06-tour-shapes/tour-shapes-build-problem-set.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": 4,
  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": 5,
  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": 6,
  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": 7,
  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": 8,
  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": 9,
 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": 10,
 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": 11,
 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": 12,
 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": 13,
 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": 14,
 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": 15,
 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": 16,
 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": 17,
 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": 18,
 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": 27,
 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": 19,
 276    "metadata": {
 277     "collapsed": true
 278    },
 279    "outputs": [],
 280    "source": [
 281     "def plot_trace(trace, colour='k', highlight_start=True,\n",
 282     "               xybounds=None, fig=None, subplot_details=None, filename=None):\n",
 283     "    plt.axis('on')\n",
 284     "    plt.axes().set_aspect('equal')\n",
 285     "        \n",
 286     "    if highlight_start:\n",
 287     "        plt.axes().add_patch(plt.Circle((trace[0].x, trace[0].y), 0.2, color=colour))\n",
 288     "        \n",
 289     "    for s, t in chunks(trace, 2):\n",
 290     "        w, h = plot_wh[t.dir]\n",
 291     "        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",
 292     "    xh, yh, xl, yl = bounds(trace)\n",
 293     "    if xybounds is not None:    \n",
 294     "        bxh, byh, bxl, byl = xybounds\n",
 295     "        plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
 296     "        plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
 297     "    else:\n",
 298     "        plt.xlim([xl-1, xh+1])\n",
 299     "        plt.ylim([yl-1, yh+1])\n",
 300     "    if filename:\n",
 301     "        plt.savefig(filename)"
 302    ]
 303   },
 304   {
 305    "cell_type": "code",
 306    "execution_count": 20,
 307    "metadata": {
 308     "collapsed": true
 309    },
 310    "outputs": [],
 311    "source": [
 312     "def trim_loop(tour, random_mistake=False):\n",
 313     "    trace = trace_tour(tour)\n",
 314     "    mistakes = mistake_positions(trace)\n",
 315     "    if random_mistake:\n",
 316     "        end_mistake_index = random.randrange(len(mistakes))\n",
 317     "    else:\n",
 318     "        end_mistake_index = 0\n",
 319     "#     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",
 320     "    # while this mistake extends to the next step in the trace...\n",
 321     "    while (mistakes[end_mistake_index].i + 1 < len(trace) and \n",
 322     "           end_mistake_index + 1 < len(mistakes) and\n",
 323     "           mistakes[end_mistake_index].i + 1 == \n",
 324     "           mistakes[end_mistake_index + 1].i):\n",
 325     "#         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",
 326     "        # push this mistake finish point later\n",
 327     "        end_mistake_index += 1\n",
 328     "    mistake = mistakes[end_mistake_index]\n",
 329     "    \n",
 330     "    # find the first location that mentions where this mistake ends (which the point where the loop starts)\n",
 331     "    mistake_loop_start = max(i for i, loc in enumerate(trace[:mistake.i])\n",
 332     "                             if (loc.x, loc.y) == (mistake.step.x, mistake.step.y))\n",
 333     "#     print('Dealing with mistake from', mistake_loop_start, 'to', mistake.i, ', trace has len', len(trace))\n",
 334     "    \n",
 335     "    # direction before entering the loop\n",
 336     "    direction_before = trace[mistake_loop_start].dir\n",
 337     "    \n",
 338     "    # find the new instruction to turn from heading before the loop to heading after the loop\n",
 339     "    new_instruction = 'F'\n",
 340     "    if (mistake.i + 1) < len(trace):\n",
 341     "        if turn_left(direction_before) == trace[mistake.i + 1].dir:\n",
 342     "            new_instruction = 'L'\n",
 343     "        if turn_right(direction_before) == trace[mistake.i + 1].dir:\n",
 344     "            new_instruction = 'R'\n",
 345     "#     if (mistake.i + 1) < len(trace):\n",
 346     "#         print('turning from', direction_before, 'to', trace[mistake.i + 1].dir, 'with', new_instruction )\n",
 347     "#     else:\n",
 348     "#         print('turning from', direction_before, 'to BEYOND END', 'with', new_instruction )\n",
 349     "    return tour[:mistake_loop_start] + new_instruction + tour[mistake.i+1:]\n",
 350     "#     return mistake, mistake_loop_start, trace[mistake_loop_start-2:mistake_loop_start+8]"
 351    ]
 352   },
 353   {
 354    "cell_type": "code",
 355    "execution_count": 21,
 356    "metadata": {
 357     "collapsed": true
 358    },
 359    "outputs": [],
 360    "source": [
 361     "def trim_all_loops(tour, mistake_reduction_attempt_limit=10):\n",
 362     "    trace = trace_tour(tour)\n",
 363     "    mistake_limit = 1\n",
 364     "    if trace[-1].x == 0 and trace[-1].y == 0:\n",
 365     "        mistake_limit = 0\n",
 366     "    mistakes = mistake_positions(trace)\n",
 367     "    \n",
 368     "    old_mistake_count = len(mistakes)\n",
 369     "    mistake_reduction_tries = 0\n",
 370     "    \n",
 371     "    while len(mistakes) > mistake_limit and mistake_reduction_tries < mistake_reduction_attempt_limit:\n",
 372     "        tour = trim_loop(tour)\n",
 373     "        trace = trace_tour(tour)\n",
 374     "        mistakes = mistake_positions(trace)\n",
 375     "        if len(mistakes) < old_mistake_count:\n",
 376     "            old_mistake_count = len(mistakes)\n",
 377     "            mistake_reduction_tries = 0\n",
 378     "        else:\n",
 379     "            mistake_reduction_tries += 1\n",
 380     "    if mistake_reduction_tries >= mistake_reduction_attempt_limit:\n",
 381     "        return ''\n",
 382     "    else:\n",
 383     "        return tour"
 384    ]
 385   },
 386   {
 387    "cell_type": "code",
 388    "execution_count": 22,
 389    "metadata": {
 390     "collapsed": true
 391    },
 392    "outputs": [],
 393    "source": [
 394     "def reverse_tour(tour):\n",
 395     "    def swap(tour_step):\n",
 396     "        if tour_step == 'R':\n",
 397     "            return 'L'\n",
 398     "        elif tour_step == 'L':\n",
 399     "            return 'R'\n",
 400     "        else:\n",
 401     "            return tour_step\n",
 402     "        \n",
 403     "    return ''.join(swap(s) for s in reversed(tour))"
 404    ]
 405   },
 406   {
 407    "cell_type": "code",
 408    "execution_count": 23,
 409    "metadata": {
 410     "collapsed": true
 411    },
 412    "outputs": [],
 413    "source": [
 414     "def wander_near(locus, current, limit=10):\n",
 415     "    valid_proposal = False\n",
 416     "    while not valid_proposal:\n",
 417     "        s = random.choice('FFFRL')\n",
 418     "        if s == 'F':\n",
 419     "            proposed = advance(current, current.dir)\n",
 420     "        elif s == 'L':\n",
 421     "            proposed = advance(current, turn_left(current.dir))\n",
 422     "        elif s == 'R':\n",
 423     "            proposed = advance(current, turn_right(current.dir))\n",
 424     "        if abs(proposed.x - locus.x) < limit and abs(proposed.y - locus.y) < limit:\n",
 425     "            valid_proposal = True\n",
 426     "#     print('At {} going to {} by step {} to {}'.format(current, locus, s, proposed))\n",
 427     "    return s, proposed"
 428    ]
 429   },
 430   {
 431    "cell_type": "code",
 432    "execution_count": 24,
 433    "metadata": {
 434     "collapsed": true
 435    },
 436    "outputs": [],
 437    "source": [
 438     "def seek(goal, current):\n",
 439     "    dx = current.x - goal.x\n",
 440     "    dy = current.y - goal.y\n",
 441     "\n",
 442     "    if dx < 0 and abs(dx) > abs(dy): # to the left\n",
 443     "        side = 'left'\n",
 444     "        if current.dir == Direction.RIGHT:\n",
 445     "            s = 'F'\n",
 446     "        elif current.dir == Direction.UP:\n",
 447     "            s = 'R'\n",
 448     "        else:\n",
 449     "            s = 'L'\n",
 450     "    elif dx > 0 and abs(dx) > abs(dy): # to the right\n",
 451     "        side = 'right'\n",
 452     "        if current.dir == Direction.LEFT:\n",
 453     "            s = 'F'\n",
 454     "        elif current.dir == Direction.UP:\n",
 455     "            s = 'L'\n",
 456     "        else:\n",
 457     "            s = 'R'\n",
 458     "    elif dy > 0 and abs(dx) <= abs(dy): # above\n",
 459     "        side = 'above'\n",
 460     "        if current.dir == Direction.DOWN:\n",
 461     "            s = 'F'\n",
 462     "        elif current.dir == Direction.RIGHT:\n",
 463     "            s = 'R'\n",
 464     "        else:\n",
 465     "            s = 'L'\n",
 466     "    else: # below\n",
 467     "        side = 'below'\n",
 468     "        if current.dir == Direction.UP:\n",
 469     "            s = 'F'\n",
 470     "        elif current.dir == Direction.LEFT:\n",
 471     "            s = 'R'\n",
 472     "        else:\n",
 473     "            s = 'L'\n",
 474     "    if s == 'F':\n",
 475     "        proposed = advance(current, current.dir)\n",
 476     "    elif s == 'L':\n",
 477     "        proposed = advance(current, turn_left(current.dir))\n",
 478     "    elif s == 'R':\n",
 479     "        proposed = advance(current, turn_right(current.dir))\n",
 480     "        \n",
 481     "#     print('At {} going to {}, currently {},  by step {} to {}'.format(current, goal, side, s, proposed))\n",
 482     "\n",
 483     "    return s, proposed"
 484    ]
 485   },
 486   {
 487    "cell_type": "code",
 488    "execution_count": 25,
 489    "metadata": {
 490     "collapsed": true
 491    },
 492    "outputs": [],
 493    "source": [
 494     "def guided_walk(loci, locus_limit=5, wander_limit=10, seek_step_limit=20, return_anyway=False):\n",
 495     "    trail = ''\n",
 496     "    current = Step(0, 0, Direction.RIGHT)    \n",
 497     "    l = 0\n",
 498     "    finished = False\n",
 499     "    while not finished:\n",
 500     "        if abs(current.x - loci[l].x) < locus_limit and abs(current.y - loci[l].y) < locus_limit:\n",
 501     "            l += 1\n",
 502     "            if l == len(loci) - 1:\n",
 503     "                finished = True\n",
 504     "        s, proposed = wander_near(loci[l], current, limit=wander_limit)\n",
 505     "        trail += s\n",
 506     "        current = proposed\n",
 507     "#     print('!! Finished loci')\n",
 508     "    seek_steps = 0\n",
 509     "    while not (current.x == loci[l].x and current.y == loci[l].y) and seek_steps < seek_step_limit:\n",
 510     "#         error = max(abs(current.x - loci[l].x), abs(current.y - loci[l].y))\n",
 511     "#         s, proposed = wander_near(loci[l], current, limit=error+1)\n",
 512     "        s, proposed = seek(loci[l], current)\n",
 513     "        trail += s\n",
 514     "        current = proposed\n",
 515     "        seek_steps += 1\n",
 516     "    if seek_steps >= seek_step_limit and not return_anyway:\n",
 517     "        return ''\n",
 518     "    else:\n",
 519     "        return trail"
 520    ]
 521   },
 522   {
 523    "cell_type": "code",
 524    "execution_count": 28,
 525    "metadata": {},
 526    "outputs": [
 527     {
 528      "data": {
 529       "image/png": 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FIBNJl6SFQEV+muMwZFu3buWGG25QGDKRAEKHIVsFPOHufxk9LykEWfRehSETqYDQYcgs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\nEKlyKgREqpwKAZEqp0JApMr9P8nYgJi0MFyGAAAAAElFTkSuQmCC\n",
 530       "text/plain": [
 531        "<matplotlib.figure.Figure at 0x7ffba4edcf60>"
 532       ]
 533      },
 534      "metadata": {},
 535      "output_type": "display_data"
 536     }
 537    ],
 538    "source": [
 539     "def square_tour(a=80):\n",
 540     "    \"a is width of square\"\n",
 541     "    return ('F' * a + 'L') * 4\n",
 542     "\n",
 543     "plot_trace(trace_tour(square_tour()))"
 544    ]
 545   },
 546   {
 547    "cell_type": "code",
 548    "execution_count": 29,
 549    "metadata": {},
 550    "outputs": [
 551     {
 552      "data": {
 553       "image/png": 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k6yMEKDzGmzHGPSUtKopIo4g8KSJxEXlbRG4WkWYReU5E+kXkuIg0rvT+6urqghdbGGPc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\nybOEYIzJ+/+3mLJIMXCXRQAAAABJRU5ErkJggg==\n",
 554       "text/plain": [
 555        "<matplotlib.figure.Figure at 0x7ffba4b355c0>"
 556       ]
 557      },
 558      "metadata": {},
 559      "output_type": "display_data"
 560     }
 561    ],
 562    "source": [
 563     "def cross_tour(a=50, b=40):\n",
 564     "    \"a is width of cross arm, b is length of cross arm\"\n",
 565     "    return ('F' *  a + 'L' + 'F' * b + 'R' + 'F' * b + 'L') * 4\n",
 566     "\n",
 567     "plot_trace(trace_tour(cross_tour()))"
 568    ]
 569   },
 570   {
 571    "cell_type": "code",
 572    "execution_count": 30,
 573    "metadata": {},
 574    "outputs": [
 575     {
 576      "data": {
 577       "image/png": 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Ukpa9WWhgqFF+bEHHGFQ509PTzM7Out0MR2hgqJGOMahqqqVkbyYaGJRySDgcrno7c7PQ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\n",
 578       "text/plain": [
 579        "<matplotlib.figure.Figure at 0x7ffba4bf1278>"
 580       ]
 581      },
 582      "metadata": {},
 583      "output_type": "display_data"
 584     }
 585    ],
 586    "source": [
 587     "def quincunx_tour(a=60, b=30, c=50):\n",
 588     "    \"a is length of indent, b is indent/outdent distance, c is outdent outer length\"\n",
 589     "    return ('F' * a + 'R' + 'F' * b + 'L' + 'F' * c + 'L' + 'F' * c + 'L' + 'F' * b + 'R') * 4\n",
 590     "plot_trace(trace_tour(quincunx_tour()))"
 591    ]
 592   },
 593   {
 594    "cell_type": "code",
 595    "execution_count": 31,
 596    "metadata": {},
 597    "outputs": [
 598     {
 599      "data": {
 600       "image/png": 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ZZ57hwIED7Nu3r84N3FRGpzCGuczMTFJSUjx/7Pv27aN79+6WU6lgVv6cyBEj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\nVBW0UCqlVBW0UCqlVBX+P0VFnoIKajtRAAAAAElFTkSuQmCC\n",
 601       "text/plain": [
 602        "<matplotlib.figure.Figure at 0x7ffba49b3710>"
 603       ]
 604      },
 605      "metadata": {},
 606      "output_type": "display_data"
 607     }
 608    ],
 609    "source": [
 610     "heart_points = [Step(60, 50, Direction.UP), Step(50, 90, Direction.UP),\n",
 611     "                Step(20, 70, Direction.UP), \n",
 612     "                Step(-40, 90, Direction.UP), Step(-60, 80, Direction.UP), \n",
 613     "                Step(0, 0, Direction.RIGHT)]\n",
 614     "\n",
 615     "heart_tour = ''\n",
 616     "current = Step(0, 0, Direction.RIGHT)\n",
 617     "\n",
 618     "for hp in heart_points:\n",
 619     "    while not (current.x == hp.x and current.y == hp.y):\n",
 620     "        s, proposed = seek(hp, current)\n",
 621     "        heart_tour += s\n",
 622     "        current = proposed\n",
 623     "\n",
 624     "plot_trace(trace_tour(heart_tour))\n",
 625     "\n",
 626     "def heart_tour_func(): return heart_tour"
 627    ]
 628   },
 629   {
 630    "cell_type": "code",
 631    "execution_count": 32,
 632    "metadata": {
 633     "collapsed": true
 634    },
 635    "outputs": [],
 636    "source": [
 637     "def trim_some_mistakes(tour, mistake_limit):\n",
 638     "    trimmed_tour = rw\n",
 639     "    mistake_count = len(mistake_positions(trace_tour(trimmed_tour)))\n",
 640     "    while len(mistake_positions(trace_tour(trimmed_tour))) > mistake_limit:\n",
 641     "        trimmed_tour = trim_loop(trimmed_tour, random_mistake=True)\n",
 642     "    return trimmed_tour"
 643    ]
 644   },
 645   {
 646    "cell_type": "code",
 647    "execution_count": 33,
 648    "metadata": {},
 649    "outputs": [
 650     {
 651      "name": "stdout",
 652      "output_type": "stream",
 653      "text": [
 654       "cross.txt\t   small-squares.txt\t  tours.txt\r\n",
 655       "large-squares.txt  tours-open.txt\t  tours-with-mistakes.txt\r\n",
 656       "quincunx.txt\t   tours-random-walk.txt\r\n"
 657      ]
 658     }
 659    ],
 660    "source": [
 661     "!ls *txt"
 662    ]
 663   },
 664   {
 665    "cell_type": "code",
 666    "execution_count": 46,
 667    "metadata": {},
 668    "outputs": [
 669     {
 670      "data": {
 671       "text/plain": [
 672        "113"
 673       ]
 674      },
 675      "execution_count": 46,
 676      "metadata": {},
 677      "output_type": "execute_result"
 678     }
 679    ],
 680    "source": [
 681     "valid_tours = [t.strip() for t in open('tours.txt').readlines() if valid(trace_tour(t.strip()))]\n",
 682     "valid_tours += [t.strip() for t in open('tours-with-mistakes.txt').readlines() if valid(trace_tour(t.strip()))]\n",
 683     "valid_tours += [t.strip() for t in open('tours-open.txt').readlines() if valid(trace_tour(t.strip()))]\n",
 684     "valid_tours += [t.strip() for t in open('tours-random-walk.txt').readlines() if valid(trace_tour(t.strip()))]\n",
 685     "\n",
 686     "len(valid_tours)"
 687    ]
 688   },
 689   {
 690    "cell_type": "code",
 691    "execution_count": 35,
 692    "metadata": {},
 693    "outputs": [
 694     {
 695      "data": {
 696       "text/plain": [
 697        "True"
 698       ]
 699      },
 700      "execution_count": 35,
 701      "metadata": {},
 702      "output_type": "execute_result"
 703     }
 704    ],
 705    "source": [
 706     "all(valid(trace_tour(t)) for t in valid_tours)"
 707    ]
 708   },
 709   {
 710    "cell_type": "code",
 711    "execution_count": 47,
 712    "metadata": {},
 713    "outputs": [
 714     {
 715      "data": {
 716       "text/plain": [
 717        "(87, 0)"
 718       ]
 719      },
 720      "execution_count": 47,
 721      "metadata": {},
 722      "output_type": "execute_result"
 723     }
 724    ],
 725    "source": [
 726     "tours_with_mistakes = [t.strip() for t in open('tours-with-mistakes.txt').readlines() \n",
 727     "                       if not valid(trace_tour(t.strip()))]\n",
 728     "len(tours_with_mistakes)"
 729    ]
 730   },
 731   {
 732    "cell_type": "code",
 733    "execution_count": 48,
 734    "metadata": {},
 735    "outputs": [
 736     {
 737      "data": {
 738       "text/plain": [
 739        "100"
 740       ]
 741      },
 742      "execution_count": 48,
 743      "metadata": {},
 744      "output_type": "execute_result"
 745     }
 746    ],
 747    "source": [
 748     "tours_open = [t.strip() for t in open('tours-open.txt').readlines() \n",
 749     "                       if not valid(trace_tour(t.strip()))]\n",
 750     "len(tours_open)"
 751    ]
 752   },
 753   {
 754    "cell_type": "code",
 755    "execution_count": 50,
 756    "metadata": {},
 757    "outputs": [
 758     {
 759      "data": {
 760       "text/plain": [
 761        "(84, 116)"
 762       ]
 763      },
 764      "execution_count": 50,
 765      "metadata": {},
 766      "output_type": "execute_result"
 767     }
 768    ],
 769    "source": [
 770     "tours_walks_loops = [t.strip() for t in open('tours-random-walk.txt').readlines() \n",
 771     "                       if len(mistake_positions(trace_tour(t.strip()))) > 1]\n",
 772     "tours_walks_unloops = [t.strip() for t in open('tours-random-walk.txt').readlines() \n",
 773     "                       if len(mistake_positions(trace_tour(t.strip()))) == 1]\n",
 774     "len(tours_walks_loops), len(tours_walks_unloops)"
 775    ]
 776   },
 777   {
 778    "cell_type": "code",
 779    "execution_count": 51,
 780    "metadata": {},
 781    "outputs": [
 782     {
 783      "data": {
 784       "image/png": 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EXnX3Y5tY1pNsSwrfAZ++Pu8RYK6ZrQS+B36XsJ5Is3S6jbQZOt1GCpZCK8FRaCU4Cq0E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\no9BKcBRaCY5CK8FRaCU4/wdDXVwAkfqwLwAAAABJRU5ErkJggg==\n",
 785       "text/plain": [
 786        "<matplotlib.figure.Figure at 0x7ffba4647c18>"
 787       ]
 788      },
 789      "metadata": {},
 790      "output_type": "display_data"
 791     }
 792    ],
 793    "source": [
 794     "plot_trace(trace_tour(tours_with_mistakes[31]))"
 795    ]
 796   },
 797   {
 798    "cell_type": "code",
 799    "execution_count": 54,
 800    "metadata": {},
 801    "outputs": [
 802     {
 803      "data": {
 804       "text/plain": [
 805        "65"
 806       ]
 807      },
 808      "execution_count": 54,
 809      "metadata": {},
 810      "output_type": "execute_result"
 811     }
 812    ],
 813    "source": [
 814     "sum(1 for t in valid_tours if len(t) > 100)"
 815    ]
 816   },
 817   {
 818    "cell_type": "code",
 819    "execution_count": 92,
 820    "metadata": {},
 821    "outputs": [
 822     {
 823      "data": {
 824       "text/plain": [
 825        "48"
 826       ]
 827      },
 828      "execution_count": 92,
 829      "metadata": {},
 830      "output_type": "execute_result"
 831     }
 832    ],
 833    "source": [
 834     "problem_set = [t for t in valid_tours if len(t) <= 100]\n",
 835     "len(problem_set)"
 836    ]
 837   },
 838   {
 839    "cell_type": "code",
 840    "execution_count": 93,
 841    "metadata": {},
 842    "outputs": [
 843     {
 844      "data": {
 845       "text/plain": [
 846        "(48, 65)"
 847       ]
 848      },
 849      "execution_count": 93,
 850      "metadata": {},
 851      "output_type": "execute_result"
 852     }
 853    ],
 854    "source": [
 855     "# problem_set += [t for t in valid_tours if len(t) > 100][0::2]\n",
 856     "valids_to_split = [t for t in valid_tours if len(t) > 100]\n",
 857     "len(problem_set), len(valids_to_split)"
 858    ]
 859   },
 860   {
 861    "cell_type": "code",
 862    "execution_count": 94,
 863    "metadata": {},
 864    "outputs": [
 865     {
 866      "data": {
 867       "text/plain": [
 868        "148"
 869       ]
 870      },
 871      "execution_count": 94,
 872      "metadata": {},
 873      "output_type": "execute_result"
 874     }
 875    ],
 876    "source": [
 877     "problem_set += random.sample(tours_with_mistakes + tours_open + tours_walks_loops + tours_walks_unloops, 100)\n",
 878     "len(problem_set)"
 879    ]
 880   },
 881   {
 882    "cell_type": "code",
 883    "execution_count": 95,
 884    "metadata": {},
 885    "outputs": [
 886     {
 887      "data": {
 888       "text/plain": [
 889        "2284"
 890       ]
 891      },
 892      "execution_count": 95,
 893      "metadata": {},
 894      "output_type": "execute_result"
 895     }
 896    ],
 897    "source": [
 898     "max(len(t) for t in valids_to_split)"
 899    ]
 900   },
 901   {
 902    "cell_type": "code",
 903    "execution_count": 96,
 904    "metadata": {},
 905    "outputs": [
 906     {
 907      "data": {
 908       "text/plain": [
 909        "1680"
 910       ]
 911      },
 912      "execution_count": 96,
 913      "metadata": {},
 914      "output_type": "execute_result"
 915     }
 916    ],
 917    "source": [
 918     "sum(len(t) for t in problem_set if valid(trace_tour(t)))"
 919    ]
 920   },
 921   {
 922    "cell_type": "code",
 923    "execution_count": 85,
 924    "metadata": {},
 925    "outputs": [
 926     {
 927      "data": {
 928       "text/plain": [
 929        "[]"
 930       ]
 931      },
 932      "execution_count": 85,
 933      "metadata": {},
 934      "output_type": "execute_result"
 935     }
 936    ],
 937    "source": [
 938     "[(i, j) \n",
 939     " for i in range(len(problem_set)) \n",
 940     " for j in range(len(problem_set))\n",
 941     " if i != j\n",
 942     " if valid(trace_tour(problem_set[i] + problem_set[j]))]"
 943    ]
 944   },
 945   {
 946    "cell_type": "code",
 947    "execution_count": 87,
 948    "metadata": {
 949     "scrolled": true
 950    },
 951    "outputs": [
 952     {
 953      "name": "stdout",
 954      "output_type": "stream",
 955      "text": [
 956       "attempting 0\n",
 957       "** found split for 0\n",
 958       "attempting 1\n",
 959       "attempting 2\n",
 960       "attempting 3\n",
 961       "attempting 4\n",
 962       "attempting 5\n",
 963       "attempting 6\n",
 964       "attempting 7\n",
 965       "attempting 8\n",
 966       "attempting 9\n",
 967       "attempting 10\n",
 968       "attempting 11\n",
 969       "** found split for 11\n",
 970       "attempting 12\n",
 971       "attempting 13\n",
 972       "attempting 14\n",
 973       "attempting 15\n",
 974       "attempting 16\n",
 975       "attempting 17\n",
 976       "** found split for 17\n",
 977       "attempting 18\n",
 978       "attempting 19\n",
 979       "attempting 20\n",
 980       "attempting 21\n",
 981       "attempting 22\n",
 982       "attempting 23\n",
 983       "attempting 24\n",
 984       "attempting 25\n",
 985       "attempting 26\n",
 986       "attempting 27\n",
 987       "attempting 28\n",
 988       "attempting 29\n",
 989       "** found split for 29\n",
 990       "attempting 30\n",
 991       "attempting 31\n",
 992       "attempting 32\n",
 993       "attempting 33\n",
 994       "attempting 34\n",
 995       "** found split for 34\n",
 996       "attempting 35\n",
 997       "attempting 36\n",
 998       "attempting 37\n",
 999       "attempting 38\n",
1000       "** found split for 38\n",
1001       "attempting 39\n",
1002       "attempting 40\n",
1003       "attempting 41\n",
1004       "** found split for 41\n",
1005       "attempting 42\n",
1006       "attempting 43\n",
1007       "attempting 44\n",
1008       "attempting 45\n",
1009       "attempting 46\n",
1010       "attempting 47\n",
1011       "attempting 48\n",
1012       "** found split for 48\n",
1013       "attempting 49\n",
1014       "** found split for 49\n",
1015       "attempting 50\n",
1016       "** found split for 50\n",
1017       "attempting 51\n",
1018       "attempting 52\n",
1019       "attempting 53\n",
1020       "attempting 54\n",
1021       "attempting 55\n",
1022       "attempting 56\n",
1023       "attempting 57\n",
1024       "** found split for 57\n",
1025       "attempting 58\n",
1026       "attempting 59\n",
1027       "** found split for 59\n",
1028       "attempting 60\n",
1029       "attempting 61\n",
1030       "attempting 62\n",
1031       "** found split for 62\n",
1032       "attempting 63\n",
1033       "attempting 64\n"
1034      ]
1035     }
1036    ],
1037    "source": [
1038     "split_valids = []\n",
1039     "unsplit_valids = []\n",
1040     "i = 0\n",
1041     "for v in valids_to_split:\n",
1042     "    can_add = False\n",
1043     "    attempts_remaining = 500\n",
1044     "    print('attempting', i)\n",
1045     "    while not can_add and attempts_remaining > 0:\n",
1046     "        # print('splitting', i, 'attempt', attempts_remaining)\n",
1047     "        attempts_remaining -= 1\n",
1048     "#         split_pos = len(v) // 2 + random.randrange(10)\n",
1049     "        split_pos = random.randint(20, len(v) - 40)\n",
1050     "        vl = v[:split_pos]\n",
1051     "        vr = v[split_pos:]\n",
1052     "        can_add = True\n",
1053     "        if valid(trace_tour(vr + vl)): can_add = False\n",
1054     "        for other in problem_set:\n",
1055     "            if can_add and valid(trace_tour(other + vl)): can_add = False\n",
1056     "            if can_add and valid(trace_tour(other + vr)): can_add = False\n",
1057     "            if can_add and valid(trace_tour(vl + other)): can_add = False\n",
1058     "            if can_add and valid(trace_tour(vr + other)): can_add = False\n",
1059     "        for other in split_valids:\n",
1060     "            if can_add and valid(trace_tour(other + vl)): can_add = False\n",
1061     "            if can_add and valid(trace_tour(other + vr)): can_add = False\n",
1062     "            if can_add and valid(trace_tour(vl + other)): can_add = False\n",
1063     "            if can_add and valid(trace_tour(vr + other)): can_add = False\n",
1064     "    if can_add:\n",
1065     "        split_valids += [vl, vr]\n",
1066     "        print('** found split for', i)\n",
1067     "    else:\n",
1068     "        unsplit_valids += [v]\n",
1069     "    i += 1"
1070    ]
1071   },
1072   {
1073    "cell_type": "code",
1074    "execution_count": 97,
1075    "metadata": {},
1076    "outputs": [
1077     {
1078      "data": {
1079       "text/plain": [
1080        "['RLFLRFRLLFFRRLFFFRFLLFFFLFLRFRFFFRFLLFRFRFFFFRFFLFLFLRRFRFFFFLFFFFFFRLFLFLFRRFFFLFRFFRRFLLFFFRFRFFLRLFFLFRFFFLFFFFLRFFFFFLFFRLFFFFFFFFRFFFFFFRFFFFFFRLFFFLFRFRFLFFFFLFFFFFFLRFFFFLRLFFRFFRFLFFFFFFFLFLRFRLFFFFFFRLRFFLFFRFRLFFFRLFRLFFFLFFRLFLFFLFRRFFFLRFFLFFLRFFRFLRFFFLFFRFFLRFFFFFRFLFRLFRRFLFFFFRRFLRLFLFFFFFFLFFFFFFRFLRLFRLFLFFRFFLFFFFFFRRFFFLLFFRFFLRFFRRLLFRFFFFFFLFFFLFFFLRFFLFRRFLRLRFFFRFLFFFFFRLRFLFLFFRRFLFFFRLLFRLLRRLFLFRFFRFLFFFFRFFFLFFLFRFRFLRFFFFFLRFLFLFFFRFFFLFRRFLFLFFLFFRFFFFFFRRFLFFRFFFLRFLFFFFFFFFLRFFRRLFFFFFLRLFFFFFRLFFFFFFFFFFFLRFFLFRFFFFLRLLFRFRLRFFFLFLFFFRFFFFFRFFRFFLFRLLFRFLRFFFFLFFLFRFFFRLFFRRFLRLFLFFFLRFLRFFFFFFLFFFRFRFFFFFF',\n",
1081        " 'LLRRLFFFFFFFLFFFRFFFFFFFLLRFFRFFFRFFFLLFFRLRFFFLFRFFRFLFRFFFRFLLFFLFFFFFFRRFLRFRLFFFLFFFFFFFFLFFRLFFFFRFFFRFFFLFFFRLR',\n",
1082        " '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',\n",
1083        " 'FLFFRRFFFFRLLFFFLFLLRRFFFRFFFLRFFFLFLFFRRFFFFLLFRFFLFRFFRFFFRFLFFFFRLFFFLRFFFFRFRLFFRLLFFFFFF']"
1084       ]
1085      },
1086      "execution_count": 97,
1087      "metadata": {},
1088      "output_type": "execute_result"
1089     }
1090    ],
1091    "source": [
1092     "split_valids[:4]"
1093    ]
1094   },
1095   {
1096    "cell_type": "code",
1097    "execution_count": 98,
1098    "metadata": {},
1099    "outputs": [
1100     {
1101      "data": {
1102       "text/plain": [
1103        "[(0, 1),\n",
1104        " (2, 3),\n",
1105        " (4, 5),\n",
1106        " (6, 7),\n",
1107        " (8, 9),\n",
1108        " (10, 11),\n",
1109        " (12, 13),\n",
1110        " (14, 15),\n",
1111        " (16, 17),\n",
1112        " (18, 19),\n",
1113        " (20, 21),\n",
1114        " (22, 23),\n",
1115        " (24, 25)]"
1116       ]
1117      },
1118      "execution_count": 98,
1119      "metadata": {},
1120      "output_type": "execute_result"
1121     }
1122    ],
1123    "source": [
1124     "[(i, j) \n",
1125     " for i in range(len(split_valids)) \n",
1126     " for j in range(len(split_valids))\n",
1127     " if i != j\n",
1128     " if valid(trace_tour(split_valids[i] + split_valids[j]))]"
1129    ]
1130   },
1131   {
1132    "cell_type": "code",
1133    "execution_count": 99,
1134    "metadata": {},
1135    "outputs": [
1136     {
1137      "data": {
1138       "text/plain": [
1139        "226"
1140       ]
1141      },
1142      "execution_count": 99,
1143      "metadata": {},
1144      "output_type": "execute_result"
1145     }
1146    ],
1147    "source": [
1148     "problem_set += (split_valids + unsplit_valids)\n",
1149     "len(problem_set)"
1150    ]
1151   },
1152   {
1153    "cell_type": "code",
1154    "execution_count": 100,
1155    "metadata": {
1156     "collapsed": true
1157    },
1158    "outputs": [],
1159    "source": [
1160     "with open('06-tours.txt', 'w') as f:\n",
1161     "    f.writelines(t + '\\n' for t in random.sample(problem_set, len(problem_set)))"
1162    ]
1163   },
1164   {
1165    "cell_type": "code",
1166    "execution_count": null,
1167    "metadata": {
1168     "collapsed": true
1169    },
1170    "outputs": [],
1171    "source": []
1172   }
1173  ],
1174  "metadata": {
1175   "kernelspec": {
1176    "display_name": "Python 3",
1177    "language": "python",
1178    "name": "python3"
1179   },
1180   "language_info": {
1181    "codemirror_mode": {
1182     "name": "ipython",
1183     "version": 3
1184    },
1185    "file_extension": ".py",
1186    "mimetype": "text/x-python",
1187    "name": "python",
1188    "nbconvert_exporter": "python",
1189    "pygments_lexer": "ipython3",
1190    "version": "3.5.2+"
1191   }
1192  },
1193  "nbformat": 4,
1194  "nbformat_minor": 2
1195 }