sonygod/gist:81842f817a06d32f88f71b77e74cd5c3

## gistfile1.txt
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0qk0nOVJTU5ufHS+ebOpugsGger1eFRGrw3QI2zcSS0fXwWflZOxFRUVFAKxb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\nJz/5CU8++SRJSV3QhlW1Uy7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11eb38f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Horizontal chords before collinear vertices =  [(6, 37), (9, 21)]\n",
      "vertical_chords =  [(21, 37), (22, 36)]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118795d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1187877f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "horizontal_chords =  [(6, 37), (9, 21), (12, 19), (13, 16), (29, 24), (31, 22), (32, 8), (33, 36)]\n",
      "vertical_chords =  [(21, 37), (22, 36), (1, 19), (2, 8), (3, 6), (10, 16), (17, 9), (27, 24)]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bffe0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d5d80f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'Please make sure that the INPUT is A CLOSED RECTILINEAR POLYGON,'\n",
    "'CONSTRUCTED WHILE GOING IN ANTI-CLOCKWISE ONLY'\n",
    "# importing libraries\n",
    "import networkx as nx\n",
    "import turtle\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "from networkx.algorithms import bipartite\n",
    "import math\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "# declaration list\n",
    "wn = turtle.Screen()\n",
    "# a turtle called gopu \n",
    "gopu = turtle.Turtle() \n",
    "# co-ordinate points\n",
    "x = [] \n",
    "y = []\n",
    "# vertex-type := rectilinear = -1; convex = 0; concave = 1 \n",
    "vertex_type = [] \n",
    "# store the bipartite graph of chords\n",
    "G = nx.Graph()\n",
    "# the line below can be commented if one needs animation\n",
    "gopu.speed(0)\n",
    "# starts recording keys being pressed\n",
    "gopu.begin_poly()\n",
    "\n",
    "# Event handlers\n",
    "stride = 25\n",
    "# Up  = up() - vertex to be deleted = -1\n",
    "def up():\n",
    "    vertex_type.append(-1)\n",
    "    gopu.forward(stride)\n",
    " \n",
    "# left = left() ; make vertex - convex = 0\n",
    "def left():\n",
    "    vertex_type.append(0)\n",
    "    gopu.setheading(gopu.heading()+90)\n",
    "    gopu.forward(stride)\n",
    " \n",
    "# right = right() ; make vertex - concave = 1\n",
    "def right():\n",
    "    vertex_type.append(1)\n",
    "    gopu.setheading(gopu.heading()-90)\n",
    "    gopu.forward(stride)\n",
    " \n",
    "# back = back() -- doing undo is allowed only once.\n",
    "def back():\n",
    "    vertex_type.pop()\n",
    "    gopu.undo()\n",
    "\n",
    "# quits the screen and outputs the plots the partitioned polygon\n",
    "def partition_polygon():\n",
    "    # closing the screen\n",
    "    wn.bye()\n",
    "    # stopped recording the polygon\n",
    "    gopu.end_poly()\n",
    "    p = gopu.get_poly()\n",
    "    p = list(p)\n",
    "    compute_partition(p)  \n",
    "    \n",
    "'''\n",
    "The movements of the turtle are recorded and the rectilinear graph thus \n",
    "obtained is converted into bipartite graph of chords\n",
    "'''\n",
    "def compute_partition(p):\n",
    "    # p now contains the list of coordinates of vertices\n",
    "    # last one is same as the origin\n",
    "    # and the origin is always going to be a convex vertex\n",
    "    p.pop()\n",
    "    vertex_type[0] = 0\n",
    "    \n",
    "    # x and y contain list of x and y coordinates respectively\n",
    "    for i,j in p:\n",
    "        x.append(i)\n",
    "        y.append(j)\n",
    "\n",
    "    # this is done as there are some very small errors in recording the \n",
    "    # position by the turtle library\n",
    "    for i in range(len(x)):\n",
    "        x[i] = int(x[i])\n",
    "        y[i] = int(y[i])\n",
    "\n",
    "    for i in range(len(x)):\n",
    "        if x[i] % stride != 0:\n",
    "            x[i] += (stride - x[i] % stride)\n",
    "        if y[i] % stride != 0:\n",
    "            y[i] += (stride - y[i] % stride)\n",
    "    \n",
    "    collinear_vertices = [i for i,val in enumerate(vertex_type) if val == -1]\n",
    "    # finding the chords inside the polygon\n",
    "    horizontal_chords = []\n",
    "    vertical_chords = []\n",
    "    concave_vertices = [i for i,val in enumerate(vertex_type) if val == 1]\n",
    "\n",
    "    # middles is used because, there are cases when there is a chord between vertices\n",
    "    # and they intersect with external chords, hence if there is any vertex in between \n",
    "    # two vertices then skip that chord. \n",
    "    for i in range(len(concave_vertices)):\n",
    "        for j in range(i+1,len(concave_vertices)):\n",
    "            if concave_vertices[j] != concave_vertices[i] + 1:\n",
    "                middles = []\n",
    "                if y[concave_vertices[i]] == y[concave_vertices[j]]:\n",
    "                    for k in range(len(x)):\n",
    "                        if y[concave_vertices[i]] == y[k] and (x[concave_vertices[i]] < x[k] and x[concave_vertices[j]] > x[k] \\\n",
    "                                                              or x[concave_vertices[i]] > x[k] and x[concave_vertices[j]] < x[k]):\n",
    "                            middles.append(k)\n",
    "                    if len(middles) == 0:\n",
    "                        horizontal_chords.append((concave_vertices[i],concave_vertices[j]))\n",
    "                middles = []\n",
    "                if x[concave_vertices[i]] == x[concave_vertices[j]]:\n",
    "                    for k in range(len(x)):\n",
    "                        if x[concave_vertices[i]] == x[k] and (y[concave_vertices[i]] < y[k] and y[concave_vertices[j]] > y[k] \\\n",
    "                                                              or y[concave_vertices[i]] > y[k] and y[concave_vertices[j]] < y[k]):\n",
    "                            middles.append(k)\n",
    "                    if len(middles) == 0:\n",
    "                        vertical_chords.append((concave_vertices[i],concave_vertices[j]))\n",
    "            \n",
    "\n",
    "    \n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x+[0], y+[0], color='black')\n",
    "    ax.scatter(x+[0], y+[0], color='black')\n",
    "    for i in range(len(x)):\n",
    "        ax.annotate(i, (x[i],y[i]))\n",
    "    plt.show()\n",
    "    plt.clf()\n",
    "    print(\"Horizontal chords before collinear vertices = \", horizontal_chords)\n",
    "    print(\"vertical_chords = \", vertical_chords)\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x+[0], y+[0], color='black')\n",
    "    ax.scatter(x+[0], y+[0], color='black')\n",
    "    for i in range(len(x)):\n",
    "        ax.annotate(i, (x[i],y[i]))\n",
    "    for i,j in horizontal_chords:\n",
    "        ax.plot([x[i],x[j]],[y[i],y[j]],color='black')\n",
    "    for i,j in vertical_chords:\n",
    "        ax.plot([x[i],x[j]],[y[i],y[j]], color='black')\n",
    "    plt.show()\n",
    "    plt.clf()\n",
    "    for i in range(len(collinear_vertices)):\n",
    "        for j in range(len(concave_vertices)):\n",
    "            middles = []\n",
    "            if y[collinear_vertices[i]] == y[concave_vertices[j]]:\n",
    "                if collinear_vertices[i] < concave_vertices[j]:\n",
    "                    for k in range(len(x)):\n",
    "                        if y[k] == y[collinear_vertices[i]] and (x[k] < x[concave_vertices[j]] \\\n",
    "                            and x[k] > x[collinear_vertices[i]] or x[k] > x[concave_vertices[j]] \\\n",
    "                            and x[k] < x[collinear_vertices[i]]):\n",
    "                            middles.append(k)\n",
    "                    if collinear_vertices[i]+1 == concave_vertices[j]:\n",
    "                        middles.append(0)\n",
    "                else:\n",
    "                    for k in range(len(x)):\n",
    "                        if y[k] == y[collinear_vertices[i]] and (x[k] > x[concave_vertices[j]] \\\n",
    "                            and x[k] < x[collinear_vertices[i]] or x[k] < x[concave_vertices[j]] \\\n",
    "                            and x[k] > x[collinear_vertices[i]]):\n",
    "                            middles.append(k)\n",
    "                    if collinear_vertices[i] == concave_vertices[j]+1:\n",
    "                        middles.append(0)\n",
    "                if len(middles) == 0:\n",
    "                    horizontal_chords.append((collinear_vertices[i],concave_vertices[j]))\n",
    "            middles = []\n",
    "            if x[collinear_vertices[i]] == x[concave_vertices[j]]:\n",
    "                if collinear_vertices[i] < concave_vertices[j]:\n",
    "                    for k in range(len(x)):\n",
    "                        if x[k] == x[collinear_vertices[i]] and (y[k] < y[concave_vertices[j]] \\\n",
    "                            and y[k] > y[collinear_vertices[i]] or y[k] > y[concave_vertices[j]] \\\n",
    "                            and y[k] < y[collinear_vertices[i]]):\n",
    "                            middles.append(k)\n",
    "                    if collinear_vertices[i]+1 == concave_vertices[j]:\n",
    "                        middles.append(0)\n",
    "                else:\n",
    "                    for k in range(len(x)):\n",
    "                        if x[k] == x[collinear_vertices[i]] and (y[k] > y[concave_vertices[j]] \\\n",
    "                            and y[k] < y[collinear_vertices[i]] or y[k] < y[concave_vertices[j]] \\\n",
    "                            and y[k] > y[collinear_vertices[i]]):\n",
    "                            middles.append(k)\n",
    "                    if collinear_vertices[i] == concave_vertices[j]+1:\n",
    "                        middles.append(0)\n",
    "                if len(middles) == 0:\n",
    "                    vertical_chords.append((collinear_vertices[i],concave_vertices[j]))\n",
    "    \n",
    "    # displaying all attributes and important parameters involved\n",
    "#     print(\"p = \",p)\n",
    "#     print(\"vertex_Type = \",vertex_type)\n",
    "#     print (\"x = \", x)\n",
    "#     print (\"y = \", y)\n",
    "#     print(\"collinear_vertices = \", collinear_vertices)\n",
    "#     print(\"concave_vertices =\", concave_vertices)\n",
    "    print(\"horizontal_chords = \" ,horizontal_chords)\n",
    "    print(\"vertical_chords = \",vertical_chords)\n",
    "    # drawing the partitioned polygon \n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x+[0], y+[0], color='black')\n",
    "    ax.scatter(x+[0], y+[0], color='black')\n",
    "    for i in range(len(x)):\n",
    "        ax.annotate(i, (x[i],y[i]))\n",
    "    for i,j in horizontal_chords:\n",
    "        ax.plot([x[i],x[j]],[y[i],y[j]],color='black')\n",
    "    for i,j in vertical_chords:\n",
    "        ax.plot([x[i],x[j]],[y[i],y[j]],color='black')\n",
    "    plt.show()\n",
    "\n",
    "# Defining the keys function\n",
    "wn.onkey(up, \"Up\")\n",
    "wn.onkey(left, \"Left\")\n",
    "wn.onkey(right, \"Right\")\n",
    "wn.onkey(back, \"Down\")\n",
    "wn.onkey(partition_polygon, \"Escape\")\n",
    "wn.listen()\n",
    "wn.mainloop()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "y=[2.56422, 3.77284,3.52623,3.51468,3.02199]\n",
    "z=[0.15, 0.3, 0.45, 0.6, 0.75]\n",
    "n=[58,651,393,203,123]\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(z, y)\n",
    "\n",
    "for i, txt in enumerate(n):\n",
    "    ax.annotate(txt, (z[i],y[i]))\n",
    "#         plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import cm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9g8vixittxiwPY8LzymfK1TyiOZEP+Dn5YuzjnHwxdmbweQEnX4z9jDhfjFX1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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118f9cac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fa65c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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jjz9u7dMmnNNvJlaHu+wc6O7zynsqUh2hc6HjobXfutkX3GVD8M/9weW7gW4h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\nb4wxHvf/AUsvGHSPUueSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d572e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pFE9D5TGiSU/6sT2qcUXTlIk7CqmkSfE0nO0RNXGWbNajGlU0TYlkEAqpJE3xzAibImpi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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d866cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f81c470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "free_vertices =  []\n",
      "maximum matching =  [(0, 9), (1, 5), (2, 8), (3, 6), (4, 7)]\n",
      "H =  {0, 1, 2, 3, 4}\n",
      "V =  {8, 9, 5, 6, 7}\n",
      "p =  [(0.00,0.00), (25.00,0.00), (25.00,25.00), (50.00,25.00), (50.00,50.00), (75.00,50.00), (100.00,50.00), (100.00,75.00), (100.00,100.00), (75.00,100.00), (75.00,125.00), (75.00,150.00), (100.00,150.00), (100.00,175.00), (75.00,175.00), (75.00,200.00), (100.00,200.00), (100.00,225.00), (75.00,225.00), (50.00,225.00), (25.00,225.00), (25.00,250.00), (0.00,250.00), (-0.00,225.00), (-0.00,200.00), (-25.00,200.00), (-25.00,175.00), (-50.00,175.00), (-50.00,150.00), (-25.00,150.00), (-25.00,125.00), (-50.00,125.00), (-50.00,100.00), (-25.00,100.00), (-0.00,100.00), (-0.00,75.00), (-25.00,75.00), (-25.00,50.00), (-0.00,50.00), (-0.00,25.00)]\n",
      "vertex_Type =  [0, 0, 1, 0, 1, -1, 0, -1, 0, 1, -1, 1, 0, 0, 1, 1, 0, 0, -1, -1, 1, 0, 0, -1, 1, 0, 1, 0, 0, 1, 1, 0, 0, -1, 1, 1, 0, 0, 1, -1]\n",
      "x =  [0, 25, 25, 50, 50, 75, 100, 100, 100, 75, 75, 75, 100, 100, 75, 75, 100, 100, 75, 50, 25, 25, 0, 0, 0, -25, -25, -50, -50, -25, -25, -50, -50, -25, 0, 0, -25, -25, 0, 0]\n",
      "y =  [0, 0, 25, 25, 50, 50, 50, 75, 100, 100, 125, 150, 150, 175, 175, 200, 200, 225, 225, 225, 225, 250, 250, 225, 200, 200, 175, 175, 150, 150, 125, 125, 100, 100, 100, 75, 75, 50, 50, 25]\n",
      "collinear_vertices =  [5, 7, 10, 18, 19, 23, 33, 39]\n",
      "concave_vertices = [2, 4, 9, 11, 14, 15, 20, 24, 26, 29, 30, 34, 35, 38]\n",
      "horizontal_chords =  [(4, 38), (9, 34), (11, 29), (14, 26), (15, 24)]\n",
      "vertical_chords =  [(2, 20), (11, 14), (24, 34), (26, 29), (35, 38)]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f7acd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rrygnJ+fqMHRyAgAMlNoB2ys/X3rkkWE/9pOf/ESnT5/WypUrtXfvXqWnp0tiiRgAcK3U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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b0efd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "maximum independent =  [4, 1, 3, 2, 0]\n",
      "Unmatched concave vertices [2, 20, 30, 35]\n",
      "nearest_chord [(2, 25), (20, -25), (30, -25), (35, -25)]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fa39cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9M4lk+0Z0JOrDWBF5GrgE6AjsAh4E/gg8A3QDtgDXq+pX4cffB4wGjgB3qurS\npv6xSUSUoPEWi30zJrpE7hsJ+zBWVUc63HWZw+MnA+n1O5UxxviYL/8y1hhjzN/ZoDfGGJ+zQW+M\nMT5ng94YY3zOBr0xxvicDXpjjPE5G/QeFSuC7/HHH6ewsJCioiImTJjgYpVNc+rjoYceIi8vj+Li\nYoqLi1myZInLlRqTWtXV1Q2v/+LiYnJycpIWi+j9MwGdoo5F8J1++unU1dVx8cUXc8UVV/DNN9+w\nePFi1q1bR3Z2Nrt37256ZS5y6gNCCVPjxo1zuUJj3NGzZ0+qqqqAUDhPXl4ew4cPT8q27B29RzlF\n8M2ZM4d7772X7OxsADp37uxmmU2KFSVojAn505/+xHnnnUcgEEjK+m3Qe1i0CL5NmzaxcuVKBg0a\nRFlZGWvWrHG7zCY5RSI+/vjj9OvXj9GjR7Nnzx6XqzTGPYsWLWLkSKeTECRAPCfESfblZE9q5hdN\nRfC99957WlRUpD//+c+1vr5e3377bQ0Gg56LRYwnEvHzzz/XI0eO6NGjR/WXv/yl3nLLLS5XbUzy\nRds3amtrtUOHDvr55583e30kKkowFRcb9PFHCQ4bNkzfeOONhp8799xzdffu3W6VfYKWRCJ++umn\nnotENCbRnPaNu+66S8vLy1u0zngHfVxRgslmZ6+MPxKxtraW2tpaunfvzqFDh1i/fj2DBg3yzHFv\np7i0QCDABx98wNChQ/mXf/kXSkpKyM3NBWD69Om8/fbbLFq0KNXlGpMyTvt427ZteeKJJ7jlllua\nvc5kRwmaBIs3ErG+vp7q6mrWrFlDRkYGPXv29MyQB+e4tC1btjBw4ECuv/56rrrqKm666SaqqqoQ\nEYLBIP/xH/+R4kqNSS2nffzQoUOMGDEiqdu2Qe8Rp0IkYmRc2h/+8IdUlmWM62Lt42eccUZSt23f\nuvEIi0szxt88HyWY7It9GBvilwg+v/RhTKJ5NkowFezD2L/zSwSfX/owJtHciBK0QzfGGONzNuiN\nMcbnbNAbY4zP2aA3xhifs0FvjDE+Z4PeGGN8zga9Mcb4nA16j3KK4LvhhhsaoseCwSDFxcUuVxqb\nUx9VVVWUlpZSXFzMgAEDWL16tcuVnjqOHj3KhRdeyFVXXeV2KS0WDAbp27dvw+snXe3du5cf/vCH\nFBYW0qtXL/7yl78kZTt2rhuPcorg++///u+Gx9xzzz1JP0fGyXLq44EHHuDBBx/kiiuuYMmSJUyY\nMMH+uCppbTWuAAANw0lEQVRFZs6cSa9evdi/f7/bpZyU5cuX07FjR7fLOCl33HEHl19+Oc899xyH\nDx/m0KFDSdmOvaP3qKYi+FSVZ555JrmpNAng1IeINAyaffv2cc4557hZ5ilj27ZtvPzyy9x6661u\nl3LK27dvH2+99RZjxowBoHXr1rRv3z4p27JB72FOEXwAK1eupEuXLhQUFLhYYXyi9TFjxgzGjx9P\n165dGTduHFOmTHG7zFPCnXfeydSpU8nISO9dX0T43ve+R0lJCXPnznW7nBb59NNP6dSpE7fccgsX\nXnght956KwcPHkzKtk7q2RaRz0TkPRGpEpF3wsvOEpHXROSj8H/PTEypp57MzEyqqqrYtm0bq1ev\nPu40v08//bTn380fE62POXPmMH36dGpqapg+fXrDuxqTPC+99BKdO3empKTE7VJO2v/+7/9SVVXF\n0qVLmTVrFm+99ZbbJTXbkSNH+Otf/8rtt9/Ou+++y3e+8x0effTR5GwsnjOfOV2Az4COjZZNBe4N\nX78X+Lem1mNnrwyJdWa7yAi+uro67dy5s9bU1LhVakzx9JGTk9OQdVtfX6/t2rVzq1xfi8whzsnJ\n0TPPPFMDgYB26dJF27RpoxUVFW6XGBenPGVV1QcffPCEeEqvitw38vPztWPHjg33vfXWW3rllVc2\na32kIjPWYdBXA7nh67lAdVPrsUEfPU+yTZs2unDhQj106JBefPHF+j//8z+qqrp06VIdMmSIyxVH\nF28fhYWFunz5clVVff3117V///7uFu5DsfJ7ly9frt///vfdLjEusV5TX3/9tQ4ePFiXLl3qdplN\nitZHRkaGTp06VVVD/2CNGzeuWeuMd9Cf1GmKReRTYB9wFPgPVZ0rIntVtX34fgH2HLvtxE5T7JzM\nJCK0adOGTp06EQwGAfjwww/Jycnx5AeYTpmxjfvYt28fmzdvRlXJyMigoKCAdu3auVBxbJs3bwbg\n/PPPd7mS5nN6LrKzsyksLKSmpoa+ffu6UFnzNPWa6ty5M4FAwIXKmsepj9atW9OzZ0/OPfdcnnrq\nKc48M/6j3anKjL1YVbeLSGfgNRH5MPJOVVURifoviYiMBcZCKGLrVOeUJ6mqDBw48LhlhYWFqSip\nRZwyYxv3ccYZZ6TFseKvv/7a7RJazOm5qK2tpX379kn7hkeixfua8jqnPurq6li/fn1St52w4BER\neQj4GrgNuERVd4pILvCmqvaM9bP2jj521qpfMmPTqY9j0jlAxS/PhfXhLOnBIyLyHRFpd+w6MBTY\nALwIjAo/bBSwuKXbOJX4JWvVL334gV+eC+sjAeI5kB/tApwLrAtf3gfuCy/vAPwJ+Ah4HTirqXXZ\nh7Ehsb5ZkE78lBlbVlamZWVlbpfRYn55Lvy0bySyDywz1rgpnQ95RPJDH37owURnmbHGGGMAG/TG\nGON7NuiNMcbnbNAbY4zP2aA3xhifs0FvjDE+Z4PeJJVTlOC6desYPHgwffv25eqrr/Z02tG3337L\npZdeSu/evSkqKmLmzJlul9QiTs+F8T8b9CapjkUJrlu3jqqqKpYtW8aqVau49dZbefTRR3nvvfcY\nPnw4jz32mNulOhIRpk2bxsaNG1m1ahWzZs1i48aNbpfVbE7PhfE/G/QmqZyiBDdt2sSQIUMAKC8v\n5/nnn3ezzJiys7Pp378/AO3ataNXr15s377d5aqar6l4SuNfNuhN0kWLEiwqKmLx4tBpkJ599llq\nampcrjI+n332Ge++++5xsY7pJFY8pfEvG/Qm6aJFCc6fP5/Zs2dTUlLCgQMHaN26tdtlNunrr7/m\nuuuuY8aMGeTk5LhdTovEiqc0/mWD3iRcZWUlq1atYsWKFQSDQSorKwFo3749l156KcuWLaOwsJBX\nX32VtWvXMnLkSM477zyXqz5RZB+BQIDvfve7VFRUMGLECLdLi1s8z4XxPxv0JqEqKysZO3ZsQ8jC\nli1buO2226isrOSbb77htddeo7CwkN27dwNQX1/Pr3/9a37yk5+4WfYJGvexdetWPvjgA7p06eJy\nZfGL97kw/mdnrzQJ5RSu0KpVK3r06MH111/PAw88wMyZM5k1axYAI0aMYMqUKZ76YDBWtGPbtm3p\n3r07HTp0cKGy+DlF1zV+Lkz6ivfslTboTUJlZGQQ7TUlItTX17tQUcs49QFQVlaW4mpaZsWKFVGX\np9tzYZylKjPWmON069Yt6jvhdMsFduojEAikzXndnX4rSbfnwpw8O0ZvEspi37zDDz2YBIknhirZ\nF4sS9Bc/xdelex9+ieAz0WFRgsZNfomv80sfxp8sStAYYwxgg94YY3zPBr0xxvicDXpjjPE5G/TG\nGONzNuiNMcbnbNCbpFu2bBk9e/bk/PPP59FHH3W7nBYZPXo0nTt3pk+fPm6XYkyz2aA3SXX06FF+\n9rOfsXTpUjZu3MjTTz+dljF8N998s53S16QtG/QmqVavXs3555/PueeeS+vWrbnxxhsbkqXSyZAh\nQzjrrLPcLsOYFrFBb5Jq+/btdO3ateF2fn5+WuatGpPOkjboReRyEakWkc0icm+ytmOMMSa2pJym\nWEQygVlAObANWCMiL6pq+h2cNc3205/+tOFc6CtXriQvL6/hvm3bth1328uOxfDV1tYSDAa58847\n3S7JmBZJ1jv6i4DNqvqJqh4GFgHXJGlbxkN++tOfMmfOnIbb9fX11NTU8KMf/YjDhw+zaNEifvCD\nH7hYYXyixfBNnDiRffv2uVyZMc2XlLNXisgPgctV9dbw7ZuAQar682iPt7NX+kdWVhZHjx6Net9p\np53G2WefTSAQSHFVzecUwweQl5fHpEmTGDNmTIqrMuZ4nk+YEpGxwFiwxBs/cRryAIMGDUphJSfH\naciLCNu2bUtxNcacnGQN+u1A14jb+eFlDVR1LjAXQu/ok1SHSbHMzMyowz4zMzOtzuluMXzGT5J1\njH4NUCAi3UWkNXAj8GKStmU8ZOzYsc1a7lUWw2f8JCmDXlWPAD8HXgE+AJ5R1feTsS3jLbNnz+b2\n228nMzMTCL2Tv/3225k9e7bLlTVPRUUFc+fOJRAIICIEAgHmzp1LRUWF26UZ02wWJWiMMWnKogSN\nMcYANuiNMcb3bNAbY4zP2aA3xhifs0FvjDE+Z4PeGGN8zga9Mcb4nA16Y4zxOU/8wZSIfAGceGIR\n93UEvnS7iBisvpNj9bWcl2uDU6e+gKp2aupBnhj0XiUi78TzV2dusfpOjtXXcl6uDay+xuzQjTHG\n+JwNemOM8Tkb9LHNdbuAJlh9J8fqazkv1wZW33HsGL0xxvicvaM3xhifs0Efg4jcIyIqIh0jlk0U\nkc0iUi0iw1yq6zER+VBE1ovI/xOR9h6r7/Lw9jeLyL1u1NConq4islxENorI+yJyR3j5WSLymoh8\nFP7vmS7XmSki74rIS16rT0Tai8hz4dfdByIy2Cv1ichd4ed1g4g8LSKnuV2biMwXkd0isiFimWNN\nyd5vbdA7EJGuwFBga8Sy3oRiEYuAy4HZIpLpQnmvAX1UtR+wCZjolfrC25sFXAH0BkaG63LTEeAe\nVe0NlAI/C9d0L/AnVS0A/hS+7aY7CCWyHeOl+mYCy1S1ELiAUJ2u1yciecD/BQaoah8gk9A+4HZt\nvye0D0aKWlMq9lsb9M6mAxOAyA8xrgEWqWqtqn4KbAYuSnVhqvpqOK4RYBWh8HWv1HcRsFlVP1HV\nw8CicF2uUdWdqvrX8PUDhIZUXriuBeGHLQCudadCEJF84PvAf0Ys9kR9InIGMASYB6Cqh1V1r1fq\nA7KANiKSBbQFdrhdm6q+BXzVaLFTTUnfb23QRyEi1wDbVXVdo7vygJqI29vCy9w0Glgavu6F+rxQ\ngyMRCQIXAm8DXVR1Z/iuz4EuLpUFMIPQG4v6iGVeqa878AXwVPjQ0n+KyHe8UJ+qbgf+ndBv3juB\nfar6qhdqi8KppqTvM1mJXFk6EZHXgbOj3HUf8EtCh21cE6s+VV0cfsx9hA5LVKaytnQlIqcDzwN3\nqup+EWm4T1VVRFz5CpqIXAXsVtW1InJJtMe4WR+hOdEf+IWqvi0iM2l0KMSt+sLHua8h9I/RXuBZ\nEfmRF2qLJdU1nbKDXlW/F225iPQl9KJZFx4E+cBfReQiYDvQNeLh+eFlKasvos6bgauAy/Tv35FN\nWX0xeKGGE4hIK0JDvlJVXwgv3iUiuaq6U0Rygd0ulfd/gB+IyJXAaUCOiCz0UH3bgG2q+nb49nOE\nBr0X6vse8KmqfgEgIi8A3/VIbY051ZT0fcYO3TSiqu+pamdVDapqkNCLvL+qfg68CNwoItki0h0o\nAFanukYRuZzQr/k/UNVDEXd5ob41QIGIdBeR1oQ+ZHoxxTUcR0L/Ys8DPlDV30Tc9SIwKnx9FLA4\n1bUBqOpEVc0Pv95uBN5Q1R95qL7PgRoR6RledBmwEW/UtxUoFZG24ef5MkKfwXihtsacakr+fquq\ndolxAT4DOkbcvg/4GKgGrnCpps2EjulVhS9Peqy+Kwl9G+hjQoea3H4OLyb0ofr6iP9nVwIdCH37\n4SPgdeAsD9R6CfBS+Lpn6gOKgXfC/w//CJzplfqAScCHwAbgD0C227UBTxP6zKCO0JvFMbFqSvZ+\na38Za4wxPmeHbowxxuds0BtjjM/ZoDfGGJ+zQW+MMT5ng94YY3zOBr0xxvicDXpjjPE5G/TGGONz\n/x9RiTpNLfoWUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d5293c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'Please make sure that the INPUT is A CLOSED RECTILINEAR POLYGON,'\n",
    "'CONSTRUCTED WHILE GOING IN ANTI-CLOCKWISE ONLY'\n",
    "# importing libraries\n",
    "import networkx as nx\n",
    "import turtle\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "from networkx.algorithms import bipartite\n",
    "import math\n",
    "import sys\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "# declaration list\n",
    "wn = turtle.Screen()\n",
    "# a turtle called gopu \n",
    "gopu = turtle.Turtle() \n",
    "# co-ordinate points\n",
    "x = [] \n",
    "y = []\n",
    "# vertex-type := rectilinear = -1; convex = 0; concave = 1 \n",
    "vertex_type = [] \n",
    "# store the bipartite graph of chords\n",
    "G = nx.Graph()\n",
    "# the line below can be commented if one needs animation\n",
    "gopu.speed(0)\n",
    "# starts recording keys being pressed\n",
    "gopu.begin_poly()\n",
    "\n",
    "# Event handlers\n",
    "stride = 25\n",
    "# Up  = up() - vertex to be deleted = -1\n",
    "def up():\n",
    "    vertex_type.append(-1)\n",
    "    gopu.forward(stride)\n",
    " \n",
    "# left = left() ; make vertex - convex = 0\n",
    "def left():\n",
    "    vertex_type.append(0)\n",
    "    gopu.setheading(gopu.heading()+90)\n",
    "    gopu.forward(stride)\n",
    " \n",
    "# right = right() ; make vertex - concave = 1\n",
    "def right():\n",
    "    vertex_type.append(1)\n",
    "    gopu.setheading(gopu.heading()-90)\n",
    "    gopu.forward(stride)\n",
    " \n",
    "# back = back() -- doing undo is allowed only once.\n",
    "def back():\n",
    "    vertex_type.pop()\n",
    "    gopu.undo()\n",
    "\n",
    "# quits the screen and outputs the plots the partitioned polygon\n",
    "def partition_polygon():\n",
    "    # closing the screen\n",
    "    wn.bye()\n",
    "    # stopped recording the polygon\n",
    "    gopu.end_poly()\n",
    "    p = gopu.get_poly()\n",
    "    p = list(p)\n",
    "    compute_partition(p)  \n",
    "    \n",
    "'''\n",
    "The movements of the turtle are recorded and the rectilinear graph thus \n",
    "obtained is converted into bipartite graph of chords\n",
    "'''\n",
    "def compute_partition(p):\n",
    "    # p now contains the list of coordinates of vertices\n",
    "    # last one is same as the origin\n",
    "    # and the origin is always going to be a convex vertex\n",
    "    if len(p) == 0:\n",
    "        print(\"No input\")\n",
    "        sys.exit()\n",
    "    p.pop()\n",
    "    vertex_type[0] = 0\n",
    "    \n",
    "    # x and y contain list of x and y coordinates respectively\n",
    "    for i,j in p:\n",
    "        x.append(i)\n",
    "        y.append(j)\n",
    "\n",
    "    # this is done as there are very small errors in recording the \n",
    "    # position accurately by the turtle library\n",
    "    for i in range(len(x)):\n",
    "        x[i] = int(x[i])\n",
    "        y[i] = int(y[i])\n",
    "\n",
    "    for i in range(len(x)):\n",
    "        if x[i] % stride != 0:\n",
    "            x[i] += (stride - x[i] % stride)\n",
    "        if y[i] % stride != 0:\n",
    "            y[i] += (stride - y[i] % stride)\n",
    "    \n",
    "    # deleting vertices that are on a straight line\n",
    "    collinear_vertices = [i for i,val in enumerate(vertex_type) if val == -1] \n",
    "    # Reverse order deletion is done so that the previous index does not \n",
    "    # overthrow the current one\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x+[0], y+[0], color='black')\n",
    "    ax.scatter(x+[0], y+[0], color='black')\n",
    "    for i in range(len(x)):\n",
    "        ax.annotate(i, (x[i],y[i]))\n",
    "    plt.show()\n",
    "    plt.clf()\n",
    "    # finding the chords inside the polygon\n",
    "    horizontal_chords = []\n",
    "    vertical_chords = []\n",
    "    concave_vertices = [i for i,val in enumerate(vertex_type) if val == 1]\n",
    "\n",
    "    # middles is used because, there are cases when there is a chord between vertices\n",
    "    # and they intersect with external chords, hence if there is any vertex in between \n",
    "    # two vertices then skip that chord. \n",
    "    for i in range(len(concave_vertices)):\n",
    "        for j in range(i+1,len(concave_vertices)):\n",
    "            if concave_vertices[j] != concave_vertices[i] + 1:\n",
    "                middles = []\n",
    "                if y[concave_vertices[i]] == y[concave_vertices[j]]:\n",
    "                    for k in range(len(x)):\n",
    "                        if y[concave_vertices[i]] == y[k] and (x[concave_vertices[i]] < x[k] and x[concave_vertices[j]] > x[k] \\\n",
    "                                                              or x[concave_vertices[i]] > x[k] and x[concave_vertices[j]] < x[k]):\n",
    "                            middles.append(k)\n",
    "                    if len(middles) == 0:\n",
    "                        horizontal_chords.append((concave_vertices[i],concave_vertices[j]))\n",
    "                middles = []\n",
    "                if x[concave_vertices[i]] == x[concave_vertices[j]]:\n",
    "                    for k in range(len(x)):\n",
    "                        if x[concave_vertices[i]] == x[k] and (y[concave_vertices[i]] < y[k] and y[concave_vertices[j]] > y[k] \\\n",
    "                                                              or y[concave_vertices[i]] > y[k] and y[concave_vertices[j]] < y[k]):\n",
    "                            middles.append(k)\n",
    "                    if len(middles) == 0:\n",
    "                        vertical_chords.append((concave_vertices[i],concave_vertices[j]))\n",
    "    \n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x+[0], y+[0], color='black')\n",
    "    ax.scatter(x+[0], y+[0], color='black')\n",
    "    for i in range(len(x)):\n",
    "        ax.annotate(i, (x[i],y[i]))\n",
    "    for i,j in horizontal_chords:\n",
    "        ax.plot([x[i],x[j]],[y[i],y[j]],color='black')\n",
    "    for i,j in vertical_chords:\n",
    "        ax.plot([x[i],x[j]],[y[i],y[j]], color='black')\n",
    "    plt.show()\n",
    "    plt.clf()\n",
    "    # Creating a bipartite graph from the set of chords\n",
    "    for i,h in enumerate(horizontal_chords):\n",
    "        y1 = y[h[0]]\n",
    "        x1 = min(x[h[0]] ,x[h[1]] )\n",
    "        x2 = max(x[h[0]] ,x[h[1]])\n",
    "        G.add_node(i, bipartite=0)\n",
    "        for j,v in enumerate(vertical_chords):\n",
    "            x3 = x[v[0]]\n",
    "            y3 = min(y[v[0]],y[v[1]])\n",
    "            y4 = max(y[v[0]],y[v[1]])\n",
    "            G.add_node(j + len(horizontal_chords),bipartite=0)\n",
    "            if x1 <= x3 and x3 <=x2 and y3 <= y1 and y1 <= y4:    \n",
    "                G.add_edge(i, j + len(horizontal_chords))\n",
    "    \n",
    "    if len(horizontal_chords) == 0:\n",
    "        for j,v in enumerate(vertical_chords):\n",
    "            x3 = x[v[0]]\n",
    "            y3 = min(y[v[0]],y[v[1]])\n",
    "            y4 = max(y[v[0]],y[v[1]])\n",
    "            G.add_node(j,bipartite=1)\n",
    "    \n",
    "    # finding the maximum matching of the bipartite graph, G.\n",
    "    M = nx.Graph()\n",
    "    maximum_matching = nx.bipartite.maximum_matching(G)\n",
    "    maximum_matching_list = []\n",
    "    for i,j in maximum_matching.items():\n",
    "        maximum_matching_list += [(i,j)]\n",
    "    M.add_edges_from(maximum_matching_list)\n",
    "    maximum_matching = M.edges()\n",
    "    # breaking up into two sets\n",
    "    H, V = bipartite.sets(G)\n",
    "    pos = dict()\n",
    "    pos.update((n, (1, i)) for i, n in enumerate(H))\n",
    "    pos.update((n,(2,i)) for i, n in enumerate(V))\n",
    "    nx.draw(G, pos=pos, with_labels = True)\n",
    "    plt.show()\n",
    "    plt.gcf().clear()\n",
    "    \n",
    "#     plotting the maximum matching of the bipartite graph\n",
    "    K = nx.Graph()\n",
    "    K.add_nodes_from(H, bipartite=0)\n",
    "    K.add_nodes_from(V, bipartite=1)\n",
    "    K.add_edges_from(maximum_matching)\n",
    "    nx.draw(K, pos=pos, with_labels = True)\n",
    "    plt.show()\n",
    "    plt.gcf().clear()\n",
    "    free_vertices = []\n",
    "    for u in H:\n",
    "        temp = []\n",
    "        for v in V:\n",
    "            if (u,v) in maximum_matching or (v,u) in maximum_matching:\n",
    "                temp += [v]\n",
    "        if len(temp) == 0:\n",
    "            free_vertices += [u]\n",
    "    for u in V:\n",
    "        temp = []\n",
    "        for v in H:\n",
    "            if (u,v) in maximum_matching or (v,u) in maximum_matching:\n",
    "                temp += [v]\n",
    "        if len(temp) == 0:\n",
    "            free_vertices += [u]\n",
    "            \n",
    "    print(\"free_vertices = \", free_vertices)\n",
    "    print(\"maximum matching = \", maximum_matching)\n",
    "    print(\"H = \", H)\n",
    "    print(\"V = \", V)\n",
    "    # finding the maximum independent set\n",
    "    max_independent = []\n",
    "    while len(free_vertices) != 0 or len(maximum_matching) != 0:\n",
    "        if len(free_vertices) != 0 :\n",
    "            u = free_vertices.pop()\n",
    "            max_independent += [u]\n",
    "        else:\n",
    "            u, v = maximum_matching.pop()\n",
    "            G.remove_edge(u,v)\n",
    "            max_independent += [u]\n",
    "\n",
    "        for v in G.neighbors(u):\n",
    "            G.remove_edge(u, v)\n",
    "            for h in G.nodes():\n",
    "                if (v,h) in maximum_matching:\n",
    "                    maximum_matching.remove((v,h))\n",
    "                    free_vertices += [h]\n",
    "                if (h,v) in maximum_matching:\n",
    "                    maximum_matching.remove((h,v))\n",
    "                    free_vertices += [h]\n",
    "\n",
    "    \n",
    "    # displaying all attributes and important parameters involved\n",
    "    print(\"p = \",p)\n",
    "    print(\"vertex_Type = \",vertex_type)\n",
    "    print (\"x = \", x)\n",
    "    print (\"y = \", y)\n",
    "    print(\"collinear_vertices = \", collinear_vertices)\n",
    "    print(\"concave_vertices =\", concave_vertices)\n",
    "    print(\"horizontal_chords = \" ,horizontal_chords)\n",
    "    print(\"vertical_chords = \",vertical_chords)\n",
    "    nx.draw(G)\n",
    "    plt.show()\n",
    "    plt.gcf().clear()\n",
    "    nx.draw(M)\n",
    "    plt.show()\n",
    "    plt.gcf().clear()\n",
    "    print(\"maximum independent = \", max_independent)\n",
    "\n",
    "    # drawing the partitioned polygon \n",
    "    ind_chords = []\n",
    "    for i in max_independent:\n",
    "        if (i >= len(horizontal_chords)):\n",
    "            ind_chords += [vertical_chords[i-len(horizontal_chords)]]\n",
    "        else:\n",
    "            ind_chords += [horizontal_chords[i]]\n",
    "    unmatched_concave_vertices = [i for i in concave_vertices]\n",
    "    for i,j in ind_chords:\n",
    "        if i in unmatched_concave_vertices:\n",
    "            unmatched_concave_vertices.remove(i)\n",
    "        if j in unmatched_concave_vertices:\n",
    "            unmatched_concave_vertices.remove(j)\n",
    "    \n",
    "    print(\"Unmatched concave vertices\", unmatched_concave_vertices)\n",
    "    nearest_chord = []\n",
    "    for i in unmatched_concave_vertices:\n",
    "        dist = 0\n",
    "        nearest_distance = math.inf\n",
    "        for j in max_independent:\n",
    "            if j < len(horizontal_chords):\n",
    "                temp1, temp2 = horizontal_chords[j]\n",
    "                if abs(y[i] - y[temp1]) < nearest_distance and \\\n",
    "                (x[i] <= x[temp1] and x[i] >= x[temp2] or x[i] >= x[temp1] and x[i] <= x[temp2]) \\\n",
    "                and abs(temp1 - i) != 1 and abs(temp2 - i) != 1:\n",
    "                    middles = []\n",
    "                    for u in range(len(x)):\n",
    "                        if x[i] == x[u] and (y[i] < y[u] and y[u] < y[temp1] or y[temp1] < y[u] and y[u] < y[i]):\n",
    "                            middles.append(u)\n",
    "                    if len(middles) == 0:\n",
    "                        nearest_distance = abs(y[i] - y[temp1])\n",
    "                        dist = y[temp1] - y[i]\n",
    "\n",
    "        if nearest_distance != math.inf:\n",
    "            nearest_chord.append((i,dist)) \n",
    "        else:\n",
    "            for k in collinear_vertices:\n",
    "                if x[k] == x[i] and abs(y[k] - y[i]) < nearest_distance and abs(k-i) != 1:\n",
    "                    middles = []\n",
    "                    for u in range(len(x)):\n",
    "                        if x[i] == x[u] and (y[i] < y[u] and y[u] < y[k] or y[k] < y[u] and y[u] < y[i]):\n",
    "                            middles.append(u)\n",
    "                    if len(middles) == 0:\n",
    "                        nearest_distance = abs(y[i] - y[k])\n",
    "                        dist = y[k] - y[i]\n",
    "            nearest_chord.append((i,dist)) \n",
    "     \n",
    "    print(\"nearest_chord\", nearest_chord)\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x+[0], y+[0], color='black')\n",
    "    ax.scatter(x+[0], y+[0], color='black')\n",
    "    for i in range(len(x)):\n",
    "        ax.annotate(i, (x[i],y[i]))\n",
    "    for i,j in ind_chords:\n",
    "        ax.plot([x[i],x[j]],[y[i],y[j]],color='black')\n",
    "    for i,dist in nearest_chord:\n",
    "        ax.plot([x[i],x[i]],[y[i], y[i]+dist],color='black')\n",
    "    plt.show()\n",
    "\n",
    "# Defining the keys function\n",
    "wn.onkey(up, \"Up\")\n",
    "wn.onkey(left, \"Left\")\n",
    "wn.onkey(right, \"Right\")\n",
    "wn.onkey(back, \"Down\")\n",
    "wn.onkey(partition_polygon, \"Escape\")\n",
    "wn.listen()\n",
    "\n",
    "wn.mainloop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial input rectillinear graph\n"
     ]
    },
    {
     "data": {
      "image/png": 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wXlWLYsz7BfCcqgYiy/0B2AN8AvxAVbd0tP6ysjKtr6/vMEcsfr+fvXv3ntfer18/CgoK\nAFi4cCHf+973aGlpYciQIUB4YOfJJx27smRMyot37AL0798fv9/Pvn37UNXWAdlBgwYxYsSInoyZ\nMMFgkJaWlpjzsrOzefDBB3nllVfYtWsXHo8Hn8/Hk08+SXZ2dtx1isg2VS3raNvdKvQich9QBkxX\nVRWRDOAiVf2ziJQCa4FCVf00xjrnAHMAcnNzS+P9wDvi8XiI1QcR4cyZM11apzEm+eIduwDjxo3r\n4TTJV1dXF7O9O7Wqs4W+y3fdiMhs4AZgYuQjBKraArREXm8TkXeAEcB5p+uqugJYAeEz+q7myM3N\njXlWkJub29VVGmN6QLxj1+fzsXnz5p4PlGTxPsH0RK3q0n30IjIVuAf4B1U9EdV+uYikRV5fDeQB\n7yYiaDzV1dV4vd42bV6vl+rq6mRu1hjTTal27Dra344u4gOrgYPASWA/cAvwNtAEhCLTk5FlKwlf\now8Bvwe+0pmBgu4MxqqGBzkyMjIUUJ/Pp4FAoFvrM8b0jFQ7dgOBgPp8PhWRhPSXRA7GJlt3BmPP\nGj9+PIArP/IZ42Z27HZdZ6/Ru+6/QDDGGNOWFXpjjHE5K/TGGONyVuiNMcblrNAbY4zLWaE3xhiX\ns0JvjDEuZ4XeGGNczgq9Mca4nBV6Y4xxOSv0xhjjclbojTHG5azQG2OMy1mhN8YYl7NCb4wxLue6\nQt/U1MSECRMoKCigsLCQZcuWAXD//fczevRoiouLmTx5MgcOHHA4qTEmWlVVFUOHDqWo6O+Ppn7h\nhRcoLCzE4/HQ3WdW9Dax+vvRRx8xadIk8vLymDRpEkeOHEnItlxX6NPT06mpqaGhoYFgMMjy5ctp\naGjg7rvv5s033yQUCnHDDTewYMECp6MaY6LMnj2bjRs3tmkrKipizZo1VFRUOJQqeWL1d9GiRUyc\nOJE9e/YwceJEFi1alJBtua7QZ2VlUVJSAkBmZib5+fk0NzczaNCg1mWOHz+OiDgV0RgTQ0VFBYMH\nD27Tlp+fz8iRIx1KlFyx+rtu3TpuvvlmAG6++WbWrl2bkG2lJ2QtvVRjYyPbt2+nvLwcgPvuu4+f\n/vSnXHzxxWzatMnhdMYY09ahQ4fIysoC4IorruDQoUMJWW+HZ/Qi8oyIHBaRnVFtg0XklyKyJ/L1\n0qh594rI2yKyS0SmJCRlB2prawkGg9TV1eH3+6mtreXYsWNUVlaydOnS1rP56upqmpqamDVrFo8/\n/nhPRDPGtOPcYzdRZ7C9VW1tLX6/H4/H02F/RSRxVx46eno4UAGUADuj2hYD8yKv5wH/HnldAOwA\nMoDhwDtAWkfbKC0t7fJT0AOBgHq9XgVap4EDB+q1116rNTU1Mb9n7969WlhY2OVtGmO6L9axO2DA\nAM3JyTlv2XHjxukbb7zhQMrE6Ux/R4wYoQcOHFBV1QMHDuiIESPaXSdQrx3UV1VFwsu2T0T8wHpV\nLYq83wWMV9WDIpIFbFbVkSJyb+SXx0OR5f4LmK+qv21v/WVlZdrVEXW/38/evXvPa8/MzOTTTz9t\nfb9nzx7y8vIAeOyxx6irq+PFF1/s0jaNMd0X79gVkfMGX0OhENdccw2ZmZk9FS/hgsEgLS0t57X3\n69ePv/3tbwDcfffdDBkyhHnz5rFo0SI++ugjFi9eHHedIrJNVcs62nZXr9EPU9WDkdfvA8Mir7OB\nYNRy+yNtsQLOAeYA5ObmdjEG7Nu3L2b70aNHKS4uBmDhwoU8/fTT7Nq1C4/Hg8/n48knn+zyNo0x\n3Rfv2FVVfvvb3+L3++nXrx979uzh5MmTvPXWW1x00UWMHj26h5MmRqwiD3Dy5ElycnJ48MEHmTdv\nHjfddBNPP/00Pp+P559/PiHb7vZgrKqqiHT8seD871sBrIDwGX1Xt5+bmxvzrMDn8xEKhVrfT5s2\nraubMMYkQXvHbmNjY88HSrJ4n2DO7e9rr72W8G139fbKQ5FLNkS+Ho60NwNXRS2XE2lLmurqarxe\nb5s2r9dLdXV1MjdrjOmmVDt2He1vZy7kA37aDsYuoe1g7OLI60LaDsa+S5IHY1XDgxwZGRkKqM/n\n00Ag0K31GWN6RiAQUJ/PpyKSEsduomsViRqMFZHVwHjgMuAQ8ACwFngeyAX2Ajep6keR5e8DqoBT\nwPdVdUNHv2y6Mxh71vjx4wHYvHlzt9ZjjDHJlMhalbDBWFWdGWfWxDjLVwPu/OxljDF9kOv+CwRj\njDFtWaE3xhiXs0JvjDEuZ4XeGGNczgq9Mca4nBV6Y4xxOSv0xhjjclbojTHG5azQG2OMy1mhN8YY\nl7NCb4wxLmeF3hhjXM4KvTHGuJwVemOMcTnXFfqmpiYmTJhAQUEBhYWFLFu2rM38mpoaRIQPP/zQ\noYSJFa+/8+fPJzs7m+LiYoqLi3nllVccTmpMxx555BEKCwspKipi5syZ/PWvf3U6UlItW7aMoqIi\nCgsLWbp0adK247pCn56eTk1NDQ0NDQSDQZYvX05DQwMQLoqvvvpqtx5G3tu019+5c+cSCoUIhUL2\nzFzT6zU3N/Poo49SX1/Pzp07OX36NM8++6zTsZJm586dPPXUU2zdupUdO3awfv163n777aRsy3WF\nPisri5KSEgAyMzPJz8+nuTn82Nq5c+eyePFiRMTJiAnVXn+N6WtOnTrFX/7yF06dOsWJEye48sor\nnY6UNH/84x8pLy/H6/WSnp7OuHHjWLNmTVK25bpCH62xsZHt27dTXl7OunXryM7OZsyYMU7HSpro\n/gI89thjjB49mqqqKo4cOeJwOmPal52dzV133UVubi5ZWVlcfPHFTJ482elYSVNUVMSWLVv485//\nzIkTJ3jllVdoampKyra6XOhFZKSIhKKmT0Xk+yIyX0Sao9oduWZw7NgxKisrWbp0Kenp6SxcuJAF\nCxY4EaVHRPd30KBB3H777bz77ruEQiGysrK48847nY5oTLuOHDnCunXreO+99zhw4ADHjx8nEAg4\nHStp8vPz+dd//VcmT57M1KlTKS4uJi0tLSnb6nKhV9VdqlqsqsVAKXAC+Hlk9iNn56lq0kcBa2tr\nCQaD1NXV4ff7WbVqFZWVlcyaNYvp06fzzjvv8N577zFmzBj8fj/79++npKSE999/P9nRkqK2tha/\n34/H44nZX4Bhw4aRlpaGx+Ph29/+Nlu3bnU4tTHni96XR4wYwZkzZ7j88svp168f06dP5ze/+Y3T\nERPq3Fo1YMAAtm3bxuuvv86ll17KiBEjkrNhVe32BEwG/l/k9Xzgrgv5/tLSUu2qQCCgXq9XgdYp\nLS1Np0yZEvd7fD6ffvDBB13eppM6298DBw60vn744Yd1xowZPR3VmHbF2pdFRJ9++mk9c+aMfvOb\n39RHH33U6ZgJE6u/AwcO1EAgoHv37tWRI0fqkSNHLmidQL12osZKeNnuEZFngN+r6uMiMh/4FvAJ\nUA/cqartXiAuKyvT+vr6Lm3b7/ezd+/eWJnwer0ADB8+nCFDhrTOCwaDlJaW0q9fvy5t00nBYJCW\nlpbz2vv160dBQQEACxcuZPXq1YRCIUQEv9/Pj3/8Y7Kysno6rjFxtXfsDhw4kIsuuoiRI0fi8bhj\nKLG9Yzc/P5+HH36YiRMnXtA6RWSbqpZ1uFx3C72I9AcOAIWqekhEhgEfEv6N9UMgS1WrYnzfHGAO\nQG5ubmmsH3hneDwe4vVh3LhxXVpnb1ZXVxezXUQ4c+ZMD6cxpuvs2A3rzrHb2UKf3qW1t/Ulwmfz\nhwDOfo2EeApYH+ubVHUFsALCZ/Rd3Xhubm7MswKfz8fmzZu7utpeK95ZkJv+NsCkBjt2w3ri2E3E\nZ6KZwOqzb0Qk+vrAjcDOBGwjrurq6tZLNGd5vV6qq6uTuVnHpFp/jXul2r7saH87cyE/3gR8Bvgz\ncHFU28+At4A3gZcJX7pJ2mCsaniQw+fzqYioz+fTQCDQrfX1doFAQDMyMhRIif4a90q1fTnRtYqe\nHIztru4Mxqaq8ePHA7jyI65JLbYvd11nr9G7YzjbGGNMXFbojTHG5azQG2OMy1mhN8YYl7NCb4wx\nLmeF3hhjXM4KvTHGuJwVemOMcTkr9MYY43JW6I0xxuWs0BtjjMtZoTfGGJezQm+MMS5nhd4YY1zO\nCr0xxricFfo+rqmpiQkTJlBQUEBhYSHLli1rnffYY48xatQoCgsLueeeexxMaUzHdu3aRXFxces0\naNAgli5d6nSspPr444/52te+xqhRo8jPz+e3v/1tUraTiGfGGgelp6dTU1NDSUkJR48epbS0lEmT\nJnHo0CHWrVvHjh07yMjI4PDhw05HNaZdI0eOJBQKAXD69Gmys7O58cYbHU6VXHfccQdTp07lxRdf\n5G9/+xsnTpxIynas0PdxWVlZZGWFH9ObmZlJfn4+zc3NPPXUU8ybN4+MjAwAhg4d6mRMYy7Ia6+9\nxjXXXIPP53M6StJ88sknvP7666xcuRKA/v37079//6Rsyy7duEhjYyPbt2+nvLyc3bt3s2XLFsrL\nyxk3bhxvvPGG0/GM6bRnn32WmTNnOh0jqd577z0uv/xyvvWtb/G5z32OW2+9lePHjydnY515sGy8\nCWgk/CDwEJGH1AKDgV8CeyJfL+1oPd19OHiqifVA5aNHj2pJSYm+9NJLqqpaWFio3/3ud/XMmTP6\nu9/9Tv1+v545c8bh5Ma0FWtfbmlp0SFDhuj777/vdLyEi344+BVXXKEej0eDwaCqqn7ve9/TH/zg\nBxe0Pjr5cPBEFPrLzmlbDMyLvJ4H/HtH67FC33mBQEC9Xq8CrdPAgQP12muv1ZqamtblpkyZor/+\n9a9b31999dV6+PBhJyIbE1Osfdnr9ercuXN10qRJTsdLuFj9FRENBAKqqvr666/rtGnTLmidnS30\nEl62a0SkEShT1Q+j2nYB41X1oIhkAZtVdWR76ykrK9P6+vou50glfr+fvXv3nteemZnJp59+2vr+\nySef5MCBAyxYsIDdu3czceJE9u3bh4j0ZFxj4oq3L3s8HvLy8rjiiiscSJU8wWCQlpaW89qvvPJK\nmpubmT9/PsePH2fJkiWdXqeIbFPVso6W6+5grAK/EpHTwI9VdQUwTFUPRua/DwyLE3AOMAcgNze3\nmzFSx759+2K2Hz16lOLiYgAWLlxIVVUVVVVVFBUV0b9/f1atWmVF3vQq8fblM2fOcNlll/VwmuSL\nVeQBDhw4wOjRo7n66qv5yU9+kpRtd/eMPltVm0VkKOHr8f8LeFlVL4la5oiqXtreeuyMvvPinQX5\nfD4aGxt7PpAxXZRq+3Iy+tvZM/pu3XWjqs2Rr4eBnwPXAYcil2yIfLUbuBOouroar9fbps3r9VJd\nXe1QImO6JtX2ZUf725kL+bEm4DNAZtTr3wBTgSW0HYxd3NG6bDD2wsS6U8GYvij6LpRU2JcTfeyS\n7MFYEbma8Fk8hK/1/19VrRaRIcDzQC6wF7hJVT9qb1126ebCjR8/HoDNmzc7msMYc2ESeewmfTBW\nVd8FxsRo/zMwsavrNcYYk1j2l7HGGONyVuiNMcblrNAbY4zLWaE3xhiXs0JvjDEuZ4XeGGNczgq9\nMca4nBV6Y4xxOSv0xhjjclbojTHG5azQG2OMy1mhN8YYl7NCb4wxLmeF3hhjXK67z4w1DmtqauKb\n3/wmhw4dQkSYM2cOd9xxBzNmzGDXrl0AfPzxx1xyySWEQiGH0xrTsdOnT1NWVkZ2djbr1693Ok5S\n+f1+MjMzSUtLIz09nWQ9l8MKfR+Xnp5OTU0NJSUlHD16lNLSUiZNmsRzzz3Xusydd97JxRdf7GBK\nYzpv2bJl5Ofn8+mnnzodpUds2rQp6Q9Dt0s3fVxWVhYlJSUAZGZmkp+fT3Nzc+t8VeX5559n5syZ\nTkU0ptP279/Pf/7nf3Lrrbc6HcVVrNC7SGNjI9u3b6e8vLy1bcuWLQwbNoy8vDwHkxnTOd///vdZ\nvHgxHk9qlCYR4Ytf/CKlpaWsWLEiadvp8r+miFwlIptEpEFE/iAid0Ta54tIs4iEItO0xMU18Rw7\ndozKykqWLl3KoEGDWttXr15tZ/OmT1i/fj1Dhw6ltLTU6Sg95r//+78JhUJs2LCB5cuX8/rrrydn\nQ515gnhbwKk+AAAK7UlEQVSsCcgCSiKvM4HdQAEwH7jrQtZVWlrarSehp5pznyS/cuVKnTx5stbU\n1LRZ7uTJkzp06FBtampyKKkx7QsEAurz+VREdNCgQXrppZeqz+fTYcOG6cCBA3XWrFlOR0yoc4/d\nQCDQOu+BBx7QJUuWXND6gHrtTL3uzEKdWhGsAyZZoU+uQCCgXq9XgdYpLS1Np0yZct6yGzZs0IqK\nCgdSGtOxWPuy1+vVQCCgmzZt0i9/+ctOR0yoWP0dOHCgBgIBPXbsmI4dO1Y3bNhwQevsbKGX8LLd\nIyJ+4HWgCPjfwLeAT4B64E5VPdLe95eVlWmybityG7/fz969e89r79evHwUFBQAsXLiQadOmMXv2\nbK6//npuu+22no5pTIfi7csZGRmMGjWKpqYmrr32WgeSJUcwGKSlpeW89n79+pGXl8c///M/c999\n913QOkVkm6qWdbhcdwu9iFwE1AHVqrpGRIYBHxL+jfVDIEtVq2J83xxgDkBubm5prB+4OZ/H4yHW\nz0xEOHPmjAOJjOmaePsywLhx43o4TfLV1dXFbO/OsdvZQt+t++hFpB/wElCrqmsAVPVQ1PyngJh/\n8aCqK4AVED6j706OVJKbmxvzLCg3N9eBNMZ0Xbx92efzsXnz5p4PlGTxPsH0xLHbnbtuBHga+KOq\nPhzVnhW12I3Azq7HM+eqrq7G6/W2afN6vVRXVzuUyJiuSbV92dH+duZCfqwJ+ALhyzNvAqHINA34\nGfBWpP1lwpdubDA2gdobuTemL0m1fTn6LqNE9JeeHIztLhuMvXDjx48HcOVHXJNabF/uus5eo0+N\nPz8zxpgUZoXeGGNczgq9Mca4nBV6Y4xxOSv0xhjjclbojTHG5azQG2OMy1mhN8YYl7NCb4wxLmeF\n3hhjXM4KvTHGuJwVemOMcTkr9MYY43JW6I0xxuWs0LvAxo0bGTlyJJ/97GdZtGiR03GSqqqqiqFD\nh1JUVOR0lKRrampiwoQJFBQUUFhYyLJly5yOlFR//etfue666xgzZgyFhYU88MADTkdyDSv0fdzp\n06f5zne+w4YNG2hoaGD16tU0NDQ4HStpZs+ezcaNG52O0SPS09OpqamhoaGBYDDI8uXLXf2zzcjI\n4Ne//jU7duwgFAqxceNGgsGg07FcwQp9H7d161Y++9nPcvXVV9O/f3++/vWvs27dOqdjJU1FRQWD\nBw92OkaPyMrKoqSkBIDMzEzy8/Npbm52OFXyiAgXXXQRACdPnuTkyZOEn1hqussKfR/X3NzMVVdd\n1fo+JyfH1cUgVTU2NrJ9+3bKy8udjpJUp0+fpri4mKFDhzJp0iTX97enJK3Qi8hUEdklIm+LyLxk\nbccYtzt27BiVlZUsXbqUQYMGOR0nqdLS0giFQuzfv5+tW7eyc+dOpyO5QlIKvYikAcuBLwEFwEwR\nKUjGtlLRv/zLv1BXV0ddXR0zZszg1VdfbZ23f/9+srOzHUyXeLW1tfj9fjweD36/n7Vr1zodKami\n++vz+fj85z/PrFmzmD59utPREq62tpZgMEhdXR1+v5/a2loALrnkEiZMmJAy4zFJ15kniF/oBIwF\n/ivq/b3AvfGWLy0t7daT0FPJ7bffrsB506xZs7SlpUVHjx6tO3fudDpmwgQCAfV6vW36OmDAAM3J\nyXE6WlLE6m96eroGAgGnoyVcrL4OHDhQA4GAnjhxQr/whS/oL37xC6dj9mpAvXaiJkt42cQSka8B\nU1X11sj7bwDlqvrdWMuXlZVpfX19wnO4UXp6OqdPn445b8CAAVxxxRX4fL4eTpU8wWCQlpaWmPP6\n9++P3+8nKyurh1MlT7z+igher5fhw4czZMgQB5IlXry+9uvXjxEjRnDTTTfxb//2bw4k6ztEZJuq\nlnW0XHpPhIlFROYAcwByc3OditHnxCvygCsHruIVeYCxY8f2YJKeEa+/qkpZWYfHc58Sr6+nTp2y\na/MJlqxC3wxcFfU+J9LWSlVXACsgfEafpByuk5aWFrPYp6WlsXnz5p4PlGR+v5+9e/ee1+7z+ay/\nfVy8vtqJX+Il666bN4A8ERkuIv2BrwMvJ2lbKWXOnDkX1N7XVVdX4/V627R5vV6qq6sdSpRcqdTf\nVOqr4zpzIb8rEzAN2A28A9zX3rI2GHthbr/9dk1LS1NA09LS9Pbbb3c6UlIFAgH1+XwqIurz+Vw5\nMBktlfqbSn1NBpwcjL1QNhhrjDEXrrODsfaXscYY43JW6I0xxuWs0BtjjMtZoTfGGJezQm+MMS5n\nhd4YY1zOCr0xxricFXpjjHG5XvEHUyLyAXD+f3qRfJcBHzqw3USx/M7qy/n7cnaw/Gf5VPXyjhbq\nFYXeKSJS35m/KuutLL+z+nL+vpwdLP+Fsks3xhjjclbojTHG5VK90K9wOkA3WX5n9eX8fTk7WP4L\nktLX6I0xJhWk+hm9Mca4XkoWehFZIiJ/EpE3ReTnInJJ1Lx7ReRtEdklIlOczNkeEZkayfi2iMxz\nOk97ROQqEdkkIg0i8gcRuSPSPlhEfikieyJfL3U6a3tEJE1EtovI+sj7PpNfRC4RkRcj+/0fRWRs\nX8kvInMj+81OEVktIgN6e3YReUZEDovIzqi2uJmTXXdSstADvwSKVHU04adg3QsgIgWEH3tYCEwF\nfiQiaY6ljCOSaTnwJaAAmBnJ3ludAu5U1QLgeuA7kbzzgNdUNQ94LfK+N7sD+GPU+76UfxmwUVVH\nAWMI96PX5xeRbOB7QJmqFgFphI/R3p59JeEaEi1m5p6oOylZ6FX1VVU9FXkbJPzwcoB/BJ5V1RZV\nfQ94G7jOiYwduA54W1XfVdW/Ac8Szt4rqepBVf195PVRwkUmm3DmVZHFVgFfdSZhx0QkB/gy8B9R\nzX0iv4hcDFQATwOo6t9U9WP6SH4gHRgoIumAFzhAL8+uqq8DH53THC9z0utOShb6c1QBGyKvs4Gm\nqHn7I229TV/JeR4R8QOfA34HDFPVg5FZ7wPDHIrVGUuBe4AzUW19Jf9w4APgJ5FLT/8hIp+hD+RX\n1Wbg/wD7gIPAJ6r6Kn0gewzxMif9eHZtoReRX0Wu6Z07/WPUMvcRvqxQ61zS1CEiFwEvAd9X1U+j\n50UedNwrbwETkRuAw6q6Ld4yvTk/4TPiEuAJVf0ccJxzLnX01vyR69j/SPiX1ZXAZ0Tkf0Yv01uz\nt6enM6f31IZ6mqp+sb35IjIbuAGYqH+/x7QZuCpqsZxIW2/TV3K2EpF+hIt8raquiTQfEpEsVT0o\nIlnAYecStut/AP8gItOAAcAgEQnQd/LvB/ar6u8i718kXOj7Qv4vAu+p6gcAIrIG+Dx9I/u54mVO\n+vHs2jP69ojIVMIfw/9BVU9EzXoZ+LqIZIjIcCAP2OpExg68AeSJyHAR6U94IOdlhzPFJSJC+Prw\nH1X14ahZLwM3R17fDKzr6Wydoar3qmqOqvoJ/1v/WlX/J30n//tAk4iMjDRNBBroG/n3AdeLiDey\nH00kPMbTF7KfK17m5NcdVU25ifBgRxMQikxPRs27D3gH2AV8yems7fRhGuE7ht4B7nM6TwdZv0D4\nY+qbUf/m04AhhO8+2AP8ChjsdNZO9GU8sD7yus/kB4qB+sjPYC1waV/JDzwI/AnYCfwMyOjt2YHV\nhMcUThL+RHVLe5mTXXfsL2ONMcblUvLSjTHGpBIr9MYY43JW6I0xxuWs0BtjjMtZoTfGGJezQm+M\nMS5nhd4YY1zOCr0xxrjc/we0EsEC8DbOkAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fa26be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "collinear_vertices =  [1, 2, 15, 18, 22, 23, 26, 27]\n",
      "concave_vertices = [4, 7, 8, 11, 12, 16, 20, 25]\n",
      "horizontal_chords =  [(8, 25), (16, 20), (22, 12), (23, 11), (26, 7), (27, 4)]\n",
      "vertical_chords =  [(4, 7), (8, 11), (20, 25), (2, 16), (15, 12)]\n",
      "The maximum partitioned rectillinear polygon\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118f75c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Arbfeyle/+lUqKyuZNGkSAFlZWUyaNAkR4eqrryYpKYlPPvnEyejGnCbaa3nm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\nuQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fa5d5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The minimum partitioned rectillinear polygon\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f7f8da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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p5Ofnc/nllzuQKnECgQCtra3ntV9xxRU0NzezYMECTpw4wdKlS2Nep4jsUNXy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\nMQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1200180b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'Please make sure that the INPUT is A CLOSED RECTILINEAR POLYGON,'\n",
    "'CONSTRUCTED WHILE GOING IN ANTI-CLOCKWISE ONLY'\n",
    "# importing libraries\n",
    "import networkx as nx\n",
    "import turtle\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "from networkx.algorithms import bipartite\n",
    "import math\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "# declaration list\n",
    "wn = turtle.Screen()\n",
    "# a turtle called gopu \n",
    "gopu = turtle.Turtle() \n",
    "# co-ordinate points\n",
    "x = [] \n",
    "y = []\n",
    "# vertex-type := rectilinear = -1; convex = 0; concave = 1 \n",
    "vertex_type = [] \n",
    "# store the bipartite graph of chords\n",
    "G = nx.Graph()\n",
    "# the line below can be commented if one needs animation\n",
    "gopu.speed(0)\n",
    "# starts recording keys being pressed\n",
    "gopu.begin_poly()\n",
    "\n",
    "# Event handlers\n",
    "stride = 25\n",
    "# Up  = up() - vertex to be deleted = -1\n",
    "def up():\n",
    "    vertex_type.append(-1)\n",
    "    gopu.forward(stride)\n",
    " \n",
    "# left = left() ; make vertex - convex = 0\n",
    "def left():\n",
    "    vertex_type.append(0)\n",
    "    gopu.setheading(gopu.heading()+90)\n",
    "    gopu.forward(stride)\n",
    " \n",
    "# right = right() ; make vertex - concave = 1\n",
    "def right():\n",
    "    vertex_type.append(1)\n",
    "    gopu.setheading(gopu.heading()-90)\n",
    "    gopu.forward(stride)\n",
    " \n",
    "# back = back() -- doing undo is allowed only once.\n",
    "def back():\n",
    "    vertex_type.pop()\n",
    "    gopu.undo()\n",
    "\n",
    "# quits the screen and outputs the plots the partitioned polygon\n",
    "def partition_polygon():\n",
    "    # closing the screen\n",
    "    wn.bye()\n",
    "    # stopped recording the polygon\n",
    "    gopu.end_poly()\n",
    "    p = gopu.get_poly()\n",
    "    p = list(p)\n",
    "    compute_partition(p)  \n",
    "    \n",
    "'''\n",
    "The movements of the turtle are recorded and the rectilinear polygon thus \n",
    "obtained is converted into bipartite graph of chords\n",
    "'''\n",
    "def compute_partition(p):\n",
    "    # p now contains the list of coordinates of vertices\n",
    "    # last one is same as the origin\n",
    "    # and the origin is always going to be a convex vertex\n",
    "    p.pop()\n",
    "    vertex_type[0] = 0\n",
    "    \n",
    "    # x and y contain list of x and y coordinates respectively\n",
    "    for i,j in p:\n",
    "        x.append(i)\n",
    "        y.append(j)\n",
    "\n",
    "    # this is done as there are some very small errors in recording the \n",
    "    # position by the turtle library\n",
    "    for i in range(len(x)):\n",
    "        x[i] = int(x[i])\n",
    "        y[i] = int(y[i])\n",
    "\n",
    "    for i in range(len(x)):\n",
    "        if x[i] % stride != 0:\n",
    "            x[i] += (stride - x[i] % stride)\n",
    "        if y[i] % stride != 0:\n",
    "            y[i] += (stride - y[i] % stride)\n",
    "\n",
    "    # separating concave and collinear vertices\n",
    "    collinear_vertices = [i for i,val in enumerate(vertex_type) if val == -1]\n",
    "    concave_vertices = [i for i,val in enumerate(vertex_type) if val == 1]\n",
    "    \n",
    "    # finding the chords inside the polygon\n",
    "    horizontal_chords = []\n",
    "    vertical_chords = []\n",
    "\n",
    "    # middles is used because, there are cases when there is a chord between vertices\n",
    "    # and they intersect with external chords, hence if there is any vertex in between \n",
    "    # two vertices then skip that chord. \n",
    "    for i in range(len(concave_vertices)):\n",
    "        for j in range(i+1,len(concave_vertices)):\n",
    "            if concave_vertices[j] != concave_vertices[i] + 1:\n",
    "                middles = []\n",
    "                if y[concave_vertices[i]] == y[concave_vertices[j]]:\n",
    "                    for k in range(len(x)):\n",
    "                        if y[concave_vertices[i]] == y[k] and (x[concave_vertices[i]] < x[k] and x[concave_vertices[j]] > x[k] \\\n",
    "                                                              or x[concave_vertices[i]] > x[k] and x[concave_vertices[j]] < x[k]):\n",
    "                            middles.append(k)\n",
    "                    if len(middles) == 0:\n",
    "                        horizontal_chords.append((concave_vertices[i],concave_vertices[j]))\n",
    "                middles = []\n",
    "                if x[concave_vertices[i]] == x[concave_vertices[j]]:\n",
    "                    for k in range(len(x)):\n",
    "                        if x[concave_vertices[i]] == x[k] and (y[concave_vertices[i]] < y[k] and y[concave_vertices[j]] > y[k] \\\n",
    "                                                              or y[concave_vertices[i]] > y[k] and y[concave_vertices[j]] < y[k]):\n",
    "                            middles.append(k)\n",
    "                    if len(middles) == 0:\n",
    "                        vertical_chords.append((concave_vertices[i],concave_vertices[j]))\n",
    "            \n",
    "\n",
    "    temp_hori = horizontal_chords[:]\n",
    "    temp_verti = vertical_chords[:]\n",
    "\n",
    "    for i in range(len(collinear_vertices)):\n",
    "        for j in range(len(concave_vertices)):\n",
    "            middles = []\n",
    "            if y[collinear_vertices[i]] == y[concave_vertices[j]]:\n",
    "                if collinear_vertices[i] < concave_vertices[j]:\n",
    "                    for k in range(len(x)):\n",
    "                        if y[k] == y[collinear_vertices[i]] and (x[k] < x[concave_vertices[j]] \\\n",
    "                            and x[k] > x[collinear_vertices[i]] or x[k] > x[concave_vertices[j]] \\\n",
    "                            and x[k] < x[collinear_vertices[i]]):\n",
    "                            middles.append(k)\n",
    "                    if collinear_vertices[i]+1 == concave_vertices[j]:\n",
    "                        middles.append(0)\n",
    "                else:\n",
    "                    for k in range(len(x)):\n",
    "                        if y[k] == y[collinear_vertices[i]] and (x[k] > x[concave_vertices[j]] \\\n",
    "                            and x[k] < x[collinear_vertices[i]] or x[k] < x[concave_vertices[j]] \\\n",
    "                            and x[k] > x[collinear_vertices[i]]):\n",
    "                            middles.append(k)\n",
    "                    if collinear_vertices[i] == concave_vertices[j]+1:\n",
    "                        middles.append(0)\n",
    "                if len(middles) == 0:\n",
    "                    horizontal_chords.append((collinear_vertices[i],concave_vertices[j]))\n",
    "            middles = []\n",
    "            if x[collinear_vertices[i]] == x[concave_vertices[j]]:\n",
    "                if collinear_vertices[i] < concave_vertices[j]:\n",
    "                    for k in range(len(x)):\n",
    "                        if x[k] == x[collinear_vertices[i]] and (y[k] < y[concave_vertices[j]] \\\n",
    "                            and y[k] > y[collinear_vertices[i]] or y[k] > y[concave_vertices[j]] \\\n",
    "                            and y[k] < y[collinear_vertices[i]]):\n",
    "                            middles.append(k)\n",
    "                    if collinear_vertices[i]+1 == concave_vertices[j]:\n",
    "                        middles.append(0)\n",
    "                else:\n",
    "                    for k in range(len(x)):\n",
    "                        if x[k] == x[collinear_vertices[i]] and (y[k] > y[concave_vertices[j]] \\\n",
    "                            and y[k] < y[collinear_vertices[i]] or y[k] < y[concave_vertices[j]] \\\n",
    "                            and y[k] > y[collinear_vertices[i]]):\n",
    "                            middles.append(k)\n",
    "                    if collinear_vertices[i] == concave_vertices[j]+1:\n",
    "                        middles.append(0)\n",
    "                if len(middles) == 0:\n",
    "                    vertical_chords.append((collinear_vertices[i],concave_vertices[j]))    \n",
    "    # displaying all attributes and important parameters involved\n",
    "    # plotting the initial input given\n",
    "    print (\"Initial input rectillinear graph\")\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x+[0], y+[0], color='black')\n",
    "    ax.scatter(x+[0], y+[0], color='black')\n",
    "    for i in range(len(x)):\n",
    "        ax.annotate(i, (x[i],y[i]))\n",
    "    plt.show()\n",
    "    plt.clf()\n",
    "    \n",
    "    print(\"collinear_vertices = \", collinear_vertices)\n",
    "    print(\"concave_vertices =\", concave_vertices)\n",
    "    print(\"horizontal_chords = \" ,horizontal_chords)\n",
    "    print(\"vertical_chords = \",vertical_chords)\n",
    "    \n",
    "    # drawing the maximum partitioned polygon \n",
    "    print(\"The maximum partitioned rectillinear polygon\")\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x+[0], y+[0], color='black')\n",
    "    ax.scatter(x+[0], y+[0], color='black')\n",
    "    for i in range(len(x)):\n",
    "        ax.annotate(i, (x[i],y[i]))\n",
    "    for i,j in horizontal_chords:\n",
    "        ax.plot([x[i],x[j]],[y[i],y[j]],color='black')\n",
    "    for i,j in vertical_chords:\n",
    "        ax.plot([x[i],x[j]],[y[i],y[j]],color='black')\n",
    "    plt.show()\n",
    "    plt.clf()\n",
    "    # MAXIMUM PARTITION CODE ENDS ---------------------------------\n",
    "\n",
    "    # MINIMUM PARTITION CODE STARTS -------------------------------\n",
    "    horizontal_chords = temp_hori[:]\n",
    "    vertical_chords = temp_verti[:]\n",
    "\n",
    "    # Creating a bipartite graph from the set of chords\n",
    "    for i,h in enumerate(horizontal_chords):\n",
    "        y1 = y[h[0]]\n",
    "        x1 = min(x[h[0]] ,x[h[1]] )\n",
    "        x2 = max(x[h[0]] ,x[h[1]])\n",
    "        G.add_node(i, bipartite=1)\n",
    "        for j,v in enumerate(vertical_chords):\n",
    "            x3 = x[v[0]]\n",
    "            y3 = min(y[v[0]],y[v[1]])\n",
    "            y4 = max(y[v[0]],y[v[1]])\n",
    "            G.add_node(j + len(horizontal_chords),bipartite=0)\n",
    "            if x1 <= x3 and x3 <=x2 and y3 <= y1 and y1 <= y4:    \n",
    "                G.add_edge(i, j + len(horizontal_chords))\n",
    "    \n",
    "    if len(horizontal_chords) == 0:\n",
    "        for j,v in enumerate(vertical_chords):\n",
    "            x3 = x[v[0]]\n",
    "            y3 = min(y[v[0]],y[v[1]])\n",
    "            y4 = max(y[v[0]],y[v[1]])\n",
    "            G.add_node(j,bipartite=0)\n",
    "    \n",
    "    # finding the maximum matching of the bipartite graph, G.\n",
    "    M = nx.Graph()\n",
    "    maximum_matching = nx.bipartite.maximum_matching(G)\n",
    "    maximum_matching_list = []\n",
    "    for i,j in maximum_matching.items():\n",
    "        maximum_matching_list += [(i,j)]\n",
    "    M.add_edges_from(maximum_matching_list)\n",
    "    maximum_matching = M.edges()\n",
    "    # breaking up into two sets\n",
    "    H, V = bipartite.sets(G)\n",
    "    free_vertices = []\n",
    "    for u in H:\n",
    "        temp = []\n",
    "        for v in V:\n",
    "            if (u,v) in maximum_matching or (v,u) in maximum_matching:\n",
    "                temp += [v]\n",
    "        if len(temp) == 0:\n",
    "            free_vertices += [u]\n",
    "    for u in V:\n",
    "        temp = []\n",
    "        for v in H:\n",
    "            if (u,v) in maximum_matching or (v,u) in maximum_matching:\n",
    "                temp += [v]\n",
    "        if len(temp) == 0:\n",
    "            free_vertices += [u]\n",
    "            \n",
    "    # finding the maximum independent set\n",
    "    max_independent = []\n",
    "    while len(free_vertices) != 0 or len(maximum_matching) != 0:\n",
    "        if len(free_vertices) != 0 :\n",
    "            u = free_vertices.pop()\n",
    "            max_independent += [u]\n",
    "        else:\n",
    "            u, v = maximum_matching.pop()\n",
    "            G.remove_edge(u,v)\n",
    "            max_independent += [u]\n",
    "\n",
    "        for v in G.neighbors(u):\n",
    "            G.remove_edge(u, v)\n",
    "            for h in G.nodes():\n",
    "                if (v,h) in maximum_matching:\n",
    "                    maximum_matching.remove((v,h))\n",
    "                    free_vertices += [h]\n",
    "                if (h,v) in maximum_matching:\n",
    "                    maximum_matching.remove((h,v))\n",
    "                    free_vertices += [h]\n",
    "\n",
    "    \n",
    "    # drawing the partitioned polygon \n",
    "    independent_chords = []\n",
    "    for i in max_independent:\n",
    "        if (i >= len(horizontal_chords)):\n",
    "            independent_chords += [vertical_chords[i-len(horizontal_chords)]]\n",
    "        else:\n",
    "            independent_chords += [horizontal_chords[i]]\n",
    "    unmatched_concave_vertices = [i for i in concave_vertices]\n",
    "    for i,j in independent_chords:\n",
    "        if i in unmatched_concave_vertices:\n",
    "            unmatched_concave_vertices.remove(i)\n",
    "        if j in unmatched_concave_vertices:\n",
    "            unmatched_concave_vertices.remove(j)\n",
    "    \n",
    "    nearest_chord = []\n",
    "    for i in unmatched_concave_vertices:\n",
    "        dist = 0\n",
    "        nearest_distance = math.inf\n",
    "        for j in max_independent:\n",
    "            if j < len(horizontal_chords):\n",
    "                temp1, temp2 = horizontal_chords[j]\n",
    "                if abs(y[i] - y[temp1]) < nearest_distance and \\\n",
    "                (x[i] <= x[temp1] and x[i] >= x[temp2] or x[i] >= x[temp1] and x[i] <= x[temp2]) \\\n",
    "                and abs(temp1 - i) != 1 and abs(temp2 - i) != 1:\n",
    "                    middles = []\n",
    "                    for u in range(len(x)):\n",
    "                        if x[i] == x[u] and (y[i] < y[u] and y[u] < y[temp1] or y[temp1] < y[u] and y[u] < y[i]):\n",
    "                            middles.append(u)\n",
    "                    if len(middles) == 0:\n",
    "                        nearest_distance = abs(y[i] - y[temp1])\n",
    "                        dist = y[temp1] - y[i]\n",
    "\n",
    "        if nearest_distance != math.inf:\n",
    "            nearest_chord.append((i,dist)) \n",
    "        else:\n",
    "            for k in collinear_vertices:\n",
    "                if x[k] == x[i] and abs(y[k] - y[i]) < nearest_distance and abs(k-i) != 1:\n",
    "                    middles = []\n",
    "                    for u in range(len(x)):\n",
    "                        if x[i] == x[u] and (y[i] < y[u] and y[u] < y[k] or y[k] < y[u] and y[u] < y[i]):\n",
    "                            middles.append(u)\n",
    "                    if len(middles) == 0:\n",
    "                        nearest_distance = abs(y[i] - y[k])\n",
    "                        dist = y[k] - y[i]\n",
    "            nearest_chord.append((i,dist)) \n",
    "     \n",
    "    print(\"The minimum partitioned rectillinear polygon\")\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x+[0], y+[0], color='black')\n",
    "    ax.scatter(x+[0], y+[0], color='black')\n",
    "    for i in range(len(x)):\n",
    "        ax.annotate(i, (x[i],y[i]))\n",
    "    for i,j in independent_chords:\n",
    "        ax.plot([x[i],x[j]],[y[i],y[j]],color='black')\n",
    "    for i,dist in nearest_chord:\n",
    "        ax.plot([x[i],x[i]],[y[i], y[i]+dist],color='black')\n",
    "    plt.show()\n",
    "    # MAXIMUM PARTITION CODE ENDS\n",
    "# Defining the keyboard keys function\n",
    "wn.onkey(up, \"Up\")\n",
    "wn.onkey(left, \"Left\")\n",
    "wn.onkey(right, \"Right\")\n",
    "wn.onkey(back, \"Down\")\n",
    "wn.onkey(partition_polygon, \"Escape\")\n",
    "wn.listen()\n",
    "wn.mainloop()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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