5 Graph Theory and Planning Algorithms.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "  # We must install required packages if we are in Google Colab\n",
    "  import google.colab\n",
    "  %pip install roboticstoolbox-python>=1.0.2\n",
    "except:\n",
    "  # We are not in Google Colab\n",
    "  # Apply custon style to notebook\n",
    "  from IPython.core.display import HTML\n",
    "  import pathlib\n",
    "  styles_path = pathlib.Path(pathlib.Path().absolute(), \"style\", \"style.css\")\n",
    "  styles = open(styles_path, \"r\").read()\n",
    "  HTML(f\"<style>{styles}</style>\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\large{\\text{Foundations of Kinematics and Algorithms in Robotics}} \\\\ \\large{\\text{Module 5: Graph Theory and Planning Algorithms}}$\n",
    "\n",
    "$\\text{By Jesse Haviland and Peter Corke}$\n",
    "\n",
    "<br>\n",
    "\n",
    "### Contents\n",
    "\n",
    "[1.0 Graphs](#1)  \n",
    "[2.0 Graph Search](#2)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We will do the imports required for this notebook here\n",
    "\n",
    "# numpy provides import array and linear algebra utilities\n",
    "import numpy as np\n",
    "np.random.seed(0)\n",
    "\n",
    "# the robotics toolbox provides robotics specific functionality\n",
    "import roboticstoolbox as rtb\n",
    "\n",
    "# spatial math provides objects for representing transformations\n",
    "import spatialmath.base as smb\n",
    "\n",
    "import pgraph as pg"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "<a id='1'></a>\n",
    "# 1.0 Graphs\n",
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A graph is an abstract representation of a set of objects connected by links and depicted visually. Mathematically, a graph is denoted by $G(V, E)$ where $V$ are the vertices or nodes, and $E$ are the links that connect pairs of vertices and are called edges or arcs. Edges can be directed (shown as arrows) or undirected (shown as line segments). Edges can have a weight or cost associated with moving from one vertex to another. A sequence of edges from one vertex to another is a path, and a sequence that starts and ends at the same vertex is a cycle. An edge from a vertex to itself is a loop. Graphs can be used to represent transport, communications or social networks, and this branch of mathematics is graph theory.\n",
    "\n",
    "We will illustrate graphs using the Python package `pgraph` that supports embedded graphs where the vertices are associated with a point in an n-dimensional space. To create a new graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = pg.UGraph()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and, by default, the vertices of the graph exist in 2-dimensional space. We can add ﬁve randomly-placed vertices to the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(5):\n",
    "    g.add_vertex(np.random.rand(2))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The method add_vertex returns a reference to the newly created vertex object, but we can obtain the reference by indexing the graph object. For example vertex 1 is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "UVertex[#1, coord=(0.6028, 0.5449)]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[1]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and is an instance of UVertex, a vertex in an undirected graph; it has the coordinate $(0.6028; 0.5449)$; and has been assigned a default name `\"#1\"` but we could specify a different name. We can also reference a vertex by its name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "UVertex[#1, coord=(0.6028, 0.5449)]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"#1\"]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can create edges between pairs of vertex objects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Edge{[#3] -- [#4], cost=0.7315}"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.add_edge(g[0], g[1])\n",
    "g.add_edge(g[0], g[2])\n",
    "g.add_edge(g[0], g[3])\n",
    "g.add_edge(g[1], g[2])\n",
    "g.add_edge(g[1], g[3])\n",
    "g.add_edge(g[3], g[4])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the `add_edge` method returns a reference to the edge object just created. By default, the edge cost is the Euclidean distance between the vertices, but this can be overridden by a third argument to add_edge.\n",
    "\n",
    "A summary of the graph can be displayed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UGraph: 5 vertices, 6 edges, 1 component\n"
     ]
    }
   ],
   "source": [
    "print(g)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This graph has one component, that is, all the vertices are connected into one network. The graph can be plotted by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g.plot()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The vertices are shown as blue circles, and the edges are shown as lines joining vertices. Many options exist to change default plotting behaviour. Note that only graphs embedded in 2- and 3-dimensional space can be plotted.\n",
    "\n",
    "The neighbors of vertex 1 are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[UVertex[#0, coord=(0.5488, 0.7152)],\n",
       " UVertex[#2, coord=(0.4237, 0.6459)],\n",
       " UVertex[#3, coord=(0.4376, 0.8918)]]"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[1].adjacent()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which is a list of neighbouring vertex objects, those connected to it by an edge. Each edge is an object and the edges connecting to vertex 1 are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[#0] -- [#1], cost=0.1786},\n",
       " Edge{[#1] -- [#2], cost=0.2056},\n",
       " Edge{[#1] -- [#3], cost=0.3842}]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[1].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and each edge has references to the vertices it connects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[UVertex[#0, coord=(0.5488, 0.7152)], UVertex[#1, coord=(0.6028, 0.5449)]]"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[1].edges()[0].endpoints"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cost or length of an edge is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1786470956951876"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[1].edges()[0].cost"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Arbitrary data can be attached to any vertex or edge by adding attributes to the vertex or edge objects, or by subclassing the UVertex and Edge classes.\n",
    "\n",
    "The vertex closest to the coordinate (0.5, 0.5) is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(UVertex[#1, coord=(0.6028, 0.5449)], 0.11213746732281339)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.closest((0.5, 0.5))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A tree is a specific type of graph with a tree-like hierarchical layout. Each node can have many child nodes but only one parent node. The root node is the only node that has no parent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make a tree using PGraph\n",
    "\n",
    "g = pg.UGraph()\n",
    "g.add_vertex(name=\"A\", coord=(0, 10))\n",
    "g.add_vertex(name=\"B\", coord=(-4, 8))\n",
    "g.add_vertex(name=\"C\", coord=(2, 8))\n",
    "g.add_vertex(name=\"D\", coord=(-6, 6))\n",
    "g.add_vertex(name=\"E\", coord=(-2, 6))\n",
    "g.add_vertex(name=\"F\", coord=(2, 6))\n",
    "\n",
    "g.add_edge(\"A\", \"B\")\n",
    "g.add_edge(\"A\", \"C\")\n",
    "g.add_edge(\"B\", \"D\")\n",
    "g.add_edge(\"B\", \"E\")\n",
    "g.add_edge(\"C\", \"F\")\n",
    "\n",
    "g.plot()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Trees are far easier to deal with than a general graph as there are no cycles or closed-loops. There is also only one solution for how to get from the root node to any other node."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "<a id='2'></a>\n",
    "# 2.0 Tree Search\n",
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As searching through trees are much easier, we will start with searching through trees.\n",
    "\n",
    "We will use the following tree for the following examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UGraph: 10 vertices, 9 edges, 1 component\n"
     ]
    }
   ],
   "source": [
    "ex_tree = pg.UGraph()\n",
    "ex_tree.add_vertex(name=\"A\")\n",
    "ex_tree.add_vertex(name=\"B\")\n",
    "ex_tree.add_vertex(name=\"C\")\n",
    "ex_tree.add_vertex(name=\"D\")\n",
    "ex_tree.add_vertex(name=\"E\")\n",
    "ex_tree.add_vertex(name=\"F\")\n",
    "ex_tree.add_vertex(name=\"G\")\n",
    "ex_tree.add_vertex(name=\"H\")\n",
    "ex_tree.add_vertex(name=\"I\")\n",
    "ex_tree.add_vertex(name=\"J\")\n",
    "\n",
    "ex_tree.add_edge(\"A\", \"B\")\n",
    "ex_tree.add_edge(\"A\", \"C\")\n",
    "ex_tree.add_edge(\"B\", \"D\")\n",
    "ex_tree.add_edge(\"B\", \"E\")\n",
    "ex_tree.add_edge(\"C\", \"F\")\n",
    "ex_tree.add_edge(\"E\", \"G\")\n",
    "ex_tree.add_edge(\"E\", \"H\")\n",
    "ex_tree.add_edge(\"F\", \"I\")\n",
    "ex_tree.add_edge(\"F\", \"J\")\n",
    "\n",
    "print(ex_tree)\n",
    "\n",
    "# You can use the showgraph method to generate a PDF of the graph\n",
    "# tree.showgraph()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"Figures/5/tree.png\" alt=\"dfs\" style=\"width: 400px\" />"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Depth First Search"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With depth-first search (DFS), we search down the tree until we reach a _leaf_ (where a leaf node is a node with no children). We then backtrack up the tree until we reach a node that has an unexplored child node. We then explore that child node and repeat the process."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A depth first traversal of the tree `ex_tree` would happen in the following order (assuming we visit the leftmost unvisited child first):\n",
    "\n",
    "A -> B -> D -> E -> G -> H -> C -> F -> I -> J"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since a tree has no cycles, we do not need to keep a visited list or frontier list (which we will introduce later) and we can solve the search problem fairly easily using recursion.\n",
    "\n",
    "We wish to find a path between A and J in the graph. We will use the following algorithm to do so:\n",
    "\n",
    "On each recursion, we check if the current node is the goal node, if it is then we return the goal node and a signal that the goal was found. If it is not the goal node, we then check if the current node has any children. If it does, we then recursively call the function on each child node. If it does not, we return a signal that the goal was not found.\n",
    "\n",
    "*Search 0*\n",
    "\n",
    "Perform search on A  \n",
    "A is not goal node  \n",
    "A has two children  \n",
    "Recursive search on B (Search 1)  \n",
    "Recursive search on C (Search 6)  \n",
    "Return A -> C -> F -> J and signal that goal was found  \n",
    "\n",
    "*Search 1*\n",
    "\n",
    "Perform search on B  \n",
    "B is not goal node  \n",
    "B has two children  \n",
    "Recursive search on D (Search 2)  \n",
    "Recursive search on E (Search 3)  \n",
    "Return signal that goal was not found  \n",
    "\n",
    "*Search 2*\n",
    "\n",
    "Perform search on D  \n",
    "D is not goal node  \n",
    "D has no children  \n",
    "Return signal that goal was not found  \n",
    "  \n",
    "*Search 3*  \n",
    "  \n",
    "Perform search on E (called from Search 1)  \n",
    "E is not goal node  \n",
    "E has two children  \n",
    "Recursive search on G (Search 4)  \n",
    "Recursive search on H (Search 5)  \n",
    "Return signal that goal was not found  \n",
    "  \n",
    "*Search 4*  \n",
    "  \n",
    "Perform search on G  \n",
    "G is not goal node  \n",
    "G has no children  \n",
    "Return signal that goal was not found  \n",
    "  \n",
    "*Search 5*  \n",
    "  \n",
    "Perform search on H (called from Search 3)  \n",
    "H is not goal node  \n",
    "H has no children  \n",
    "Return signal that goal was not found  \n",
    "  \n",
    "*Search 6*  \n",
    "  \n",
    "Perform search on C (called from Search 0)  \n",
    "C is not goal node  \n",
    "C has one child  \n",
    "Recursive search on F (Search 7)  \n",
    "  \n",
    "Return C -> F -> J and signal that goal was found  \n",
    "  \n",
    "*Search 7*  \n",
    "  \n",
    "Perform search on F  \n",
    "F is not goal node  \n",
    "F has two children  \n",
    "Recursive search on I (Search 8)  \n",
    "Recursive search on J (Search 9)  \n",
    "  \n",
    "Return F -> J and signal that goal was found  \n",
    "  \n",
    "*Search 8*  \n",
    "  \n",
    "Perform search on I  \n",
    "I is not goal node  \n",
    "I has no children  \n",
    "Return signal that goal was not found  \n",
    "  \n",
    "*Search 9*  \n",
    "  \n",
    "Perform search on J (called from Search 7)  \n",
    "J is goal node  \n",
    "Return J and signal that goal was found  \n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After 10 recursive calls of our search function we have obtained the path A -> C -> F -> J."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Breadth First Search"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With breadth first search (BFS), we search across the tree level by level. We start at the root node and search all of its children. We then search all of the children of those children and so on. We can think of this as searching the tree in a wave-like pattern.\n",
    "\n",
    "A breadth first traversal of the tree `ex_tree` would happen in the following order:\n",
    "\n",
    "A -> B -> C -> D -> E -> F -> G -> H -> I -> J\n",
    "\n",
    "We keep a frontier list which is a first in - first out (fifo) queue and keeps track of where we need to go next. We will also keep track of the parent node that took us to the child node so we can reconstruct the path later. We will call this the parents list and store pairs (node, parent) in it.\n",
    "\n",
    "We wish to find a path between A and J in the graph. We will use the following algorithm to do so:\n",
    "\n",
    "On each loop, we take the first value from the frontier list. If it is not the goal node, we then check if the current node has any children. If it does, we then add each child to the frontier list. If it is the goal node, then we reconstruct the path by following from the goal node back to the root node using the parents list.\n",
    "\n",
    "Initialise frontier with root node  \n",
    "frontier = [A]  \n",
    "parents = {A: None}  \n",
    "  \n",
    "*Iteration 0*  \n",
    "  \n",
    "Take first element from frontier list: A  \n",
    "A is not goal node and has two children  \n",
    "Add B and C to frontier list  \n",
    "frontier = [B, C]  \n",
    "parents = {A: None, B: A, C: A}  \n",
    "  \n",
    "*Iteration 1*  \n",
    "  \n",
    "Take first element from frontier list: B  \n",
    "B is not goal node and has two children  \n",
    "Add D and E to frontier list  \n",
    "frontier = [C, D, E]  \n",
    "parents = {A: None, B: A, C: A, D: B, E: B}  \n",
    "  \n",
    "*Iteration 2*  \n",
    "  \n",
    "Take first element from frontier list: C  \n",
    "C is not goal node and has one child  \n",
    "Add F to frontier list  \n",
    "frontier = [D, E, F]  \n",
    "parents = {A: None, B: A, C: A, D: B, E: B, F: C}  \n",
    "  \n",
    "*Iteration 3*  \n",
    "  \n",
    "Take first element from frontier list: D  \n",
    "D is not goal node and has no children  \n",
    "frontier = [E, F]  \n",
    "parents = {A: None, B: A, C: A, D: B, E: B, F: C}  \n",
    "  \n",
    "*Iteration 4*  \n",
    "  \n",
    "Take first element from frontier list: E  \n",
    "E is not goal node and has two children  \n",
    "Add G and H to frontier list  \n",
    "frontier = [F, G, H]  \n",
    "parents = {A: None, B: A, C: A, D: B, E: B, F: C, G: E, H: E}  \n",
    "  \n",
    "*Iteration 5*  \n",
    "  \n",
    "Take first element from frontier list: F  \n",
    "F is not goal node and has two children  \n",
    "Add I and J to frontier list  \n",
    "frontier = [G, H, I, J]  \n",
    "parents = {A: None, B: A, C: A, D: B, E: B, F: C, G: E, H: E, I: F, J: F}  \n",
    "  \n",
    "*Iteration 6*  \n",
    "  \n",
    "Take first element from frontier list: G  \n",
    "G is not goal node and has no children  \n",
    "frontier = [H, I, J]  \n",
    "parents = {A: None, B: A, C: A, D: B, E: B, F: C, G: E, H: E, I: F, J: F}  \n",
    "  \n",
    "*Iteration 7*  \n",
    "  \n",
    "Take first element from frontier list: H  \n",
    "H is not goal node and has no children  \n",
    "frontier = [I, J]  \n",
    "parents = {A: None, B: A, C: A, D: B, E: B, F: C, G: E, H: E, I: F, J: F}  \n",
    "  \n",
    "*Iteration 8*  \n",
    "  \n",
    "Take first element from frontier list: I  \n",
    "I is not goal node and has no children  \n",
    "frontier = [J]  \n",
    "parents = {A: None, B: A, C: A, D: B, E: B, F: C, G: E, H: E, I: F, J: F}  \n",
    "  \n",
    "*Iteration 9*  \n",
    "  \n",
    "Take first element from frontier list: J  \n",
    "J is goal node  \n",
    "  \n",
    "Reconstruct the path by following the parent nodes back to the root node using the parents list  \n",
    "J -> F  \n",
    "F -> C  \n",
    "C -> A  \n",
    "  \n",
    "The path is A -> C -> F -> J  \n",
    "  \n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "<a id='3'></a>\n",
    "# 3.0 Graph Search\n",
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have the following map of Queensland"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"./Figures/5/fig5_7.jpg\" width=\"700\">"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this example, we consider the towns and cities shown in the figure above, and we import a datafile included with the Toolbox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = rtb.rtb_load_jsonfile(\"data/queensland.json\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where data is a dictionary containing two items. Firstly, `data[\"places\"]` is a dictionary that maps place names to a dictionary of attributes such as latitude, longitude and UTM map coordinates in units of kilometres. We can easily plot these places, along with their names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for name, info in data[\"places\"].items():\n",
    "    smb.plot_point(info[\"utm\"], text=name)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Secondly, `data[\"routes\"]` is a list of dictionaries that each define a graph edge: the name of its start and end place, the route length and the driving speed. For example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'start': 'Camooweal', 'end': 'Mount Isa', 'distance': 188, 'speed': 100}"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[\"routes\"][0]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the Python `pgraph` package to create a graph representation of the data. The first step is to create an undirected graph object and then add vertices and edges from the data we just loaded"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = pg.UGraph()\n",
    "\n",
    "for name, info in data[\"places\"].items():\n",
    "    g.add_vertex(name=name, coord=info[\"utm\"])\n",
    "\n",
    "for route in data[\"routes\"]:\n",
    "    g.add_edge(route[\"start\"], route[\"end\"], cost=route[\"distance\"])\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `UGraph` object has many methods, for example, we can plot the graph we just created"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g.plot()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can retrieve a vertex by its name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "UVertex[Brisbane, coord=(1096, 6947)]"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Brisbane\"]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which is an object of UVertex class which represents a vertex in an undirected graph. Its neighbors, or adjacent vertices, are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[UVertex[Rockhampton, coord=(858.9, 7410)], UVertex[Roma, coord=(677.7, 7060)]]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Brisbane\"].adjacent()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can obtain references to the Edge objects that represent the edges. A list of the edges from the Brisbane vertex is given by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Edge{[Rockhampton] -- [Brisbane], cost=682}, Edge{[Brisbane] -- [Roma], cost=482}]\n"
     ]
    }
   ],
   "source": [
    "edges = g[\"Brisbane\"].edges()\n",
    "print(edges)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and each edge has references to its endpoints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[UVertex[Rockhampton, coord=(858.9, 7410)],\n",
       " UVertex[Brisbane, coord=(1096, 6947)]]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "edges[0].endpoints"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we are ready to plan a path, and will consider the specific example of a journey from Brisbane to Barcaldine. A simple-minded solution would be to randomly choose one of the neighbouring vertices, move there, and repeat the process. We might eventually reach our goal – but there is no guarantee of that – and it is extremely unlikely that the path would be optimal. A more systematic approach is required and we are fortunate this problem has been well-studied – it is the well-known graph search problem."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting at Brisbane, there are just two roads we can take to get to a neighbouring place. From one of those places, say Roma, we can visit in turn each of its neighbors. However, one of those neighbors is Brisbane, our starting point, and backtracking cannot lead to an optimal path. We need some means of keeping track of where we have been. The frontier (or open set) contains all the vertices that are scheduled for exploration, and the explored set (or closed set) contains all the vertices that we have explored and are finished with."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use BFS and then introduce two new algorithms and step through the solutions."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Breadth First Search"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will start at Brisbane and we want to travel to Barcaldine. With a graph instead of a tree, we will also keep a visited list to keep track of where we've already been. As we traverse through the graph, through the parents list, we are essentially constructing a tree from the graph where the root node is the staring node. Once we find the goal node, we can traverse back up through the tree to find the shortest path from the goal node to the starting node. At each iteration, we take the first node from the Frontier and add it to the Visited List.\n",
    "\n",
    "Add brisbane to the frontier as our start node  \n",
    "frontier = [Brisbane]  \n",
    "visited = []  \n",
    "parents = {Brisbane: None}  \n",
    "  \n",
    "**Iteration 0**:  \n",
    "  \n",
    "Move Brisbane to visited  \n",
    "Add Brisbane's neighbouring nodes to frontier  \n",
    "frontier = [Roma, Rockhampton]  \n",
    "visited = [Brisbane]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane}  \n",
    "  \n",
    "**Iteration 1**:  \n",
    "  \n",
    "Move Roma to visited  \n",
    "Add Roma's neighbouring nodes to the frontier (excluding those in visited)  \n",
    "frontier = [Rockhampton, Charleville]  \n",
    "visited = [Brisbane, Roma]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma}  \n",
    "  \n",
    "**Iteration 2**:  \n",
    "  \n",
    "Move Rockhampton to visited  \n",
    "Add Rockhampton's neighbouring nodes to the frontier (excluding those in visited)  \n",
    "frontier = [Charleville, Emerald, Mackay]  \n",
    "visited = [Brisbane, Roma, Rockhampton]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma, Emerald: Rockhampton, Mackay: Rockhampton}  \n",
    "  \n",
    "**Iteration 3**:  \n",
    "  \n",
    "Move Charleville to visited  \n",
    "Add Charleville's neighbouring nodes to the frontier (excluding those in visited)  \n",
    "frontier = [Emerald, Mackay, Blackall]  \n",
    "visited = [Brisbane, Roma, Rockhampton, Charleville]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma, Emerald: Rockhampton, Mackay: Rockhampton, Blackall:   Charleville}\n",
    "  \n",
    "**Iteration 4**:  \n",
    "  \n",
    "Move Emerald to visited  \n",
    "Add Emerald's neighbouring nodes to the frontier (excluding those in visited)  \n",
    "frontier = [Mackay, Blackall, Barcaldine]  \n",
    "visited = [Brisbane, Roma, Rockhampton, Charleville, Emerald]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma, Emerald: Rockhampton, Mackay: Rockhampton, Blackall:   Charleville, Barcaldine: Emerald}\n",
    "  \n",
    "  \n",
    "And we have found our goal node Barcaldine, so we stop. We can then use the parents list to find the path that led to the goal node:  \n",
    "  \n",
    "Brisbane -> Rockhampton -> Emerald -> Barcaldine\n",
    "\n",
    "We can see that the path we found is the shortest in terms of nodes visited from Brisbane to Barcaldine. Other solutions exist with more nodes, such as the path:\n",
    "\n",
    "Brisbane -> Roma -> Charleville -> Blackall -> Barcaldine"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While BFS will always find the shortest path in terms of total nodes in the path, it is not guaranteed to find the smallest path in terms of cost, or in this context, distance travelled."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Uniform Cost Search"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A variation of BFS is uniform-cost-search (UCS). In BFS, we expanded vertices from the frontier on a first-in first-out basis, but now we will choose the frontier vertex that has the lowest cumulative distance from the start – the lowest cost to come.\n",
    "\n",
    "We will start with Brisbane in the Frontier and in the brackets we will show the cumulative distance from the start node to this node.\n",
    "\n",
    "Add brisbane to the frontier as our start node  \n",
    "frontier = [Brisbane (0)]  \n",
    "visited = []  \n",
    "parents = {Brisbane: None}  "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At each iteration, we take the vertex with the lowest cumulative distance from Brisbane from the Frontier and add it to the Visited List. We then add all the neighbours of that node to the Frontier. We repeat this process until we reach the goal node.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Rockhampton] -- [Brisbane], cost=682},\n",
       " Edge{[Brisbane] -- [Roma], cost=482}]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check Brisbane's edges\n",
    "g[\"Brisbane\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Iteration 0**:\n",
    "\n",
    "Move Brisbane to visited  \n",
    "Add Brisbane's neighbouring nodes to the frontier (and record the cumulative distance from the start node)  \n",
    "\n",
    "frontier = [Roma (482), Rockhampton (682)]  \n",
    "visited = [Brisbane]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane}  \n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Iteration 1**:\n",
    "\n",
    "We will expand Roma as it has the lowest cumulative distance from Brisbane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Brisbane] -- [Roma], cost=482}, Edge{[Roma] -- [Charleville], cost=266}]"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Roma\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "frontier = [Rockhampton (682), Charleville (482 + 266 = 748)]  \n",
    "visited = [Brisbane (0), Roma (482)]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma}  "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Iteration 2**:\n",
    "\n",
    "The next lowest cumulative distance is Rockhampton"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Mackay] -- [Rockhampton], cost=334},\n",
       " Edge{[Rockhampton] -- [Brisbane], cost=682},\n",
       " Edge{[Rockhampton] -- [Emerald], cost=270}]"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Rockhampton\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "frontier = [Charleville (748), Emerald (682 + 270 = 952), Mackay (682 + 334 = 1016)]  \n",
    "visited = [Brisbane (0), Roma (482), Rockhampton (682)]\n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma, Emerald: Rockhampton, Mackay: Rockhampton}"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Iteration 3**:\n",
    "\n",
    "The next lowest cumulative distance is Charleville"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Roma] -- [Charleville], cost=266},\n",
       " Edge{[Charleville] -- [Blackall], cost=305}]"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Charleville\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "frontier = [Emerald (952), Mackay (1016), Blackall (748 + 305 = 1053)]  \n",
    "visited = [Brisbane, Roma (482), Rockhampton (682), Charleville (748)]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma, Emerald: Rockhampton, Mackay: Rockhampton, Blackall: Charleville}"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Iteration 4**:\n",
    "\n",
    "The next lowest cumulative distance is Emerald"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Mackay] -- [Emerald], cost=384},\n",
       " Edge{[Rockhampton] -- [Emerald], cost=270},\n",
       " Edge{[Barcaldine] -- [Emerald], cost=307}]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Emerald\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "frontier = [Mackay (1016), Blackall (1053), Barcaldine (952 + 307 = 1259), Mackay (952 + 384 = 1336), Rockhampthon (952 + 270 = 1222)]  \n",
    "visited = [Brisbane, Roma (482), Rockhampton (682), Charleville (748), Emerald (952)]  \n",
    "\n",
    "_Remove the **new** Rockhampton and Mackay from frontier we already have paths to them with a lower cumulative distance_\n",
    "\n",
    "frontier = [Mackay (1016), Blackall (1053), Barcaldine (1259)]  \n",
    "visited = [Brisbane, Roma (482), Rockhampton (682), Charleville (748), Emerald (952)]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma, Emerald: Rockhampton, Mackay: Rockhampton, Blackall: Charleville, Barcaldine: Emerald} "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With UCS, we may encounter places that are already on our frontier or visited lists. In this scenario, we will replace the existing node with the new node if the new node has a lower cumulative distance from Brisbane. Since the new routes to Mackay and Rockhampton are both longer than the existing routes, we will not replace them.\n",
    "\n",
    "We have found our goal node Barcaldine, but we do not stop with UCS until all nodes are visited."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Iteration 5**:\n",
    "\n",
    "The next lowest cumulative distance is Mackay"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Townsville] -- [Mackay], cost=388},\n",
       " Edge{[Mackay] -- [Rockhampton], cost=334},\n",
       " Edge{[Mackay] -- [Emerald], cost=384}]"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Mackay\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "frontier = [Blackall (1053), Barcaldine (1259), Townsville (1016 + 388 = 1404), Emerald (1016 + 384 = 1400)]  \n",
    "visited = [Brisbane, Roma (482), Rockhampton (682), Charleville (748), Emerald (952), Mackay (1016)]\n",
    "\n",
    "Remove the new Emerald from frontier as it is already in visited with a lower cumulative distance.\n",
    "\n",
    "frontier = [Blackall (1053), Barcaldine (1259), Townsville (1404)]  \n",
    "visited = [Brisbane, Roma (482), Rockhampton (682), Charleville (748), Emerald (952), Mackay (1016)]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma, Emerald: Rockhampton, Mackay: Rockhampton, Blackall: Charleville, Barcaldine: Emerald, Townsville: Mackay}"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Iteration 6**:\n",
    "\n",
    "The next lowest cumulative distance is Blackall"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Charleville] -- [Blackall], cost=305},\n",
       " Edge{[Blackall] -- [Barcaldine], cost=106},\n",
       " Edge{[Blackall] -- [Windorah], cost=530}]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Blackall\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "frontier = [Barcaldine (1259), Townsville (1404), Windorah (1053 + 530 = 1583), Barcaldine (1053 + 106 = 1159)]  \n",
    "visited = [Brisbane, Roma (482), Rockhampton (682), Charleville (748), Emerald (952), Mackay (1016), Blackall (1053)]  \n",
    "\n",
    "Remove the old Barcaldine from the frontier as the new route has a lower cumulative distance. We will also re-parent Barcaldine in the parents list to reflect this change\n",
    "\n",
    "frontier = [Townsville (1404), Windorah (1583), Barcaldine (1159)]  \n",
    "visited = [Brisbane, Roma (482), Rockhampton (682), Charleville (748), Emerald (952), Mackay (1016), Blackall (1053)]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma, Emerald: Rockhampton, Mackay: Rockhampton, Blackall: Charleville, Barcaldine: Blackall, Townsville: Mackay, Windorah: Blackall}"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And our new best route to Barcaldine is:\n",
    "\n",
    "Brisbane -> Roma -> Charleville -> Blackall -> Barcaldine with a total cost of 1159\n",
    "\n",
    "The UCS search will continue until all nodes in the graph has been visited. This can be expensive for very large graphs. This type of algorithm is known as a **brute force** algorithm. It is guaranteed to find the best solution, but it search the whole solution space to do so, which can be very computationally expensive.\n",
    "\n",
    "Once we have finished the search, we use the parents list to reconstruct the path from goal node to the start node:\n",
    "\n",
    "Barcaldine -> Blackall -> Charleville -> Roma -> Brisbane\n",
    "\n",
    "which gives us the path from Brisbane to Barcaldine with the lowest cost:\n",
    "\n",
    "Brisbane -> Roma -> Charleville -> Blackall -> Barcaldine with a total cost of 1159"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can perform this search using `PGraph`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1159"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path, length, parents = g.path_UCS(\"Brisbane\", \"Barcaldine\")\n",
    "length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Brisbane, Roma, Charleville, Blackall, Barcaldine'"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\", \".join([p.name for p in path])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parents list describes a tree rooted at the start node, with the shortest path to each node from the start node. We can plot this tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "tree = pg.DGraph.Dict(parents)\n",
    "tree.showgraph()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"./Figures/5/tree_2.png\" width=\"400\">"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 A* Search\n",
    "\n",
    "A* is a variation on the UCS algorithm but we use a _heuristic_ to guide our path. A commonly used heuristic is the distance \"as the crow flies\" or Euclidean distance – easily computed since our graph is embedded and the position of every vertex is known.\n",
    "\n",
    "To calculate the Euclidean distance between each node and Barcaldine, we simply loop through nodes in the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Barcaldine: 0.0\n",
      "Bedourie: 601.0\n",
      "Birdsville: 656.0\n",
      "Blackall: 97.0\n",
      "Boulia: 557.0\n",
      "Brisbane: 890.0\n",
      "Camooweal: 847.0\n",
      "Charleville: 329.0\n",
      "Charters Towers: 398.0\n",
      "Cloncurry: 587.0\n",
      "Emerald: 293.0\n",
      "Hughenden: 320.0\n",
      "Longreach: 107.0\n",
      "Mackay: 481.0\n",
      "Mount Isa: 677.0\n",
      "Rockhampton: 533.0\n",
      "Roma: 485.0\n",
      "Townsville: 501.0\n",
      "Windorah: 338.0\n",
      "Winton: 265.0\n"
     ]
    }
   ],
   "source": [
    "barcaldine_coords = g[\"Barcaldine\"].coord\n",
    "\n",
    "for name in sorted([n.name for n in g]):\n",
    "    euc_dist = np.linalg.norm(barcaldine_coords - g[name].coord)\n",
    "    print(f\"{g[name].name}: {np.round(euc_dist)}\")\n",
    "    "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we will use these numbers as our heuristic. The total cost we will use for each node is the cumulative distance from Brisbane plus the Euclidean distance to Barcaldine."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start with Brisbane in the frontier list as our start node and in brackets we add the cumulative distance to the Heuristic value.\n",
    "\n",
    "frontier = [Brisbane (0 + 890 = 890)]  \n",
    "visited = []  \n",
    "parents = {Brisbane: None}  \n",
    "\n",
    "**Iteration 0**:\n",
    "\n",
    "We move Brisbane to visited, and add Brisbane's neighbouring nodes to the frontier\n",
    "\n",
    "frontier [Roma (485 + 482 = 967), Rockhampton (533 + 682 = 1215)]\n",
    "visited = [Brisbane]\n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Rockhampton] -- [Brisbane], cost=682},\n",
       " Edge{[Brisbane] -- [Roma], cost=482}]"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Brisbane\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Iteration 1**:\n",
    "\n",
    "We move Roma to visited, and add Roma's neighbouring nodes to the frontier\n",
    "\n",
    "frontier = [Rockhampton (533 + 682 = 1215), Charleville (329 + 482 + 266 = 1077)]  \n",
    "visited = [Brisbane, Roma (485 + 482 = 967)]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma}  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Brisbane] -- [Roma], cost=482}, Edge{[Roma] -- [Charleville], cost=266}]"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Roma\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Iteration 2**:\n",
    "\n",
    "We move Charleville to visited, and add Charleville's neighbouring nodes to the frontier\n",
    "\n",
    "frontier = [Rockhampton (533 + 682 = 1215), Blackall (97 + 482 + 266 + 305 = 1150)]  \n",
    "visited = [Brisbane, Roma (485 + 482 = 967), Charleville (329 + 482 + 266 = 1077)]  \n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma, Blackall: Charleville}  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Roma] -- [Charleville], cost=266},\n",
       " Edge{[Charleville] -- [Blackall], cost=305}]"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Charleville\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Iteration 3**:\n",
    "\n",
    "We move Blackall to visited, and add Blackall's neighbouring nodes to the frontier\n",
    "\n",
    "frontier = [Rockhampton (533 + 682 = 1215), Barcaldine (0 + 482 + 266 + 305 + 106 = 1159), Windorah (338 + 482 + 266 + 305 + 530 = 1921)]\n",
    "visited = [Brisbane, Roma (485 + 482 = 967), Charleville (329 + 482 + 266 = 1077), Blackall (97 + 482 + 266 + 305 = 1150)]\n",
    "parents = {Brisbane: None, Roma: Brisbane, Rockhampton: Brisbane, Charleville: Roma, Blackall: Charleville, Barcaldine: Blackall, Windorah: Blackall}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Edge{[Charleville] -- [Blackall], cost=305},\n",
       " Edge{[Blackall] -- [Barcaldine], cost=106},\n",
       " Edge{[Blackall] -- [Windorah], cost=530}]"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g[\"Blackall\"].edges()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we have found our goal node Barcaldine, so we stop.\n",
    "\n",
    "We can then use the parents list to find the path that led to the goal node:\n",
    "\n",
    "Brisbane -> Roma -> Charleville -> Blackall -> Barcaldine with a total cost of 1159 which is the lowest cost solution, and we found it in just 4 iterations (the same as BFS)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can do this search using `PGraph`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1159"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path, length, parents = g.path_Astar(\"Brisbane\", \"Barcaldine\")\n",
    "length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Brisbane, Roma, Charleville, Blackall, Barcaldine'"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\", \".join([p.name for p in path])"
   ]
  },
  {
   "attachments": {},
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    "The performance of A* depends critically on the heuristic. A* is guaranteed to return the lowest-cost path only if the heuristic is admissible, that is, it does not overestimate the cost of reaching the goal. The Euclidean distance is an admissible heuristic since it is the minimum possible cost and by definition cannot be an overestimate. As the heuristic cost component increases from zero up to its maximum admissible value, the efficiency increases as fewer vertices are explored. A non-admissible heuristic may lead to a non-optimal path."
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