{ "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", "* If we try to add a node that already exists, do we just do nothing?\n", " * Yes\n", "* If we try to delete a node that doesn't exist, do we just do nothing?\n", " * Yes\n", "* Can we assume this fits memory?\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", "* incoming edge count (useful for algorithms such as topological sort)\n", "* adjacent nodes and edge weights\n", "\n", "#### add_neighhbor\n", "\n", "* If the neighbor doesn't already exist as an adjacent node\n", " * Update the adjancet nodes and edge weights\n", " * Increment the neighbor's incoming edge count\n", "\n", "Complexity:\n", "* Time: O(1)\n", "* Space: O(1)\n", "\n", "#### remove_neighhbor\n", "\n", "* If the neighbor exists as an adjacent node\n", " * Decrement the neighbor's incoming edge count\n", " * Remove the neighbor as an adjacent node\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", "\n", "#### add_node\n", "\n", "* If node already exists, return it\n", "* Create a node with the given id\n", "* Add the newly created node to the collection 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 collection of nodes, add it\n", "* If the dest node is not in the collection of nodes, add it\n", "* Add a connection from the source node to the dest node with the given edge weight\n", "\n", "#### add_undirected_edge\n", "\n", "* Call add_edge\n", "* Also add a connection from the dest node to the source 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, key):\n", " self.key = key\n", " self.visit_state = State.unvisited\n", " self.incoming_edges = 0\n", " self.adj_nodes = {} # Key = key, val = Node\n", " self.adj_weights = {} # Key = key, val = weight\n", "\n", " def __repr__(self):\n", " return str(self.key)\n", "\n", " def __lt__(self, other):\n", " return self.key < other.key\n", "\n", " def add_neighbor(self, neighbor, weight=0):\n", " if neighbor is None:\n", " raise Exception('Invalid neighbor')\n", " neighbor.incoming_edges += 1\n", " self.adj_weights[neighbor.key] = weight\n", " self.adj_nodes[neighbor.key] = neighbor\n", "\n", " def remove_neighbor(self, neighbor):\n", " if neighbor is None:\n", " raise Exception('Invalid neighbor')\n", " if neighbor.key in self.adj_nodes:\n", " neighbor.incoming_edges -= 1\n", " del self.adj_weights[neighbor.key]\n", " del self.adj_nodes[neighbor.key]\n", " else:\n", " raise Exception('Invalid neighbor')\n", "\n", "\n", "class Graph:\n", "\n", " def __init__(self):\n", " self.nodes = {} # Key = key, val = Node\n", "\n", " def add_node(self, key):\n", " if key is None:\n", " raise Exception('Invalid key')\n", " if key in self.nodes:\n", " return self.nodes[key]\n", " self.nodes[key] = Node(key)\n", " return self.nodes[key]\n", "\n", " def add_edge(self, source_key, dest_key, weight=0):\n", " if source_key is None or dest_key is None:\n", " raise Exception('Invalid key')\n", " if source_key not in self.nodes:\n", " self.add_node(source_key)\n", " if dest_key not in self.nodes:\n", " self.add_node(dest_key)\n", " self.nodes[source_key].add_neighbor(self.nodes[dest_key],\n", " weight)\n", "\n", " def add_undirected_edge(self, source_key, dest_key, weight=0):\n", " if source_key is None or dest_key is None:\n", " raise Exception('Invalid key')\n", " self.add_edge(source_key, dest_key, weight)\n", " self.nodes[dest_key].add_neighbor(self.nodes[source_key],\n", " 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 key in range(0, 6):\n", " graph.add_node(key)\n", " return graph\n", "\n", " def test_graph(self):\n", " graph = self.create_graph()\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].adj_weights[graph.nodes[1].key], 5)\n", " assert_equal(graph.nodes[0].adj_weights[graph.nodes[5].key], 2)\n", " assert_equal(graph.nodes[1].adj_weights[graph.nodes[2].key], 3)\n", " assert_equal(graph.nodes[2].adj_weights[graph.nodes[3].key], 4)\n", " assert_equal(graph.nodes[3].adj_weights[graph.nodes[4].key], 5)\n", " assert_equal(graph.nodes[3].adj_weights[graph.nodes[5].key], 6)\n", " assert_equal(graph.nodes[4].adj_weights[graph.nodes[0].key], 7)\n", " assert_equal(graph.nodes[5].adj_weights[graph.nodes[4].key], 8)\n", " assert_equal(graph.nodes[5].adj_weights[graph.nodes[2].key], 9)\n", "\n", " assert_equal(graph.nodes[0].incoming_edges, 1)\n", " assert_equal(graph.nodes[1].incoming_edges, 1)\n", " assert_equal(graph.nodes[2].incoming_edges, 2)\n", " assert_equal(graph.nodes[3].incoming_edges, 1)\n", " assert_equal(graph.nodes[4].incoming_edges, 2)\n", " assert_equal(graph.nodes[5].incoming_edges, 2)\n", "\n", " graph.nodes[0].remove_neighbor(graph.nodes[1])\n", " assert_equal(graph.nodes[1].incoming_edges, 0)\n", " graph.nodes[3].remove_neighbor(graph.nodes[4])\n", " assert_equal(graph.nodes[4].incoming_edges, 1)\n", "\n", " assert_equal(graph.nodes[0] < graph.nodes[1], True)\n", "\n", " print('Success: test_graph')\n", "\n", " def test_graph_undirected(self):\n", " graph = self.create_graph()\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].adj_weights[graph.nodes[1].key], 5)\n", " assert_equal(graph.nodes[1].adj_weights[graph.nodes[0].key], 5)\n", " assert_equal(graph.nodes[0].adj_weights[graph.nodes[5].key], 2)\n", " assert_equal(graph.nodes[5].adj_weights[graph.nodes[0].key], 2)\n", " assert_equal(graph.nodes[1].adj_weights[graph.nodes[2].key], 3)\n", " assert_equal(graph.nodes[2].adj_weights[graph.nodes[1].key], 3)\n", "\n", " print('Success: test_graph_undirected')\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_undirected\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 }