06-tour-shapes/tour-shapes-sample-tours.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "markdown",
   5    "metadata": {},
   6    "source": [
   7     "Given a sequence of {F|L|R}, each of which is \"move forward one step\", \"turn left, then move forward one step\", \"turn right, then move forward one step\":\n",
   8     "1. which tours are closed?\n",
   9     "2. what is the area enclosed by the tour?"
  10    ]
  11   },
  12   {
  13    "cell_type": "code",
  14    "execution_count": 1,
  15    "metadata": {
  16     "collapsed": true
  17    },
  18    "outputs": [],
  19    "source": [
  20     "import collections\n",
  21     "import enum\n",
  22     "import random\n",
  23     "import os\n",
  24     "\n",
  25     "import matplotlib.pyplot as plt\n",
  26     "%matplotlib inline\n"
  27    ]
  28   },
  29   {
  30    "cell_type": "code",
  31    "execution_count": 2,
  32    "metadata": {
  33     "collapsed": true
  34    },
  35    "outputs": [],
  36    "source": [
  37     "class Direction(enum.Enum):\n",
  38     "    UP = 1\n",
  39     "    RIGHT = 2\n",
  40     "    DOWN = 3\n",
  41     "    LEFT = 4\n",
  42     "    \n",
  43     "turn_lefts = {Direction.UP: Direction.LEFT, Direction.LEFT: Direction.DOWN,\n",
  44     "              Direction.DOWN: Direction.RIGHT, Direction.RIGHT: Direction.UP}\n",
  45     "\n",
  46     "turn_rights = {Direction.UP: Direction.RIGHT, Direction.RIGHT: Direction.DOWN,\n",
  47     "               Direction.DOWN: Direction.LEFT, Direction.LEFT: Direction.UP}\n",
  48     "\n",
  49     "def turn_left(d):\n",
  50     "    return turn_lefts[d]\n",
  51     "\n",
  52     "def turn_right(d):\n",
  53     "    return turn_rights[d]\n"
  54    ]
  55   },
  56   {
  57    "cell_type": "code",
  58    "execution_count": 3,
  59    "metadata": {
  60     "collapsed": true
  61    },
  62    "outputs": [],
  63    "source": [
  64     "Step = collections.namedtuple('Step', ['x', 'y', 'dir'])\n",
  65     "Mistake = collections.namedtuple('Mistake', ['i', 'step'])"
  66    ]
  67   },
  68   {
  69    "cell_type": "code",
  70    "execution_count": 4,
  71    "metadata": {
  72     "collapsed": true
  73    },
  74    "outputs": [],
  75    "source": [
  76     "def advance(step, d):\n",
  77     "    if d == Direction.UP:\n",
  78     "        return Step(step.x, step.y+1, d)\n",
  79     "    elif d == Direction.DOWN:\n",
  80     "        return Step(step.x, step.y-1, d)\n",
  81     "    elif d == Direction.LEFT:\n",
  82     "        return Step(step.x-1, step.y, d)\n",
  83     "    elif d == Direction.RIGHT:\n",
  84     "        return Step(step.x+1, step.y, d)"
  85    ]
  86   },
  87   {
  88    "cell_type": "code",
  89    "execution_count": 5,
  90    "metadata": {
  91     "collapsed": true
  92    },
  93    "outputs": [],
  94    "source": [
  95     "def step(s, current):\n",
  96     "    if s == 'F':\n",
  97     "        return advance(current, current.dir)\n",
  98     "    elif s == 'L':\n",
  99     "        return advance(current, turn_left(current.dir))\n",
 100     "    elif s == 'R':\n",
 101     "        return advance(current, turn_right(current.dir))\n",
 102     "    else:\n",
 103     "        raise ValueError"
 104    ]
 105   },
 106   {
 107    "cell_type": "code",
 108    "execution_count": 6,
 109    "metadata": {
 110     "collapsed": true
 111    },
 112    "outputs": [],
 113    "source": [
 114     "def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
 115     "    current = Step(startx, starty, startdir)\n",
 116     "    trace = [current]\n",
 117     "    for s in tour:\n",
 118     "        current = step(s, current)\n",
 119     "        trace += [current]\n",
 120     "    return trace    "
 121    ]
 122   },
 123   {
 124    "cell_type": "code",
 125    "execution_count": 7,
 126    "metadata": {
 127     "collapsed": true
 128    },
 129    "outputs": [],
 130    "source": [
 131     "def positions(trace):\n",
 132     "    return [(s.x, s.y) for s in trace]"
 133    ]
 134   },
 135   {
 136    "cell_type": "code",
 137    "execution_count": 8,
 138    "metadata": {
 139     "collapsed": true
 140    },
 141    "outputs": [],
 142    "source": [
 143     "def valid(trace):\n",
 144     "    return (trace[-1].x == 0 \n",
 145     "            and trace[-1].y == 0 \n",
 146     "            and len(set(positions(trace))) + 1 == len(trace))"
 147    ]
 148   },
 149   {
 150    "cell_type": "code",
 151    "execution_count": 9,
 152    "metadata": {
 153     "collapsed": true
 154    },
 155    "outputs": [],
 156    "source": [
 157     "def valid_prefix(tour):\n",
 158     "    current = Step(0, 0, Direction.RIGHT)\n",
 159     "    prefix = []\n",
 160     "    posns = []\n",
 161     "    for s in tour:\n",
 162     "        current = step(s, current)\n",
 163     "        prefix += [s]\n",
 164     "        if (current.x, current.y) in posns:\n",
 165     "            return ''\n",
 166     "        elif current.x == 0 and current.y == 0: \n",
 167     "            return ''.join(prefix)\n",
 168     "        posns += [(current.x, current.y)]\n",
 169     "    if current.x == 0 and current.y == 0:\n",
 170     "        return ''.join(prefix)\n",
 171     "    else:\n",
 172     "        return ''"
 173    ]
 174   },
 175   {
 176    "cell_type": "code",
 177    "execution_count": 10,
 178    "metadata": {
 179     "collapsed": true
 180    },
 181    "outputs": [],
 182    "source": [
 183     "def mistake_positions(trace, debug=False):\n",
 184     "    mistakes = []\n",
 185     "    current = trace[0]\n",
 186     "    posns = [(0, 0)]\n",
 187     "    for i, current in enumerate(trace[1:]):\n",
 188     "        if (current.x, current.y) in posns:\n",
 189     "            if debug: print(i, current)\n",
 190     "            mistakes += [Mistake(i+1, current)]\n",
 191     "        posns += [(current.x, current.y)]\n",
 192     "    if (current.x, current.y) == (0, 0):\n",
 193     "        return mistakes[:-1]\n",
 194     "    else:\n",
 195     "        return mistakes + [Mistake(len(trace)+1, current)]"
 196    ]
 197   },
 198   {
 199    "cell_type": "code",
 200    "execution_count": 11,
 201    "metadata": {
 202     "collapsed": true
 203    },
 204    "outputs": [],
 205    "source": [
 206     "def returns_to_origin(mistake_positions):\n",
 207     "    return [i for i, m in mistake_positions\n",
 208     "           if (m.x, m.y) == (0, 0)]"
 209    ]
 210   },
 211   {
 212    "cell_type": "code",
 213    "execution_count": 12,
 214    "metadata": {
 215     "collapsed": true
 216    },
 217    "outputs": [],
 218    "source": [
 219     "sample_tours = ['FFLRLLFLRL', 'FLLFFLFFFLFFLFLLRRFR', 'FFRLLFRLLFFFRFLLRLLRRLLRLL']"
 220    ]
 221   },
 222   {
 223    "cell_type": "code",
 224    "execution_count": 13,
 225    "metadata": {
 226     "collapsed": true
 227    },
 228    "outputs": [],
 229    "source": [
 230     "def random_walk(steps=1000):\n",
 231     "    return ''.join(random.choice('FFLR') for _ in range(steps))"
 232    ]
 233   },
 234   {
 235    "cell_type": "code",
 236    "execution_count": 14,
 237    "metadata": {
 238     "collapsed": true
 239    },
 240    "outputs": [],
 241    "source": [
 242     "def bounds(trace):\n",
 243     "    return (max(s.x for s in trace),\n",
 244     "            max(s.y for s in trace),\n",
 245     "            min(s.x for s in trace),\n",
 246     "            min(s.y for s in trace))"
 247    ]
 248   },
 249   {
 250    "cell_type": "code",
 251    "execution_count": 15,
 252    "metadata": {
 253     "collapsed": true
 254    },
 255    "outputs": [],
 256    "source": [
 257     "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
 258     "           Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
 259    ]
 260   },
 261   {
 262    "cell_type": "code",
 263    "execution_count": 16,
 264    "metadata": {
 265     "collapsed": true
 266    },
 267    "outputs": [],
 268    "source": [
 269     "def chunks(items, n=2):\n",
 270     "    return [items[i:i+n] for i in range(len(items) - n + 1)]"
 271    ]
 272   },
 273   {
 274    "cell_type": "code",
 275    "execution_count": 17,
 276    "metadata": {
 277     "collapsed": true
 278    },
 279    "outputs": [],
 280    "source": [
 281     "def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None, filename=None, show_axis=False):\n",
 282     "    if show_axis:\n",
 283     "        plt.axis('on')\n",
 284     "    else:\n",
 285     "        plt.axis('off')\n",
 286     "    plt.axes().set_aspect('equal')\n",
 287     "    for s, t in chunks(trace, 2):\n",
 288     "        w, h = plot_wh[t.dir]\n",
 289     "        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",
 290     "    xh, yh, xl, yl = bounds(trace)\n",
 291     "    if xybounds is not None:    \n",
 292     "        bxh, byh, bxl, byl = xybounds\n",
 293     "        plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
 294     "        plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
 295     "    else:\n",
 296     "        plt.xlim([xl-1, xh+1])\n",
 297     "        plt.ylim([yl-1, yh+1])\n",
 298     "    if filename:\n",
 299     "        plt.savefig(filename)"
 300    ]
 301   },
 302   {
 303    "cell_type": "code",
 304    "execution_count": 18,
 305    "metadata": {
 306     "collapsed": true
 307    },
 308    "outputs": [],
 309    "source": [
 310     "def trim_loop(tour, random_mistake=False):\n",
 311     "    trace = trace_tour(tour)\n",
 312     "    mistakes = mistake_positions(trace)\n",
 313     "    if random_mistake:\n",
 314     "        end_mistake_index = random.randrange(len(mistakes))\n",
 315     "    else:\n",
 316     "        end_mistake_index = 0\n",
 317     "#     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",
 318     "    # while this mistake extends to the next step in the trace...\n",
 319     "    while (mistakes[end_mistake_index].i + 1 < len(trace) and \n",
 320     "           end_mistake_index + 1 < len(mistakes) and\n",
 321     "           mistakes[end_mistake_index].i + 1 == \n",
 322     "           mistakes[end_mistake_index + 1].i):\n",
 323     "#         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",
 324     "        # push this mistake finish point later\n",
 325     "        end_mistake_index += 1\n",
 326     "    mistake = mistakes[end_mistake_index]\n",
 327     "    \n",
 328     "    # find the first location that mentions where this mistake ends (which the point where the loop starts)\n",
 329     "    mistake_loop_start = max(i for i, loc in enumerate(trace[:mistake.i])\n",
 330     "                             if (loc.x, loc.y) == (mistake.step.x, mistake.step.y))\n",
 331     "#     print('Dealing with mistake from', mistake_loop_start, 'to', mistake.i, ', trace has len', len(trace))\n",
 332     "    \n",
 333     "    # direction before entering the loop\n",
 334     "    direction_before = trace[mistake_loop_start].dir\n",
 335     "    \n",
 336     "    # find the new instruction to turn from heading before the loop to heading after the loop\n",
 337     "    new_instruction = 'F'\n",
 338     "    if (mistake.i + 1) < len(trace):\n",
 339     "        if turn_left(direction_before) == trace[mistake.i + 1].dir:\n",
 340     "            new_instruction = 'L'\n",
 341     "        if turn_right(direction_before) == trace[mistake.i + 1].dir:\n",
 342     "            new_instruction = 'R'\n",
 343     "#     if (mistake.i + 1) < len(trace):\n",
 344     "#         print('turning from', direction_before, 'to', trace[mistake.i + 1].dir, 'with', new_instruction )\n",
 345     "#     else:\n",
 346     "#         print('turning from', direction_before, 'to BEYOND END', 'with', new_instruction )\n",
 347     "    return tour[:mistake_loop_start] + new_instruction + tour[mistake.i+1:]\n",
 348     "#     return mistake, mistake_loop_start, trace[mistake_loop_start-2:mistake_loop_start+8]"
 349    ]
 350   },
 351   {
 352    "cell_type": "code",
 353    "execution_count": 19,
 354    "metadata": {
 355     "collapsed": true
 356    },
 357    "outputs": [],
 358    "source": [
 359     "def trim_all_loops(tour, mistake_reduction_attempt_limit=10):\n",
 360     "    trace = trace_tour(tour)\n",
 361     "    mistake_limit = 1\n",
 362     "    if trace[-1].x == 0 and trace[-1].y == 0:\n",
 363     "        mistake_limit = 0\n",
 364     "    mistakes = mistake_positions(trace)\n",
 365     "    \n",
 366     "    old_mistake_count = len(mistakes)\n",
 367     "    mistake_reduction_tries = 0\n",
 368     "    \n",
 369     "    while len(mistakes) > mistake_limit and mistake_reduction_tries < mistake_reduction_attempt_limit:\n",
 370     "        tour = trim_loop(tour)\n",
 371     "        trace = trace_tour(tour)\n",
 372     "        mistakes = mistake_positions(trace)\n",
 373     "        if len(mistakes) < old_mistake_count:\n",
 374     "            old_mistake_count = len(mistakes)\n",
 375     "            mistake_reduction_tries = 0\n",
 376     "        else:\n",
 377     "            mistake_reduction_tries += 1\n",
 378     "    if mistake_reduction_tries >= mistake_reduction_attempt_limit:\n",
 379     "        return ''\n",
 380     "    else:\n",
 381     "        return tour"
 382    ]
 383   },
 384   {
 385    "cell_type": "code",
 386    "execution_count": 20,
 387    "metadata": {
 388     "collapsed": true
 389    },
 390    "outputs": [],
 391    "source": [
 392     "def reverse_tour(tour):\n",
 393     "    def swap(tour_step):\n",
 394     "        if tour_step == 'R':\n",
 395     "            return 'L'\n",
 396     "        elif tour_step == 'L':\n",
 397     "            return 'R'\n",
 398     "        else:\n",
 399     "            return tour_step\n",
 400     "        \n",
 401     "    return ''.join(swap(s) for s in reversed(tour))"
 402    ]
 403   },
 404   {
 405    "cell_type": "code",
 406    "execution_count": 21,
 407    "metadata": {
 408     "collapsed": true
 409    },
 410    "outputs": [],
 411    "source": [
 412     "def wander_near(locus, current, limit=10):\n",
 413     "    valid_proposal = False\n",
 414     "    while not valid_proposal:\n",
 415     "        s = random.choice('FFFRL')\n",
 416     "        if s == 'F':\n",
 417     "            proposed = advance(current, current.dir)\n",
 418     "        elif s == 'L':\n",
 419     "            proposed = advance(current, turn_left(current.dir))\n",
 420     "        elif s == 'R':\n",
 421     "            proposed = advance(current, turn_right(current.dir))\n",
 422     "        if abs(proposed.x - locus.x) < limit and abs(proposed.y - locus.y) < limit:\n",
 423     "            valid_proposal = True\n",
 424     "#     print('At {} going to {} by step {} to {}'.format(current, locus, s, proposed))\n",
 425     "    return s, proposed"
 426    ]
 427   },
 428   {
 429    "cell_type": "code",
 430    "execution_count": 22,
 431    "metadata": {
 432     "collapsed": true
 433    },
 434    "outputs": [],
 435    "source": [
 436     "def seek(goal, current):\n",
 437     "    dx = current.x - goal.x\n",
 438     "    dy = current.y - goal.y\n",
 439     "\n",
 440     "    if dx < 0 and abs(dx) > abs(dy): # to the left\n",
 441     "        side = 'left'\n",
 442     "        if current.dir == Direction.RIGHT:\n",
 443     "            s = 'F'\n",
 444     "        elif current.dir == Direction.UP:\n",
 445     "            s = 'R'\n",
 446     "        else:\n",
 447     "            s = 'L'\n",
 448     "    elif dx > 0 and abs(dx) > abs(dy): # to the right\n",
 449     "        side = 'right'\n",
 450     "        if current.dir == Direction.LEFT:\n",
 451     "            s = 'F'\n",
 452     "        elif current.dir == Direction.UP:\n",
 453     "            s = 'L'\n",
 454     "        else:\n",
 455     "            s = 'R'\n",
 456     "    elif dy > 0 and abs(dx) <= abs(dy): # above\n",
 457     "        side = 'above'\n",
 458     "        if current.dir == Direction.DOWN:\n",
 459     "            s = 'F'\n",
 460     "        elif current.dir == Direction.RIGHT:\n",
 461     "            s = 'R'\n",
 462     "        else:\n",
 463     "            s = 'L'\n",
 464     "    else: # below\n",
 465     "        side = 'below'\n",
 466     "        if current.dir == Direction.UP:\n",
 467     "            s = 'F'\n",
 468     "        elif current.dir == Direction.LEFT:\n",
 469     "            s = 'R'\n",
 470     "        else:\n",
 471     "            s = 'L'\n",
 472     "    if s == 'F':\n",
 473     "        proposed = advance(current, current.dir)\n",
 474     "    elif s == 'L':\n",
 475     "        proposed = advance(current, turn_left(current.dir))\n",
 476     "    elif s == 'R':\n",
 477     "        proposed = advance(current, turn_right(current.dir))\n",
 478     "        \n",
 479     "#     print('At {} going to {}, currently {},  by step {} to {}'.format(current, goal, side, s, proposed))\n",
 480     "\n",
 481     "    return s, proposed"
 482    ]
 483   },
 484   {
 485    "cell_type": "code",
 486    "execution_count": 24,
 487    "metadata": {
 488     "collapsed": true
 489    },
 490    "outputs": [],
 491    "source": [
 492     "def guided_walk(loci, locus_limit=5, wander_limit=10, seek_step_limit=20, return_anyway=False):\n",
 493     "    trail = ''\n",
 494     "    current = Step(0, 0, Direction.RIGHT)    \n",
 495     "    l = 0\n",
 496     "    finished = False\n",
 497     "    while not finished:\n",
 498     "        if abs(current.x - loci[l].x) < locus_limit and abs(current.y - loci[l].y) < locus_limit:\n",
 499     "            l += 1\n",
 500     "            if l == len(loci) - 1:\n",
 501     "                finished = True\n",
 502     "        s, proposed = wander_near(loci[l], current, limit=wander_limit)\n",
 503     "        trail += s\n",
 504     "        current = proposed\n",
 505     "#     print('!! Finished loci')\n",
 506     "    seek_steps = 0\n",
 507     "    while not (current.x == loci[l].x and current.y == loci[l].y) and seek_steps < seek_step_limit:\n",
 508     "#         error = max(abs(current.x - loci[l].x), abs(current.y - loci[l].y))\n",
 509     "#         s, proposed = wander_near(loci[l], current, limit=error+1)\n",
 510     "        s, proposed = seek(loci[l], current)\n",
 511     "        trail += s\n",
 512     "        current = proposed\n",
 513     "        seek_steps += 1\n",
 514     "    if seek_steps >= seek_step_limit and not return_anyway:\n",
 515     "        return ''\n",
 516     "    else:\n",
 517     "        return trail"
 518    ]
 519   },
 520   {
 521    "cell_type": "code",
 522    "execution_count": 23,
 523    "metadata": {},
 524    "outputs": [
 525     {
 526      "data": {
 527       "image/png": "iVBORw0KGgoAAAANSUhEUgAAANgAAAEACAYAAADROrgbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
 528       "text/plain": [
 529        "<matplotlib.figure.Figure at 0x7fcb73ad0978>"
 530       ]
 531      },
 532      "metadata": {},
 533      "output_type": "display_data"
 534     }
 535    ],
 536    "source": [
 537     "plot_trace(trace_tour('LFFRLFFFFRLRRFFFFRFFRLFRRRFRFFLLRLRLRL'))"
 538    ]
 539   },
 540   {
 541    "cell_type": "code",
 542    "execution_count": 25,
 543    "metadata": {},
 544    "outputs": [
 545     {
 546      "data": {
 547       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAD7CAYAAABqkiE2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJ7EMO+IfAAAAAElFTkSuQmCC\n",
 548       "text/plain": [
 549        "<matplotlib.figure.Figure at 0x7fdea71b8cc0>"
 550       ]
 551      },
 552      "metadata": {},
 553      "output_type": "display_data"
 554     }
 555    ],
 556    "source": [
 557     "def square_tour(a=80):\n",
 558     "    \"a is width of square\"\n",
 559     "    return ('F' * a + 'L') * 4\n",
 560     "\n",
 561     "plot_trace(trace_tour(square_tour()))"
 562    ]
 563   },
 564   {
 565    "cell_type": "code",
 566    "execution_count": 26,
 567    "metadata": {},
 568    "outputs": [
 569     {
 570      "data": {
 571       "image/png": 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t38g6ESeYLYRY/hX4EfDHHFXHt4BzEz8hXWSXSZOprHTbHpAulEOOakMbfH059NFFNumb\n9hsdb9JD0sUG6WJcJl3UF7ttT0nJ5Bnp4p98zWj/yfdrORrd+YfEuklKaHD09x/VDv4ezcwWgqQx\nnzJIGjMhSBozIUgaMyFIGjMhSBozIUgaMyFIGjMhSBozIUgaMyFIGjMhSBozIUgaMyFIGjMhSBoz\nIUgaMyFIGjMhSBozIUgaMyFIGjMhSBozIUga+39B5c93LYMfSQAAAABJRU5ErkJggg==\n",
 572       "text/plain": [
 573        "<matplotlib.figure.Figure at 0x7fdea71dde10>"
 574       ]
 575      },
 576      "metadata": {},
 577      "output_type": "display_data"
 578     }
 579    ],
 580    "source": [
 581     "def cross_tour(a=50, b=40):\n",
 582     "    \"a is width of cross arm, b is length of cross arm\"\n",
 583     "    return ('F' *  a + 'L' + 'F' * b + 'R' + 'F' * b + 'L') * 4\n",
 584     "\n",
 585     "plot_trace(trace_tour(cross_tour()))"
 586    ]
 587   },
 588   {
 589    "cell_type": "code",
 590    "execution_count": 27,
 591    "metadata": {},
 592    "outputs": [
 593     {
 594      "data": {
 595       "image/png": 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nEvOQAd2izoOgzsuuu3sOPO27E4k5xfLxGrmnwHbfnUjM49gCjhi07DaBT/vuRGKuYfn4\nQUtp+wzVVZz5WBUtH5/SjuepRJ3rpLsDwrRoTVg+fuBcJ90dYfKxKlo+PqURg7UH6lwn3T3A0m5V\nt4C7bQukFBhS6ksqXCfdXcPp9lUbhDxDo5ROJfx0rDPH0J3l4+teYfn4QTPH0N0bLB9fZfn4gTMw\ndPch5hiqLB8/cAbL7lLax1NxA8vHa+S2McdQdUgo79YopWjqsLnOEUN3K6T1AZiCQyL3lUgpMDhi\nqPNrtu7uA5/03YnE3GdAU6ItH19nsOzuHa7HqkGVj/c7+zpPr7rbxlvUVe0xoKsrPZ/WRbiG5eOr\njgnXkDRKKTCozu3T3V0sH181qPLxKZ3WpMLy8d0dE7nEeIQyIsdbSgejB0FdSoF7qCwfX7dD5NhP\naccz0aaLsEEYOmsiJ5LTSykwqM5g2d0NTD5WPSJy/UhKpxKbWZatEL62LCPaKuE76Kz498uEU47y\ngMmmll3h/UhYtlW+9tLU801tvy2ey6b+nQtoe2Xq+ayhbfAr3Hk4Ap5lWfaQ5vXdtm1XeX+fnN4H\nc8K2L5+fbqtt2/6xbTP1+mzq75z395v8jLan98mcyKl7SoHhD313IEHec7G73wJ/CvzUd0cS829t\nT2Z57vQBSe8zxyCpxsAgqcbAIKnGwCCpxsAgqcbAIKnGwCCpxsAgqcbAIKnGwCCpxsAgqcbAIKnG\nwCCpxsAgqcbAIKnGwCCpxsAgqcbAIKnGwCCpxsAgqcbAIKnm/wGyPjyrfbBoQAAAAABJRU5ErkJg\ngg==\n",
 596       "text/plain": [
 597        "<matplotlib.figure.Figure at 0x7fdea6f8a160>"
 598       ]
 599      },
 600      "metadata": {},
 601      "output_type": "display_data"
 602     }
 603    ],
 604    "source": [
 605     "def quincunx_tour(a=60, b=30, c=50):\n",
 606     "    \"a is length of indent, b is indent/outdent distance, c is outdent outer length\"\n",
 607     "    return ('F' * a + 'R' + 'F' * b + 'L' + 'F' * c + 'L' + 'F' * c + 'L' + 'F' * b + 'R') * 4\n",
 608     "plot_trace(trace_tour(quincunx_tour()))"
 609    ]
 610   },
 611   {
 612    "cell_type": "code",
 613    "execution_count": 28,
 614    "metadata": {},
 615    "outputs": [
 616     {
 617      "data": {
 618       "image/png": 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qgIj4Ual4zGwwM127PV1tukZJRFzdU+DZpGhAZjYTZ+XjeaRJElqWKCewIF8I/nrpQMxs\ncpK27CncXFfZvtt06t1N0tbALsCZwEtGfY3DzGZG0l6k5HgI8AxwdUSsrmTfbU2UHZIWAdsBS4BL\nI+KPCodkZl3yDcH+BdgWmFtiUONEmZr/fhvYFMAjS7N66SncfC8i3lx5DG1PlB2SZpFuLbFRfupJ\nrw03K0fSHGA2sAJYHhHFiq9tL+Z064wkV+R/ny4Yi1mr5aa7z5CORYCiBVePKCeQh/p3RMQupWMx\na6t8HG4D/BJSU8lSsXhE+cJ2dvNfs2rlprtPdl2XXB1ZybicKCe2H3AlsAg3/zWr0meADYCfAl+J\niEcKxwP41HtSko4gVcSPAp6KiO8WDslsLEnalnR3gpOAXeo2+6Qt3YMGdUvengUg6T0RcXrBeMzG\n1YNdH5/7gl9ViE+9JxERd/WsDX9V0YDMxtuf5OPtiNKB9HKinJ7j3fzXbDgk7dGzdvuXRQOahE+9\np+6lwJ8Av4+b/5oNw+F5ezKwLCJqOwBxMWeaJJ0OvBv4KrAoIj5SOCSzRpG0M/ARYA/g1XUr3EzE\niXKaJO0P/LDrqb0jorJ2T2ZN17N2++KIqP0UPF+jnKaI+FFPgWfDogGZNdN38nFU+yQJTpTDcEW+\nIH1m6UDM6krSvJ7CzdVFA5omn3rPgKQtgJ2A84DNm3CtxawESbuR5iX/LvAscGNVTXeHwYlyCCQ9\nAmxB6nSyICLeVTgks1rITXf/Fdge2KCpgwknyiGQ9FrgP4HNwM1/zTp6CjcLIqKRU+ucKIdI0kbA\nctLoMkg3ZPcP2FpH0gakQucS4LmImF04pBlxMWe4VubtEuBR4JMFYzErIjfdfZJ0HAD8R8FwhsIj\nyhHJpxw3RsSepWMxq1r++98RuA/KNt0dBo8oR6uzltXNf23sSTpQ0jNd1yVX1aHp7jB4rffo7AN8\nCpiPm/9aO5wMzAGuBW6OiAcKxzM0PvUeMUlHkW6MdAzpzo7fLByS2VBJ2g74PeB44JXjOOvDI8rR\n+0nefgVA0uyI+GrBeMyGbVHXx+cVi2KEfI1yxCLiZz1rw3cuGpDZaByX/87fWjqQUXCirN5Hc4HH\n99+xxpK0e8/a7Qcn/YaG86l3tV4KHA28k9QA2KypXp+3HwUej4hvlwxm1FzMKUDSt4AjgbOB+yLi\n/xQOyWxKJL2SlBx3BV41joWbiThRFiDpQGBh11N7RMRNpeIxm6omNt0dBp96FxARPwAEa/7w1i8b\nkdm0XBQRbyodRJVczKmHq/OF8TNKB2LWS9LcnsLNDyf9hjHkU+/CJG0GbEc6Fd+kLdd8rDkk7Qjc\nTboZ2ErgjiY13R0GJ8qakPRrYBNgFel+IkcWDslaLl9LPx3YAVinzW/iTpQ1kZv/ngVsBW7+a+VJ\nehbo9JE8PyJaO6XNibJm8n14HiE101gFPDwO3VesOSRtDMwF7gVm+U3bxZw6eiJvHwAeAj5WMBZr\np8dJf3+zSKferecRZY3lKuOVEbF/6VisPfLf3W7A7dD8prvD4BFl/e3n5r82arnp7squKUArx6Xp\n7jB4wnm9/Q7wd6SW+q1YAWHFnEjKB/9Fmv7z87Lh1ItPvRtA0h+T7o38fuCJiGj8zZqsHiRtDxwO\n/CktWrs9XR5RNsM1efvPAJKedqd0G5Lu2zWcXyyKmvM1ygaIiFt7mv++rGhANm5OyH9frZ0n2Y8T\nZTN93M1/bVCSdu1Zu31fyXiawKfezbMD8A7Szco8ArBBHJS3fwGsiIhvlQymCVzMaShJFwBvARYA\nd0XEnxcOyWpO0qtJCxheDuzqws3UOVE2VG5Y8H1yX0tgl4i4o2BIVnM9TXcviYg3FAumYXzq3VC5\n+e86sOYAmFM2ImuIhRFxcOkgmsbFnPFxU75A/5XSgVh9SNqwp3CzcNJvsAn51HsMSJoLbAn8FJjj\na0/WIWkbYDHwCuA50s3sWtV0dxg8ohwDEbEsIu4EAtKpuKSxvn2oTS6v3V5ESpJExJ0RcY+T5GCc\nKMfLm3j+RvRHlAzEiruQdIsRAM+3nSGfeo+hvH73AXy61Tpdl2FuADb0ZZjh8IhyPC3L25+Rbgr1\n0YKxWLWWkn7vGwJnFo5lbHh60BiKiOWsfd9wTwdpl70i4vrSQYwTjyjb4RA3/x1fkg6QtKprCtAz\nRQMaQx5Rjr89gb8B/gdu/juujicNehYAd0fELYXjGTsu5rSEpA8CXyA1QlgeEV8uHJLNUC7aHQm8\nG9jDhZvR8YiyPTorMk4BkPRYRJxTMB6bue6muxcUi6IFfI2yJSLi5p7mvzsUDciG5aT8ez28dCDj\nzImyvU7JBZ7vlA7Epk7SK3rWbvsmYBXwqXc77QAcBnwAeFvhWGx69snbzo3mvl4ymLZwMafFJF0G\nHEK6ReltEfGBshHZC5H028DJwG8Br3DhplpOlC0m6SDgcmBWfmrHiLi3YEj2Anqa7l4cEZ7qVSGf\nerdYRCwk/w3kA3FdScqf8zto/VwXEXuXDqKNXMyxbncCqwHPsawBSev3FG4uKxpQi/nU2wCQtDEw\nlzw3z9fAysudgJYC84FVwMMe6ZfhEaUBqZFGRCxi7ea/7mNYQG66+zApSRIRiyJisZNkOU6U1ut1\nwH2kEYzvG17Gd4CtSb8Dd6qvAZ9624QkvQK4A9gDWAnc4ea/oyVpM1JX8suBeb78UR8eUdoLWZK3\nNwK3Ah8uGEtbPEr6ec8DvlY4Fuvi6UE2oYh4jLWb/+5fNqLWOCAiflQ6CFubR5Q2VYflAs+C0oGM\nE0n790wBeqpoQDYhjyhtKl4NnAi8Enhz4VjGTWfZ6NnAooi4oWQwNjEXc2zKJJ0AfIp0s7JfR8QX\nC4fUWJLmA/+L1HjXTXdrzonSpkzSnqTboHa8NSLOKxVPk/Ws3V4QEYcVC8b68jVKm7KI+ElP899t\niwbUfH+ff55OkjXnRGkz8f9yIcKToqdA0st6Cjd3FA3IpszFHBvUfOD1pPmVRxSOpSn2yNtjgKci\n4hslg7Gp8zVKmxFJVwH7AtcCN0bE+wqHVDuSfodUBJsP7OTCTfM4UdqMSDoYuASYnZ/aNiIWFwyp\ndnoKN5dGxKHFgrGBOFHa0OSEMB94ENz8tyP/XG6JiFeVjsUG42KODUWnMzqpn+Vq4EsFwylO0uye\nws1FRQOyGfGI0oZG0gbAhqSGGk9HxAaFQypG0nrA08AWpB6fj3mE3VweUdrQRMRTEfFofti5jUGr\nJqRLOkjSElKSJCIejYhfOUk2mxOljcLBwM9JDR4OLxxL1c4CNgdWAN8qHIsNiU+9bWQk7U7qr/i7\nwLOk6UNj2fxX0hbATqSO5Ft7CtB48YRzG6XONKGr8vb/Ap8pFMuoPdL1sSeSjxknShuZiFjC2s1/\n9ykb0ci9ISIuKR2EDZ+vUVqVjhyn5r+S9u2ZArSiaEA2Mh5RWlV2BT5CWu88Ls1/j83brwIPRsRV\nk32xNZeLOVYpSX8DnAScDCyNiFPKRjR9uenuscBhwJ4u3Iw/J0qrlKTXANd3PfWWiLiwVDyDcNPd\n9vE1SqtURNzQ0/x3y6IBDe5zbrrbHk6UVtq/54LI2aUDmYyk3+op3Py0aEBWKRdzrKTtSfcL/zvg\nDwrH0s+ueXsUacVRq5Zmtp2vUVpxkn5CqobfAlwbEe8tHNIakvYlTZLfHpjvwk07OVFacZJeC1wI\nrJ+f2iwiHisX0fN6CjeXRMQbigVjxThRWq3kxLQ58BiUb/6b47k7Il5WMg4ry8Ucq42u5r+Pkpr/\nnloojlk9hZvzS8Rh9eERpdWKpDmk+++sIE1In1cojgA2JjXdfbL0yNbK8ojSaiUino2IJ/LDF+eR\n3QVV7FvSwZKWdo0kn4yIJ5wkzYnS6uog4FZgGfCWivb578Bc0q0svj6uvTNt+nzqbbWWp+dcBRzS\n86kgtXDrbFcBc/J2NWkQsApYD3iu67mJXqPzudOB7T0FyHp5wrnV3QN5e3lF+/PtG+w3eERpZtaH\nr1GamfXhRGlm1ocTpZlZH06UZmZ9OFGamfXhRGlm1ocTpZlZH06UZmZ9OFGamfXhRGlm1ocTpZlZ\nH06UZmZ9OFGamfXhRGlm1ocTpZlZH06UZmZ9OFGamfXhRGlm1ocTpZlZH06UZmZ9OFGamfXhRGlm\n1sd/Aw+RJa+eq45oAAAAAElFTkSuQmCC\n",
 619       "text/plain": [
 620        "<matplotlib.figure.Figure at 0x7fdea6d354e0>"
 621       ]
 622      },
 623      "metadata": {},
 624      "output_type": "display_data"
 625     }
 626    ],
 627    "source": [
 628     "heart_points = [Step(60, 50, Direction.UP), Step(50, 90, Direction.UP),\n",
 629     "                Step(20, 70, Direction.UP), \n",
 630     "                Step(-40, 90, Direction.UP), Step(-60, 80, Direction.UP), \n",
 631     "                Step(0, 0, Direction.RIGHT)]\n",
 632     "\n",
 633     "heart_tour = ''\n",
 634     "current = Step(0, 0, Direction.RIGHT)\n",
 635     "\n",
 636     "for hp in heart_points:\n",
 637     "    while not (current.x == hp.x and current.y == hp.y):\n",
 638     "        s, proposed = seek(hp, current)\n",
 639     "        heart_tour += s\n",
 640     "        current = proposed\n",
 641     "\n",
 642     "plot_trace(trace_tour(heart_tour))\n",
 643     "\n",
 644     "def heart_tour_func(): return heart_tour"
 645    ]
 646   },
 647   {
 648    "cell_type": "code",
 649    "execution_count": 29,
 650    "metadata": {
 651     "collapsed": true
 652    },
 653    "outputs": [],
 654    "source": [
 655     "def trim_some_mistakes(tour, mistake_limit):\n",
 656     "    trimmed_tour = rw\n",
 657     "    mistake_count = len(mistake_positions(trace_tour(trimmed_tour)))\n",
 658     "    while len(mistake_positions(trace_tour(trimmed_tour))) > mistake_limit:\n",
 659     "        trimmed_tour = trim_loop(trimmed_tour, random_mistake=True)\n",
 660     "    return trimmed_tour"
 661    ]
 662   },
 663   {
 664    "cell_type": "code",
 665    "execution_count": 68,
 666    "metadata": {},
 667    "outputs": [
 668     {
 669      "data": {
 670       "text/plain": [
 671        "10"
 672       ]
 673      },
 674      "execution_count": 68,
 675      "metadata": {},
 676      "output_type": "execute_result"
 677     },
 678     {
 679      "data": {
 680       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUQAAAEACAYAAADLIw+8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJogA7b/FLob4OhrHyQAAAABJRU5ErkJggg==\n",
 681       "text/plain": [
 682        "<matplotlib.figure.Figure at 0x7fdea6b5b1d0>"
 683       ]
 684      },
 685      "metadata": {},
 686      "output_type": "display_data"
 687     }
 688    ],
 689    "source": [
 690     "plot_trace(trace_tour(sample_tours[0]))\n",
 691     "len(sample_tours[0])"
 692    ]
 693   },
 694   {
 695    "cell_type": "code",
 696    "execution_count": 31,
 697    "metadata": {},
 698    "outputs": [
 699     {
 700      "data": {
 701       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN4AAAEACAYAAADcJMhcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
 702       "text/plain": [
 703        "<matplotlib.figure.Figure at 0x7fdea6ff01d0>"
 704       ]
 705      },
 706      "metadata": {},
 707      "output_type": "display_data"
 708     }
 709    ],
 710    "source": [
 711     "plot_trace(trace_tour(sample_tours[1]))"
 712    ]
 713   },
 714   {
 715    "cell_type": "code",
 716    "execution_count": 32,
 717    "metadata": {},
 718    "outputs": [
 719     {
 720      "data": {
 721       "image/png": "iVBORw0KGgoAAAANSUhEUgAAASMAAAEACAYAAAD4GBC1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
 722       "text/plain": [
 723        "<matplotlib.figure.Figure at 0x7fdea700c4e0>"
 724       ]
 725      },
 726      "metadata": {},
 727      "output_type": "display_data"
 728     }
 729    ],
 730    "source": [
 731     "plot_trace(trace_tour(sample_tours[2]))"
 732    ]
 733   },
 734   {
 735    "cell_type": "code",
 736    "execution_count": 40,
 737    "metadata": {},
 738    "outputs": [
 739     {
 740      "data": {
 741       "text/plain": [
 742        "['FLRFRFFFRFFFRFFR',\n",
 743        " 'FFFRFRFRLR',\n",
 744        " 'FFFFRFRFRLFR',\n",
 745        " 'FFFLFFLFFLFF',\n",
 746        " 'FFRRFLRRFR',\n",
 747        " 'RLRFFRFRFFFR',\n",
 748        " 'LFRFLLFFFLFFLF',\n",
 749        " 'RLFFLFLFLR',\n",
 750        " 'RFFFLLRFFFLLRRLLFFFF',\n",
 751        " 'FLFFLFFLFLRL']"
 752       ]
 753      },
 754      "execution_count": 40,
 755      "metadata": {},
 756      "output_type": "execute_result"
 757     }
 758    ],
 759    "source": [
 760     "samples = []\n",
 761     "while len(samples) < 10:\n",
 762     "    t = valid_prefix(random_walk())\n",
 763     "    if len(t) > 8 and len(t) < 25:\n",
 764     "        samples += [t]\n",
 765     "samples"
 766    ]
 767   },
 768   {
 769    "cell_type": "code",
 770    "execution_count": 43,
 771    "metadata": {},
 772    "outputs": [
 773     {
 774      "data": {
 775       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEACAYAAACwB81wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAACaRJREFUeJzt2m2o5nldx/HPd/Zu1t1ctS1voRS8CVSIiu7YjEx9YndE\nQvnAniQEoQibwYBi1gqyLII9CKIHkVAUm6gkK4hsbA90AxFiRZJYEnNrc8V2mN2Zmt3z7cF1DTMt\naTtnrjm/M9f39YJhz3XYgc+fOefN7/zOVd0dAPbfidUDADgagg8whOADDCH4AEMIPsAQgg8whOAD\nDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8w\nhOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQ\ngg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMI\nPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4XLaq+lhV/UFVPW/1ll2r\nqlur6rNV9c6qunH1nl2rqldV1f1V9daqqtV7dq2q3lJVn6mqH1m95TgSfA7jF5PcmeRf9zD8tyV5\nQ5J7snm+fQv/a5L8ZJK/TPKVPQz/TyV5S5IHqupzwv+/VXev3jBGVb0iyfNX79iBzye5Yfvx2SQH\nST6S5NNJzq8atSMvSvI3SW7avj6TzTO+P8mXkjy1aNeu/HySU0meu319Jsk3krwvycOrRu3Qe5K8\nfftxZ/Nv94Ukp7r7wWWrjgnBPyJV9YYkf7d6B4fSSfbpFPxMB9v/7utP/AfZPNuLu/vfV49ZaV//\ngY+jDyd5OskHuruu5T9JTl/yXGeS/FOSX0hyYvW2HTzby5I8uX22CyfE+5P86OptO3q+X0ry+Pb5\nzic5l+RjSV6xetuOnu+Dl3xtnk3yRJIPbV8/N8MJ/hGoqjuSvDbJdUnurKp9+MI7m03ofz3JD3X3\n33bvzY+LN2UT/fuT3NHdb+zuLy7etEvPySb0f5HkNd39m939tcWbdunpbEJ/T5KXdff7Fu85Nq5f\nPWCIu5Pcsv34umzuGX9/3ZwrduG+99N7FPkLHktyV5JP7VnkL3gwm6/HP9mzyF9wbza/Z/mj7v7P\n1WOOm9q/79fjZXu6vy8Xg59srkFe2t2n/++/BexSVXWSV3f3V1dvWcmVztX3h9n8CH3hF2MHSW5O\n8tvLFgEjudK5+u5K8mNJXp/kbdm8vS9JPrFsETCSK50jUlU/m+T+7TsJgCPkSmfDlQ7AEIIPMITg\nAwwh+ABDCD7AEIIPMITgAwwh+ABDCD7AEIIPMITgAwwh+ABDCD7AEIIPMITgAwwh+ABDCD7AEIIP\nMITgAwwh+ABDCD7AEIIPMITgAwwh+ABDCD7AEIIPMITgAwwh+ABDCD7AEIIPMITgAwwh+ABDCD7A\nEIIPMITgAwwh+ABDCD7AEIIPMITgAwwh+ABDCD7AEIIPMITgA3upqt5TVY9V1WPbT31x+/qPlw5b\n6PrVAwCukm8keU6Sm7evb01yQ5JHly1azAl/saqq1Ruupn1/Po61e5P8xzM+dz7JRxZsORYEf5Gq\nOllV707yzar6tdV7dq2qbq+qu5M8VlWvXb2Hebr7IMl7k5zZfupsknu6+/F1q9YS/CN2SegfSXJX\nkucl+YG1q3bnktB/LcnvJLkpyfetXcVg9yb51vbjpzP4dJ+4w1/hkSQ3Jrll+/qpJHdW1avWTdqp\nt2dzkDi5fX02yV1V9dC6STvxZJL3d/fp1UN49rr7oKrem+SvMvx0nyTV3as3jFBVtyX5xyQvzObU\ne8FB9ucnrTPZHCJO/n//4zXqwe7+idUjuDxVdSKb0/3ruvtaP3hckX0JzbG3PVm8PMlvJHk4F+8V\nn07yu91d1/qfbK5ufi/Jt5M8sX2+x5P83OptV/hcP7N9ntdX1Q8f4ZcNO7C9y0+S/1465BgQ/CPU\n3Qfd/fEkr0zyjmzCf93aVbvT3ee6+6NJXpLkVDbh/561q3bi7myu4G5K8uHFW+DQXOkstP1R881J\nPr+Pd4tVdTLJm5J8prvPr95zGFV1R5L7cvF3LmeT/HR3f2ndKi5XVXWSV3f3V1dvWUnw4buoqi8k\n+fFLPnWQ5HPd/eZFkzgEwd9wpQPfQVX9YDaxP51N6J/K5i7/TVXlraZcc7wtE76D7v6XqnpjNm+j\nvS+bA9LbkjzZ3d9cOg4OwZUOPAvbK4Ez3b0Pv4Qex5XOhisdgCEEH2AIwQcYQvABhhB8gCEEH2AI\nwQcYQvABhhB8gCEEH2AIwQcYQvABhhB8gCEEH2AIwQcYQvABhhB8gCEEH2AIwQcYQvABhhB8gCEE\nH2AIwQcYQvABhhB8gCEEH2AIwQcYQvABhhB8gCEEH2AIwQcYQvABhhB8gCEEH2AIwQcYQvABhhB8\ngCEEH2AIwQcYQvABhhB8gCGuXz0A4GqoqhuS3HbJp15QVbcnOdPd5xbNWsoJH9hXH0zyaJKvb18/\nkOTfkvz1skWLCT6wr+5LcjbJye3rG5KcS/LJZYsWE3w4pKo6UVUvXr3jaqmqk1X1vat3HFZ3P5Dk\ny8/49JNJ/nzBnGNB8OEybUP/q0n+OcnXq+rW1Zt2aRv6dyV5JMk/rN5zhe5M8sT24zNJTnX3+YV7\nlhJ8uAyXhP7Pkrw8yUH25PvoGaH/UJLnJ7ll7aor091/n+Sh7cvRp/skqe5evQGOvap6PMnNSf4r\nyV6d6LceSvLSJDfmGo/8d/Fb3f2nq0estBcnEzgCv5LNOzy4Nn0iw0/3iRM+PGtVdSLJLye5O8n3\nZ3PSP5/k9u4+vXLbLlTVySTvTPKBXDzpP9rdL1q5i91xwodnqbsPuvvjSV6Z5B1JHs7me+hg6bAd\n6e5z3f3RJC9JcirJt3PxF57sASd8OKTtif+F3b2XVz3bE/8t3f2t1VvYDcEHGMKVDsAQgg8whOAD\nDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8w\nhOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQ\ngg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMI\nPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4\nAEMIPsAQgg8whOADDCH4AEMIPsAQgg8whOADDCH4AEP8D59AFpXbgft5AAAAAElFTkSuQmCC\n",
 776       "text/plain": [
 777        "<matplotlib.figure.Figure at 0x7fdea6ba2c50>"
 778       ]
 779      },
 780      "metadata": {},
 781      "output_type": "display_data"
 782     }
 783    ],
 784    "source": [
 785     "plot_trace(trace_tour(samples[2]))"
 786    ]
 787   },
 788   {
 789    "cell_type": "code",
 790    "execution_count": 44,
 791    "metadata": {},
 792    "outputs": [
 793     {
 794      "data": {
 795       "text/plain": [
 796        "1"
 797       ]
 798      },
 799      "execution_count": 44,
 800      "metadata": {},
 801      "output_type": "execute_result"
 802     }
 803    ],
 804    "source": [
 805     "mistakes = [t.strip() for t in open('tours-random-walk.txt').readlines()\n",
 806     "           if len(t) > 8\n",
 807     "           if len(t) < 26]\n",
 808     "len(mistakes)"
 809    ]
 810   },
 811   {
 812    "cell_type": "code",
 813    "execution_count": 45,
 814    "metadata": {},
 815    "outputs": [
 816     {
 817      "data": {
 818       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQMAAAEACAYAAAC3RRNlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEwOgEgNgEwOgEgNgEwOgEgNgEwOgqv8F9Hl5y6i1C9AAAAAASUVORK5CYII=\n",
 819       "text/plain": [
 820        "<matplotlib.figure.Figure at 0x7fdea7040b70>"
 821       ]
 822      },
 823      "metadata": {},
 824      "output_type": "display_data"
 825     }
 826    ],
 827    "source": [
 828     "plot_trace(trace_tour(mistakes[0]))"
 829    ]
 830   },
 831   {
 832    "cell_type": "code",
 833    "execution_count": 48,
 834    "metadata": {},
 835    "outputs": [
 836     {
 837      "data": {
 838       "text/plain": [
 839        "(212,\n",
 840        " 94,\n",
 841        " 'FFRFLLFFFRLRRFFFLFLRRFLLFFFFFRFLFFFFFRLLFRFRLLFFFFFFLRFFRLLFRFFFLFFLFFRFRRLLFFRLFFFFFLLFFRFRFL')"
 842       ]
 843      },
 844      "execution_count": 48,
 845      "metadata": {},
 846      "output_type": "execute_result"
 847     },
 848     {
 849      "data": {
 850       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAEACAYAAACTecuMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
 851       "text/plain": [
 852        "<matplotlib.figure.Figure at 0x7fdea7095780>"
 853       ]
 854      },
 855      "metadata": {},
 856      "output_type": "display_data"
 857     }
 858    ],
 859    "source": [
 860     "lc = trace_tour(square_tour(a=10))\n",
 861     "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
 862     "rw_trimmed = trim_all_loops(rw)\n",
 863     "plot_trace(trace_tour(rw_trimmed))\n",
 864     "len(rw), len(rw_trimmed), rw_trimmed"
 865    ]
 866   },
 867   {
 868    "cell_type": "code",
 869    "execution_count": 66,
 870    "metadata": {},
 871    "outputs": [
 872     {
 873      "data": {
 874       "text/plain": [
 875        "['LFLLFFFFLLLFFRFRFF',\n",
 876        " 'LFFLLFFL',\n",
 877        " 'FRFFRRFFFFFFLLRLRLRLLFFF',\n",
 878        " 'RFFRRRFLFFFFLFLFRLLF',\n",
 879        " 'LFFRFRFFFFFRFFRLRFRF',\n",
 880        " 'LFFRFRFRFL',\n",
 881        " 'FLFFLLFFRLLL',\n",
 882        " 'FLLFFLLF',\n",
 883        " 'FFLLRLRLLFLR',\n",
 884        " 'FRRLLFLFFFFLFFFLLFFRRFLL',\n",
 885        " 'FRFRRFFF',\n",
 886        " 'FFFRFRRFFFFFFLFLFFFLRR',\n",
 887        " 'FFRRRFFLRLFRLFLFLFRFLF',\n",
 888        " 'RFFRRFFR',\n",
 889        " 'LFFFFRRRFLFFFL',\n",
 890        " 'FFLLLRRLLL',\n",
 891        " 'FFRFFRFRFRLL',\n",
 892        " 'RFLFFFFRRFFFFFRFFLLLLR',\n",
 893        " 'RRLLRRFFRFRFLR',\n",
 894        " 'FFRFRFFRFR']"
 895       ]
 896      },
 897      "execution_count": 66,
 898      "metadata": {},
 899      "output_type": "execute_result"
 900     }
 901    ],
 902    "source": [
 903     "mistakes = []\n",
 904     "while len(mistakes) < 20:\n",
 905     "    lc = trace_tour(square_tour(a=8))\n",
 906     "    rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
 907     "    rw_trimmed = trim_some_mistakes(rw, 2)\n",
 908     "    if len(rw_trimmed) > 6 and len(rw_trimmed) < 25:\n",
 909     "        mistakes += [rw_trimmed]\n",
 910     "mistakes"
 911    ]
 912   },
 913   {
 914    "cell_type": "code",
 915    "execution_count": 67,
 916    "metadata": {},
 917    "outputs": [
 918     {
 919      "data": {
 920       "text/plain": [
 921        "317"
 922       ]
 923      },
 924      "execution_count": 67,
 925      "metadata": {},
 926      "output_type": "execute_result"
 927     }
 928    ],
 929    "source": [
 930     "open('mistakes.txt', 'w').write('\\n'.join(mistakes))"
 931    ]
 932   },
 933   {
 934    "cell_type": "code",
 935    "execution_count": 69,
 936    "metadata": {},
 937    "outputs": [
 938     {
 939      "data": {
 940       "text/plain": [
 941        "137"
 942       ]
 943      },
 944      "execution_count": 69,
 945      "metadata": {},
 946      "output_type": "execute_result"
 947     }
 948    ],
 949    "source": [
 950     "open('samples.txt', 'w').write('\\n'.join(samples))"
 951    ]
 952   },
 953   {
 954    "cell_type": "code",
 955    "execution_count": 71,
 956    "metadata": {},
 957    "outputs": [
 958     {
 959      "data": {
 960       "text/plain": [
 961        "('FFRRFLRRFR', 10)"
 962       ]
 963      },
 964      "execution_count": 71,
 965      "metadata": {},
 966      "output_type": "execute_result"
 967     }
 968    ],
 969    "source": [
 970     "samples[4], len(samples[4])"
 971    ]
 972   },
 973   {
 974    "cell_type": "code",
 975    "execution_count": 83,
 976    "metadata": {},
 977    "outputs": [
 978     {
 979      "data": {
 980       "text/plain": [
 981        "('RRLLRRFFRFRFLR', 14)"
 982       ]
 983      },
 984      "execution_count": 83,
 985      "metadata": {},
 986      "output_type": "execute_result"
 987     }
 988    ],
 989    "source": [
 990     "mistakes[18], len(mistakes[18])"
 991    ]
 992   },
 993   {
 994    "cell_type": "code",
 995    "execution_count": 74,
 996    "metadata": {},
 997    "outputs": [
 998     {
 999      "data": {
1000       "text/plain": [
1001        "'RRFFLLFFFFLF'"
1002       ]
1003      },
1004      "execution_count": 74,
1005      "metadata": {},
1006      "output_type": "execute_result"
1007     },
1008     {
1009      "data": {
1010       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAADgCAYAAAAANN1GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
1011       "text/plain": [
1012        "<matplotlib.figure.Figure at 0x7fdea6e5cac8>"
1013       ]
1014      },
1015      "metadata": {},
1016      "output_type": "display_data"
1017     }
1018    ],
1019    "source": [
1020     "t = trim_all_loops(random_walk(20))\n",
1021     "plot_trace(trace_tour(t))\n",
1022     "t"
1023    ]
1024   },
1025   {
1026    "cell_type": "code",
1027    "execution_count": 76,
1028    "metadata": {
1029     "collapsed": true
1030    },
1031    "outputs": [],
1032    "source": [
1033     "t2 = 'FFRFLLFFFRLRRFFFLFLRRFLLFFFFFRFLFFFFFRLLFRFRLLFFFFFFLRFFRLLFRFFFLFFLFFRFRRLLFFRLFFFFFLLFFRFRFL'\n",
1034     "t2a = t2[:51]\n",
1035     "t2b = t2[51:]"
1036    ]
1037   },
1038   {
1039    "cell_type": "code",
1040    "execution_count": 80,
1041    "metadata": {},
1042    "outputs": [
1043     {
1044      "data": {
1045       "text/plain": [
1046        "'FFRFLLFFFRLRRFFFLFLRRFLLFFFFFRFLFFFFFRLLFRFRLLFFFFF'"
1047       ]
1048      },
1049      "execution_count": 80,
1050      "metadata": {},
1051      "output_type": "execute_result"
1052     },
1053     {
1054      "data": {
1055       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMwAAAEACAYAAAD/f5mJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
1056       "text/plain": [
1057        "<matplotlib.figure.Figure at 0x7fdea6fc12e8>"
1058       ]
1059      },
1060      "metadata": {},
1061      "output_type": "display_data"
1062     }
1063    ],
1064    "source": [
1065     "plot_trace(trace_tour(t2a))\n",
1066     "t2a"
1067    ]
1068   },
1069   {
1070    "cell_type": "code",
1071    "execution_count": 81,
1072    "metadata": {},
1073    "outputs": [
1074     {
1075      "data": {
1076       "text/plain": [
1077        "'FLRFFRLLFRFFFLFFLFFRFRRLLFFRLFFFFFLLFFRFRFL'"
1078       ]
1079      },
1080      "execution_count": 81,
1081      "metadata": {},
1082      "output_type": "execute_result"
1083     },
1084     {
1085      "data": {
1086       "image/png": "iVBORw0KGgoAAAANSUhEUgAAALUAAAEACAYAAAD1IzfbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
1087       "text/plain": [
1088        "<matplotlib.figure.Figure at 0x7fdea6c4e550>"
1089       ]
1090      },
1091      "metadata": {},
1092      "output_type": "display_data"
1093     }
1094    ],
1095    "source": [
1096     "plot_trace(trace_tour(t2b))\n",
1097     "t2b"
1098    ]
1099   },
1100   {
1101    "cell_type": "code",
1102    "execution_count": 84,
1103    "metadata": {},
1104    "outputs": [
1105     {
1106      "data": {
1107       "text/plain": [
1108        "(94,\n",
1109        " 'FFRFLLFFFRLRRFFFLFLRRFLLFFFFFRFLFFFFFRLLFRFRLLFFFFFFLRFFRLLFRFFFLFFLFFRFRRLLFFRLFFFFFLLFFRFRFL')"
1110       ]
1111      },
1112      "execution_count": 84,
1113      "metadata": {},
1114      "output_type": "execute_result"
1115     },
1116     {
1117      "data": {
1118       "image/png": 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N4AeQHghylqSv1HrKzTJIS4svkfSP7v5463pqIvhAQPzjHhAQwQcCIvhAQAQfCIjgAwER\nfCAggg8ERPCBgAg+EBDBBwIi+EBABB8IiOADARF8ICCCDwRE8IGACD4QEMEHAiL4QEAEHwiI4AMB\nEXwgIIIPBETwgYAIPhAQwQcCIvhAQAQfCIjgAwERfCAggg8E9H9g3ys8YjIz8gAAAABJRU5ErkJg\ngg==\n",
1119       "text/plain": [
1120        "<matplotlib.figure.Figure at 0x7fdea6e6ca20>"
1121       ]
1122      },
1123      "metadata": {},
1124      "output_type": "display_data"
1125     }
1126    ],
1127    "source": [
1128     "plot_trace(trace_tour(t2a + t2b))\n",
1129     "len(t2a + t2b), t2a + t2b"
1130    ]
1131   },
1132   {
1133    "cell_type": "code",
1134    "execution_count": null,
1135    "metadata": {
1136     "collapsed": true
1137    },
1138    "outputs": [],
1139    "source": []
1140   }
1141  ],
1142  "metadata": {
1143   "kernelspec": {
1144    "display_name": "Python 3",
1145    "language": "python",
1146    "name": "python3"
1147   },
1148   "language_info": {
1149    "codemirror_mode": {
1150     "name": "ipython",
1151     "version": 3
1152    },
1153    "file_extension": ".py",
1154    "mimetype": "text/x-python",
1155    "name": "python",
1156    "nbconvert_exporter": "python",
1157    "pygments_lexer": "ipython3",
1158    "version": "3.5.2+"
1159   }
1160  },
1161  "nbformat": 4,
1162  "nbformat_minor": 2
1163 }