06-tour-shapes/tour-creation-for-background.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"
  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 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": 6,
 112    "metadata": {
 113     "collapsed": true
 114    },
 115    "outputs": [],
 116    "source": [
 117     "def positions(trace):\n",
 118     "    return [(s.x, s.y) for s in trace]"
 119    ]
 120   },
 121   {
 122    "cell_type": "code",
 123    "execution_count": 7,
 124    "metadata": {
 125     "collapsed": true
 126    },
 127    "outputs": [],
 128    "source": [
 129     "def valid(trace):\n",
 130     "    return (trace[-1].x == 0 \n",
 131     "            and trace[-1].y == 0 \n",
 132     "            and len(set(positions(trace))) + 1 == len(trace))"
 133    ]
 134   },
 135   {
 136    "cell_type": "code",
 137    "execution_count": 8,
 138    "metadata": {
 139     "collapsed": true
 140    },
 141    "outputs": [],
 142    "source": [
 143     "def chunks(items, n=2):\n",
 144     "    return [items[i:i+n] for i in range(len(items) - n + 1)]"
 145    ]
 146   },
 147   {
 148    "cell_type": "markdown",
 149    "metadata": {},
 150    "source": [
 151     "Using the [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula)"
 152    ]
 153   },
 154   {
 155    "cell_type": "code",
 156    "execution_count": 9,
 157    "metadata": {
 158     "collapsed": true
 159    },
 160    "outputs": [],
 161    "source": [
 162     "def shoelace(trace):\n",
 163     "    return abs(sum(s.x * t.y - t.x * s.y for s, t in chunks(trace, 2))) // 2"
 164    ]
 165   },
 166   {
 167    "cell_type": "code",
 168    "execution_count": 10,
 169    "metadata": {
 170     "collapsed": true
 171    },
 172    "outputs": [],
 173    "source": [
 174     "def step(s, current):\n",
 175     "    if s == 'F':\n",
 176     "        return advance(current, current.dir)\n",
 177     "    elif s == 'L':\n",
 178     "        return advance(current, turn_left(current.dir))\n",
 179     "    elif s == 'R':\n",
 180     "        return advance(current, turn_right(current.dir))\n",
 181     "    else:\n",
 182     "        raise ValueError"
 183    ]
 184   },
 185   {
 186    "cell_type": "code",
 187    "execution_count": 11,
 188    "metadata": {
 189     "collapsed": true
 190    },
 191    "outputs": [],
 192    "source": [
 193     "def valid_prefix(tour):\n",
 194     "    current = Step(0, 0, Direction.RIGHT)\n",
 195     "    prefix = []\n",
 196     "    posns = []\n",
 197     "    for s in tour:\n",
 198     "        current = step(s, current)\n",
 199     "        prefix += [s]\n",
 200     "        if (current.x, current.y) in posns:\n",
 201     "            return ''\n",
 202     "        elif current.x == 0 and current.y == 0: \n",
 203     "            return ''.join(prefix)\n",
 204     "        posns += [(current.x, current.y)]\n",
 205     "    if current.x == 0 and current.y == 0:\n",
 206     "        return ''.join(prefix)\n",
 207     "    else:\n",
 208     "        return ''"
 209    ]
 210   },
 211   {
 212    "cell_type": "code",
 213    "execution_count": 12,
 214    "metadata": {
 215     "collapsed": true
 216    },
 217    "outputs": [],
 218    "source": [
 219     "def mistake_positions(trace, debug=False):\n",
 220     "    mistakes = []\n",
 221     "    current = trace[0]\n",
 222     "    posns = [(0, 0)]\n",
 223     "    for i, current in enumerate(trace[1:]):\n",
 224     "        if (current.x, current.y) in posns:\n",
 225     "            if debug: print(i, current)\n",
 226     "            mistakes += [Mistake(i+1, current)]\n",
 227     "        posns += [(current.x, current.y)]\n",
 228     "    if (current.x, current.y) == (0, 0):\n",
 229     "        return mistakes[:-1]\n",
 230     "    else:\n",
 231     "        return mistakes + [Mistake(len(trace)+1, current)]"
 232    ]
 233   },
 234   {
 235    "cell_type": "code",
 236    "execution_count": 13,
 237    "metadata": {
 238     "collapsed": true
 239    },
 240    "outputs": [],
 241    "source": [
 242     "def returns_to_origin(mistake_positions):\n",
 243     "    return [i for i, m in mistake_positions\n",
 244     "           if (m.x, m.y) == (0, 0)]"
 245    ]
 246   },
 247   {
 248    "cell_type": "code",
 249    "execution_count": 14,
 250    "metadata": {
 251     "collapsed": true
 252    },
 253    "outputs": [],
 254    "source": [
 255     "def random_walk(steps=1000):\n",
 256     "    return ''.join(random.choice('FFLR') for _ in range(steps))"
 257    ]
 258   },
 259   {
 260    "cell_type": "code",
 261    "execution_count": 15,
 262    "metadata": {
 263     "collapsed": true
 264    },
 265    "outputs": [],
 266    "source": [
 267     "def bounds(trace):\n",
 268     "    return (max(s.x for s in trace),\n",
 269     "            max(s.y for s in trace),\n",
 270     "            min(s.x for s in trace),\n",
 271     "            min(s.y for s in trace))"
 272    ]
 273   },
 274   {
 275    "cell_type": "code",
 276    "execution_count": 1,
 277    "metadata": {},
 278    "outputs": [
 279     {
 280      "ename": "NameError",
 281      "evalue": "name 'Direction' is not defined",
 282      "output_type": "error",
 283      "traceback": [
 284       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
 285       "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
 286       "\u001b[0;32m<ipython-input-1-f5ea591d6161>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n\u001b[0m\u001b[1;32m      2\u001b[0m            Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}\n",
 287       "\u001b[0;31mNameError\u001b[0m: name 'Direction' is not defined"
 288      ]
 289     }
 290    ],
 291    "source": [
 292     "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
 293     "           Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
 294    ]
 295   },
 296   {
 297    "cell_type": "code",
 298    "execution_count": 16,
 299    "metadata": {
 300     "collapsed": true
 301    },
 302    "outputs": [],
 303    "source": [
 304     "def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None, filename=None):\n",
 305     "    plt.axis('on')\n",
 306     "    plt.axes().set_aspect('equal')\n",
 307     "    for s, t in chunks(trace, 2):\n",
 308     "        w, h = plot_wh[t.dir]\n",
 309     "        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",
 310     "    xh, yh, xl, yl = bounds(trace)\n",
 311     "    if xybounds is not None:    \n",
 312     "        bxh, byh, bxl, byl = xybounds\n",
 313     "        plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
 314     "        plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
 315     "    else:\n",
 316     "        plt.xlim([xl-1, xh+1])\n",
 317     "        plt.ylim([yl-1, yh+1])\n",
 318     "    if filename:\n",
 319     "        plt.savefig(filename)"
 320    ]
 321   },
 322   {
 323    "cell_type": "code",
 324    "execution_count": 17,
 325    "metadata": {
 326     "collapsed": true
 327    },
 328    "outputs": [],
 329    "source": [
 330     "def trim_loop(tour):\n",
 331     "    trace = trace_tour(tour)\n",
 332     "    mistakes = mistake_positions(trace)\n",
 333     "    end_mistake_index = 0\n",
 334     "#     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",
 335     "    # while this mistake extends to the next step in the trace...\n",
 336     "    while (mistakes[end_mistake_index].i + 1 < len(trace) and \n",
 337     "           end_mistake_index + 1 < len(mistakes) and\n",
 338     "           mistakes[end_mistake_index].i + 1 == \n",
 339     "           mistakes[end_mistake_index + 1].i):\n",
 340     "#         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",
 341     "        # push this mistake finish point later\n",
 342     "        end_mistake_index += 1\n",
 343     "    mistake = mistakes[end_mistake_index]\n",
 344     "    \n",
 345     "    # find the first location that mentions where this mistake ends (which the point where the loop starts)\n",
 346     "    mistake_loop_start = max(i for i, loc in enumerate(trace[:mistake.i])\n",
 347     "                             if (loc.x, loc.y) == (mistake.step.x, mistake.step.y))\n",
 348     "#     print('Dealing with mistake from', mistake_loop_start, 'to', mistake.i, ', trace has len', len(trace))\n",
 349     "    \n",
 350     "    # direction before entering the loop\n",
 351     "    direction_before = trace[mistake_loop_start].dir\n",
 352     "    \n",
 353     "    # find the new instruction to turn from heading before the loop to heading after the loop\n",
 354     "    new_instruction = 'F'\n",
 355     "    if (mistake.i + 1) < len(trace):\n",
 356     "        if turn_left(direction_before) == trace[mistake.i + 1].dir:\n",
 357     "            new_instruction = 'L'\n",
 358     "        if turn_right(direction_before) == trace[mistake.i + 1].dir:\n",
 359     "            new_instruction = 'R'\n",
 360     "#     if (mistake.i + 1) < len(trace):\n",
 361     "#         print('turning from', direction_before, 'to', trace[mistake.i + 1].dir, 'with', new_instruction )\n",
 362     "#     else:\n",
 363     "#         print('turning from', direction_before, 'to BEYOND END', 'with', new_instruction )\n",
 364     "    return tour[:mistake_loop_start] + new_instruction + tour[mistake.i+1:]\n",
 365     "#     return mistake, mistake_loop_start, trace[mistake_loop_start-2:mistake_loop_start+8]"
 366    ]
 367   },
 368   {
 369    "cell_type": "code",
 370    "execution_count": 18,
 371    "metadata": {
 372     "collapsed": true
 373    },
 374    "outputs": [],
 375    "source": [
 376     "def trim_all_loops(tour, mistake_reduction_attempt_limit=10):\n",
 377     "    trace = trace_tour(tour)\n",
 378     "    mistake_limit = 1\n",
 379     "    if trace[-1].x == 0 and trace[-1].y == 0:\n",
 380     "        mistake_limit = 0\n",
 381     "    mistakes = mistake_positions(trace)\n",
 382     "    \n",
 383     "    old_mistake_count = len(mistakes)\n",
 384     "    mistake_reduction_tries = 0\n",
 385     "    \n",
 386     "    while len(mistakes) > mistake_limit and mistake_reduction_tries < mistake_reduction_attempt_limit:\n",
 387     "        tour = trim_loop(tour)\n",
 388     "        trace = trace_tour(tour)\n",
 389     "        mistakes = mistake_positions(trace)\n",
 390     "        if len(mistakes) < old_mistake_count:\n",
 391     "            old_mistake_count = len(mistakes)\n",
 392     "            mistake_reduction_tries = 0\n",
 393     "        else:\n",
 394     "            mistake_reduction_tries += 1\n",
 395     "    if mistake_reduction_tries >= mistake_reduction_attempt_limit:\n",
 396     "        return ''\n",
 397     "    else:\n",
 398     "        return tour"
 399    ]
 400   },
 401   {
 402    "cell_type": "code",
 403    "execution_count": 19,
 404    "metadata": {
 405     "collapsed": true
 406    },
 407    "outputs": [],
 408    "source": [
 409     "def reverse_tour(tour):\n",
 410     "    def swap(tour_step):\n",
 411     "        if tour_step == 'R':\n",
 412     "            return 'L'\n",
 413     "        elif tour_step == 'L':\n",
 414     "            return 'R'\n",
 415     "        else:\n",
 416     "            return tour_step\n",
 417     "        \n",
 418     "    return ''.join(swap(s) for s in reversed(tour))"
 419    ]
 420   },
 421   {
 422    "cell_type": "code",
 423    "execution_count": 20,
 424    "metadata": {
 425     "collapsed": true
 426    },
 427    "outputs": [],
 428    "source": [
 429     "def wander_near(locus, current, limit=10):\n",
 430     "    valid_proposal = False\n",
 431     "    while not valid_proposal:\n",
 432     "        s = random.choice('FFFRL')\n",
 433     "        if s == 'F':\n",
 434     "            proposed = advance(current, current.dir)\n",
 435     "        elif s == 'L':\n",
 436     "            proposed = advance(current, turn_left(current.dir))\n",
 437     "        elif s == 'R':\n",
 438     "            proposed = advance(current, turn_right(current.dir))\n",
 439     "        if abs(proposed.x - locus.x) < limit and abs(proposed.y - locus.y) < limit:\n",
 440     "            valid_proposal = True\n",
 441     "#     print('At {} going to {} by step {} to {}'.format(current, locus, s, proposed))\n",
 442     "    return s, proposed"
 443    ]
 444   },
 445   {
 446    "cell_type": "code",
 447    "execution_count": 21,
 448    "metadata": {
 449     "collapsed": true
 450    },
 451    "outputs": [],
 452    "source": [
 453     "def seek(goal, current):\n",
 454     "    dx = current.x - goal.x\n",
 455     "    dy = current.y - goal.y\n",
 456     "\n",
 457     "    if dx < 0 and abs(dx) > abs(dy): # to the left\n",
 458     "        side = 'left'\n",
 459     "        if current.dir == Direction.RIGHT:\n",
 460     "            s = 'F'\n",
 461     "        elif current.dir == Direction.UP:\n",
 462     "            s = 'R'\n",
 463     "        else:\n",
 464     "            s = 'L'\n",
 465     "    elif dx > 0 and abs(dx) > abs(dy): # to the right\n",
 466     "        side = 'right'\n",
 467     "        if current.dir == Direction.LEFT:\n",
 468     "            s = 'F'\n",
 469     "        elif current.dir == Direction.UP:\n",
 470     "            s = 'L'\n",
 471     "        else:\n",
 472     "            s = 'R'\n",
 473     "    elif dy > 0 and abs(dx) <= abs(dy): # above\n",
 474     "        side = 'above'\n",
 475     "        if current.dir == Direction.DOWN:\n",
 476     "            s = 'F'\n",
 477     "        elif current.dir == Direction.RIGHT:\n",
 478     "            s = 'R'\n",
 479     "        else:\n",
 480     "            s = 'L'\n",
 481     "    else: # below\n",
 482     "        side = 'below'\n",
 483     "        if current.dir == Direction.UP:\n",
 484     "            s = 'F'\n",
 485     "        elif current.dir == Direction.LEFT:\n",
 486     "            s = 'R'\n",
 487     "        else:\n",
 488     "            s = 'L'\n",
 489     "    if s == 'F':\n",
 490     "        proposed = advance(current, current.dir)\n",
 491     "    elif s == 'L':\n",
 492     "        proposed = advance(current, turn_left(current.dir))\n",
 493     "    elif s == 'R':\n",
 494     "        proposed = advance(current, turn_right(current.dir))\n",
 495     "        \n",
 496     "#     print('At {} going to {}, currently {},  by step {} to {}'.format(current, goal, side, s, proposed))\n",
 497     "\n",
 498     "    return s, proposed"
 499    ]
 500   },
 501   {
 502    "cell_type": "code",
 503    "execution_count": 22,
 504    "metadata": {
 505     "collapsed": true
 506    },
 507    "outputs": [],
 508    "source": [
 509     "def guided_walk(loci, locus_limit=5, wander_limit=10, seek_step_limit=20):\n",
 510     "    trail = ''\n",
 511     "    current = Step(0, 0, Direction.RIGHT)    \n",
 512     "    l = 0\n",
 513     "    finished = False\n",
 514     "    while not finished:\n",
 515     "        if abs(current.x - loci[l].x) < locus_limit and abs(current.y - loci[l].y) < locus_limit:\n",
 516     "            l += 1\n",
 517     "            if l == len(loci) - 1:\n",
 518     "                finished = True\n",
 519     "        s, proposed = wander_near(loci[l], current, limit=wander_limit)\n",
 520     "        trail += s\n",
 521     "        current = proposed\n",
 522     "#     print('!! Finished loci')\n",
 523     "    seek_steps = 0\n",
 524     "    while not (current.x == loci[l].x and current.y == loci[l].y) and seek_steps < seek_step_limit:\n",
 525     "#         error = max(abs(current.x - loci[l].x), abs(current.y - loci[l].y))\n",
 526     "#         s, proposed = wander_near(loci[l], current, limit=error+1)\n",
 527     "        s, proposed = seek(loci[l], current)\n",
 528     "        trail += s\n",
 529     "        current = proposed\n",
 530     "        seek_steps += 1\n",
 531     "    if seek_steps >= seek_step_limit:\n",
 532     "        return ''\n",
 533     "    else:\n",
 534     "        return trail"
 535    ]
 536   },
 537   {
 538    "cell_type": "code",
 539    "execution_count": 24,
 540    "metadata": {
 541     "collapsed": true
 542    },
 543    "outputs": [],
 544    "source": [
 545     "def square_tour(a=80):\n",
 546     "    \"a is width of square\"\n",
 547     "    return ('F' * a + 'L') * 4"
 548    ]
 549   },
 550   {
 551    "cell_type": "code",
 552    "execution_count": 25,
 553    "metadata": {
 554     "collapsed": true
 555    },
 556    "outputs": [],
 557    "source": [
 558     "def cross_tour(a=50, b=40):\n",
 559     "    \"a is width of cross arm, b is length of cross arm\"\n",
 560     "    return ('F' *  a + 'L' + 'F' * b + 'R' + 'F' * b + 'L') * 4"
 561    ]
 562   },
 563   {
 564    "cell_type": "code",
 565    "execution_count": 26,
 566    "metadata": {
 567     "collapsed": true
 568    },
 569    "outputs": [],
 570    "source": [
 571     "def quincunx_tour(a=60, b=30, c=50):\n",
 572     "    \"a is length of indent, b is indent/outdent distance, c is outdent outer length\"\n",
 573     "    return ('F' * a + 'R' + 'F' * b + 'L' + 'F' * c + 'L' + 'F' * c + 'L' + 'F' * b + 'R') * 4\n"
 574    ]
 575   },
 576   {
 577    "cell_type": "code",
 578    "execution_count": 27,
 579    "metadata": {
 580     "collapsed": true
 581    },
 582    "outputs": [],
 583    "source": [
 584     "heart_points = [Step(60, 50, Direction.UP), Step(50, 90, Direction.UP),\n",
 585     "                Step(20, 70, Direction.UP), \n",
 586     "                Step(-40, 90, Direction.UP), Step(-60, 80, Direction.UP), \n",
 587     "                Step(0, 0, Direction.RIGHT)]\n",
 588     "\n",
 589     "heart_tour = ''\n",
 590     "current = Step(0, 0, Direction.RIGHT)\n",
 591     "\n",
 592     "for hp in heart_points:\n",
 593     "    while not (current.x == hp.x and current.y == hp.y):\n",
 594     "        s, proposed = seek(hp, current)\n",
 595     "        heart_tour += s\n",
 596     "        current = proposed\n",
 597     "\n",
 598     "def heart_tour_func(): return heart_tour"
 599    ]
 600   },
 601   {
 602    "cell_type": "code",
 603    "execution_count": 28,
 604    "metadata": {
 605     "collapsed": true
 606    },
 607    "outputs": [],
 608    "source": [
 609     "# success_count = 0\n",
 610     "# while success_count <= 20:\n",
 611     "#     lc = trace_tour(square_tour(a=10))\n",
 612     "#     rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
 613     "#     if rw:\n",
 614     "#         rw_trimmed = trim_all_loops(rw)\n",
 615     "#         if len(rw_trimmed) > 10:\n",
 616     "#             with open('small-squares.txt', 'a') as f:\n",
 617     "#                 f.write(rw_trimmed + '\\n')\n",
 618     "#                 success_count += 1"
 619    ]
 620   },
 621   {
 622    "cell_type": "code",
 623    "execution_count": 29,
 624    "metadata": {
 625     "collapsed": true
 626    },
 627    "outputs": [],
 628    "source": [
 629     "# success_count = 0\n",
 630     "# while success_count <= 20:\n",
 631     "#     lc = trace_tour(square_tour())\n",
 632     "#     rw = guided_walk(lc)\n",
 633     "#     if rw:\n",
 634     "#         rw_trimmed = trim_all_loops(rw)\n",
 635     "#         if len(rw_trimmed) > 10:\n",
 636     "#             with open('large-squares.txt', 'a') as f:\n",
 637     "#                 f.write(rw_trimmed + '\\n')\n",
 638     "#                 success_count += 1"
 639    ]
 640   },
 641   {
 642    "cell_type": "code",
 643    "execution_count": 30,
 644    "metadata": {
 645     "collapsed": true
 646    },
 647    "outputs": [],
 648    "source": [
 649     "# success_count = 0\n",
 650     "# while success_count <= 20:\n",
 651     "#     lc = trace_tour(cross_tour())\n",
 652     "#     rw = guided_walk(lc)\n",
 653     "#     if rw:\n",
 654     "#         rw_trimmed = trim_all_loops(rw)\n",
 655     "#         if len(rw_trimmed) > 10:\n",
 656     "#             with open('cross.txt', 'a') as f:\n",
 657     "#                 f.write(rw_trimmed + '\\n')\n",
 658     "#                 success_count += 1"
 659    ]
 660   },
 661   {
 662    "cell_type": "code",
 663    "execution_count": 31,
 664    "metadata": {
 665     "collapsed": true
 666    },
 667    "outputs": [],
 668    "source": [
 669     "# success_count = 0\n",
 670     "# while success_count <= 20:\n",
 671     "#     lc = trace_tour(quincunx_tour())\n",
 672     "#     rw = guided_walk(lc)\n",
 673     "#     if rw:\n",
 674     "#         rw_trimmed = trim_all_loops(rw)\n",
 675     "#         if len(rw_trimmed) > 10:\n",
 676     "#             with open('quincunx.txt', 'a') as f:\n",
 677     "#                 f.write(rw_trimmed + '\\n')\n",
 678     "#                 success_count += 1"
 679    ]
 680   },
 681   {
 682    "cell_type": "code",
 683    "execution_count": 32,
 684    "metadata": {
 685     "collapsed": true
 686    },
 687    "outputs": [],
 688    "source": [
 689     "patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
 690     "tours_filename = 'tours.txt'\n",
 691     "\n",
 692     "try:\n",
 693     "    os.remove(tours_filename)\n",
 694     "except OSError:\n",
 695     "    pass\n",
 696     "\n",
 697     "success_count = 0\n",
 698     "while success_count < 100:\n",
 699     "    lc = trace_tour(random.choice(patterns)())\n",
 700     "    rw = guided_walk(lc)\n",
 701     "    if rw:\n",
 702     "        rw_trimmed = trim_all_loops(rw)\n",
 703     "        if len(rw_trimmed) > 10:\n",
 704     "            with open(tours_filename, 'a') as f:\n",
 705     "                f.write(rw_trimmed + '\\n')\n",
 706     "                success_count += 1"
 707    ]
 708   },
 709   {
 710    "cell_type": "code",
 711    "execution_count": null,
 712    "metadata": {
 713     "collapsed": true
 714    },
 715    "outputs": [],
 716    "source": []
 717   }
 718  ],
 719  "metadata": {
 720   "kernelspec": {
 721    "display_name": "Python 3",
 722    "language": "python",
 723    "name": "python3"
 724   },
 725   "language_info": {
 726    "codemirror_mode": {
 727     "name": "ipython",
 728     "version": 3
 729    },
 730    "file_extension": ".py",
 731    "mimetype": "text/x-python",
 732    "name": "python",
 733    "nbconvert_exporter": "python",
 734    "pygments_lexer": "ipython3",
 735    "version": "3.5.2+"
 736   }
 737  },
 738  "nbformat": 4,
 739  "nbformat_minor": 2
 740 }