--- /dev/null
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "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",
+ "1. which tours are closed?\n",
+ "2. what is the area enclosed by the tour?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "import collections\n",
+ "import enum\n",
+ "import random\n",
+ "import os\n",
+ "\n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "class Direction(enum.Enum):\n",
+ " UP = 1\n",
+ " RIGHT = 2\n",
+ " DOWN = 3\n",
+ " LEFT = 4\n",
+ " \n",
+ "turn_lefts = {Direction.UP: Direction.LEFT, Direction.LEFT: Direction.DOWN,\n",
+ " Direction.DOWN: Direction.RIGHT, Direction.RIGHT: Direction.UP}\n",
+ "\n",
+ "turn_rights = {Direction.UP: Direction.RIGHT, Direction.RIGHT: Direction.DOWN,\n",
+ " Direction.DOWN: Direction.LEFT, Direction.LEFT: Direction.UP}\n",
+ "\n",
+ "def turn_left(d):\n",
+ " return turn_lefts[d]\n",
+ "\n",
+ "def turn_right(d):\n",
+ " return turn_rights[d]\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "Step = collections.namedtuple('Step', ['x', 'y', 'dir'])\n",
+ "Mistake = collections.namedtuple('Mistake', ['i', 'step'])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def advance(step, d):\n",
+ " if d == Direction.UP:\n",
+ " return Step(step.x, step.y+1, d)\n",
+ " elif d == Direction.DOWN:\n",
+ " return Step(step.x, step.y-1, d)\n",
+ " elif d == Direction.LEFT:\n",
+ " return Step(step.x-1, step.y, d)\n",
+ " elif d == Direction.RIGHT:\n",
+ " return Step(step.x+1, step.y, d)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
+ " current = Step(startx, starty, startdir)\n",
+ " trace = [current]\n",
+ " for s in tour:\n",
+ " if s == 'F':\n",
+ " current = advance(current, current.dir)\n",
+ " elif s == 'L':\n",
+ " current = advance(current, turn_left(current.dir))\n",
+ " elif s == 'R':\n",
+ " current = advance(current, turn_right(current.dir))\n",
+ " trace += [current]\n",
+ " return trace "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def positions(trace):\n",
+ " return [(s.x, s.y) for s in trace]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def valid(trace):\n",
+ " return (trace[-1].x == 0 \n",
+ " and trace[-1].y == 0 \n",
+ " and len(set(positions(trace))) + 1 == len(trace))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def chunks(items, n=2):\n",
+ " return [items[i:i+n] for i in range(len(items) - n + 1)]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Using the [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def shoelace(trace):\n",
+ " return abs(sum(s.x * t.y - t.x * s.y for s, t in chunks(trace, 2))) // 2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def step(s, current):\n",
+ " if s == 'F':\n",
+ " return advance(current, current.dir)\n",
+ " elif s == 'L':\n",
+ " return advance(current, turn_left(current.dir))\n",
+ " elif s == 'R':\n",
+ " return advance(current, turn_right(current.dir))\n",
+ " else:\n",
+ " raise ValueError"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def valid_prefix(tour):\n",
+ " current = Step(0, 0, Direction.RIGHT)\n",
+ " prefix = []\n",
+ " posns = []\n",
+ " for s in tour:\n",
+ " current = step(s, current)\n",
+ " prefix += [s]\n",
+ " if (current.x, current.y) in posns:\n",
+ " return ''\n",
+ " elif current.x == 0 and current.y == 0: \n",
+ " return ''.join(prefix)\n",
+ " posns += [(current.x, current.y)]\n",
+ " if current.x == 0 and current.y == 0:\n",
+ " return ''.join(prefix)\n",
+ " else:\n",
+ " return ''"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def mistake_positions(trace, debug=False):\n",
+ " mistakes = []\n",
+ " current = trace[0]\n",
+ " posns = [(0, 0)]\n",
+ " for i, current in enumerate(trace[1:]):\n",
+ " if (current.x, current.y) in posns:\n",
+ " if debug: print(i, current)\n",
+ " mistakes += [Mistake(i+1, current)]\n",
+ " posns += [(current.x, current.y)]\n",
+ " if (current.x, current.y) == (0, 0):\n",
+ " return mistakes[:-1]\n",
+ " else:\n",
+ " return mistakes + [Mistake(len(trace)+1, current)]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def returns_to_origin(mistake_positions):\n",
+ " return [i for i, m in mistake_positions\n",
+ " if (m.x, m.y) == (0, 0)]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def random_walk(steps=1000):\n",
+ " return ''.join(random.choice('FFLR') for _ in range(steps))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def bounds(trace):\n",
+ " return (max(s.x for s in trace),\n",
+ " max(s.y for s in trace),\n",
+ " min(s.x for s in trace),\n",
+ " min(s.y for s in trace))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None, filename=None):\n",
+ " plt.axis('on')\n",
+ " plt.axes().set_aspect('equal')\n",
+ " for s, t in chunks(trace, 2):\n",
+ " w, h = plot_wh[t.dir]\n",
+ " 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",
+ " xh, yh, xl, yl = bounds(trace)\n",
+ " if xybounds is not None: \n",
+ " bxh, byh, bxl, byl = xybounds\n",
+ " plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
+ " plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
+ " else:\n",
+ " plt.xlim([xl-1, xh+1])\n",
+ " plt.ylim([yl-1, yh+1])\n",
+ " if filename:\n",
+ " plt.savefig(filename)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def trim_loop(tour):\n",
+ " trace = trace_tour(tour)\n",
+ " mistakes = mistake_positions(trace)\n",
+ " end_mistake_index = 0\n",
+ "# 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",
+ " # while this mistake extends to the next step in the trace...\n",
+ " while (mistakes[end_mistake_index].i + 1 < len(trace) and \n",
+ " end_mistake_index + 1 < len(mistakes) and\n",
+ " mistakes[end_mistake_index].i + 1 == \n",
+ " mistakes[end_mistake_index + 1].i):\n",
+ "# 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",
+ " # push this mistake finish point later\n",
+ " end_mistake_index += 1\n",
+ " mistake = mistakes[end_mistake_index]\n",
+ " \n",
+ " # find the first location that mentions where this mistake ends (which the point where the loop starts)\n",
+ " mistake_loop_start = max(i for i, loc in enumerate(trace[:mistake.i])\n",
+ " if (loc.x, loc.y) == (mistake.step.x, mistake.step.y))\n",
+ "# print('Dealing with mistake from', mistake_loop_start, 'to', mistake.i, ', trace has len', len(trace))\n",
+ " \n",
+ " # direction before entering the loop\n",
+ " direction_before = trace[mistake_loop_start].dir\n",
+ " \n",
+ " # find the new instruction to turn from heading before the loop to heading after the loop\n",
+ " new_instruction = 'F'\n",
+ " if (mistake.i + 1) < len(trace):\n",
+ " if turn_left(direction_before) == trace[mistake.i + 1].dir:\n",
+ " new_instruction = 'L'\n",
+ " if turn_right(direction_before) == trace[mistake.i + 1].dir:\n",
+ " new_instruction = 'R'\n",
+ "# if (mistake.i + 1) < len(trace):\n",
+ "# print('turning from', direction_before, 'to', trace[mistake.i + 1].dir, 'with', new_instruction )\n",
+ "# else:\n",
+ "# print('turning from', direction_before, 'to BEYOND END', 'with', new_instruction )\n",
+ " return tour[:mistake_loop_start] + new_instruction + tour[mistake.i+1:]\n",
+ "# return mistake, mistake_loop_start, trace[mistake_loop_start-2:mistake_loop_start+8]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def trim_all_loops(tour, mistake_reduction_attempt_limit=10):\n",
+ " trace = trace_tour(tour)\n",
+ " mistake_limit = 1\n",
+ " if trace[-1].x == 0 and trace[-1].y == 0:\n",
+ " mistake_limit = 0\n",
+ " mistakes = mistake_positions(trace)\n",
+ " \n",
+ " old_mistake_count = len(mistakes)\n",
+ " mistake_reduction_tries = 0\n",
+ " \n",
+ " while len(mistakes) > mistake_limit and mistake_reduction_tries < mistake_reduction_attempt_limit:\n",
+ " tour = trim_loop(tour)\n",
+ " trace = trace_tour(tour)\n",
+ " mistakes = mistake_positions(trace)\n",
+ " if len(mistakes) < old_mistake_count:\n",
+ " old_mistake_count = len(mistakes)\n",
+ " mistake_reduction_tries = 0\n",
+ " else:\n",
+ " mistake_reduction_tries += 1\n",
+ " if mistake_reduction_tries >= mistake_reduction_attempt_limit:\n",
+ " return ''\n",
+ " else:\n",
+ " return tour"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def reverse_tour(tour):\n",
+ " def swap(tour_step):\n",
+ " if tour_step == 'R':\n",
+ " return 'L'\n",
+ " elif tour_step == 'L':\n",
+ " return 'R'\n",
+ " else:\n",
+ " return tour_step\n",
+ " \n",
+ " return ''.join(swap(s) for s in reversed(tour))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def wander_near(locus, current, limit=10):\n",
+ " valid_proposal = False\n",
+ " while not valid_proposal:\n",
+ " s = random.choice('FFFRL')\n",
+ " if s == 'F':\n",
+ " proposed = advance(current, current.dir)\n",
+ " elif s == 'L':\n",
+ " proposed = advance(current, turn_left(current.dir))\n",
+ " elif s == 'R':\n",
+ " proposed = advance(current, turn_right(current.dir))\n",
+ " if abs(proposed.x - locus.x) < limit and abs(proposed.y - locus.y) < limit:\n",
+ " valid_proposal = True\n",
+ "# print('At {} going to {} by step {} to {}'.format(current, locus, s, proposed))\n",
+ " return s, proposed"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def seek(goal, current):\n",
+ " dx = current.x - goal.x\n",
+ " dy = current.y - goal.y\n",
+ "\n",
+ " if dx < 0 and abs(dx) > abs(dy): # to the left\n",
+ " side = 'left'\n",
+ " if current.dir == Direction.RIGHT:\n",
+ " s = 'F'\n",
+ " elif current.dir == Direction.UP:\n",
+ " s = 'R'\n",
+ " else:\n",
+ " s = 'L'\n",
+ " elif dx > 0 and abs(dx) > abs(dy): # to the right\n",
+ " side = 'right'\n",
+ " if current.dir == Direction.LEFT:\n",
+ " s = 'F'\n",
+ " elif current.dir == Direction.UP:\n",
+ " s = 'L'\n",
+ " else:\n",
+ " s = 'R'\n",
+ " elif dy > 0 and abs(dx) <= abs(dy): # above\n",
+ " side = 'above'\n",
+ " if current.dir == Direction.DOWN:\n",
+ " s = 'F'\n",
+ " elif current.dir == Direction.RIGHT:\n",
+ " s = 'R'\n",
+ " else:\n",
+ " s = 'L'\n",
+ " else: # below\n",
+ " side = 'below'\n",
+ " if current.dir == Direction.UP:\n",
+ " s = 'F'\n",
+ " elif current.dir == Direction.LEFT:\n",
+ " s = 'R'\n",
+ " else:\n",
+ " s = 'L'\n",
+ " if s == 'F':\n",
+ " proposed = advance(current, current.dir)\n",
+ " elif s == 'L':\n",
+ " proposed = advance(current, turn_left(current.dir))\n",
+ " elif s == 'R':\n",
+ " proposed = advance(current, turn_right(current.dir))\n",
+ " \n",
+ "# print('At {} going to {}, currently {}, by step {} to {}'.format(current, goal, side, s, proposed))\n",
+ "\n",
+ " return s, proposed"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def guided_walk(loci, locus_limit=5, wander_limit=10, seek_step_limit=20):\n",
+ " trail = ''\n",
+ " current = Step(0, 0, Direction.RIGHT) \n",
+ " l = 0\n",
+ " finished = False\n",
+ " while not finished:\n",
+ " if abs(current.x - loci[l].x) < locus_limit and abs(current.y - loci[l].y) < locus_limit:\n",
+ " l += 1\n",
+ " if l == len(loci) - 1:\n",
+ " finished = True\n",
+ " s, proposed = wander_near(loci[l], current, limit=wander_limit)\n",
+ " trail += s\n",
+ " current = proposed\n",
+ "# print('!! Finished loci')\n",
+ " seek_steps = 0\n",
+ " while not (current.x == loci[l].x and current.y == loci[l].y) and seek_steps < seek_step_limit:\n",
+ "# error = max(abs(current.x - loci[l].x), abs(current.y - loci[l].y))\n",
+ "# s, proposed = wander_near(loci[l], current, limit=error+1)\n",
+ " s, proposed = seek(loci[l], current)\n",
+ " trail += s\n",
+ " current = proposed\n",
+ " seek_steps += 1\n",
+ " if seek_steps >= seek_step_limit:\n",
+ " return ''\n",
+ " else:\n",
+ " return trail"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def square_tour(a=80):\n",
+ " \"a is width of square\"\n",
+ " return ('F' * a + 'L') * 4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def cross_tour(a=50, b=40):\n",
+ " \"a is width of cross arm, b is length of cross arm\"\n",
+ " return ('F' * a + 'L' + 'F' * b + 'R' + 'F' * b + 'L') * 4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def quincunx_tour(a=60, b=30, c=50):\n",
+ " \"a is length of indent, b is indent/outdent distance, c is outdent outer length\"\n",
+ " return ('F' * a + 'R' + 'F' * b + 'L' + 'F' * c + 'L' + 'F' * c + 'L' + 'F' * b + 'R') * 4\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "heart_points = [Step(60, 50, Direction.UP), Step(50, 90, Direction.UP),\n",
+ " Step(20, 70, Direction.UP), \n",
+ " Step(-40, 90, Direction.UP), Step(-60, 80, Direction.UP), \n",
+ " Step(0, 0, Direction.RIGHT)]\n",
+ "\n",
+ "heart_tour = ''\n",
+ "current = Step(0, 0, Direction.RIGHT)\n",
+ "\n",
+ "for hp in heart_points:\n",
+ " while not (current.x == hp.x and current.y == hp.y):\n",
+ " s, proposed = seek(hp, current)\n",
+ " heart_tour += s\n",
+ " current = proposed\n",
+ "\n",
+ "def heart_tour_func(): return heart_tour"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# success_count = 0\n",
+ "# while success_count <= 20:\n",
+ "# lc = trace_tour(square_tour(a=10))\n",
+ "# rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
+ "# if rw:\n",
+ "# rw_trimmed = trim_all_loops(rw)\n",
+ "# if len(rw_trimmed) > 10:\n",
+ "# with open('small-squares.txt', 'a') as f:\n",
+ "# f.write(rw_trimmed + '\\n')\n",
+ "# success_count += 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# success_count = 0\n",
+ "# while success_count <= 20:\n",
+ "# lc = trace_tour(square_tour())\n",
+ "# rw = guided_walk(lc)\n",
+ "# if rw:\n",
+ "# rw_trimmed = trim_all_loops(rw)\n",
+ "# if len(rw_trimmed) > 10:\n",
+ "# with open('large-squares.txt', 'a') as f:\n",
+ "# f.write(rw_trimmed + '\\n')\n",
+ "# success_count += 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# success_count = 0\n",
+ "# while success_count <= 20:\n",
+ "# lc = trace_tour(cross_tour())\n",
+ "# rw = guided_walk(lc)\n",
+ "# if rw:\n",
+ "# rw_trimmed = trim_all_loops(rw)\n",
+ "# if len(rw_trimmed) > 10:\n",
+ "# with open('cross.txt', 'a') as f:\n",
+ "# f.write(rw_trimmed + '\\n')\n",
+ "# success_count += 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# success_count = 0\n",
+ "# while success_count <= 20:\n",
+ "# lc = trace_tour(quincunx_tour())\n",
+ "# rw = guided_walk(lc)\n",
+ "# if rw:\n",
+ "# rw_trimmed = trim_all_loops(rw)\n",
+ "# if len(rw_trimmed) > 10:\n",
+ "# with open('quincunx.txt', 'a') as f:\n",
+ "# f.write(rw_trimmed + '\\n')\n",
+ "# success_count += 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
+ "tours_filename = 'tours.txt'\n",
+ "\n",
+ "try:\n",
+ " os.remove(tours_filename)\n",
+ "except OSError:\n",
+ " pass\n",
+ "\n",
+ "success_count = 0\n",
+ "while success_count < 100:\n",
+ " lc = trace_tour(random.choice(patterns)())\n",
+ " rw = guided_walk(lc)\n",
+ " if rw:\n",
+ " rw_trimmed = trim_all_loops(rw)\n",
+ " if len(rw_trimmed) > 10:\n",
+ " with open(tours_filename, 'a') as f:\n",
+ " f.write(rw_trimmed + '\\n')\n",
+ " success_count += 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.5.2+"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
projects / ou-summer-of-code-2017.git / blobdiff