Travelling_Salesman.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Travelling Salesman Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>\"Given a list of cities (nodes) and distances between each pair of cities (edges), what is the shortest possible route that visits each city and returns to the original city\"</i>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Packages"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* **random** - For generating random numbers to be used as the nodes.\n",
    "* **pandas** - Popular data analysis package in python\n",
    "* **numpy** - Popular package in python for handling arrays \n",
    "* **pulp** - Optimization package that is used in one of the solutions\n",
    "* **time** - Package used get time and calculate computational time.\n",
    "* **matplotlib** - Used for plotting data \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import pulp\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An object that generates nodes and stores metadata regarding said nodes. It also caclulates the distances between a pair of nodes and can show a plot of the nodes with a solution from an algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Change self.permutations into {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Space():\n",
    "    def __init__(self):\n",
    "        self.nodes = {}\n",
    "        self.solutions = {}\n",
    "        self.solution_total_dist = {}\n",
    "        self.distances = None\n",
    "        self.nodes_df = None\n",
    "        self.totalDistances = {}\n",
    "        self.permutations = []\n",
    "        \n",
    "        \n",
    "    def __len__(self):\n",
    "        '''\n",
    "        Returns the number of nodes available in the Space Object.\n",
    "        '''\n",
    "        \n",
    "        return len(self.nodes)\n",
    "    \n",
    "    \n",
    "    def posToChar(self,pos):\n",
    "        '''\n",
    "        Converts position (int) to a character starting with 'A'.\n",
    "        \n",
    "        pos: integer\n",
    "        '''\n",
    "        \n",
    "        return chr(pos + 65) \n",
    "    \n",
    "    \n",
    "    def intToChar(self,inte):\n",
    "        '''\n",
    "        Converts integer into an only alphabet character string \n",
    "        starting with 'A'.\n",
    "        \n",
    "        inte: integer\n",
    "        '''\n",
    "        \n",
    "        div = (inte//26)\n",
    "        rem = inte%26\n",
    "        \n",
    "        if div == 0:\n",
    "            return self.posToChar(rem)\n",
    "        else:\n",
    "            return self.posToChar(div-1) + self.posToChar(rem)\n",
    "    \n",
    "    \n",
    "    def generateNodes(self,nums):\n",
    "        '''\n",
    "        Generates unique random cooordinates given a number of nodes.\n",
    "        \n",
    "        nums: integer\n",
    "        '''\n",
    "        \n",
    "        assert len(self.nodes)==0,'Nodes already available'\n",
    "        assert nums%1 == 0, 'Input not an integer. Try again.'\n",
    "        assert nums>3,'Input must be greater than 3. Try again'\n",
    "        \n",
    "        num = 0\n",
    "        while len(self)<nums:\n",
    "            coordinates = random.sample(range(1,100), 2)\n",
    "            if coordinates not in self.nodes.values():\n",
    "                self.nodes[self.intToChar(num)] = coordinates\n",
    "                num+=1\n",
    "\n",
    "                \n",
    "    def nodesToDF(self):\n",
    "        '''\n",
    "        Creates a pandas DataFrame od distance from dictionary of nodes.\n",
    "        '''\n",
    "        assert len(self.nodes)>0,'No nodes available.'\n",
    "        \n",
    "        self.nodes_df = pd.DataFrame(list(self.nodes.values())\n",
    "                                     ,index=list(self.nodes.keys())) \\\n",
    "                                     .rename(columns = {0:'x',1:'y'})\n",
    "        return self.nodes_df\n",
    "\n",
    "        \n",
    "    def getDistances(self):\n",
    "        '''\n",
    "        Converts dictionary of node coordinates into a table of distances\n",
    "        '''\n",
    "        \n",
    "        #X's\n",
    "        dfx = self.nodes_df['x']\n",
    "        df1_x = pd.concat([dfx]*len(self), axis=1)\n",
    "        df1_x.columns = df1_x.index\n",
    "        df2_x = df1_x.T\n",
    "        \n",
    "        #Y's\n",
    "        dfy = self.nodes_df['y']\n",
    "        df1_y = pd.concat([dfy]*len(self), axis=1)\n",
    "        df1_y.columns = df1_y.index\n",
    "        df2_y = df1_y.T\n",
    "        \n",
    "        self.distances = (((df1_x-df2_x)**2) + ((df1_y-df2_y)**2))**(1/2)\n",
    "        \n",
    "        for i in self.distances.columns:\n",
    "            for j in self.distances.index:\n",
    "                self.totalDistances[(i,j)] = self.distances[i][j]\n",
    "                \n",
    "        self.distances = self.distances.replace(0,100)\n",
    "\n",
    "        return self.distances\n",
    "    \n",
    "    \n",
    "    def getDistance(self,order,end,total_distance):\n",
    "        '''\n",
    "        Outputs the distances from an input list. Uses memoization the store \n",
    "        previous calculations.\n",
    "        \n",
    "        order: tuple of node names in their respective order\n",
    "        end: end of range to get distance\n",
    "        total_distance: total distance (output)\n",
    "        '''\n",
    "        \n",
    "        if end == len(order)+1:\n",
    "            return total_distance\n",
    "        \n",
    "        elif order[:end] in self.totalDistances:\n",
    "            total_distance = self.totalDistances[order[:end]]\n",
    "            return self.getDistance(order,end+1,total_distance)\n",
    "        else:\n",
    "            total_distance = self.totalDistances[order[:end-1]] + \\\n",
    "                             self.distances[order[end-2]][order[end-1]]\n",
    "            self.totalDistances[order[:end]] = total_distance\n",
    "            \n",
    "            return self.getDistance(order,end+1,total_distance)\n",
    "\n",
    "        \n",
    "    def getTotalDistance(self,order,solution_key=None):\n",
    "        '''\n",
    "        Outputs the total distances including the closing connection. Stores \n",
    "        output in solution_total_dist dictionary under the solution_key.\n",
    "        \n",
    "        order: order of nodes to calculate\n",
    "        solution_key: name of this order\n",
    "        '''\n",
    "        \n",
    "        order = tuple(order)\n",
    "        self.total_distance = self.getDistance(order,2,0)\n",
    "        self.total_distance += self.distances[order[-1]][order[0]]\n",
    "        \n",
    "        if solution_key is not None:\n",
    "            self.solution_total_dist[solution_key] = self.total_distance \n",
    "            \n",
    "        return self.total_distance\n",
    "        \n",
    "        \n",
    "    def plot(self,solution_key,kind):\n",
    "        '''\n",
    "        Plots all nodes and edges (depending on solution_key) in space.\n",
    "        \n",
    "        solution_key: name of solution\n",
    "        kind: 'char' - only shows node name\n",
    "              'coor' - only shows coordinates of node\n",
    "              'both' - shows both name and coordinates of nodes\n",
    "        '''\n",
    "        \n",
    "        solution_total_dist = str(np.round(self.solution_total_dist[solution_key]\n",
    "                                           ,2)) \n",
    "        \n",
    "        fig, ax = plt.subplots(figsize=(10,10))\n",
    "        self.nodes_df.plot(kind='scatter', \n",
    "                           x='x', y='y',\n",
    "                           title=str(solution_key) +': '+ solution_total_dist, \n",
    "                           grid=True,\n",
    "                           fontsize=10, \n",
    "                           ax=ax,\n",
    "                           xlim = (0,100),\n",
    "                           ylim=(0,100)) \n",
    "        \n",
    "        for i in range(-1,len(self.solutions[solution_key])-1):\n",
    "            j = self.solutions[solution_key][i]\n",
    "            k = self.solutions[solution_key][i+1]\n",
    "            \n",
    "            ax.plot((self.nodes[j][0],self.nodes[k][0]),\n",
    "                    (self.nodes[j][1],self.nodes[k][1]), 'r--')\n",
    "\n",
    "            if kind == 'char':\n",
    "                ax.annotate(j, (self.nodes[j][0],self.nodes[j][1]))\n",
    "            elif kind == 'coor':\n",
    "                ax.annotate((self.nodes[j][0],self.nodes[j][1]), \n",
    "                            (self.nodes[j][0],self.nodes[j][1]))\n",
    "            elif kind == 'both':\n",
    "                ax.annotate(str(j)+ ': ' + str((self.nodes[j][0],self.nodes[j][1])),\n",
    "                           (self.nodes[j][0],self.nodes[j][1]), \n",
    "                            (self.nodes[j][0],self.nodes[j][1]))\n",
    "            \n",
    "            dist = int(self.distances[j][k])\n",
    "            x = (self.nodes[j][0]+self.nodes[k][0])/2\n",
    "            y = (self.nodes[j][1]+self.nodes[k][1])/2\n",
    "            ax.annotate(dist, (x,y),color='green')    \n",
    "            \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "S = Space()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "S.generateNodes(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': [60, 6],\n",
       " 'B': [86, 40],\n",
       " 'C': [25, 9],\n",
       " 'D': [25, 80],\n",
       " 'E': [87, 88],\n",
       " 'F': [52, 41]}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>25</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>86</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>87</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>25</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>60</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>52</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    x   y\n",
       "C  25   9\n",
       "B  86  40\n",
       "E  87  88\n",
       "D  25  80\n",
       "A  60   6\n",
       "F  52  41"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.nodesToDF()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>C</th>\n",
       "      <th>B</th>\n",
       "      <th>E</th>\n",
       "      <th>D</th>\n",
       "      <th>A</th>\n",
       "      <th>F</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>68.425142</td>\n",
       "      <td>100.424101</td>\n",
       "      <td>71.000000</td>\n",
       "      <td>35.128336</td>\n",
       "      <td>41.868843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>68.425142</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>48.010416</td>\n",
       "      <td>72.945185</td>\n",
       "      <td>42.801869</td>\n",
       "      <td>34.014703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>100.424101</td>\n",
       "      <td>48.010416</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>62.513998</td>\n",
       "      <td>86.330759</td>\n",
       "      <td>58.600341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>71.000000</td>\n",
       "      <td>72.945185</td>\n",
       "      <td>62.513998</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>81.859636</td>\n",
       "      <td>47.434165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>35.128336</td>\n",
       "      <td>42.801869</td>\n",
       "      <td>86.330759</td>\n",
       "      <td>81.859636</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>35.902646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>41.868843</td>\n",
       "      <td>34.014703</td>\n",
       "      <td>58.600341</td>\n",
       "      <td>47.434165</td>\n",
       "      <td>35.902646</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            C           B           E           D           A           F\n",
       "C  100.000000   68.425142  100.424101   71.000000   35.128336   41.868843\n",
       "B   68.425142  100.000000   48.010416   72.945185   42.801869   34.014703\n",
       "E  100.424101   48.010416  100.000000   62.513998   86.330759   58.600341\n",
       "D   71.000000   72.945185   62.513998  100.000000   81.859636   47.434165\n",
       "A   35.128336   42.801869   86.330759   81.859636  100.000000   35.902646\n",
       "F   41.868843   34.014703   58.600341   47.434165   35.902646  100.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.getDistances()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Algorithms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parent class of the algorithms with different advantages and disadvantages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Algorithm(object):\n",
    "    '''\n",
    "    Parent class of all solutions\n",
    "    '''\n",
    "    def __init__(self):\n",
    "        self.time = None\n",
    "        \n",
    "    def checkSpace(self,obj):\n",
    "        assert isinstance(obj,Space),'Input must be Space object'\n",
    "    \n",
    "    def solveWithTimer(self,Space,verbose=False):\n",
    "        '''\n",
    "        Input space and saves time in time variable.\n",
    "        '''\n",
    "        start = time.time()\n",
    "        solution = self.solve(Space,verbose)\n",
    "        end = time.time()\n",
    "        self.time = end - start\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Naive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First algorithm is the brute force solution which has two parts. First part is a recursive function that gets all permutations of the sequence of nodes. The second part is calculating the total distance for each sequence while finding the sequence with lowest total distance.\n",
    "\n",
    "***O(n!) *** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Naive(Algorithm):\n",
    "    def __str__(self):\n",
    "        return \"Naive\"\n",
    "    \n",
    "    def permutation(self, order): \n",
    "        '''\n",
    "        Recursive function that returns a list of all permutations of input.\n",
    "        '''\n",
    "        if len(order) == 0: \n",
    "            return [] \n",
    "\n",
    "        if len(order) == 1: \n",
    "            return [order] \n",
    "\n",
    "        current = [] \n",
    "\n",
    "        for i in range(len(order)): \n",
    "            m = order[i] \n",
    "\n",
    "            remaining = order[:i] + order[i+1:] \n",
    "\n",
    "            for p in self.permutation(remaining): \n",
    "                current.append([m] + p) \n",
    "                \n",
    "        return current \n",
    "\n",
    "    \n",
    "    def getPermutations(self, Space):\n",
    "        '''\n",
    "        We will be only using sequences that have the same first element \n",
    "        so that all the solutions will have the same starting and end node.\n",
    "        By doing this we are reducing the total number of permutations \n",
    "        by the number of nodes (N! permutations to N!/N permutations). \n",
    "        To do this, we will only calculates the permutations from the 2nd\n",
    "        node and retain the same first node.\n",
    "        \n",
    "        '''\n",
    "        \n",
    "        node_names = list(Space.nodes.keys())\n",
    "        first = node_names.pop(0)\n",
    "        \n",
    "        Space.permutations = self.permutation(node_names)\n",
    "        \n",
    "        for i in range(len(Space.permutations)):\n",
    "            Space.permutations[i].insert(0,first)\n",
    "            \n",
    "        return Space.permutations\n",
    "\n",
    "    \n",
    "    def getBest(self, Space, verbose):\n",
    "        '''\n",
    "        Loops through all permutations and finds the permutation that \n",
    "        has the least distance.\n",
    "        \n",
    "        verbose: Boolean, show log or not\n",
    "        '''\n",
    "        lowest = 10000000 \n",
    "        lowest_perm = []\n",
    "        total = 0\n",
    "        \n",
    "        if verbose == True:\n",
    "            print('Total Permutations: ', len(Space.permutations))\n",
    "            print()\n",
    "        \n",
    "        for perm in Space.permutations:\n",
    "            perm_dist = Space.getTotalDistance(tuple(perm),'Naive')\n",
    "\n",
    "            if lowest > perm_dist:\n",
    "                if verbose == True:\n",
    "                    \n",
    "                    print('lowest: ',lowest)\n",
    "                    print('lowest_perm: ',lowest_perm)\n",
    "                    print()\n",
    "                lowest = perm_dist\n",
    "                lowest_perm = perm\n",
    "                \n",
    "            total += perm_dist\n",
    "        \n",
    "        Space.getTotalDistance(tuple(lowest_perm),'Naive')\n",
    "        if verbose == True:\n",
    "            print('total distance of all solutions: ',total)\n",
    "        \n",
    "        Space.solution_total_dist['Average'] = total/len(Space.permutations)\n",
    "        if verbose == True:\n",
    "            print('average distance of any solution: ',\n",
    "                  Space.solution_total_dist['Average'])\n",
    "        \n",
    "        \n",
    "        if verbose == True:\n",
    "            print(Space.solution_total_dist['Naive'])\n",
    "            \n",
    "        return lowest_perm\n",
    "    \n",
    "    \n",
    "    def solve(self, Space, verbose=True):\n",
    "        '''\n",
    "        Brute force solution\n",
    "        \n",
    "        verbose: Boolean, show log or not\n",
    "        '''\n",
    "        self.checkSpace(Space)\n",
    "        \n",
    "        self.permutations = self.getPermutations(Space)\n",
    "        naive_solution = self.getBest(Space,verbose)\n",
    "        \n",
    "        Space.solutions['Naive'] = naive_solution\n",
    "        Space.getTotalDistance(Space.solutions['Naive'],'Naive')\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Hashset of distances for memoization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(S.totalDistances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total Permutations:  120\n",
      "\n",
      "lowest:  10000000\n",
      "lowest_perm:  []\n",
      "\n",
      "lowest:  338.58068048318677\n",
      "lowest_perm:  ['C', 'B', 'E', 'D', 'A', 'F']\n",
      "\n",
      "lowest:  297.41470273226514\n",
      "lowest_perm:  ['C', 'B', 'E', 'D', 'F', 'A']\n",
      "\n",
      "lowest:  286.57009895490535\n",
      "lowest_perm:  ['C', 'D', 'E', 'B', 'F', 'A']\n",
      "\n",
      "total distance of all solutions:  42588.486697360684\n",
      "average distance of any solution:  354.90405581133905\n",
      "277.75762696099065\n"
     ]
    }
   ],
   "source": [
    "N = Naive()\n",
    "N.solve(S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Hashmap has increased its length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "356"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(S.totalDistances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x7wpCRsCDm7X2e2PM28BPQDLwM/AKUBKYb4y5AfgbyB//SkqBUKFkUdfK9sRj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\nXH01rFypnjbJlHrcRCR7bN1qe9piYuyQkIhYv/9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7ny0+Hj76yK4kFZFzpjluIuciIQHu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\n7GrWggXtmbXpPf105s+dNg22bTuxR69aNXuf59nevK1b0861BVvMDR9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      "text/plain": [
       "<matplotlib.figure.Figure at 0x15b86a6fc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "S.plot('Naive','both')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Greedy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finds whats the best decision momentarily but may not necesarily be the best results in the overall structure of the problem. This strategy does not get the most optimal solution however it is extremely fast.\n",
    "\n",
    "***O(n^2) to O(n)***  Getting min is O(n) * total number of nodes (n),  but n is decreasing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Greedy(Algorithm):\n",
    "    def __str__(self):\n",
    "        return \"Greedy\"\n",
    "    \n",
    "    def getMinRowCol(self, df):\n",
    "        '''\n",
    "        Get minimum distance value between any two nodes in the Dataframe\n",
    "        \n",
    "        df: pandas dataframe of distances from col name to row index or vice versa.\n",
    "        '''\n",
    "        row, col = df.stack().idxmin()\n",
    "        return row,col\n",
    "\n",
    "    def solve(self, Space, verbose=True):\n",
    "        '''\n",
    "        Gets minimum distance value between any two nodes and then finds the \n",
    "        least distance to the next node for every succeeding nodes.\n",
    "        \n",
    "        verbose: Boolean, show log or not\n",
    "        \n",
    "        '''\n",
    "        \n",
    "        self.checkSpace(Space)\n",
    "        \n",
    "        visited_list = list()\n",
    "\n",
    "        row,col = self.getMinRowCol(Space.distances)\n",
    "        latest = col\n",
    "        visited_list.append(row)\n",
    "        visited_list.append(latest)\n",
    "        \n",
    "        if verbose == True:\n",
    "            print('minimum distance from any two nodes:')\n",
    "            print(str(row) + ' to ' + str(col) + ': ' + \\\n",
    "                  str(Space.distances[row][col]))\n",
    "            print('')\n",
    "            print('minimum distance following prev node:')\n",
    "                \n",
    "        for i in range(len(Space.distances.columns)-2):\n",
    "            latest = Space.distances.drop(visited_list).idxmin()[latest]\n",
    "            visited_list.append(latest)\n",
    "            if verbose == True:\n",
    "                print(str(visited_list[-2]) \n",
    "                      + ' to ' \n",
    "                      + str(visited_list[-1]) \n",
    "                      + ': ' \n",
    "                      + str(Space.distances[visited_list[-2]][visited_list[-1]]))\n",
    "                \n",
    "        Space.solutions['Greedy'] = visited_list    \n",
    "        Space.getTotalDistance(Space.solutions['Greedy'],'Greedy')\n",
    "        \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = Greedy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum distance from any two nodes:\n",
      "B to F: 34.0147027033899\n",
      "\n",
      "minimum distance following prev node:\n",
      "F to A: 35.90264614203248\n",
      "A to C: 35.12833614050059\n",
      "C to D: 71.0\n",
      "D to E: 62.51399843235114\n"
     ]
    }
   ],
   "source": [
    "G.solve(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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89540fLi0erXvSkKD4AYAAKqH7UCSjuCGcLj3XjcAAPHDBrxJR3BDOLz6qhsA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15b88d7fac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "S.plot('Greedy','char')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimization: Integer Programming"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Integer programming is when you minimize/maximize an objective function by adjusting its the weights which can only be integers. Constraints are the different rules that has to be followed in the optimization process. In this application, we put weights (0 or 1) on each edge and that will be our objective function. As for the constraints we have two: \n",
    "\n",
    "* Only one path can exit each node\n",
    "* Only one path can enter each node\n",
    "\n",
    "Given that we optimize using the above constraints, we will encounter the issue of subtours. This is when the solution is only locally connected (ie (A->B),(B->A),(C->D),(D->C)). To rectify this, we will more add contstraints that are specific to each subtour (ie (A->B) + (B->A) <= 1) and optimize again. As we add constraints that eliminates subtours, it is likely that more subtour will emerge. We will keep repeating this process until all subtours are eliminated then we will have an optimal solution.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Optimization(Algorithm):\n",
    "    def __str__(self):\n",
    "        return \"Optimization\"\n",
    "    \n",
    "    \n",
    "    def solutionToTuple(self, model):\n",
    "        '''\n",
    "        model: pulp object\n",
    "        '''\n",
    "        output = []\n",
    "        for v in model.variables():\n",
    "            if v.varValue>0:\n",
    "                name = v.name[5:]\n",
    "                r = name[name.rfind('_to_')+4:]\n",
    "                l = name[:name.rfind('_to_')]\n",
    "                output.append((l,r))\n",
    "                \n",
    "        return output\n",
    "\n",
    "\n",
    "    def identifySubtourFromTuples(self, Space, list_of_tuples):\n",
    "        '''\n",
    "        Outputs a list of subtours from list a list of touples\n",
    "        \n",
    "        list_of_tuples: list of tuples where 0th index of each tuple is the \n",
    "        starting node and the 1st index is the end node. Each tuple represents \n",
    "        an edge.  \n",
    "        \n",
    "        '''\n",
    "        subtours = []\n",
    "        subtour = []\n",
    "\n",
    "        i = 0\n",
    "\n",
    "        while len(list_of_tuples)>0:\n",
    "            next_node = list_of_tuples[i][1]\n",
    "            subtour.append(list_of_tuples[i])\n",
    "            list_of_tuples.pop(i)\n",
    "            j = 0\n",
    "            subtour_end = False\n",
    "            while subtour_end == False:\n",
    "                j = 0\n",
    "                while (j < len(list_of_tuples)):\n",
    "                    if next_node == list_of_tuples[j][0]:\n",
    "                        subtour.append(list_of_tuples[j])\n",
    "                        next_node = list_of_tuples[j][1]\n",
    "                        list_of_tuples.pop(j)\n",
    "                        j = 0\n",
    "                        break\n",
    "                    j += 1\n",
    "\n",
    "                if j == len(list_of_tuples):\n",
    "                    subtour_end = True\n",
    "\n",
    "            subtours.append(subtour)\n",
    "            subtour = []\n",
    "            \n",
    "        return subtours\n",
    "\n",
    "    \n",
    "    def getColInd(self,node_tuple,Space):\n",
    "        '''\n",
    "        Input a tuple of node names and returns the row and column index\n",
    "        \n",
    "        node_tuple: tuple of two nodes that signify an edge\n",
    "        '''\n",
    "        col = list(Space.distances.columns).index(node_tuple[0])\n",
    "        row = list(Space.distances.index).index(node_tuple[1])\n",
    "        \n",
    "        return col,row\n",
    "    \n",
    "    \n",
    "    def addNewConstraints(self,Space,subtours):\n",
    "        '''\n",
    "        Adds new contraints to eliminate subtours\n",
    "        \n",
    "        subtours: list of subtours\n",
    "        '''\n",
    "        new_constraints = []\n",
    "        for subtour in subtours:\n",
    "            new_constraint = np.zeros(Space.distances.shape)\n",
    "            for node in subtour:\n",
    "                row,col = self.getColInd(node,Space)\n",
    "                new_constraint[row][col] = 1\n",
    "            new_constraints.append(new_constraint.flatten())\n",
    "            \n",
    "        return new_constraints\n",
    "    \n",
    "    \n",
    "    def tupleToSolution(self,subtours):#subtourToSolution\n",
    "        '''\n",
    "        Converts list tuples into solution format\n",
    "        '''\n",
    "        solution = []\n",
    "        for subtour in subtours[0]:\n",
    "            solution.append(subtour[0])\n",
    "\n",
    "        return solution\n",
    "    \n",
    "    \n",
    "    def solve(self,Space,verbose=True):\n",
    "        '''\n",
    "        Solve using integer programming. Iteratively adds more constraints \n",
    "        until an acceptable solution is found.\n",
    "        '''\n",
    "        \n",
    "        self.checkSpace(Space)\n",
    "        \n",
    "        constraint = np.zeros([len(Space), len(Space)**2])\n",
    "\n",
    "        constraint1 = constraint.copy()#only one edge enter one node\n",
    "        constraint2 = constraint.copy()#only one path that exit one node\n",
    "    \n",
    "        for i in range(len(Space)):\n",
    "            constraint1[i][i*len(Space):(i+1)*len(Space)] += 1\n",
    "        for i in range(len(Space)):\n",
    "            constraint2[:,(i)*len(Space):(i+1)*len(Space)] += \\\n",
    "            np.identity(len(Space))\n",
    "        \n",
    "\n",
    "        constraints = np.concatenate([constraint1,constraint2],axis=0)\n",
    "\n",
    "        model = pulp.LpProblem(\"TSP\", pulp.LpMinimize)\n",
    "\n",
    "        path_names = []\n",
    "\n",
    "        for i in Space.distances.columns:\n",
    "            for j in Space.distances.index:\n",
    "                path_names.append(i + ' to ' + j)\n",
    "\n",
    "        costs = []\n",
    "\n",
    "        for row in Space.distances:\n",
    "            costs.extend(Space.distances[row].values)\n",
    "\n",
    "        costs_dict = dict(zip(path_names,costs))\n",
    "\n",
    "        path_vars = pulp.LpVariable.dicts(\"path\", path_names,\n",
    "                                          lowBound=0, cat='Integer')\n",
    "\n",
    "        model += pulp.lpSum([costs_dict[i]*path_vars[i] for i in path_names])\n",
    "\n",
    "        for i in range(constraints.shape[0]):\n",
    "            model += pulp.lpSum([constraints[i][j] * path_vars[path_names[j]] for j in range(len(path_names))]) >= 1, \"constraints_\"+str(i)\n",
    "        \n",
    "        if verbose == True:\n",
    "            print(model)\n",
    "\n",
    "        tsp_iteration = 0\n",
    "        num_subtour = 1000\n",
    "\n",
    "        while (num_subtour>1):\n",
    "            model.solve()\n",
    "            if verbose == True:\n",
    "                print()\n",
    "                print()\n",
    "                print(\"Status:\", pulp.LpStatus[model.status])\n",
    "                print('TSP iteration: ', tsp_iteration)\n",
    "                print('total distance: ', str(pulp.value(model.objective)))\n",
    "\n",
    "            solution = []\n",
    "            for v in model.variables():\n",
    "                solution.append(v.name)\n",
    "\n",
    "            list_of_tuples = self.solutionToTuple(model)\n",
    "\n",
    "            subtours = self.identifySubtourFromTuples(Space,list_of_tuples)\n",
    "            num_subtour = len(subtours)\n",
    "            if verbose == True:\n",
    "                print('subtours: ')\n",
    "                for subtour in subtours:\n",
    "                    print(subtour)\n",
    "                print()\n",
    "\n",
    "            new_constraints = self.addNewConstraints(Space,subtours)\n",
    "\n",
    "            tsp_iteration += 1\n",
    "            new_constraint_names = []\n",
    "            for i in range(len(new_constraints)):\n",
    "                new_constraint_name = \"subtour_constraints_\" + str(tsp_iteration) + '_'+str(i) \n",
    "                new_constraint_names.append(new_constraint_name)\n",
    "    \n",
    "                model += pulp.lpSum([new_constraints[i][j] * path_vars[path_names[j]] for j in range(len(path_names))]) <= sum(new_constraints[i])-1, new_constraint_name\n",
    "            \n",
    "            if verbose == True:\n",
    "                print('new constraints: ',len(model.constraints))\n",
    "                for constraint_name in new_constraint_names:\n",
    "                    print(model.constraints[constraint_name])\n",
    "                \n",
    "                print('===============================================================================')\n",
    "                print()\n",
    "\n",
    "        if verbose == True:\n",
    "            print('total distance: '+str(pulp.value(model.objective)))\n",
    "            for subtour in subtours:\n",
    "                    print(subtour)\n",
    "                    \n",
    "        Space.solutions['Optimization'] = self.tupleToSolution(subtours)\n",
    "        Space.getTotalDistance(Space.solutions['Optimization'], 'Optimization')\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "O = Optimization()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TSP:\n",
      "MINIMIZE\n",
      "100.0*path_A_to_A + 42.80186911806539*path_A_to_B + 35.12833614050059*path_A_to_C + 81.85963596303125*path_A_to_D + 86.33075929238663*path_A_to_E + 35.90264614203248*path_A_to_F + 42.80186911806539*path_B_to_A + 100.0*path_B_to_B + 68.42514157822401*path_B_to_C + 72.94518489934754*path_B_to_D + 48.010415536631214*path_B_to_E + 34.0147027033899*path_B_to_F + 35.12833614050059*path_C_to_A + 68.42514157822401*path_C_to_B + 100.0*path_C_to_C + 71.0*path_C_to_D + 100.42410069301094*path_C_to_E + 41.86884283091664*path_C_to_F + 81.85963596303125*path_D_to_A + 72.94518489934754*path_D_to_B + 71.0*path_D_to_C + 100.0*path_D_to_D + 62.51399843235114*path_D_to_E + 47.43416490252569*path_D_to_F + 86.33075929238663*path_E_to_A + 48.010415536631214*path_E_to_B + 100.42410069301094*path_E_to_C + 62.51399843235114*path_E_to_D + 100.0*path_E_to_E + 58.60034129593445*path_E_to_F + 35.90264614203248*path_F_to_A + 34.0147027033899*path_F_to_B + 41.86884283091664*path_F_to_C + 47.43416490252569*path_F_to_D + 58.60034129593445*path_F_to_E + 100.0*path_F_to_F + 0.0\n",
      "SUBJECT TO\n",
      "constraints_0: path_C_to_A + path_C_to_B + path_C_to_C + path_C_to_D\n",
      " + path_C_to_E + path_C_to_F >= 1\n",
      "\n",
      "constraints_1: path_B_to_A + path_B_to_B + path_B_to_C + path_B_to_D\n",
      " + path_B_to_E + path_B_to_F >= 1\n",
      "\n",
      "constraints_2: path_E_to_A + path_E_to_B + path_E_to_C + path_E_to_D\n",
      " + path_E_to_E + path_E_to_F >= 1\n",
      "\n",
      "constraints_3: path_D_to_A + path_D_to_B + path_D_to_C + path_D_to_D\n",
      " + path_D_to_E + path_D_to_F >= 1\n",
      "\n",
      "constraints_4: path_A_to_A + path_A_to_B + path_A_to_C + path_A_to_D\n",
      " + path_A_to_E + path_A_to_F >= 1\n",
      "\n",
      "constraints_5: path_F_to_A + path_F_to_B + path_F_to_C + path_F_to_D\n",
      " + path_F_to_E + path_F_to_F >= 1\n",
      "\n",
      "constraints_6: path_A_to_C + path_B_to_C + path_C_to_C + path_D_to_C\n",
      " + path_E_to_C + path_F_to_C >= 1\n",
      "\n",
      "constraints_7: path_A_to_B + path_B_to_B + path_C_to_B + path_D_to_B\n",
      " + path_E_to_B + path_F_to_B >= 1\n",
      "\n",
      "constraints_8: path_A_to_E + path_B_to_E + path_C_to_E + path_D_to_E\n",
      " + path_E_to_E + path_F_to_E >= 1\n",
      "\n",
      "constraints_9: path_A_to_D + path_B_to_D + path_C_to_D + path_D_to_D\n",
      " + path_E_to_D + path_F_to_D >= 1\n",
      "\n",
      "constraints_10: path_A_to_A + path_B_to_A + path_C_to_A + path_D_to_A\n",
      " + path_E_to_A + path_F_to_A >= 1\n",
      "\n",
      "constraints_11: path_A_to_F + path_B_to_F + path_C_to_F + path_D_to_F\n",
      " + path_E_to_F + path_F_to_F >= 1\n",
      "\n",
      "VARIABLES\n",
      "0 <= path_A_to_A Integer\n",
      "0 <= path_A_to_B Integer\n",
      "0 <= path_A_to_C Integer\n",
      "0 <= path_A_to_D Integer\n",
      "0 <= path_A_to_E Integer\n",
      "0 <= path_A_to_F Integer\n",
      "0 <= path_B_to_A Integer\n",
      "0 <= path_B_to_B Integer\n",
      "0 <= path_B_to_C Integer\n",
      "0 <= path_B_to_D Integer\n",
      "0 <= path_B_to_E Integer\n",
      "0 <= path_B_to_F Integer\n",
      "0 <= path_C_to_A Integer\n",
      "0 <= path_C_to_B Integer\n",
      "0 <= path_C_to_C Integer\n",
      "0 <= path_C_to_D Integer\n",
      "0 <= path_C_to_E Integer\n",
      "0 <= path_C_to_F Integer\n",
      "0 <= path_D_to_A Integer\n",
      "0 <= path_D_to_B Integer\n",
      "0 <= path_D_to_C Integer\n",
      "0 <= path_D_to_D Integer\n",
      "0 <= path_D_to_E Integer\n",
      "0 <= path_D_to_F Integer\n",
      "0 <= path_E_to_A Integer\n",
      "0 <= path_E_to_B Integer\n",
      "0 <= path_E_to_C Integer\n",
      "0 <= path_E_to_D Integer\n",
      "0 <= path_E_to_E Integer\n",
      "0 <= path_E_to_F Integer\n",
      "0 <= path_F_to_A Integer\n",
      "0 <= path_F_to_B Integer\n",
      "0 <= path_F_to_C Integer\n",
      "0 <= path_F_to_D Integer\n",
      "0 <= path_F_to_E Integer\n",
      "0 <= path_F_to_F Integer\n",
      "\n",
      "\n",
      "\n",
      "Status: Optimal\n",
      "TSP iteration:  0\n",
      "total distance:  261.145833159315\n",
      "subtours: \n",
      "[('A', 'C'), ('C', 'A')]\n",
      "[('B', 'E'), ('E', 'B')]\n",
      "[('D', 'F'), ('F', 'D')]\n",
      "\n",
      "new constraints:  15\n",
      "path_A_to_C + path_C_to_A <= 1.0\n",
      "path_B_to_E + path_E_to_B <= 1.0\n",
      "path_D_to_F + path_F_to_D <= 1.0\n",
      "===============================================================================\n",
      "\n",
      "\n",
      "\n",
      "Status: Optimal\n",
      "TSP iteration:  1\n",
      "total distance:  277.75762696099065\n",
      "subtours: \n",
      "[('A', 'B'), ('B', 'E'), ('E', 'D'), ('D', 'F'), ('F', 'C'), ('C', 'A')]\n",
      "\n",
      "new constraints:  16\n",
      "path_A_to_B + path_B_to_E + path_C_to_A + path_D_to_F + path_E_to_D + path_F_to_C <= 5.0\n",
      "===============================================================================\n",
      "\n",
      "total distance: 277.75762696099065\n",
      "[('A', 'B'), ('B', 'E'), ('E', 'D'), ('D', 'F'), ('F', 'C'), ('C', 'A')]\n"
     ]
    }
   ],
   "source": [
    "O.solve(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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ZrVruvBtucB8FJSUFgFrVK0A+QxtAjRo1jjnj1AvDhw/3uoTjUnATERHxUkpKVjCLjHQt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15b88d6be80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "S.plot('Optimization','both')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def benchmark(low,high,step=1,include_naive=True):\n",
    "    '''\n",
    "    Plots computational time of different algorithms and their accuracies given a range.\n",
    "    \n",
    "    low: lower bound of range to compute\n",
    "    high: upper bound of range to compute\n",
    "    '''\n",
    "    \n",
    "    time_df = pd.DataFrame()\n",
    "    dist_df = pd.DataFrame()\n",
    "    \n",
    "\n",
    "    for i in range(low,high,step):\n",
    "        print('Calculating with Nodes:', i)\n",
    "        S = Space()\n",
    "        S.generateNodes(i)\n",
    "        S.nodesToDF()\n",
    "        S.getDistances()\n",
    "        \n",
    "        algorithms = []\n",
    "        for cls in Algorithm.__subclasses__():\n",
    "            if str(cls.__name__) == 'Naive':\n",
    "                if include_naive == True:\n",
    "                    algorithms.append(cls())\n",
    "                else:\n",
    "                    pass\n",
    "            else:\n",
    "                algorithms.append(cls())\n",
    "\n",
    "        for algorithm in algorithms:\n",
    "            algorithm.solveWithTimer(S)\n",
    "        \n",
    "        time_dict = {}\n",
    "        dist_dict = {}\n",
    "        for algorithm in algorithms:\n",
    "            time_dict[str(algorithm)] = [algorithm.time]\n",
    "            dist_dict[str(algorithm)] = [S.solution_total_dist[str(algorithm)]]\n",
    "            \n",
    "        if include_naive == True:\n",
    "            dist_dict['Average'] = [S.solution_total_dist['Average']]\n",
    "        \n",
    "        time_df = time_df.append(pd.DataFrame(data = time_dict,index = [i]))\n",
    "        dist_df = dist_df.append(pd.DataFrame(data = dist_dict,index = [i]))\n",
    "        \n",
    "        \n",
    "    axes = ()*len(algorithms)\n",
    "    fig,axes  = plt.subplots(1,len(algorithms))\n",
    "    fig.suptitle('Computational Time')\n",
    "    fig.legends\n",
    "    fig.set_figwidth(15)\n",
    "\n",
    "    counter = 0\n",
    "    for ax in axes:\n",
    "        ax.plot(time_df[str(algorithms[counter])])\n",
    "        ax.legend(loc=\"upper right\")\n",
    "        ax.set_xlabel('Num of Nodes')\n",
    "        ax.set_ylabel('Time (Sec)')\n",
    "        counter +=1\n",
    "\n",
    "    \n",
    "    if include_naive == True:\n",
    "        bench = \"Naive\"\n",
    "    else:\n",
    "        bench = \"Optimization\"\n",
    "        \n",
    "    bench_df = dist_df[bench]\n",
    "    dist_df = dist_df.subtract(dist_df[bench], axis=0)\n",
    "    dist_df = dist_df.div(bench_df, axis=0)\n",
    "    dist_df.drop(bench, axis=1, inplace=True)\n",
    "    dist_df.plot(kind='line', title='Percent Error vs ' + str(bench), ylim=(-.1,1.1), figsize=(12,4))\n",
    "        \n",
    "    del algorithms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating with Nodes: 4\n",
      "Calculating with Nodes: 5\n",
      "Calculating with Nodes: 6\n",
      "Calculating with Nodes: 7\n",
      "Calculating with Nodes: 8\n",
      "Calculating with Nodes: 9\n",
      "Calculating with Nodes: 10\n"
     ]
    },
    {
     "data": {
      "image/png": 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MT9s65RWHZLpvWwGMqlB2BBhWm7iNaS42p+WwKS2HByYO8HUoxhjTaPzrs21k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\n07ZdVVxx/5vsrKrh4WunMLQF+eTIvl354zc+x40nD+fJJaW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ZdOuUS7dOOXTvlEuPzh0Y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15bf0e49fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4cttBnrxmOD+5dLACsvhUc0aSdwFJXrcTPce83Qb8xjor7rYZY3YAg4CvW6RK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\nkiRJLYZkSZIkqcWQLEmSJLX8HzFDPJG0eQo7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15b88aed400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "benchmark(4,11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating with Nodes: 10\n",
      "Calculating with Nodes: 15\n",
      "Calculating with Nodes: 20\n",
      "Calculating with Nodes: 25\n",
      "Calculating with Nodes: 30\n",
      "Calculating with Nodes: 35\n"
     ]
    },
    {
     "data": {
      "image/png": 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Te7ehSWpsj8aKnWkIRSTm/OvL1Xy9agsPnT+QNo1jd6x8ZZT2Jp58RBtuenke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\ni3lzLBUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15b853f87b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uOSMe1CBNtpQSTW3HeCRnpLm5/RgAc0sKWVtXNfSAk0uWzqOwYPij1V9JSB7T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\npHGgFiIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15b88d75d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "benchmark(10,40,5,False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}