "rw = guided_walk(lc, seek_step_limit=0, return_anyway=True)\n",
3095     "plot_trace(trace_tour(rw))"
3096    ]
3097   },
3098   {
3099    "cell_type": "code",
3100    "execution_count": 139,
3101    "metadata": {},
3102    "outputs": [
3103     {
3104      "data": {
3105       "image/png": 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3Dzu2nsOsWbMoLy8HYO7cuV201mjsixOrl9laOZSXl5Ofn8+BAwesFkWjCQvD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\nDhqNxi9aOWg0Gr/8f+oSxfuPC6HEAAAAAElFTkSuQmCC\n",
3106       "text/plain": [
3107        "<matplotlib.figure.Figure at 0x7f10341ba780>"
3108       ]
3109      },
3110      "metadata": {},
3111      "output_type": "display_data"
3112     }
3113    ],
3114    "source": [
3115     "rw_trimmed = trim_some_mistakes(rw, 1)\n",
3116     "plot_trace(trace_tour(rw_trimmed))"
3117    ]
3118   },
3119   {
3120    "cell_type": "code",
3121    "execution_count": 140,
3122    "metadata": {},
3123    "outputs": [
3124     {
3125      "data": {
3126       "text/plain": [
3127        "[Mistake(i=702, step=Step(x=-1, y=1, dir=<Direction.RIGHT: 2>))]"
3128       ]
3129      },
3130      "execution_count": 140,
3131      "metadata": {},
3132      "output_type": "execute_result"
3133     }
3134    ],
3135    "source": [
3136     "mistake_positions(trace_tour(rw_trimmed))"
3137    ]
3138   },
3139   {
3140    "cell_type": "code",
3141    "execution_count": 141,
3142    "metadata": {
3143     "collapsed": true
3144    },
3145    "outputs": [],
3146    "source": [
3147     "patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
3148     "tours_filename = 'tours-open.txt'\n",
3149     "\n",
3150     "try:\n",
3151     "    os.remove(tours_filename)\n",
3152     "except OSError:\n",
3153     "    pass\n",
3154     "\n",
3155     "success_count = 0\n",
3156     "while success_count < 100:\n",
3157     "    lc = trace_tour(random.choice(patterns)())\n",
3158     "    rw = guided_walk(lc, seek_step_limit=0, return_anyway=True)\n",
3159     "    if rw:\n",
3160     "        rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
3161     "        if len(rw_trimmed) > 10:\n",
3162     "            with open(tours_filename, 'a') as f:\n",
3163     "                f.write(rw_trimmed + '\\n')\n",
3164     "                success_count += 1"
3165    ]
3166   },
3167   {
3168    "cell_type": "code",
3169    "execution_count": null,
3170    "metadata": {
3171     "collapsed": true
3172    },
3173    "outputs": [],
3174    "source": []
3175   }
3176  ],
3177  "metadata": {
3178   "kernelspec": {
3179    "display_name": "Python 3",
3180    "language": "python",
3181    "name": "python3"
3182   },
3183   "language_info": {
3184    "codemirror_mode": {
3185     "name": "ipython",
3186     "version": 3
3187    },
3188    "file_extension": ".py",
3189    "mimetype": "text/x-python",
3190    "name": "python",
3191    "nbconvert_exporter": "python",
3192    "pygments_lexer": "ipython3",
3193    "version": "3.5.2+"
3194   }
3195  },
3196  "nbformat": 4,
3197  "nbformat_minor": 2
3198 }