From 43eb3f84fa9778a37c10627f9f5e06ca6dfcae13 Mon Sep 17 00:00:00 2001 From: Donne Martin Date: Tue, 4 Aug 2015 20:01:59 -0400 Subject: [PATCH] Added graph dfs challenge. --- README.md | 1 + graphs_trees/graph_dfs/__init__.py | 0 graphs_trees/graph_dfs/dfs_challenge.ipynb | 209 +++++++++++++++++++ graphs_trees/graph_dfs/dfs_solution.ipynb | 231 +++++++++++++++++++++ graphs_trees/graph_dfs/test_dfs.py | 34 +++ 5 files changed, 475 insertions(+) create mode 100644 graphs_trees/graph_dfs/__init__.py create mode 100644 graphs_trees/graph_dfs/dfs_challenge.ipynb create mode 100644 graphs_trees/graph_dfs/dfs_solution.ipynb create mode 100644 graphs_trees/graph_dfs/test_dfs.py diff --git a/README.md b/README.md index eb37991..e7fb5ed 100644 --- a/README.md +++ b/README.md @@ -208,6 +208,7 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup | Implement breadth-first search on a tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_bfs/bfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_bfs/bfs_solution.ipynb) | | Determine the height of a tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_solution.ipynb) | | Implement a graph | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph/graph_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph/graph_solution.ipynb) | +| Implement depth-first search on a graph | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_dfs/dfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_dfs/dfs_solution.ipynb) | | Print a tree using pre-order traversal without recursion | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) | | Determine the lowest common ancestor of two nodes | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) | | Transform a binary tree into a heap | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) | diff --git a/graphs_trees/graph_dfs/__init__.py b/graphs_trees/graph_dfs/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/graphs_trees/graph_dfs/dfs_challenge.ipynb b/graphs_trees/graph_dfs/dfs_challenge.ipynb new file mode 100644 index 0000000..a8fa189 --- /dev/null +++ b/graphs_trees/graph_dfs/dfs_challenge.ipynb @@ -0,0 +1,209 @@ +{ + "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": [ + "# Challenge Notebook" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem: Implement depth-first search on a graph.\n", + "\n", + "* [Constraints](#Constraints)\n", + "* [Test Cases](#Test-Cases)\n", + "* [Algorithm](#Algorithm)\n", + "* [Code](#Code)\n", + "* [Unit Test](#Unit-Test)\n", + "* [Solution Notebook](#Solution-Notebook)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constraints\n", + "\n", + "* Is the graph directed?\n", + " * Yes\n", + "* Can we assume we already have Graph and Node classes?\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, 4, 3)\n", + "graph.add_edge(0, 5, 2)\n", + "graph.add_edge(1, 3, 5)\n", + "graph.add_edge(1, 4, 4)\n", + "graph.add_edge(2, 1, 6)\n", + "graph.add_edge(3, 2, 7)\n", + "graph.add_edge(3, 4, 8)\n", + "```\n", + "\n", + "Result:\n", + "* Order of nodes visited: [0, 1, 3, 2, 4, 5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_dfs/dfs_solution.ipynb). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%run ../graph/graph.py\n", + "%load ../graph/graph.py" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def dfs(root, visit_func):\n", + " # TODO: Implement me\n", + " pass" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**The following unit test is expected to fail until you solve the challenge.**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%run ../utils/results.py" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# %load test_dfs.py\n", + "from nose.tools import assert_equal\n", + "\n", + "\n", + "class TestDfs(object):\n", + "\n", + " def __init__(self):\n", + " self.results = Results()\n", + "\n", + " def test_dfs(self):\n", + " nodes = []\n", + " graph = Graph()\n", + " for id in range(0, 6):\n", + " nodes.append(graph.add_node(id))\n", + " graph.add_edge(0, 1, 5)\n", + " graph.add_edge(0, 4, 3)\n", + " graph.add_edge(0, 5, 2)\n", + " graph.add_edge(1, 3, 5)\n", + " graph.add_edge(1, 4, 4)\n", + " graph.add_edge(2, 1, 6)\n", + " graph.add_edge(3, 2, 7)\n", + " graph.add_edge(3, 4, 8)\n", + " dfs(nodes[0], self.results.add_result)\n", + " assert_equal(str(self.results), \"[0, 1, 3, 2, 4, 5]\")\n", + "\n", + " print('Success: test_dfs')\n", + "\n", + "\n", + "def main():\n", + " test = TestDfs()\n", + " test.test_dfs()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solution Notebook\n", + "\n", + "Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_dfs/dfs_solution.ipynb) for a discussion on algorithms and code solutions." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/graphs_trees/graph_dfs/dfs_solution.ipynb b/graphs_trees/graph_dfs/dfs_solution.ipynb new file mode 100644 index 0000000..ff497d5 --- /dev/null +++ b/graphs_trees/graph_dfs/dfs_solution.ipynb @@ -0,0 +1,231 @@ +{ + "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 depth-first search on 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", + " * Yes\n", + "* Can we assume we already have Graph and Node classes?\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, 4, 3)\n", + "graph.add_edge(0, 5, 2)\n", + "graph.add_edge(1, 3, 5)\n", + "graph.add_edge(1, 4, 4)\n", + "graph.add_edge(2, 1, 6)\n", + "graph.add_edge(3, 2, 7)\n", + "graph.add_edge(3, 4, 8)\n", + "```\n", + "\n", + "Result:\n", + "* Order of nodes visited: [0, 1, 3, 2, 4, 5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "If we want to visit every node in a graph, we generally prefer depth-first search since it is simpler (no need to use a queue). For shortest path, we generally use breadth-first search.\n", + "\n", + "* Visit the current node and mark it visited\n", + "* Iterate through each adjacent node\n", + " * If the node has not been visited, call dfs on it\n", + "\n", + "Complexity:\n", + "* Time: O(V + E), where V = number of vertices and E = number of edges\n", + "* Space: O(V + E)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%run ../graph/graph.py" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def dfs(root, visit_func):\n", + " if root is None:\n", + " return\n", + " visit_func(root.id)\n", + " root.visited = True\n", + " for node in root.adjacent:\n", + " if not node.visited:\n", + " dfs(node, visit_func)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%run ../utils/results.py" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting test_dfs.py\n" + ] + } + ], + "source": [ + "%%writefile test_dfs.py\n", + "from nose.tools import assert_equal\n", + "\n", + "\n", + "class TestDfs(object):\n", + "\n", + " def __init__(self):\n", + " self.results = Results()\n", + "\n", + " def test_dfs(self):\n", + " nodes = []\n", + " graph = Graph()\n", + " for id in range(0, 6):\n", + " nodes.append(graph.add_node(id))\n", + " graph.add_edge(0, 1, 5)\n", + " graph.add_edge(0, 4, 3)\n", + " graph.add_edge(0, 5, 2)\n", + " graph.add_edge(1, 3, 5)\n", + " graph.add_edge(1, 4, 4)\n", + " graph.add_edge(2, 1, 6)\n", + " graph.add_edge(3, 2, 7)\n", + " graph.add_edge(3, 4, 8)\n", + " dfs(nodes[0], self.results.add_result)\n", + " assert_equal(str(self.results), \"[0, 1, 3, 2, 4, 5]\")\n", + "\n", + " print('Success: test_dfs')\n", + "\n", + "\n", + "def main():\n", + " test = TestDfs()\n", + " test.test_dfs()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Success: test_dfs\n" + ] + } + ], + "source": [ + "%run -i test_dfs.py" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/graphs_trees/graph_dfs/test_dfs.py b/graphs_trees/graph_dfs/test_dfs.py new file mode 100644 index 0000000..2830387 --- /dev/null +++ b/graphs_trees/graph_dfs/test_dfs.py @@ -0,0 +1,34 @@ +from nose.tools import assert_equal + + +class TestDfs(object): + + def __init__(self): + self.results = Results() + + def test_dfs(self): + nodes = [] + graph = Graph() + for id in range(0, 6): + nodes.append(graph.add_node(id)) + graph.add_edge(0, 1, 5) + graph.add_edge(0, 4, 3) + graph.add_edge(0, 5, 2) + graph.add_edge(1, 3, 5) + graph.add_edge(1, 4, 4) + graph.add_edge(2, 1, 6) + graph.add_edge(3, 2, 7) + graph.add_edge(3, 4, 8) + dfs(nodes[0], self.results.add_result) + assert_equal(str(self.results), "[0, 1, 3, 2, 4, 5]") + + print('Success: test_dfs') + + +def main(): + test = TestDfs() + test.test_dfs() + + +if __name__ == '__main__': + main() \ No newline at end of file