cost-allocation-breaks.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ride Share Allocation\n",
    "## Implementation of Gopalakrishnan et al.(2016) Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This algorithm intake a list of passengers and their destination, and designs a specific graph who's max flow min cost reduction is isomorphic to the best route to take.\n",
    "\n",
    "The biggest problem is that this algorithm assumes uncapacitated vehicles, and takes the pickup order as inputted. For the first problem we can assume now that this is a bus-sharing problem (think Google sending shuttles to pick up their employees), and for the second we can do some sorting on the input. To turn the algorithm into returning paths for capacitated vehicles, we would need to modify the max_flow_min_cost algorithm for a graph, which is fairly complicated/involved.\n",
    "\n",
    "Code can be found [on Arya's Github](www.github.com/misingnoglic/cost-allocation)\n",
    "\n",
    "Authors:\n",
    "Arya Boudaie;\n",
    "Kiranmayi P;\n",
    "Nidhi Rathi.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Backend Logic Code:\n",
    "\n",
    "This part of the code deals with backend functions. Feel free to just read the comments under the function headers, or just skip to Main Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "__author__ = \"Arya\"\n",
    "import networkx as nx # Graph Library\n",
    "import matplotlib.pyplot as plt # Plotting library\n",
    "from matplotlib.colors import cnames\n",
    "from itertools import cycle\n",
    "import random\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def new_round(num, digits):\n",
    "    '''\n",
    "    Because nx.nextwork_simplex doesnt work for \n",
    "    floats, this function just multiplies num\n",
    "    by digits and turns in into an integer\n",
    "    '''\n",
    "    return int(num*(10**digits))\n",
    "\n",
    "def node_numbers(node):\n",
    "    '''\n",
    "    Numbers the nodes, to allow for sorting \n",
    "    when printing them\n",
    "    '''\n",
    "    \n",
    "    if node[0]=='source': return 0\n",
    "    if node[0]=='sink': return 1\n",
    "    if node[0]=='destination': return float('inf')\n",
    "    else:\n",
    "        if node[0][0]==\"d\": print node\n",
    "        cost= 2+2*int(node[0][0])\n",
    "        if node[0][1:]=='out': cost+=1\n",
    "        return cost\n",
    "\n",
    "def sort_nodes(nodes):\n",
    "    '''Sorts a list of nodes'''\n",
    "    return sorted(nodes,key=node_numbers)\n",
    "\n",
    "def sort_edges(edges):\n",
    "    '''sorts a list of edges'''\n",
    "    return sorted(edges, key = lambda x:node_numbers([x[0]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic functions integral to the construction\n",
    "\n",
    "These are the building functions that are used in the algorithm. We can replace them, as the main algorithm doesn't make any assumptions on these.  It might be interesting to use other distance functions for instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "def distance(node1,node2):\n",
    "    '''Simple euclidian distance formula between two points'''\n",
    "    x1 = node1[0]\n",
    "    x2 = node2[0]\n",
    "    y1 = node1[1]\n",
    "    y2 = node2[1]\n",
    "    return sqrt((x2-x1)**2 + (y2-y1)**2)\n",
    "\n",
    "def max_distance(points):\n",
    "    '''Gets the max distance between two points in the graph'''\n",
    "    current = 0\n",
    "    for node1 in points:\n",
    "        for node2 in points:\n",
    "            d = distance(node1,node2) # distance from n1 & n2\n",
    "            if d>current: \n",
    "                current=d # store larger distance\n",
    "    return current\n",
    "\n",
    "# Used in main algorithm to see which m' has lowest cost\n",
    "def cost_of_min_cost(G):\n",
    "    '''\n",
    "    Given a graph, it gives the cost of the paths \n",
    "    in the max flow min cost over the graph.\n",
    "    It also returns the paths from source to \n",
    "    destination as a list, for convenience\n",
    "    '''\n",
    "    \n",
    "    # Gets the max flow min cost path from source to sink\n",
    "    flow_path = nx.max_flow_min_cost(G,'source','sink',weight='cost')\n",
    "    \n",
    "    # The beginning has the directions for where each cab starts\n",
    "    beginning = flow_path['source'] \n",
    "    \n",
    "    total_cost = 0\n",
    "    # each node which the flow_path indicates to go\n",
    "    start_paths = [n[0] for n in beginning.items() if n[1]==1] \n",
    "    paths = []\n",
    "    \n",
    "    # For each node that a cab goes to in order to start\n",
    "    for start_node in start_paths: \n",
    "        path = [start_node]\n",
    "        curr_node=start_node\n",
    "        path_cost = 0\n",
    "        # Loop through the path until you reach the destination\n",
    "        while curr_node!='destination': \n",
    "            # Node that current node travels to\n",
    "            next_node = [n for n in \n",
    "                         flow_path[curr_node].items() \n",
    "                         if n[1]==1][0][0] \n",
    "            # Add the cost of the edge from the current node \n",
    "            #to the next node\n",
    "            path_cost += G.edge[curr_node][next_node]['cost'] \n",
    "            # Switch current node to be the node travelled to\n",
    "            curr_node = next_node \n",
    "            if G.node[curr_node]['type']=='passenger in': \n",
    "                path.append(curr_node)\n",
    "        # When that node is finished, add it to the total cost \n",
    "        # and start over\n",
    "        total_cost += path_cost \n",
    "        # add destination to end of path\n",
    "        paths.append(path+['destination']) \n",
    "    return total_cost, paths  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Main Algorithm\n",
    "\n",
    "In the code I include comments on what part of the \n",
    "paper is being represented by the code\n",
    "\n",
    "1. The algorithm takes a list of passengers (x,y position tuples), and a destination (x,y) tuple. Passengers are listed in  pickup order\n",
    "\n",
    "2. From that, it creates a source node, a sink node, a destination node, and two nodes for every passenger (an in and an out node)\n",
    "\n",
    "3. For each passenger it adds an edge from its in node to its out node (cost 0, capacity 1)\n",
    "\n",
    "4. Add an edge from the source to every in node (cost 0, capacity 1)\n",
    "\n",
    "5. Calculate a value L, which is larger than the maximum distance between two points multiplied by the number of passengers.\n",
    "\n",
    "6. Create an edge from each out node to the destination with the cost being the distance between the passenger and the destination\n",
    "\n",
    "7. Add an edge from each out/in pair (where the index of the out is less than the index of the in) where the cost is the distance between the two passengers minus L."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def generate_graph(passengers, destination, \n",
    "                   annotate=False, complete=False, mistake=False):\n",
    "    '''\n",
    "    This code generates the graph described by Raga in \n",
    "    section 7.3 steps 1 through 5.\n",
    "    The code is annotated with what it is doing in comments\n",
    "    passengers = List of x,y coordinates for each passenger\n",
    "    destination = x,y tuple with coord. of destination\n",
    "    annotate=True if you want print statements\n",
    "    complete=True if you want to do unordered paths\n",
    "    \n",
    "    '''\n",
    "    \n",
    "    G=nx.DiGraph() # Create a directed graph\n",
    "    \n",
    "    # The rest of the algorithm closely follows Raga's paper\n",
    "    # I quote the steps directly\n",
    "    \n",
    "    # Step 1\n",
    "    # \"s and t denote the source and sink vertices, respectively\"\n",
    "    G.add_node(\"source\", type=\"meta\")\n",
    "    G.add_node(\"sink\", type=\"meta\")\n",
    "    \n",
    "    # Step 2\n",
    "    # For each passenger/pickup location u ∈ N , we create \n",
    "    # two vertices and an edge: an entry vertex u_in, an exit \n",
    "    # vertex u_out, and an edge of cost 0 and capacity 1 directed\n",
    "    # from u_in to u_out. We also create a vertex n+1 \n",
    "    # corresponding to the dropoff location.\n",
    "    i = 1\n",
    "    for passenger in passengers:\n",
    "        # {}in.format(x) will give the node the name xin, \n",
    "        # for any integer x\n",
    "        G.add_node(\"{}in\".format(i), number=i, x=passenger[0], \n",
    "                   y=passenger[1], type=\"passenger in\")\n",
    "        G.add_node(\"{}out\".format(i),number=i, x=passenger[0], \n",
    "                   y=passenger[1], type=\"passenger out\")\n",
    "        G.add_edge(\"{}in\".format(i), \"{}out\".format(i), cost=0, \n",
    "                   capacity=1)\n",
    "        i+=1\n",
    "    G.add_node(\"destination\", x=destination[0], y=destination[1], \n",
    "               type=\"destination\")\n",
    "    \n",
    "    # Step 3\n",
    "    # We create n edges, one each of cost 0 and capacity 1 from \n",
    "    # the source vertex s to each of the entry vertices u_in, \n",
    "    # u ∈ N.\n",
    "    for node in G.nodes(data=True):\n",
    "        if node[1]['type']==\"passenger in\":\n",
    "            G.add_edge(\"source\", node[0], cost=0, capacity=1)\n",
    "    \n",
    "    # Calculating L\n",
    "    # passengers + [destination] is the concatonation of the \n",
    "    # two lists\n",
    "    L = len(passengers)*max_distance(passengers + \n",
    "                                     [destination]) + 1 \n",
    "    if annotate: print \"L = {}\".format(L)   \n",
    "        \n",
    "    # Step 4\n",
    "    # We create n edges, one each of cost SuD and capacity 1 \n",
    "    # from each of the exit vertices uout, u ∈ N, to the \n",
    "    # dropoff vertex n + 1\n",
    "    for node in G.nodes(data=True):\n",
    "        if node[1]['type']==\"passenger out\":\n",
    "            # Calculating SuD\n",
    "            cost = distance(destination, (node[1]['x'],\n",
    "                                          node[1]['y']))-L \n",
    "            \n",
    "            if mistake: cost+=L\n",
    "            cost = new_round(cost, 2)\n",
    "            node_name = node[0]\n",
    "            # Creating the edge with that cost\n",
    "            G.add_edge(node_name,\"destination\", cost=cost, \n",
    "                       capacity=1) \n",
    "    # Step 5\n",
    "    # To encode the pickup order, for each 1 ≤ u < v ≤ n we \n",
    "    # create an edge of cost (SuSv − L) and capacity 1 directed \n",
    "    # from u_out to v_in, where L is a sufficiently large number \n",
    "    # satisfying L > 2*max [u,v∈N∪{n+1} SuSv].    \n",
    "    \n",
    "    for u in range(1,len(passengers)+1): # For each u\n",
    "        # If we want a complete graph we will do every v, \n",
    "        # otherwise just v>u\n",
    "        if complete: \n",
    "            start = 1\n",
    "        else: \n",
    "            start = u+1\n",
    "        for v in range(start, len(passengers)+1):\n",
    "            if u!=v:\n",
    "                G.add_edge(\"{}out\".format(u), \"{}in\".format(v), \n",
    "                           cost=new_round(distance(\n",
    "                            passengers[u-1], passengers[v-1])-L, \n",
    "                                          2), capacity=1) \n",
    "    # pass this graph to step 6\n",
    "    return allocation(G, annotate=annotate) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 6:\n",
    "Finally, it creates a separate graph for each of n passengers, with each one having\n",
    "an edge from destination to sink with cost 0 and capacity m' (for each value m'\n",
    "from 1 to n).\n",
    "\n",
    "After the graphs are generated, it iterates over each graph and calculate the cost for n passengers pick up and  returns the path with minimum cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def allocation(G, annotate=False):\n",
    "    '''\n",
    "    Given the G in the generate_graph algo, it gives the graph w/\n",
    "    a node from destination to source m' with the minimum cost\n",
    "    for traversing the max flow min cost graph.\n",
    "    annotate=True if you want print statements\n",
    "    '''        \n",
    "    # Step 6\n",
    "    # We add a final edge of cost 0 and capacity m′ \n",
    "    # from the dropoff vertex n + 1 to the\n",
    "    # sink vertex t, thereby limiting the maximum flow \n",
    "    # in the network to m′ units.\n",
    "    \n",
    "    # In this implementation, we make n copies of this graph, \n",
    "    # and give each one an m' from i to n\n",
    "    passengers = [node for node in G.nodes(data=True) \n",
    "                  if node[1]['type']=='passenger in']\n",
    "    possible_graphs = [G.copy() for i in range(len(passengers))]\n",
    "    \n",
    "    for i, pg in enumerate(possible_graphs, 1):\n",
    "        # All the different m' values\n",
    "        pg.add_edge(\"destination\", \"sink\", cost=0, capacity=i) \n",
    "        \n",
    "    \n",
    "    # Now over these graphs we have to find the one \n",
    "    # with the lowest cost in the min cost max flow algorithm\n",
    "    # In other words which m' gives the lowest cost\n",
    "    min_cost = float('inf')\n",
    "    min_flow_graph = None\n",
    "    costs = []\n",
    "    paths = []\n",
    "    optimal = 0\n",
    "    \n",
    "    for index, pg in enumerate(possible_graphs):\n",
    "        if annotate: print \"{} cabs: \".format(index+1),\n",
    "        # For each possible graph, calculate the cost. \n",
    "        c, path = cost_of_min_cost(pg)\n",
    "        c = new_round(c,2)\n",
    "        paths.append(path)\n",
    "        costs.append(c)\n",
    "        if annotate:\n",
    "            print \"path: \",path,\"--\",\n",
    "            print \"cost: \",c/10000.0\n",
    "        \n",
    "        # If the cost is less than previous graphs, store it\n",
    "        if c<min_cost:\n",
    "            min_cost=c\n",
    "            min_flow_graph=pg\n",
    "            optimal = index\n",
    "    if annotate: print \"Optimal path with {} cabs\".format(\n",
    "            optimal+1), paths[optimal]\n",
    "    return min_flow_graph,paths[optimal]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Frontend Functions\n",
    "\n",
    "The following functions allow the user to interract with the algorithm and visually inspect the output. (They are not commented, as they aren't important to the algorithm.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def allocation_interractive(**kwargs):\n",
    "    '''\n",
    "    Interractive version of the function\n",
    "    '''\n",
    "    players = int(raw_input(\"How many players are there: \"))\n",
    "    player_coordinates = []\n",
    "    for i in range(1,players+1):\n",
    "        coord = raw_input('''What are the x and y \n",
    "                          coordinates for player {}: '''.format(i))\n",
    "        coord = [int(x) for x in coord.split()]\n",
    "        player_coordinates.append((coord[0],coord[1]))\n",
    "    destination = raw_input('''What are the x and y coordinates \n",
    "                                for the destination: ''')\n",
    "    destination = [int(x) for x in destination.split()]\n",
    "    return generate_graph(player_coordinates, \n",
    "                    (destination[0], destination[1]), **kwargs)\n",
    "\n",
    "def draw_paths(G, paths=None, title=\"Graph of optimal routes\"):\n",
    "    '''\n",
    "    Given a graph and paths through the graph, it plots \n",
    "    them w/ arrows. If path not given, it gets the path with \n",
    "    min cost max flow.\n",
    "    '''\n",
    "    if paths == None:\n",
    "        paths = cost_of_min_cost(G)[1]\n",
    "    \n",
    "    # Way of getting random colors\n",
    "    color_names = list(\"gbrcmyk\")\n",
    "    new_colors=[]\n",
    "    if len(paths) > len(color_names):\n",
    "        new_colors = [c for c in cnames.keys() \n",
    "                      if not(\"light\" in c)]\n",
    "        random.shuffle(new_colors)\n",
    "    #iterator through colors (so it will repeat)\n",
    "    colors = cycle(color_names+new_colors) \n",
    "    \n",
    "    # plot labels\n",
    "    plt.xlabel(\"X\")\n",
    "    plt.ylabel(\"Y\") \n",
    "    plt.title(title+\" - {} cabs\".format(len(paths)))\n",
    "    \n",
    "    # add all the x,y points of the passengers\n",
    "    xs = []\n",
    "    ys = []\n",
    "    for n in G.nodes(data=True):\n",
    "        if n[1]['type'] == 'passenger in':\n",
    "            xs.append(n[1]['x'])\n",
    "            ys.append(n[1]['y'])\n",
    "    plt.plot(xs,ys,'ro')\n",
    "    \n",
    "    # plot the destination\n",
    "    destination = G.node['destination']\n",
    "    plt.plot(destination['x'], destination['y'], 'bo')\n",
    "    xs.append(destination['x'])\n",
    "    ys.append(destination['y'])\n",
    "    \n",
    "    # determine the axis\n",
    "    plt.axis([min(xs)-1,max(xs)+1,min(ys)-1,max(ys)+1])\n",
    "    \n",
    "    for path in paths: # for each path\n",
    "        c = colors.next() # choose a random color\n",
    "        for i in range(len(path)-1): # for each pair in the path\n",
    "            from_node = G.node[path[i]] \n",
    "            to_node = G.node[path[i+1]]\n",
    "            try:\n",
    "                # draw an arrow from from_node to to_node\n",
    "                plt.arrow(from_node['x'], from_node['y'], \n",
    "                          (to_node['x']-from_node['x']),  \n",
    "                      (to_node['y']-from_node['y']), \n",
    "                          head_width=0.2, head_length=0.05, \n",
    "                      length_includes_head=True,fc=c, ec=c)\n",
    "            except: \n",
    "                # if error is thrown, it means that the point \n",
    "                # was repeated\n",
    "                continue\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Running the cell below allows you to interractively give the program a set of passengers and a destination. For example, try the simple case - two passengers at (0,0) and (1,0) - destination (2,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "How many players are there: 2\n",
      "What are the x and y coordinates for player 1: 0 0\n",
      "What are the x and y coordinates for player 2: 1 0\n",
      "What are the x and y coordinates for the destination: 2 0\n",
      "L = 5.0\n",
      "1 cabs:  path:  [['1in', '2in', 'destination']] -- cost:  -8.0\n",
      "2 cabs:  path:  [['2in', 'destination'], ['1in', 'destination']] -- cost:  -7.0\n",
      "Optimal path with 1 cabs [['1in', '2in', 'destination']]\n"
     ]
    },
    {
     "data": {
      "image/png": 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ly38MzCdcQbUUeAX49ADVsl0rDM6eP2cOzRs3snX4cCbPmOGgbR+tGw93NA/ltCXjeNOw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\nkiRJkiRJkiRJ0qD1/xg/9x1J98GeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c44ab50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run this cell to run the interractive simulation\n",
    "a, paths = allocation_interractive(annotate=True)\n",
    "draw_paths(a,paths)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### List of all the nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('source', {'type': 'meta'}),\n",
       " ('sink', {'type': 'meta'}),\n",
       " ('1in', {'number': 1, 'type': 'passenger in', 'x': 0, 'y': 0}),\n",
       " ('1out', {'number': 1, 'type': 'passenger out', 'x': 0, 'y': 0}),\n",
       " ('2in', {'number': 2, 'type': 'passenger in', 'x': 1, 'y': 0}),\n",
       " ('2out', {'number': 2, 'type': 'passenger out', 'x': 1, 'y': 0}),\n",
       " ('destination', {'type': 'destination', 'x': 2, 'y': 0})]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort_nodes(a.nodes(data=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### List of all the edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('source', '2in', {'capacity': 1, 'cost': 0}),\n",
       " ('source', '1in', {'capacity': 1, 'cost': 0}),\n",
       " ('1in', '1out', {'capacity': 1, 'cost': 0}),\n",
       " ('1out', '2in', {'capacity': 1, 'cost': -400}),\n",
       " ('1out', 'destination', {'capacity': 1, 'cost': -300}),\n",
       " ('2in', '2out', {'capacity': 1, 'cost': 0}),\n",
       " ('2out', 'destination', {'capacity': 1, 'cost': -400}),\n",
       " ('destination', 'sink', {'capacity': 1, 'cost': 0})]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# All the edges in the graph\n",
    "sort_edges(a.edges(data=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Drawing of the constructed graph\n",
    "This gets quite complicated with large number of players, but shows the graph constructed by the algorithm, with the source, sink, destination, and in/out nodes, as well as all the edges. Layout is random."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CPT2i5C2FbzEVFxdH7dq1Wb58OfXr17+rfWRmZjJw4EBOnTrFkiVL9Nu6FFvB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\nCPEeyYSZOBoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c67ced0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(a, with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'1in': {'1out': 1},\n",
       " '1out': {'2in': 1, 'destination': 0},\n",
       " '2in': {'2out': 1},\n",
       " '2out': {'destination': 1},\n",
       " 'destination': {'sink': 1},\n",
       " 'sink': {},\n",
       " 'source': {'1in': 1, '2in': 0}}"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The path that should be taken \n",
    "# Starting from the source, a 1 in the node in the dictionary \n",
    "# means send 1 cab there\n",
    "nx.max_flow_min_cost(a,'source','sink',weight='cost')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More examples\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RDA1JUjRDQ5IUzdCQJEUzNCRJ0QwNSVI0Q0OSFM3QkCRFMzQkSdEMDUlSNENDkhTN0JAk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\nkiRJkiRJdev/ATXRlnmRQjv1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c09cb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "passengers = [(0,0), (1,0)]\n",
    "destination = (2,0)\n",
    "a, paths = generate_graph(passengers, destination)\n",
    "draw_paths(a,paths, title=\"Simple Example\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c04ac10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "passengers = [(2,0), (1,0), (0,2), (0,1), (0,-2), (0,-1)]\n",
    "destination = (0,0)\n",
    "a, paths = generate_graph(passengers, destination)\n",
    "draw_paths(a,paths, title=\"Three cabs needed\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bV97Ys12hADNnwuTJ4fbLL8Ps2TV8JtLgODwlDdKyZ5Yx7eZpAPzwoz+k/YT20AyOPx7W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\nJNWt/w9FYHZVUzoLFAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103a45b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "passengers = [(1,1), (-1,1), (-1,-1), (1,-1)]\n",
    "destination = (0,0)\n",
    "a, paths = generate_graph(passengers, destination)\n",
    "draw_paths(a,paths, title=\"Points in Square\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OGAOhSNlslr9s+AsrX17JAy8+wPIXl/PC+hc4ZlErK//UssP4Ew7dhX2v+RSfPOiTTBg5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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c0c3b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "passengers = [(2,2), (1,1), (1,0), (1,-1), (3,1), (3,0), (3,-1)]\n",
    "destination = (2,-2)\n",
    "a, paths = generate_graph(passengers, destination)\n",
    "draw_paths(a,paths, title=\"Points in hexagon\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ug2iu0cD7QHfXgYiIiOHqDOEjoB3wuX39JvDfjmIRERERERG/GQ2swZw5/DTO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c0a0590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "passengers = [(2,2), (1,1), (1,0), (1,-1), (3,1), (3,0), (3,-1)]\n",
    "destination = (2,0)\n",
    "a, paths = generate_graph(passengers, destination)\n",
    "draw_paths(a,paths, title=\"hexagon with destination in middle\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below graphs are completely random (except for destination being 0,0) - feel free to change the variables in the below cell to get different graphs. The first random graph will have non optimal paths, as the ordering is set, but the second graph shows the paths when we order the pickups by distance from destination (largest first). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Constraints for random graphs\n",
    "n = 50 # number of passengers\n",
    "min_x = -30\n",
    "max_x = 30\n",
    "min_y = -30\n",
    "max_y = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VD/r1497Onb0tjqKZUZsyUGai5sKyZfJ9507vyqFoFObRwH0HD3pZEkVLQymD5kJEhHyf\nNMm7cigazeu97a3ZrlC4F6UMmhOPPw5q8rHJ82g3uYb7mpwcL0uiaEmoOQMP4LGUEeXlEBICq1fD\nuHGuL1/hMTQpKXQMCODMiBEeu2ZTTm2iqB++GnTWIrCbMsL02eV/NHN8wQ03QGWla8tWeJRHunZl\n8enTHrueR+upwidRZiI34/EUxf/+N+h0yquoifPCeecBsKuoyCPXU6m0FUoZuBmHKSPKytxzwcce\nk+/Ll7unfIVHCPf3J2zrVp4YO5b5cXHMiY8nLSnJbdfzeD1V+BzKTORmHKaMSEuDbdvg8stde0Gt\nSb9PmwZTp7q2bIXHSEtK4pZ33+XDkyct29xptnFYTzXFUHwMwnq5/JoK30KNDNyM3ZQRkZGMARg+\nHAYMAL3etRf9/HP5bjC4tlyF26k0GjlYWkrCG29UUQTgXrONw9Qm998FBfvg9I9gUAkQmzNqZOBm\nzL24uUuW4FdejiE4mHEPP0xM377Qty8cOAABATJ6+LbbXHPRO+6AO++EhQth1izXlKloEKUGA+ll\nZRwqK+NwtddJByYZW2Jzc+1ud1dGWks9feN5/MpKMbTpKuvp+PGgL4GzqXBmI4R2h4jBbpFB4V2U\na6k3MRigWzc4c8a6LS8PTNkrG0Xr1lBU1OImkl3tHpmv01ka8eoN+zmdzqky/TUazg8JqfHqExJC\nj6Ag/LVa761VcW4z6Aqh63U19xUehCLTJHP7ERDYxn1yKNyCci31Vfz8IDMTFi2CJ56Q2yIiYP58\nmDevcWV//z1ccw2UlkJoaKNFbQo4co8UQtBvzJgaPXTzq8BJc1qoVkufkBD6hIbWaNg7BwaibUSi\nubEzZjA7Pb3mCmjezEjbuh+E9YbM9ZD1MwS0gfZXgkqo1yxoqk+xeYwMbDl0SJqNbDl8GKrZcRuE\nRgPTp8PSpY2TrYngqDc9bNgwdrz2msPzIv397fbUzw8JoV1AgNeyh1oy0prMi2PMZht3UtvIwJbS\n05D3h/wceQmEdHSvXAqXoLKWNhWMRmk2ysy0brvpJvjuO+d6XwMGyDmJ5niv7DAvNpYFaWk1ts8Z\nOZIX7WxXVCUtKYl1/16Af3kZ+tZd6jaxCSOcTQNDKaCBzmNAW39jg4p49jy1KYOmimjWvPGGELIJ\nt77S0hpezp498tysLNfL6IMMHzas5n0DMSc+3tui+TypiYliVnR0lfs2KzpapCYm1n1yea4Qp5Lk\nqzDd/ddTOA3Q7HqG3r6n7uevv6x/lMBA+d6zpxAVFQ0rB4SYONEtIvoSk/bsEWEvvyweP++8Kg3M\ns6qBqRezx461r0jHjBKiIr/uV3meEOe2WZVC6dlaj589+hqluL0AtSgDNYHsq/TpY/U2ysyEMWNg\n/XoICoKPPqp/QNk118DKlW4V1dssOnmSb7OzWT5tGr0uvLCmG68yPdSJwwjkorNysrih5O6o/XrF\n5+xfz02us4q6UcrAl9FqISOjqrfRFVfI6OJp0yArC9q1q72M5cuhe3c4cgSaYZ78Dbm5PJGezvQu\nXZjSqROMH68afydwGIHcpqvdyeQ67f1Fh6HwL/lZG0Tauk2s+/B/+Ffq0AcGcKao1P71zMkWFYp6\n4u3Rluc5dMg6nP7wQ+vnp5+u+1wQ4vLL3S+jh0kvLRUkJ4tB27d7W5Qmjz0bviMTm0N7/7efCHHu\nF6upyPRK/XiemNWzc5XjH+vUSdzbqZMy6XkYajETNdVZZdPvamHYehtNmybjB955R+7bvx/697d/\n3t13w2efNSuvomK9nvDNmwEQcXHeFaaZUF9XVocBcbEX80LCC+AXDK16ymhlv0DmjInjxQ2pNY6f\nfvHFRLZv71nX2RaOCjprLpjNRm++KVc1A0hPl7EIAwbIeYW1a2u6oS5dKpXBjh1w6aWel9vFCCEs\niqAyJsbL0jQfYupjYhNG/Ivtr8DmR7hdk5K/g0Dt9uHhzHdnNLWiQahEdU2Rxx6TQWogFUFKCrz7\nrpxg1mrluy1tTGkDbr7Zo2K6i2BTzEDWlVcSoFVV2CPoSyBzA2SsQe9vtHuII3t/Q49vTqQlJTEn\nPt4jachbKl62vPkIBoMQXbpIm+u0aUKUlQnRvr38HhUlRGmp9dinn5bbmzjj//hDkJwsfi8s9LYo\nLYPik1XnAIqONmh+QZTnyDmD87q1uPkBX4ylwEfnDLoDnwAdkAL+B3gbiARWAD2BY8CtQH61c02/\nSwHAW29ZF7UpLoatW6XJCOSI4Z//hIoKuSxmUhJcV0eqAR/llePHmXX0KF9ecAG3dejgbXGaL0YD\n5O2C8rPyu8ZP5iAKCLccUq/5BUMZnEmW3kQ7yz2fWsPLeC3ZYC34ajqKTqbXLiAM+A24CZgGZAOv\nAc8AEcDMaucqZVCdw4dlbAJIs1FMDFx7rZxDADhzhrROnVgH+MfGNrnw/x9zchi/Zw9PdOvGv88/\n39viNGkcuoVWFppiCkz/rZDOEHGhVAYNRRggw1T3ulzb4pLZrVq1ircmTiTFzr75sbHMT7G3x/00\nlXQUq4DRwAHAnPWqk+l7dbw2zPJpqpuNhBBi/34hQKSCmBUc7FND1vpysKREkJwshu3Y4W1Rmjx2\nTRfn9RCpH8+zmoJKTjfuIkajtSyj3iVyNxUSEhLMphhxmVbrc1HWNIF0FL2A40A4kGezXVPtuxmv\n3cwmwZtvWitfcbEQQojZvXr5XMWsDwU6nSA5WZCc7G1RmgUO007EDRNCV+Kai2RskIpAX+aa8poA\n77//vkUJdOjQQWRmZtpVvLeAmPf4416TEx9PRxEGfAs8AhRV2+dQ+Pnz51s+x8XFEad8za08+ihM\nmCDNRmFhkJKCf8+ecOxYjUN9OfzfKARtTC6kOuVC6hIcpp0QoeDvgnUvcn8HYwW0u0LGGzRzFi9e\nzKOPPgpAdHQ027ZtIyoqCoBOdlY5zM7JYcGiRUyZPp3eHsgIkJKSQoqXTFINJQBYCzxqs+0A0jwE\n0BllJnIeg0GIrl2FADHbbD5qQiMD84ggp7LS26I0GxyODFxRD4qOyhFB8YnGl+XjvPjii5aRwJAh\nQ0R+fn69zzWfp9Pp3Chhrde2izedtDXAB8A+4C2b7f8D7jF9vgc5l6BwBq0WTp2CN99kbEYGs6vt\nnhUdzRhvrpxVC6N37QJgz6WXEhkQ4GVpmg8OF75vbD2oyIGCfTLquFX3xpXlowghmDlzJhqNhjlz\n5jBixAiKi4vZtWsXbdrUfwnQ0lKZlynAx+q1N2eVrwLSgN1YtdWzwHbgK6AHyrXUdRw+TFqfPqwH\n/IYMwdCpk8+6980/epQFx4/z7cCB3Ny+vbfFaXakJSWx/u238Cs8g6FN18bXA30ZnE0Gv1DoFOcy\nOX0Fo9HIjBkzeMeU+iU+Pp5Vq1YR3Iigud27dzNkyBD+8Y9/8J///MdVotZJU/EmaggeH141CwwG\nIbqZgn+mTvW2NHZZlZUlSE4Ws9Prt0iKwkkqi6RJp7EY9FbPoWaGXq8XU6ZMsZh1Jk2aJCpdaLJc\ntGiRAERSkufuHT4adNYYTL9L4RS2QWpFRXKS2QfYW1LCoF9/JbZNG1Iuusjb4jRvdMVwLq3utY5r\nQwjIWC0/dxkHmuaRGkSn03H77bfz3XffAXDPPffwwQcf4OfnRLxFHQwZMoTdu3dz5swZOnZ0/zrS\nvhp01hiUMmgstkFqycngZW+sPJ2OyJ/lIioqC6kHcIUyyFgHQg+dRoGf/fUQmhLl5eXceOONrDNF\nDU+fPp23334brRvzXwkhLOUbjUZzY+02alMGzUOVKxrO+edbV1K7+mqZEttLGISwKAJ9bKzX5FA0\ngJzfpCJof2WTVwQlJSWMGDGCkJAQ1q1bx7PPPovRaGTp0qVuVQQgG+fc3FwAevTo4dZr1YVSBi0Z\nrRZOnpRmo48/likDios9LoZ/qsx1n3/VVfi1sLQFTZKiIzJvUcQQCGzrbWmcpqCggCFDhhAWFsaW\nLVt44YUXEELw8ssvu72HbktERASpqamcOnWqSvyUp1HKQAGPPCLNRgDh4TK3kYe4cudOAPYPG0Yb\nf1+IgVTUSnkWFB4wLV7T1dvSOEVOTg69e/embdu27N69mzfffBMhBHPmzPGaTDExMTz11FMsWLCA\nX375xSsyNNVumJozcAdGI/TsKWMTpk6Fjz5y6+Vmpqez8ORJ/jdoENfXtZazwrU4M2egL4GzqeAf\nDh1Huk82N3HmzBkuvPBCsrKyAHj//ff5+9//7mWpqhIREUF+fj4FBQW0bt3a5eWrOQNF/TCbjRYv\ndrvZ6Otz51h48iTP9+qlFEFTwKiXigCanCI4ceIEoaGhdO7cmaysLBISEhBC+JwiADlqARoUxOYq\n1MhAYZ/0dDnJDLBxo5xkdhG7i4sZsmMH8RERrBkyxGXlKupHWlIS6xa/iX/RWfStu9SdyryJupAe\nPnyYPmaPOWDlypXcdNNNXpSofmRkZNC1a1euvPJKfjY5VrgKFXSmcA6DQYju3WWQ2j33uKTI7MpK\nQXKy0KgspF7BqdW3Tv1oykJa4TlBG8Gff/5pCRQDxJo1a7wtUoP57rvvBCCWLVvm0nJpAimsG4pL\nb5CiDhYvtjYeRUVOF6MzGCzJ5wxGowsFVNSXBieqy9ouFUFFgWcFdYLffvutihJITU31tkiN4q67\n7hKA2Ldvn8vKxEcT1SmaCjNmVPU2Sk52qpgA00L2hVddhVa5kHoFhyms7aUyLzoMFVkQMRQCXT+Z\n6Sq2bNmCRqPhkksuAWD79u0IIYhp4mnPP/30UwAuuOACKhw8N1eilIGifkRHyyC17t3hmmukt1ED\nuGjHDgAOXXYZ4cqF1Gvog+wHiBmqJ10rPweFf0Gr8yC0iwckazg//fQTGo2GESNGADL5mxCCYcOG\neVky12FWAo1JildflDJQ1B+tFk6ckN5Gy5fX29vo0UOH2FVczJoLL+T8UBcsoKJwmnqlsNYVQ84O\nCGgDbQd4WMK6SUxMRKPRMHr0aAAOHjyIEILBgwd7WTLXExgYyIEDckmX22+/3a3XaqpjdZP5S+E1\njhyRowWo1dso4exZ7tq/n4W9e/O0l8PtFZK0pCTW26y+VSWFtVEHmevl58bkLXIDX331Fbfddhsg\n1wL466+/6NWrl3eF8hDvv/8+999/P1999RW33HKL0+WoRHUK92A0wnnnydHClClytGDDb0VFXPrb\nb9wYFcWqZthra3b4qAvpxx9/zDRT7qyIiAj+/PNPunTxTdOVO7n66qtJSUnhxIkTdO/u3AJCShko\n3MuSJXKSGSwpsc9VVtJxyxZCtVpKmvhEXovh9I/yvfNo0AZ6VxZg6dKlPGwyX/Xo0YMdO3bQvoUv\ndmTOmaTX651Kqa2UgcL92JiNKjduJMhUaY2xsR5N+qVwkqxfoDIXOoyEgHCvirJw4UJmzpwJSE+a\nn3/+mbZtm25CPFdSXFxMeHg4rVq1otiJ7AAqHYXC7aTt38+csWOZHxTEiKefJmzrVopHjlSKoClQ\n+JdUBJEXe00RCCGYO3cuGo2GmTNnctlll1FUVMTevXuVIrAhLCyM7du3U1JSwmPmBapaOC4LwlA0\nHntRrU9ptSK1kUFqCg9QmimDyvIPeOXyRqNRPProo5ZAsVGjRonS0lKvyNKUePHFFwUgNm7c2KDz\nUMteKtzJnPh4XjStDmXLXOAFgJ9+krEJCt9CVwTnNkFgJLQf7tFLG41G7r//fj744AMAbrzxRr76\n6isCA70/V9FUiI6O5siRI+Tk5BAZGVmvc5SZSOFWHEa1xsTIlNijRsE993hYKkWtGHVSEYBHFYFe\nr+f222/Hz8+PDz74gMmTJ6PT6Vi1apVSBA3ksCkrQFRUFK7oHCtloGg0DqNaQ0Lg2DF4+2345BMZ\npFZU5FnhfIi0pCTmxMczPy6OOfHxpCUleUcQIayxBF2u9cglKysrmTBhAgEBAaxYsYIHHngAg8HA\nZ599hr+KSHcKjUbDuXPnABg4cKCXpfEe7jDDKZzE3pzBLV26iLCXXxYFOp08KD3duv+nn7wrsBdw\nKluouziVJF+GSrdfqqSkRMTExFjmBJ588klhVEkKXcratWsFIF577bU6j0XNGSjcTfWo1r5//ztT\nTIvWLO90OJ7iAAAgAElEQVTfnymdOskgtd694fhxuPtuOVpoITiaV3kk8gruH/M+gR0CCegQIN/b\nBxDQPsCyzb+Nv+u8ss79DLoC6BADAWGuKdMORUVFxMXFsdO0rOn8+fN57rnnlHeZm3jooYd45513\n2LlzJxdddJHD41ScgcIrCCEY/ccfbMzPp7WfH1kjRhCo1cLSpWDOhVNYKDOhNnPmx8UxPzW1xvZH\nGcJNvOXSa2lDtDUUSmCHQNqPyab1BTkUHukLIR0siscvpOHBS47Iy8tj+PDh/PXXXwC8/vrrPPnk\nky4rX+EYf39/DAYDxcXFtGrVyu4xtSkDZaxTuA2NRsNPQ4eyOT+fkbt2EZSWxurBgxn30ENw3XUy\nSK116xbhbeRoXiU8vhNxa+JqPddYaUSXraPyXCW6c9Z3XZaOyqyq2yrPVWIsMVJxooKKE9aJ/fYT\n9LR+pJIjCwM4seQUcMrp3+Lf1p99Idv4s/Qbgvz16EOCGHjJJOakLORswVkA3pr7Fv966F8ERAU4\nfZ36kJaUxLq338a/ogJ9UFDdq7Y1Y8rLywkICKBTWBiPjB3b4HuiRgYKj2AQgn7btpFeXs6FrVrx\n+6WXohVCKoRjx+Cuu8CUv705kpaUxNpHHuGl9HTLtlnR0YxbvNj9jZeuEM5thqB20O6yKruEEBiK\nDVKx1FPZ/GnYyhGWsogMSzm3AT8CDzGTeOKdl1WD1VzmwGxm3vbLzvVsmP0EL9vc09nR0cR74p76\nKF9/+CHf3HcfK2y22d4TXzYTfQiMB84B5kxmkcAKoCdwDLgVyK92nlIGTZRVWVlM3LsXgG0XX8xl\nrVu3GLNRWlISKyYsIChET6uYDlWzhboLQyWc2SA/uygLqcO4kvh4Xlizpso2YRDocnX1Vjb6PH29\n5fiKp1jGjnrJ0VKo69n4spnoI2AJYDuTOBNYD7wGPGP6PtPzoincwU3t21M6ciThmzZx+c6dXB8V\nxffTp6MZP15OLrduDRs2yNiEZkbM+PEYaUWXe7vQd2lf919QGK2KwIUupPmnT9vdbm+1NI2fhsD2\ngQS2D6TVBfbt2M6SEtcKak7DYMxsue7LDVrJrhrejjPYBORV23YDYM6FvBy4yaMSKdxOiJ8f+rg4\n/q9vX37IyUGbmspfHTvKldTOOw9Gj5beRs2UiFERnrlQhql33HmsjPFoJMXFxfj7+7PNNLKrTo3V\n0tyMo3mY/N06tnTegqHc4FF5fIF6r2RnB28rA3t0BM6aPp81fVc0Q+7v0oVc05KF/bZvZ/rhwzL7\n6dKl8NlnzS5IzagzAtA2zgOJ186aoos7xoK28QaA119/nfDwcAwGA/e99lrdq6V5AEertl234HEq\nz1SyKWQTGe9nODi7eVKvlewc4O05A4BewA9Y5wzyANuuUy5yHsEWMW/ePMuXuLg44uLi3Cehwu3M\nP3qUBcePA5BxxRV0zsiQZiNoNmajgp8L+P2q34kTce69UP5eKDkOUcMguHH5/0+cOEHPnj0BuO22\n2/jiiy/QaDS1r5bmQRzJIYyCP8b+Qf5PcrrxyrNXEtihZaS7sL0n6aWl+J9/Pj37SrPkggULwEcn\nkKGmMjgAxAFngM5AMtC/2jlqArkZcqq8nO6//ALAK+edx8zu3eH88+Ho0WbhbXTs+WMcm3fMvcqg\n9DTk/QGt+0N4b6eLEUIwZcoUPvvsMwCOHj3aJJeYLNlXwq8DfwWg64yuZI79q0W7otY2gewL9AL2\n2Hw3TxyDnDh+1c457onrVvgE0/bvFyQnC5KTZTqLpUutaRwKC70tntPsjNkpkkl23wUq8mSaiewd\njSpm27ZtlvQRL730kouE8y6HnjgklvCyeIwuvpESxEvgw+kovgBigXbI+YHngO+Br4AeKNfSFsu+\nkhIG/ip7dB/37889ZWVN3myUokkBcM/IwFABZ34CjR90cc7PX6/XM2TIEPbt2wdAQUEBrVu3dqWU\nXmXW1WN4OWVDje0tyRXVl1NY3wF0AQKB7khX01xgNNAXGEtNRaBoAVzQqhXG2FhGt23L1AMHCD91\nigqdTiqE0aOl2agJ0vYaN0weC6NUBCA9h5xgxYoVBAQEsG/fPr755huEEM1KEQAECp3d7fVxu2wJ\neFsZKBQO0Wg0rB86lM0XXUSxwUDw5s2s3r5dehslJDRJbyO3uJU2woU0Pz8fjUbD7bffztChQ9Hp\ndEyaNMn1MvoAjXG7bAkoZaDweUa0aYM+NpY+ISFct2cPg4YNw2hOQWDObdREcLkyOGOKuuoY12AX\n0ueff56ICCnPr7/+yu+//96s1xZojNtlS8DbcwbOouYMWij/y87mxj//BOCXoUO5/JJLZGzC5Mky\nNsFHqcyuZEv7LcToYtD6u6gPlrcHSk9Cu8shKKrepx05coRoU6M4depUPvroI9fI0wQwpwQJiTQS\nMqyd11xivYUv5yZyFqUMWjDlBgOtN29GJwTXRUaSuHkzmunT5U4fzW107utz7Lt1n+smj0tOQv4e\naHMBhPWq1ylCCCZNmsTKlSsBOHXqFF27dnWNPE2IFE0KUTdEMfj7wXUf3Mzw5QlkhaLBBPv5URkb\ny3/69uXH3Fy0F1zAXwcPyp0+ajbK+6l61pVGUJknFUFI53orgk2bNqHValm5ciWLFi1CCNEiFYHC\nMUoZKJos/+jShTxzOouMDB48cMBnvY3MkbCNxlAOWVtBGwiRjle0MlNZWUmvXr2IiYkhNDSU4uJi\nHnvsMdfIomhWKGWgaNK0DQhAxMUxv1cv3s3MRPPBB2T+3//5nLdR2eEyAjs1Mh2CMMCZjfJzp7rj\nLJYvX05QUBDHjx8nMTGRkpIShytgKRRKGSiaBfN69eLUFVcA0KVvX175/Xe5w5wS2weIGN0ITyIh\nIGOt/NwlvlYX0pycHDQaDVOnTuWqq67CYDAwvgVNkiqcQykDRbOha1AQIi6O+zp1YlZ+PprkZAoG\nDYIxY6S3kZdpO6oRAWdnk+V7p6tllLEDnnnmGdq1awfA7t27LXMFCkVdqFqiaHb8t39/9g0bBkDb\nJUv46LPP4PPPvWY2Mnu+OR1jkPuHnCtoNxz8QuwecuDAATQaDa+99hrTp09HCMHgwS3PW0bhPM03\nwkTRohlgSmcxbvdu7gUeSkkhd8wYglq3hvXr5SSzhyjZWwJAcHcnIl1LjkPZaWg7CIIiaywAP+bh\nh3np7bdZv349AGfOnKFjR+eWAHG0uLxadL5loJSBotmi0WhYO2QIWwoKGPH77wSvW0fi4sWMHzMG\n7rhDjhY8gNOeRBW5cm2C0G7QqgdpSUmsfeQRXrJZAP62devYCrz77rv885//dFpGe2XPTk/nz19/\n5fRnn9XYDiiFoPAJvJQAVtFU0RuNou8vvwiSk8UFa9YIg0bjsZTYu6/f3fDU1bpSmY46c6Nl0+yx\nY6ukXza/nh0zptEyOip7UlBbu9vnxMc3+preIplksfuG3d4WwytQSwprNWegaBH4aTQcvPxy/jdo\nEPuCgvDbuJFtAwZ4xNsob0MDA86EwTph3DHOstnRYueBlZVOSmbFUdnBFfYzfRatPUOKJoUUTQq7\nr93NqcWnKD1YapkfUTQ9mrWZSNk6FdW5vl07ykaOpM3mzQxftoxr9+whacwYNG40GxnLjIRdHFa/\ng2txIT2Rk2P3FFdk3XSU0VMXFQw5JTW2+/dtQ9tubcnfmE/umlxy1+TaPb9tXFsix0USeW0krQa3\nMqdDUPggzVYZOLKBgrJ1tnSC/fyoiI3lvxkZ/APQJidzYMoU+mk0UFAgRwsupt6eRGdMo5RO11Rx\nIb3++utJ+fNPCA3lw9JSy/ZZ0dGMc0HWzbEzZjA7Pb3K/2VWdDSxd93F7GpzBrOio7lh0dMMHT+0\nShlCCMoOl0nlsFq+8lPyyU/J58jMIzWu2frK1lJRjIsk/JJwNFqlKLxJU737oq7h6Jz4eF5ct67G\n9pa0qpGibvJ1OiJ+/hmAB77/nvfeesvl3kYpmhQuXHshkWMjaz8wZyeUn4H2V0KgjEkoLy8nJES6\nk3766af0iIhw20L0jhaXd7S9oZQdKyNvbZ5lJGEsNzo8NvzScKuiuDzcdZleUYnqaGlZS+fHxTE/\nNbXm9thY5qekuEksRVPlhWPHeO7YMQBO/+1vdBk71iVmI0OpgU2tNjGyZCR+oY6DxSg+CgX7oe2F\n0KobAHv37mXQoEEAHD582JJ2ujlScbqC3HW5FkVhKDQ4PLbVoFYWRdHmqjZog+qvKNKSkvhywnxC\nIwXBl0a1ONNxbcqg2ZqJ1KpGioYwt1cv7u3cmW5bt9L1m2948b//ZbYLzEYFmwsAalcEFdlSEYT2\nsCiCZcuWMd2UlruyspKAgACnZWgKBHUNovO0znSe1rnGvspzleStt44oSv4soeTPEk7++2SNY0P6\nhlgURdvYtlXuu9l0vIx0ubjuOmU6tqXZjgzSkpJ4Z8IEVthsuxU42r8/v+7f71bhFE2b+w8e5P3M\nTADyJ0ygzcqVMqWFE6Q/k87J1046XsdAXwpnU8C/FXSMBWDkyJFs3ryZKVOmsHz5cqeu21LQ5evI\n/ymfnNU55K7OpTLDsWfVN8HPsLR8e43tLcl03CJHBsdycvgRmD1mDAGVlRiCg7l8+HC+XrCA3r17\nc+RIzQkthQLgP/368Xi3bgz49VfaJibywWuvce+HH8IXXzS4rFrXMTDqpSIA6BhLcXEx4aaFeVau\nXMlNN93khPQti4C2AbSf1J72k9rX2Kcv1pOfbPV28j9i333Wr7zc3WI2CZrtyMDswlb9uE2bNhET\nE0NISAglJSVedXVTrq++jRCC63bvZk1eHsEVFeRdfz3B2dkNMhulaFLQhmiJKY2pXjhkrJafu4xj\nx287GWbKp3Ty5Em6devmqp+hMKGcSmofGTRVao2yy87OFoDYvHmz3f07d+40R+IJo9HoquC+BpGa\nmChmRUdXieqcFR0tUhMTvSKPwjFb8vMFycmC5GTxw/DhQqxbV+9zk0kWu6+3E+16eo2MMNaXi1df\nfVUAIjQ0VOj1ehdKrrDF3n/u2Rb2n6OWCOSmSq0/ePTo0aKuYw4cOGBRCJ7+A2ZnZ4upAwc2uzD/\n5ozeaBT9Teks+n/8sdDfcUe9zksmWZx862TVjdm/CnEqSRjL88SAAQMEIB5++GE3SK2oTmpioniQ\nYeLRgKFiTnx8i1IEQtSuDJrlnMGGDRuYMmVKrcf069ePEydO0KNHD/z9/amoqCAwsJErUVXj4MGD\nrFy5kpUrV7J9e9WJq1gH5yj7pW/ip9Gw//LLSczO5nrA//772TJwIFds3Vqn2ajKOgZF6VB+juLA\n8wkPloFoa9euZezYsW6UXmEmZvx4jLQiICqAEWtGeFscn6LZKYNVq1YB8N5779V5bPfu3Tl79iwd\nO3YkKiiI6aNGEazXN8h+r9fr2bx5s6XRP3myprsbQFRUFBMnTmTixImMGjWKF264AezYL5Xrq28z\nwZTOInLzZq585x1iZ8xgxJ9/EhAWVqPelJ+Uir3VQNNSk+VZUHiQU/kBdB/UD4CzZ8/SoUMHr/wW\nhaI5UNcwqEFDp6QVK8St1cw11e33BQUF4osvvhC33HKL8Pf3t1yn+mvgwIFi7ty5YufOnbXORyj7\nZdNn9vLl4tYuXRzWm4yPMqzZSnXFQpxKEqd2rhCA6Natm9fmq1o6ySSLzZ3szyc2d2iCZqJxwFuA\nH/BfYGF9TioyrWK1evXqBl1sywcfVIlHAHgpPZ1hEyaww8E5o0ePZuLEidx444107dq1QdcDa5DL\nXJsw/3EuTC2g8AAJCazIyKiy6aX0dOYuWULM+PHWdQyMejgro+G7XXwbc+fO5fnnn/e0tApFrfii\nMvADlgKjgdPAr8D/AIeRYmYXzYM7d3IpEGpwHMoOYDQa2bZtm8W00/XwYbvHhWs03H3XXUycOJGx\nY8fSqlUrJ3+SfWLGj1eNfxPGUdpn3enTJCWl8fxXK6jAn45Xf8GMe/ty431Ps3nzZkaMULZqb5GW\nlMRXzCcoR8/q+A7KnduG2pTBauBB4KiHZDFzGXAYOGb6/iVwIw6Ugd3spI88AsAlcXGsXbvW0uiX\nlNRMxQvQJSQEyspqbC8SgvPPP5+JEyc6/2sUzRZHKU++rQjgvbs/p6DSNG+VBhs23cHnX/ygFIEX\nqZKOQodKR9EAbgH+AmYDnkyM8jfgfZvvdwFLqh1jsYE5WqHpUjv2/JEjR4pFixaJI0eOVLGjObLf\n3zRqlOXc9PR0T5v3FD6OvXozs3dv0br7dfaqpIiPn+NtkVs0jtqKluTOjZNzBl8jRwfPATuAT20K\nEsCiejfvDaNeQRHz588HYPPBg6QAcdX2DxswgJ9++YXW9YgWdWS/f3n8eE6dOkX37t2Jjo5m4sSJ\nfPvtt2qBjhaOXl9MYeHPdO2/iQ5TBX97H8qy4VwpHDhyhOLzL7V7Xnl5LcnqFG7HkVmvObtzp6Sk\nkFLPLM11zRnogGIgGAgHHCcgdx2nge4237sDp6ofZFYGc7ZuJe748RqFRPXoUS9FYMaR/b5bt24I\nIXjzzTd5/PHH0Wq1pKWlMXLkyHqXrWhaGAzlFBVtIy8vmfz8ZAoK0jAYYMcOuUKm3VUy/f0I/O4B\nKicMRTMuDWFnGqpQlJBTXklUsGvjWRT1oyVmMo6LiyMuLs7yfcGCBU6VMw7Yh/TkCXWFYPXEH0gH\negGBwC5gQLVjLMMeT7poFhcXi5CQEAGInj17ioqKCpdfQ+F+DAadKCj4RRw79orYtWusSEkJEMnJ\nWF7LlyPuvhvRubN992FATJw4UXzzzTcit6xIXKNLFFT+R76WpolpQzuLqJA7qlgjevWeKeZ8+J1Y\ndSxDrDqWIU4Vl3r7NrQ4lDt37Wai2uwdm4B/Anuda9MbxbVYXUs/AF6ptt/0uySuWompviQlJTFh\nwgQAPv74Y+655x63XUvRcIQwUlKyx9Kzz89PxmAoqnFccTFs2iR7+jt32i9ryJAhTJ48mdtvv53u\n3a0D1kJRSaw+kV3IdYlvOz6UFX0u5cZ+z3JVj//S/a5lfPT5HspzNxEc1oGHn3iI8eNjKNXr2ZiR\njcFUfwdFhBPdup7rIysajafbCl/D2ZXONPhuUqMqysAbGI1GRo4cyZYtWwDIzs4mKirKqzI1FRqb\nrVUIQWnpQUtDn5+fjE6X7fB4oxEOHerNxo2hJCYeorS0pu04PDycyZMnM3nyZK688kq0WvurZ2WJ\nMi7Rr+Qk0jPtNe1l6BYOYfZsGHnRPm5oF8OVdz/NlXc/LU/4qy0YC6B/1fpaaTCy6Uw2xXrpBt07\nvBWDIsLVfJTCrbTIZS89xe7duxkyZAgAzzzzDK+++qqXJfJt7LoCR0cTv3hxFYVQVnasSmNfUVFj\n2qgKISH9iIi4mqKigaxencmKFf/jzz//tHtsfHw8kydP5qabbrKsH1AXJ0UxA/RfU4IegP/6jeQ+\nbX9Gj4affoInHjfSaY9MK/HkOhvFVPQ9nL4J+umrLHBvxmAUbM/K5Vy5XJSlU0gQw9pHoFVKQeEG\nlDLwANOnT2fZsmUA7N+/n/79+3tZIt/EUU756cPgltccnxcU1JOIiKtp2/Zq2raNw2hsxw8//EBC\nQgI//PCD3XP69OnD5MmTufPOO+nTp49T8h4U+fTXf235/rXfKP6m7Y3BAP4m94tvvoG8H4aRn3GU\nR/53goDgalNsBzTQcQlEPOTwOkIIducWcqy4FIA2Af6M6BRFgIMRikLhDEoZeIgzZ87QubNcw3Xs\n2LGsWbNGDfurMT8ujvmpqTW2PzY0gH8kTDI19lcTEnI+Go0GIQQ7duwgISGBhIQEsrNrmoP8/Pws\nJp5rrrkGf//GB9bvFNlcol9p+b7O71rGaOWCM9nZ0N60sNbevUDm1/y48F9Mevkrzrv0mpqFHTDV\ngf5111khBIcKS9ifL+c4ArUa4jq3J8RfuaUqGk+LXPbSG3Tq1AkhBO+++y4PPvggWq2W9evXM3r0\naG+L5jM4cu8L63gNUVFvsWLFChIS7qqR8tvMyJEjufPOO7nlllvcMkeTZswk1pBo+b7V7waGazta\nvu/cCZdcIj8XFEAAebzz6L/oMXSkfUUA0PEdODtd+q/U0TnQaDT0bRNG3zZhnCwuZWdOAetOnwPg\n6s7taB3oyfhPRUuiqXZbfXJkYEtZWRndu3cnJyeHdu3acfLkSYKbsT9zfUlLSmLNjBm8bLMG9a3I\n6MZim+O6du1q6e0PHjzY7SOsRONxrjdYzVe7/ScxWBNZ5Zjly2HqVAgKgtJS0Grh32PbAfDE2izH\nMgoDHPSHrt9BeMNTm5wrq2DruVzL9ys7RtI+2L5SVShqQ5mJvMj69estC5e89957PPDAA16WyLPs\n3bvXYuI5ceIEAGFAf6AVUAJEjRjBP598kmuvvZYgByMHd5FgPMxdhmQAtGj4y/9WojU1gxX//nf4\n4AOYNEnOEQCse+txdv/4Cf/4ZCdtOvWo/UIHNKANh76FTstaUKkjJdNqJrukXVu6tQpxujxFy0Mp\nAy8jhCA+Pp7169cDcm6hY8eOdZzVtMjLy+Pbb78lISHBYfj7xRdfbPHZ79Kli2cFrMYywz6mG38G\noD3B7PK/mS6amllphYDu3eH0aViyBB4yzQGfPbybTx+8hpH3zuXy2x+p+4JZsyDnlXrNG9RFqd5A\nSmYWOqMs64K24fRpo2IVFHWjlIGPsH//fi644AJAeh8tXbrUyxI1HIPBQGpqqqW3X2En30tERITF\nxHP55Zf7zCS6EIKXjL8z1/gbAP1owxb/G4jU2DfflZaCOWv5pk1w1VXys9FgYNG1UplXcSOtDWMZ\n/BUKPbdCyPBG/Q4zOqORzWdyKNRJd9deYaFcGNnaZ+63wvdQysDHePrpp3n99dcBGacwePBgL0tk\nn6NHj5KQkMDnn3/O/v32l5O47rrrmDx5MjfccANhYb7ZOxVC8LjxF94yyriDK+jAOv/rCNM4now9\nehR695afT58G24HMe3deSHF2Bo8mnsI/sAHzQAc0EDgAeu9z5mc4xCAEO7LyOFMmFXPH4CCGdYjA\nTykFRTWUMvBBsrOzaW/yTxwxYgRpaWkOo17dTUlJCd9//z0JCQn8+OOPdo/p378/kydP5o477iA6\nOtrDEjqHQRi515DGJ+IQABM03fnGbwxBdoK/bFm7FsaNk58rKiDQJq/cnrWfs/aNGdy68Dt6XBTT\nMIEy7oHCT1xiKrKHEII9eYUcLZKxCuEB/lzVMYpAPxWroJDUpgyaKh5I6eQZPvroI0vys0Q3J8wy\nGo1i69at4qGHHhIRERF2E7AFBQWJadOmiQ0bNgi9Xu9WedxFuVEvJuhWW5LHTdElC73RUK9zX3xR\n5jAbOrTmvpL8bPH6mCjxzaxbnRNMlyXEfoSoOOzc+Q3gUH6RJSle4vFMUaLTuf2aCt8HJxPV+TKm\n39U8qKyspE+fPpw4cYKQkBCysrIavcRmZmYmX375JQkJCfz22292j4mLi2Py5MlMmjSJiIiIRl3P\nFygROsbof2Qr0i//Ee0g3tQOr7cN/ZprIDkZnnwSTFa8KpjdSOs9T2CPAxoIHQ091jtfRgM4VVLG\nb9n5lu9xndvRRsUqtFiUmaiJkJaWRmxsLACLFi3iscceq/OciooKVq9eTUJCAt+YfR6r0aNHD0ta\nhkGDBrlUZl8gT1Rwhf57DlIAwPPaS5ijvajeSkCvhwBT+/jtt3DzzTWPWf36dPauX8EDCbsJb98I\nT6gTo6B0o9tMRY7ILq/g57PWWIUrOkTSIUTFKrQ0lDJoQgghuPnmm1m1ahUAJ0+etCyws2fPHosX\nz+nTp+2ef9tttzF58mTi4+MJDGzei6hkilKG6L8lC7lS1RLtlTzkN7BBZdimlti3DwZUXzkDyDy4\nk4SHxxJ3//Nc+rcHGyd05SE40hf6ZIOf57PcFlbqSLaJVbgoqg09wjy5XInCmyhl0MTIzc1l2bJl\nzJ0717KteqCWsU8f7nnoIW699VY6derkJUm9wxFRSB/9VxhN5s9P/eK4S9vwRHS//QaXmlaoLCgA\newvjGQ16Fl3bCa1/AI//mNkYsa0c0ECbqdD5I9eU5wRlegMpmdlUGuXihf1NKTCUW2rzRuUm8lEM\nBgMbN2609Pb1en2NY0JDQ9GWlnIdsMJm+2yjkaHR0S1KEfwpchms/9by/Qe/sUzQ9nSqrI8/hmnT\nICQESkocpwx693Y50njk+5pLqzpNQF8o+NiryiDE349ru3dEZzSy5WwuBwqKOVBQTM+wEIZEtlFK\noQXSVJ94kxsZHD582NLoHzp0yO4x119/PZMnT+aqq65i7969bN++ne3bt5OzZg0/63Q1jp8bH88L\na9a4W3Svs814juGG7y3fU/wmEKvt7HR5990HH34It9wCX33l+Lg/kpazfvET3P7GD3QbfIXT16tB\n6RY4MQL6loHWN/JVGU2xCpmmWIX2wYFc3j4SP21TbSIU9lBmokbQ0FW5iouLWblyJQkJCaxdu9bu\nMV27dqV79+6Ulpaye/fuOmWIBVLsbJ8fG8t8B6kfmgPrjacYa1ht+b7D/yYu0bR3ujwhoGtXyMyE\npUth+nTHx5bknePd2y7g/BHjuWnecqev6ZADGoiaA+1faPTKb65ECMHe/CLSC+VKbmH+fozs1E7F\nKjQTlJnISeyuymX6PPK669iyZYult19YWP8EZKdPn64yAXzxxRdz+eWXc9lll3HZZZfRr18//Pys\ngVFz4uPBzoIwhmaaBfVb41H+Zthg+X7A/xb6ado2qkzb1BKbN8OIEbUf/+5tMm2IWxQBgCYUcl4k\nbftwh3XMGwpBo9EwKKI1gyJak15Ywp95haw+dRatBq7p3J5WAarJUPgWHgnQmD12rIxAqva61E6w\nlr1X+/btxfjx48WCBQvE6tWrRVZWllNypCYmilnR0VVkeDY6WqS6OUjN03xgOGAJFGtV+aE4bixy\nSTcRaakAAB8hSURBVLnp6dZbl5FR9/H/e/E+8fqYKFGUXY+DnaXgGyH247COzYmPd9+1G8jp4lJL\nANuqYxkit7zC2yIpnIRags6Umq8FfztJ2EB69PTp04eYmBhLb37gwIEEBLgnmMfcQ5y7ZAl+5eUY\ngoMZ9/DDXjMluJo3DLt50rgNgO60Yof/RDpoXJOaefVquO46+bl6agl7nN67nYOpqxj10ELCopyf\nl6iTcBnMUJlhf51mv/Jy9127gXRpFcKNrULIKa9k89kc0s7kADC8QwQdQ5rn6LQlopRBLThalWuk\nFyZuY8aPbzaNP0jb9BzjDl427gJgKFGk+E+gjcZ1sREvvADPPQcXXSRXKKsLg17HF49dR2BoGBfd\ncJ/L5KhOwZkTrJp/N1lHojidcc6+LD5oAowKDuTGnp0p0unZmJHFL+fyABga2Yae4SpWoamjJpBr\nwd6cwazoaMYtXtysGmZPYhSC6cafec8os6Beo+lCol88IRrX9kvi4iA1FZ5+GhYurN85i2/sia6s\nhMd+zMTP37WjPKNBz+aPX2b7irct2y4aNwxt0Bo2vBndJOtYucFAamY25QYZq9CvTRj9VKyCT6Mm\nkJ2kuZtnPIlOGJls2MjX4igAf9Ocx+d+1xCgca2Xim1qie++g4n1XGVy5/f/RVdWwp1vrXapIjjx\nexpfPWPNb9G2y3nc/OIXRHY737Icpl/Hycz977YmV8eC/fyI79YRvdHI1nO5HCwo5mBBMd1bhTA0\nqg1apRSaFE31aXlkZKBoPGVCz/WGtfwkMgB4QNufZdqr3NJQ2KaW2L8f+vev33nFOZm8d8dg+sfd\nzIRZ/2m0HKUFOSS9+gDHf0uxbIt/4m0Gx99Z8+ADGtBGQt+cRl/X2xiFYGd2PqdL5XxHVFAgwztE\n4O+l1OyKmqg4AwXQ8JiJxlAoKonTJ/I7spF7VjuUl7SXus2EsGMHDBsmPztKLeEIV2QjFULw23fv\nkfJ/1hQi/WJvZOyjbxHUKtzxieeegtx/ezxxnTsRQrA/v4hDpliFUD8/YjpHEeRX+zoSCvejzESK\nWmMmXKkQskQZl+pXcYJiAF7TXsZTfkNcVr49PvoI7r0XwsKgsNBxagl7rJx3NwD/WuHc6mPn0vfw\n9cy/UVYglV5gaBi3vPodnftfXL8C2s2XyqBsB4Rc6pQMvoZGo+GCiNZcENGao0Ul7M4tZM0pOVE+\nqkt7wlSsgk/irZHBLcB8ZO61YYCtr8ezwL2AAZgB1Iy2UiODBjNzdDyv/lTzVs4eE89L6xrvGXVS\nFHOB/huKkWkz3vcbyd+19bTTNIJp02Seodtugy+/bNi5J3dvYcWTNzD20UVceN2Uep9XWVbChiVP\nsW+DNZfFyHvnctmtD6NxxiRyQANBF8J5fzT83CZCZmk527PyLN9HdooiMqh5Z9X1RXxxZLAHmAj8\nX7XtFwC3md67AhuAvoDRo9I1I8yZOWOxHzPx8/pyNBq45BK5oMvVVzes/L9EPv30X1u+f+03ir9p\nezdG5HohBHTuDGfPwjvvwIMNzCytr6xgxZM3ENImqoYicGRO27/xG5Je/afluG4XXsn1s96nVWTH\nxv2Y8NuhqIGarInROTSYG3t2Jreikk1ncthkilW4rH0EnUN9z422KeBLaUxcQTJgO55+FnjG5vsa\nYLid87wUv9c0MBqFeOWVqkGt9w2xH+n68BXxYtSomrumThXixAnH19hpzLJEC1P5H7HWcNJjv6+k\nxCrnzz87V8Yb4zqK18dECYO+6nKQ9qK9HwoPFjOGhonXx0SJ18dEifRt613wK2zQnTEth3nUteX6\nMEWVOvG9TVTzkcJib4vUpLBXT2fVIysBtUQge5vqymAJMNnm+3+BSXbO89Atb1pkZwsxfLi1fpx/\nvrVBr09KC71eiE8+EaJjx6qKQaMR4t//FqKsTIhUQ0YVJbDVcMajv/HwYatcmZnOlbH966Xi9TFR\nIuPAbzX2OUoP8a8BvYW+0o1pGPYjxInr3Fe+j1Ku14t1p85alMLe3AJhNBq9LZbP42waE7yUjmI9\nYC/Z/izghwaUY1f4+fPnWz7HxcURFxfXgCKbFz/9BKNHW78//ji89hrYOm/UJ2bCzw/uvlu+APLy\n4JVXpPnoyZ9O8OSMtXImB3hv+yTuvzKyQZO1jeXHH8EsbmWlNZ6gIRSeO03qf+YxcMztdO5n7YeU\n5meT8p/nyNy+0e55HTp0xy/AjTbukKug5Ef3le+jBPn5MaZrB/RGI9vO5XGosIRDhSV0DQ3m4nZt\nVayCAxylyqmexiQlJYWUemY29vadTgaewDqBPNP0/qrpfQ0wD9hW7TyTkms5VLcPjpo+g6S08bzx\nhvWYDRtg1CjXXvdz42EmG5IB0AoNVz1wK2kfV/XbvPNOePFFOO88117bluefh3nz5NzGjh0NO9f2\n3h3a8zPtegSz+Pci8jOOsm7xE5z4Pc1y7N59ej46XVCjDLevHVFxAI4OgD654Bfhvuv4OEYh2JVT\nwMmSMgAiAgO4omMkASpWoQpPjRnD6xs21NheVz2tbQLZ2yQDl9h8vwDYBQQC5wHp2BfcI0MxX8Ge\niedWokUYiWL4cCGcTIZaK+/o91pMQe0rPxGnjVVtugaDEF98IUS3bjVHq6+8IkRpqetkiYmR5c6c\n2fBz7c8BBFWZA1jx1ESRd/qIw+M9liF2P0Jk3u/+6zQBjEaj2J9XaDEfrTl5RpTp9d4Wyyc4V1ou\nFn74iXisV68G11N8cM5gInASKAPOAKtt9s0CDgMHgHgH53votvsGjuyDs12c5thoNIoX9L9ZlEDf\nyhUix1hWr3Pz84WYNaummP37C5GYKCe1G4pOZy1n5cqGny+E43v3QN/uoiTPvhZNTUwUc+LjxbzY\nWDEnPt5zqcIPnycVgqIKxwpLqqTQLqzU1X1SMyW7rEKsOpYhfjp9TqQmJop/xMSJGcOvqHc9xQeV\nQWPxwG33HebFxtpt0ObFxrqkfKPRKB7Tb7EogeGVq0SRsbJRZe7dK8QNN9QU+5ZbhDh0yP45qYmJ\nYvbYsWJebKx4Mm6sCCNRgBAHDjgvh7vvnUspSZHKwFDubUl8kjOlZVWUQnZZy1pXIa+8Uqw6liH+\nv717j46quhc4/j0zE/JOyIs8IICmiIDKQ7Q+QCM0EIpAqde2t1fXUqztqpZ4u5a2VrCirdXq9Vax\nq3Zdr+312iutrUXR8IqFEEVEsSDyFCJvSCDvdzJzzrl/nEkySWaSkMzkzDn5fdbKypkzk2FvMpnf\nnP3b+7c3neqctNEeGPoL2c/A2gKV0h5smWNV17hHLeFV3diTeaGSzZvOPCKVwZcNmDwZ3vZuW6zr\nRtG4hx6Cv/7V+Gr3xBNGwvvT4p4rpE9Syt1vwMSJA587Har/u5CIudn4XvUMpD7a+2OHofRoY61C\nTaubbWUVfFBurFW4JnUkWbHB2f8iXNW1GX12KQrzxgxyXYvNhCLwhq1gj2O3ah59kXtjx5XAne4t\nultTg9zqwOrqdH3Vqq4f1mcSmh2/LLdL3MEIGSrqp4Y2t/7Oic4rhaO19lyrUNfm7uhjd3JlMMwE\nq5R2o+5mnmc9H2LUiXnAcQW/cVw35PXn4+ONmUGPPWbcPnwYVs5qBT914ga745flypBnvQpnv2uE\nLZlW2avYCBe3js2kTdV4v6yCfdV17KuuIyc+lilJ8bbYV6HJY2wkBLB4rL+Z+sFj1f8tb5AT/VGt\nt3KD520OYUyZfMJxNSsd08Pqj2Xl/Pn8cnPP2kkhn9IZbnQdDjsg4xUYuczs1liKqunsvFDFhZY2\nADKjI5mZlmTZtQrNHpXNZ4wPbovHZvj9e337xDniI1zMyUrr13OGY20iMQTK9Camet7kPMan69WO\n61nuvMLkVvk3r6CAFaWlPXf8Wr7cxFaZoP0PvuweCQYXyelQuCE9BV3X+ayqjhMNTbxzsoyRI1zc\nkJ5iqbUKLWrfgSDYrBky5cqgV8f0OiZ43kD1Dg++5szlDscEk1vVt5LCQop8hnPywnk4J5Qqn4UL\nP7HVHgdm0HWdL+oaOFRjlFMf4XCQm5lKtCu891VoUzU2nC4H+g4EwbwykGBgI/v1Kq7wvNlxe51z\nHosc40xskRgQ3QOHI2DMRogLtNRGXIyTDU3sruxcWX5LZioJI4K7z3UwuDWN9aeMQLBobEafQ1wy\nTCS62Kmd5zr17Y7bxc5budmRaWKLxKAo3j/Lc3fBhHOmNsUuxsbFMDYuhvPNrew4X8XWc8ZshRvT\nk0mN8j/9eKh5fALBrf0IBMEmwcDC3tPOkKd2Fjfb5foGVyv9+4QgwlzSA1D9gtmtsJ1R0ZEsGZdJ\nbZub4nMVbC+vAmBm6khGm7hWQdV1Cr2BYGF2Bk4Tkt4yTGRBf9eOcZvaWaTqoOt2LldGmtgiEXRq\nPRxJgPF7ICq024YOZ00eD1vPVuDxvp9MSYrnKwlxQ9oGTdd552QZAF/PTr+oRLfkDIZpMPijdphl\nqlFhMxYXB1y3M1YZ2heuGDolv1fY/HoCLsd0W+xkFc7aVI3t5ZXUuT0AXBIfw5VJCSGfxeMbCBaM\nSWeE8+JmPEnOYJh5Tt3Lg5pRxTubWHa5ljJKsffy++GupLCQTU/H8uSJOmAbACu8024lIATfCKeD\nW7LSUHWdT85Xc6y+iWP1TWR41yqEYthG9wkE+WNGXXQgCDa5MghTuq6zUtvFr7Q9AEwjhWLXrSQq\nson4cCCL8Myl6zqfV9dxrL4JgIQIF7MygrdWQdd11nkDwbzRowY83VWuDGxM03Xu17bze+0gAHOU\nLN51zidakV/VcNLfnaxEaCiKwlXJiVyVnMiR2gYO1NSz/lQ5EYpCblYaMYNYq+AbCPJGp4XNugd5\nhwkTbl3jDnULb+jHALhNGc8a51wiFOusmhTBY6lqqzY3ITGOCYlxnG5s5tOKGoq8K4NzM1NJHMBa\nhfZAMDcrjRhX+LwFh09LhqkW3cMidRPv6WcB+L7jcl5yzLJsPRURHFKeI/yMiY1mTGw0F1pa+bC8\nimLvWoUbRiWTFt2/tQrvegPBLZmpxEWE19uvVd9xLJ8zqNPbuMXzLv/EqMn+sGMqv3JcE1bF44S5\nSgoLKXr6VpzapajxE4ZveY4wVdfm7li8BjAjJZHsuJiAj990upwWVePmjFRGRgZn9bNMLbVwMLig\nN3ON5y1OYNRLecZxLQ85ZR65COCQAmnPQsqDIf+nSgoL2bx6Na7WVpnKehGaPSrF5ypo0zQAJo2M\nZ0JCbJcPdv84c54Gj8rsjBSSI4M3CUQSyBZ0Sm9giudv1OMG4GXnbL7nuNzkVglhKCnsudOcTGXt\nn2iXkwXZ6bg1Y63CwZp6DtbUMy4uhqnJCbxfVkmDR+WG9OSgBoJgk2AQYl/oNUz0dO7z+FfnXP7F\ncamJLRKip82rV3cJBABPlpby6IsvSjDopwiHg9zMNDRdZ9eFak40NHGiwZiaem3aSNLCpAZSIBIM\nQmS3XsEMz9qO25ucC5jnGGNii4QILOBU1qpNcOwqiFsK8UshcqrswNYHh6Jw7ahkdpZXUubdaOfj\nCzXEueqZnZFq+uKyQCQYBNn72jluUt/tuP2hczHXO2QDa3HxSgoL2fwUuPSX8MQVhXQMP/BU1kho\n/dz4qnyi653OVG+Q+CbEzoFeFkQOt3zEPyuqKWtpY0bKSLLjoimta2RfdR0bTpfjVBTmZKWG1bRS\nkGAQNOu1kyxUN3Xc3uu6jSuVZBNbJKyscwwf4Evgy5CO4QecyvrTF+Byn3+v9SA0vAX1a6HlE6h9\n2fjqLm6RESjiFlGyaeewykd8VlnLqcYWpiUnkh1nlI3JSYglJyGWs43NfFJRQ9EZY1/jYM4sGiyr\nXu+FzWyiNdpRvqtuBcCBwheub5GjJJjcKmF1ActRzIJf+HnvDYaSYij6P3C2ghoJef8GN+UO/nlX\nfg9+ub3neTuW1thfXcfRukauSEogJyE24OMqW9r4oLyy4/Z1o5JIj774BYUymygMvKQe4D7NeIWn\nEsVnrm+SpQT+5QtxMQKO4fs/HRQ35Qbnzb87V5v/83YrrXG4pp6jdY1MGhnfayAASIkawZJxmdS7\n3Ww5W8FH56sBmJaSyLhe1iqEkgSDPnQf66y6fyEvLTAu/S4jkR2uxSQrUiJABFfAMfzk+XC5tT5N\ne5LmAz2vcuxUWuNoXQOHahu4LCGWyxL7X1Y+PiKCJeMyafGobCurYE9lLXsqa5mYGMfExLghXYQq\nwaAX/uZef7t0NzP1H7B18c+JU8JjrE/Yj53KUdipL/4cq29kf3U9l8bHMClpYEPEUS4n88cYaxV2\nlFdxuLaBw7UNjI2NZlpK4pAEBbOCwbPArUAbUArcDbTvVv0zYBmgAgX4+0gxRPzNvf5L6QUefekT\n4pZIIBCh055YffTFF3G2tKBGRZFv0XIUdupLdycbmthbVce42GiuTE4c9PNFOBzclJmKpuv8s6KG\nk43NnGxsJjVyBF8dlYzLEbqgYFYCOQ/4B6ABT3vPPQxMBl4HrgFGA+8Bl3kf52tIEsircnNZtW1b\nj/OLZk/hj9t2kSrDQ0IMW2cam9lVUcPomChmpiWF5N/QdZ0D3lwEQKzLyeyMFCKdTkoKC/nTr58l\n2t1GfEJ8v6brhmMCucjneCdwm/d4CbAGcAPHgaPAtcBHQ9m4doHGbcuiddI8rwGw2bmAPFlMJsSw\nUtbUwq6KGtKjIkMWCMB4856SlMCUpASO1Teyt6qOjafPc3jLe1Q/+Tj/FcTpuuGwFG4ZsN57nAWc\n9rnvNMYVginmFRSwIieny7lHcnJ4ruAZtjiN//B56gYU98v8WN2Bqne/gBFC2M355lZ2XqgmJTKC\n69KHbi3RJfGxLBmXybVpSRz94ys85ad8SNGLLw74+UN5ZVAEZPg5/wjwjvd4BUbe4PVensfveNCq\nVas6jnNzc8nNzR1IG3vV11in7riXKr2FxZ7NPK/t43ltH+OJY5trkWxUL4QNVba0seN8FYkRLmZl\npJrShsyYKLICfIzvPl23uLiY4uLifj2vmYvO7gLuBeYC7T142Pu9PY+wEXgMYyjJV9gsOmun6zr/\noe3lJ9rHHef+4pzDtxw5vfyUEMIqqlvbKCmrJMblJG/0KFPbMtA9snvLGZg1TJQPPISRI/ANZeuA\n7wAjgEuACcDHPX46DCmKwkPOqegR9/KpaykK8G11C4r7Ze70bKVVV81uohBigGrb3JSUVTLCoZge\nCCDwEHbeIKbrmnVlcATjDb/Ke3sHcJ/3+BGMPIIHeADY1OOnw/DKwJ9G3c0d6lbe0k8AEEcEO11L\nmKyELuEkhAiuereHLWcvoACLx2Wa3ZwOJYWFFPkMYfdnJzzZ6SwM/EE7zD1qScft3zlu5IfOySa2\nSAjRl0a3h/fOGkXlFo/NsPy2tBIMwsgRvZYbPeu44B0dy1fG8IZzLvG9lP8VQgy9Zo/K5jPnAXsE\nApBgEJbadJX71O28oh/uOPeRcwlfdZg/HinEcNeiqmw6ba9AABIMwt5b2nGWqp3r8J5wXM1Kx3Tb\nvACFsJJWVWPj6XLAXoEAJBhYxlm9ka951nOQGgCuJpUNrnzSlGiTWyaEvbVXJ3a0tFCmK3zl7nt4\n8K47cNgoEIAEA8vRdJ0V2ic8rX3WcW6jM5/5jmwTWyWEPfmrTvxITg75L7xgi2J6viQYWNg27Ry5\nPnsqFzim8JzjOlxKOFQSEcL6BrqAy4rCcdGZ6KebHZnoEfdS6bqT2WSwWttPhOcVxrvXcEKvN7t5\nQljal/WN1NTW+b3Pbjux9UU2t7GIZCWKkohF6LrOf2qf86C2k/GePwOwxjmH70jZCyH6RdN1dlfW\ncLrReLMPuKucjXZi6w8ZJrKw3XoFMz1voXlr+f2rksMfnDcRpUiMF6K7Zo/KB2WVNKlGaZismChm\npI5k+/r1kjMIdNICJBj4aNTd3KluZa237EUMLj52LWGKMnTldYUIV5UtbXxQXtlx+4qkhB4b1g+k\ntIMVSTAYRv5H+4K71c7d2X7ruIH7nVNMbJEQ5viyrpHPqzvzATemJ5Ma5X9IaLiQYDAMHdFrmeVZ\nx3lv2Ys8ZTR/c36NBCl7IWysfe/gM03G6z7a6WB2RirRLqfJLQsPEgyGMbeucb+6nZf1Qx3nPnQu\n5npHuomtEiK4AuUDnDZbNDZYEgwEAOu0EyxRO+dTr3LM4OeOGbZabi+Gl/7kA0QnCQbDTPvSeldr\nK57ISOYVFHRJhp3VG8nzrOeAt+zFdFLY6FrAKCl7ISyitK6RfZIPuGi9BQOZg2gz/pbWr/AetweE\nLCWW/RG3o+k6K7VdPKXtId3zJwA2OPPJl7IXIgyp3nzAWW8+IMbpZFZGiuQDgkSuDGwm0NL6u+fP\n4tkNRaQq/hfSlGjnuNmn7MWPHJP5jeN6KXshTNfsUXm/rIJmVQNgdEwU0yUfMCByZTCMuFpb/Z4/\n1lROmue1LudmKqksVcaz1DGe2UoGesS9VOutfMOzmd9qB/itdoBsYilxLWK8Eg/0PQQlRLBUtLSy\nvbyq47bkA0JLgoHNBFpaPzvmUja5lrFVP8ta/ThrtePs0ivYpVewQtvV5bGjieF+ZRIa8JJ+kEu8\nZS9WbYS2H/+61yEoIQarez5gVnoKKVEyJTrUrHqdJcNEAQykHK+u6+ylirWaEST2UuX3cTMXPs8n\nRQd6nLdjdUcxtCQfMDRkmGgYaX/Df9RnaX1+H0vrFUVhKilMdaawynl1l/vO6U2s006wVj9OS4vb\n788Pt+qOIni65wPGxEYxPWWk7TaVsQIJBjZ008KFQRu2yVRi+IFzEj9gEiujnweO9HjMcKvuKAav\nez7gyqQELpV8gKkkGIh+m1dQwIrS0p5DUMuXm9gqYSWldQ3sq+7ch0PyAeHDqtdikjMwyXCp7iiC\nR9V1Pr1QzblmY6ZbjMvJ7PQUoiQfMORkBbIQYsg1e1RKyipo6cgHRDM9JVHyASaSBLIQYsj0yAck\nJ3BpvOQDwp0EAyHEoOm6Tml9I/slH2BZZgWDXwCLAR2oBO4CTnnv+xmwDFCBAqBnbQUhRFjong+I\ndTmZJfkASzJr8C4eaP8IsRyYCnwPmAy8DlwDjAbeAy4DtG4/LzkDIYaIvxIk18zP75IPyI6NZprk\nA8JeOOYM6n2O44AK7/ESYA3gBo4DR4FrgY+GsnFCCIO/Fe0PHP6Cjx57golzvsZVyQlcIvkAWzCz\nJOWTwEmMIaKnvOeygNM+jzmNcYUghDDB5tWruwQCgBdOHKdyzWssGZcpgcBGQnllUARk+Dn/CPAO\nsML79TDwPHB3gOfxOx60atWqjuPc3Fxyc3MH3tIwVFxcbLs+dSd9DH+BquBGt7UB1u9ff1i5j8XF\nxRQXF/frsaEMBnn9fNzrwHrv8RnAd2eVMd5zPfgGAzuy8guwv6SP4S9QFdz2EiRW719/WLmP3T8o\nP/744wEfa9Yw0QSf4yXAbu/xOuA7wAjgEu/jPh7apgkh2s0rKGBFTk6Xc4/k5JAnJUhsx6wE8lPA\nRIzpo6XAD73nDwBveL97gPsIMEwkhAi9gVTBFdZk1XlgezCmowohhOi/bUCu2Y0QQgghhBBCCCGE\nECJIfgF8hpEz+Addp6H+DGMbrkPAvKFvWtA8CxzE6OffgUSf++zQx9uB/RiTB2Z0u88O/WuXj9GP\nI8BPTW5LsPwBKAc+9zmXjLGm6AuMOmIjTWhXMGUDWzFeo/sw6qOB/fppefE+x8uB//YeT8YIEBHA\neIwyFmaurh6MPDrb/rT3C+zTx8sx6k1tpWswsEv/AJwY7R+P0Z89wCQzGxQks4HpdA0GzwA/8R7/\nlM7Xq1VlANO8x3HAYYzfnd362YPV/tgutqaRFRXRWZhvJ8bCO7BPHw9hfLrqzi79A6PdRzH64Qb+\njNE/q3sfqO52bjHwqvf4VeAbQ9qi4CvDCN4ADRhX6aOxXz97sFowgOFV02gZnauz7drHdnbq32g6\nS7KDtfvSl3SMoSO839NNbEuwjce4EtqJvfsJhOfmNiGtaRQm+uojGH1swyjXEUi49rE//euPcO1f\nX6za7sHSsU/f44A3gQfoOiIB9upnh3AMBiGtaRQm+urjXcDXgbk+56zUx/7+Dn1ZqX996d6XbLpe\n9dhJOUbgLwMygfPmNicoIjACwWvAW95zduynpfnWNFqO8cuCzuRje02jUqy7ujofYyZDarfzduoj\nGAnkq31u26l/Loz2j8foj10SyGD0qXsCuX221MNYP7GqAP8L/Kbbebv10/L+hvFC3IMRuUf53PcI\nRtLuEDB/6JsWNEeAExjF+3YDv/O5zw59XIoxnt6M8Slrg899duhfuwUYM1GOYkyZtYM1wFmM4ctT\nGEO0yRg7EtplyuUsjAkce+j8G8zHfv0UQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIEVrZwJdA\nkvd2kvf2WNNaJMRFcJrdACFsog5jtfG3gHeBFzAWKa3v7YeEEELYjwtjU6J/x1gpLx+2hBBimJqP\nUc5gbl8PFCKcWHE/AyHC2QKM+j1Xmt0QIYQQ5piGsW9uNkaxQX97OgghhLAxBdhB5/DQj4A/mdcc\nIYQQZvg+Ronndg7gU4xN5IUQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghrOP/ARyU\nkOAreGWoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bee77d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "passengers = [(random.randint(min_x,max_x), \n",
    "               random.randint(min_y,max_y)) for i in range(n)]\n",
    "destination = (0,0)\n",
    "a, paths = generate_graph(passengers, destination)\n",
    "draw_paths(a,paths, title='''Completely random graph \n",
    "           of {} passengers'''.format(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we order the passengers and the paths taken are much more optimal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ex6rPmvQEpsTF8UZSUpn9jvarrFkDAwbIEPmNGjmsGIXWPP88zJ8PW7ZAd+sT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\nb9+eDb//XmZFw0lRUdyqfAZugccrAxOnTi3kwIG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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c4768d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "passengers = sorted(passengers, key = \n",
    "                    lambda x : distance(x, destination), \n",
    "                    reverse=True)\n",
    "a, paths = generate_graph(passengers, destination)\n",
    "draw_paths(a,paths, title=\"Same graph with sorted passengers\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## The bug we found in the paper\n",
    "As described in the presentation, the original cost of the edge from a passenger's out node to the destination was just the distance between the passenger and the destination. This subtle bug caused the optimal number of cabs to always be 1, and we fixed it by subtracting the same L from the cost.\n",
    "\n",
    "This is not a formal proof, but since the problem was only found in the implementation, we have recreated the results of the mistake below with the mistake=True flag - on graphs which we have already seen the best path for."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/AGzt5efeA1iVc381oTfRVZuxGBqqYnPnLtomMACam6/gL79zCDt/bQUbP9pINptl4oiJ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\nJEmSJEmSJEk16/8DKOroZLputdYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c06da50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "passengers = [(1,1), (-1,1), (-1,-1), (1,-1)]\n",
    "destination = (0,0)\n",
    "a, paths = generate_graph(passengers, destination, mistake=True)\n",
    "draw_paths(a,paths, title=\"Square Mistake\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6z2Wo11Auv7zM27C3OJJywmDRuUUAGV79Ym9jz/67pu+DsZA0LMIglZEXkK/7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\nUXZMWV+LkSv3Mu+Jx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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b486790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "passengers = [(random.randint(min_x,max_x), \n",
    "               random.randint(min_y,max_y)) for i in range(n)]\n",
    "destination = (0,0)\n",
    "a, paths = generate_graph(passengers, destination, mistake=True)\n",
    "draw_paths(a,paths, title=\"Random graph with mistake\".format(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unused work\n",
    "We tried to make progress in calculating costs, but as the min cost max flow algorithm is not based on individual rationality, the output of optimal path need not satisy SIR. \n",
    "However, the following part of code can be used to verify if the resultant path is SIR compliant or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def operational_cost(G, route, meter_fare = 8):\n",
    "    oc = 0\n",
    "    oc_values = []\n",
    "    players_on_route = 1\n",
    "    for i in range(len(route)-1):\n",
    "        first = G.node[route[i]]\n",
    "        second = G.node[route[i+1]]\n",
    "        oc += meter_fare*(distance( (first['x'], first['y']), \n",
    "        (second['x'], second['y']) ) / float(players_on_route) )\n",
    "        oc_values.append((distance( (first['x'], first['y']), \n",
    "        (second['x'], second['y']) ) / float(players_on_route) ))\n",
    "        players_on_route +=1\n",
    "    return oc\n",
    "    \n",
    "def shared_cost_per_player(G, route, meter_fare=8):\n",
    "    operational_costs = []\n",
    "    inconvenience_costs = [0]\n",
    "    for i in range(len(route)-1):\n",
    "        operational_costs.append(operational_cost(G, route[i:], \n",
    "                                                  meter_fare)) \n",
    "    \n",
    "    #IC(i) is the inconvenience cost caused due to \n",
    "    # player(i) to other players\n",
    "    for i in range(1,len(route)-1):\n",
    "        first = G.node[route[i-1]]\n",
    "        second = G.node[route[i]]\n",
    "        destination = G.node[\"destination\"]\n",
    "        new_distance = (distance( (first['x'], first['y']), \n",
    "                                 (second['x'], second['y']) )+\n",
    "                             distance( (second['x'], second['y']), \n",
    "                                      (destination['x'], \n",
    "                                       destination['y']) ))\n",
    "        original_distance = distance( (first['x'], first['y']), \n",
    "                                     (destination['x'], \n",
    "                                      destination['y']) )\n",
    "        \n",
    "        inconvenience_costs.append(\n",
    "            (new_distance-original_distance)*meter_fare)\n",
    "    \n",
    "    total_cost = []\n",
    "    for i in range(len(route)-1):\n",
    "        total_cost.append(\n",
    "            operational_costs[i]+i*inconvenience_costs[i])\n",
    "    \n",
    "    return total_cost\n",
    "    \n",
    "def original_cost_per_player(G, meter_fare=8):\n",
    "    costs = []\n",
    "    players = [n for n in G.nodes(data=True) \n",
    "               if n[1]['type']=='passenger in']\n",
    "    destination = G.node[\"destination\"]\n",
    "    for player in players:\n",
    "        costs.append(\n",
    "            meter_fare*(distance((player[1]['x'], player[1]['y']), \n",
    "                        (destination['x'], destination['y']) )))\n",
    "    return costs"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
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