{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Solution Notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: Implement a graph.\n", "\n", "* [Constraints](#Constraints)\n", "* [Test Cases](#Test-Cases)\n", "* [Algorithm](#Algorithm)\n", "* [Code](#Code)\n", "* [Unit Test](#Unit-Test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constraints\n", "\n", "* Is the graph directed?\n", " * Implement both\n", "* Do the edges have weights?\n", " * Yes\n", "* Can we assume the inputs are valid?\n", " * Yes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test Cases\n", "\n", "Input:\n", "* `add_edge(source, destination, weight)`\n", "\n", "```\n", "graph.add_edge(0, 1, 5)\n", "graph.add_edge(0, 5, 2)\n", "graph.add_edge(1, 2, 3)\n", "graph.add_edge(2, 3, 4)\n", "graph.add_edge(3, 4, 5)\n", "graph.add_edge(3, 5, 6)\n", "graph.add_edge(4, 0, 7)\n", "graph.add_edge(5, 4, 8)\n", "graph.add_edge(5, 2, 9)\n", "```\n", "\n", "Result:\n", "* `source` and `destination` nodes within `graph` are connected with specified `weight`.\n", "\n", "Note: \n", "* The Graph class will be used as a building block for more complex graph challenges." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm\n", "\n", "### Node\n", "\n", "Node will keep track of its:\n", "* id\n", "* visit state\n", "* adjacent\n", " * key: node\n", " * value: weight\n", "\n", "#### add_neighhbor\n", "\n", "* Add the neighbor as a key and the weight as the value to `adjacent`\n", "\n", "Complexity:\n", "* Time: O(1)\n", "* Space: O(1)\n", "\n", "### Graph\n", "\n", "Graph will keep track of its:\n", "* nodes\n", " * key: node id\n", " * value: node\n", "\n", "#### add_node\n", "\n", "* Create a node with the input id\n", "* Add the newly created node to the list of nodes\n", "\n", "Complexity:\n", "* Time: O(1)\n", "* Space: O(1)\n", "\n", "#### add_edge\n", "\n", "* If the source node is not in the list of nodes, add it\n", "* If the dest node is not in the list of nodes, add it\n", "* Add a connection from the source node to the dest node with the given edge weight\n", "\n", "Complexity:\n", "* Time: O(1)\n", "* Space: O(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting graph.py\n" ] } ], "source": [ "%%writefile graph.py\n", "from enum import Enum # Python 2 users: Run pip install enum34\n", "\n", "\n", "class State(Enum):\n", " unvisited = 0\n", " visiting = 1\n", " visited = 2\n", "\n", "\n", "class Node:\n", "\n", " def __init__(self, id):\n", " self.id = id\n", " self.visit_state = State.unvisited\n", " self.adjacent = {} # key = node, val = weight\n", "\n", " def __str__(self):\n", " return str(self.id)\n", "\n", " def add_neighbor(self, neighbor, weight=0):\n", " self.adjacent[neighbor] = weight\n", "\n", "\n", "class Graph:\n", "\n", " def __init__(self):\n", " self.nodes = {} # key = node id, val = node\n", "\n", " def add_node(self, id):\n", " node = Node(id)\n", " self.nodes[id] = node\n", " return node\n", "\n", " def add_edge(self, id_source, id_dest, weight=0):\n", " if id_source not in self.nodes:\n", " self.add_node(id_source)\n", " if id_dest not in self.nodes:\n", " self.add_node(id_dest)\n", " self.nodes[id_source].add_neighbor(self.nodes[id_dest], weight)\n", "\n", " def add_undirected_edge(self, source, dest, weight=0):\n", " self.add_edge(source, dest, weight)\n", " self.nodes[dest].add_neighbor(self.nodes[source], weight)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%run graph.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unit Test" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting test_graph.py\n" ] } ], "source": [ "%%writefile test_graph.py\n", "from nose.tools import assert_equal\n", "\n", "\n", "class TestGraph(object):\n", "\n", " def create_graph(self):\n", " graph = Graph()\n", " for id in range(0, 6):\n", " graph.add_node(id)\n", " return graph\n", "\n", " def test_graph(self):\n", " graph = self.create_graph()\n", "\n", " graph.add_edge(0, 1, weight=5)\n", " graph.add_edge(0, 5, weight=2)\n", " graph.add_edge(1, 2, weight=3)\n", " graph.add_edge(2, 3, weight=4)\n", " graph.add_edge(3, 4, weight=5)\n", " graph.add_edge(3, 5, weight=6)\n", " graph.add_edge(4, 0, weight=7)\n", " graph.add_edge(5, 4, weight=8)\n", " graph.add_edge(5, 2, weight=9)\n", "\n", " assert_equal(graph.nodes[0].adjacent[graph.nodes[1]], 5)\n", " assert_equal(graph.nodes[0].adjacent[graph.nodes[5]], 2)\n", " assert_equal(graph.nodes[1].adjacent[graph.nodes[2]], 3)\n", " assert_equal(graph.nodes[2].adjacent[graph.nodes[3]], 4)\n", " assert_equal(graph.nodes[3].adjacent[graph.nodes[4]], 5)\n", " assert_equal(graph.nodes[3].adjacent[graph.nodes[5]], 6)\n", " assert_equal(graph.nodes[4].adjacent[graph.nodes[0]], 7)\n", " assert_equal(graph.nodes[5].adjacent[graph.nodes[4]], 8)\n", " assert_equal(graph.nodes[5].adjacent[graph.nodes[2]], 9)\n", "\n", " print('Success: test_graph')\n", "\n", " def test_graph_undirected(self):\n", " graph = self.create_graph()\n", "\n", " graph.add_undirected_edge(0, 1, weight=5)\n", " graph.add_undirected_edge(0, 5, weight=2)\n", " graph.add_undirected_edge(1, 2, weight=3)\n", "\n", " assert_equal(graph.nodes[0].adjacent[graph.nodes[1]], 5)\n", " assert_equal(graph.nodes[1].adjacent[graph.nodes[0]], 5)\n", " assert_equal(graph.nodes[0].adjacent[graph.nodes[5]], 2)\n", " assert_equal(graph.nodes[5].adjacent[graph.nodes[0]], 2)\n", " assert_equal(graph.nodes[1].adjacent[graph.nodes[2]], 3)\n", " assert_equal(graph.nodes[2].adjacent[graph.nodes[1]], 3)\n", "\n", " print('Success: test_graph')\n", "\n", "\n", "def main():\n", " test = TestGraph()\n", " test.test_graph()\n", " test.test_graph_undirected()\n", "\n", "\n", "if __name__ == '__main__':\n", " main()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Success: test_graph\n", "Success: test_graph\n" ] } ], "source": [ "%run -i test_graph.py" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.0" } }, "nbformat": 4, "nbformat_minor": 0 }