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https://github.com/donnemartin/interactive-coding-challenges.git
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Add graph shortest path challenge
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Donne Martin
parent
3837b5a8cc
commit
3e0d78f685
0
graphs_trees/graph_shortest_path/__init__.py
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graphs_trees/graph_shortest_path/__init__.py
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Challenge Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Find the shortest path between two nodes in a graph.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)\n",
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"* [Solution Notebook](#Solution-Notebook)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Is this a directional graph?\n",
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" * Yes\n",
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"* Could the graph have cycles?\n",
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" * Yes\n",
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" * Note: If the answer were no, this would be a DAG. \n",
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" * DAGs can be solved with a [topological sort](http://www.geeksforgeeks.org/shortest-path-for-directed-acyclic-graphs/)\n",
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"* Are the edges weighted?\n",
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" * Yes\n",
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" * Note: If the edges were not weighted, we could do a BFS\n",
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"* Are the edges all non-negative numbers?\n",
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" * Yes\n",
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" * Note: Graphs with negative edges can be done with Bellman-Ford\n",
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" * Graphs with negative cost cycles do not have a defined shortest path\n",
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"* Do we have to check for non-negative edges?\n",
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" * No\n",
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"* Can we assume this is a connected graph?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Can we assume we already have a graph class?\n",
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" * Yes\n",
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"* Can we assume we already have a priority queue class?\n",
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" * Yes\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"The constaints state we don't have to check for negative edges, so we test with the general case.\n",
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"\n",
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"<pre>\n",
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"graph.add_edge('a', 'b', weight=5)\n",
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"graph.add_edge('a', 'c', weight=3)\n",
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"graph.add_edge('a', 'e', weight=2)\n",
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"graph.add_edge('b', 'd', weight=2)\n",
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"graph.add_edge('c', 'b', weight=1)\n",
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"graph.add_edge('c', 'd', weight=1)\n",
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"graph.add_edge('d', 'a', weight=1)\n",
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"graph.add_edge('d', 'g', weight=2)\n",
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"graph.add_edge('d', 'h', weight=1)\n",
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"graph.add_edge('e', 'a', weight=1)\n",
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"graph.add_edge('e', 'h', weight=4)\n",
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"graph.add_edge('e', 'i', weight=7)\n",
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"graph.add_edge('f', 'b', weight=3)\n",
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"graph.add_edge('f', 'g', weight=1)\n",
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"graph.add_edge('g', 'c', weight=3)\n",
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"graph.add_edge('g', 'i', weight=2)\n",
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"graph.add_edge('h', 'c', weight=2)\n",
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"graph.add_edge('h', 'f', weight=2)\n",
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"graph.add_edge('h', 'g', weight=2)\n",
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"shortest_path = ShortestPath(graph)\n",
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"result = shortest_path.find_shortest_path('a', 'i')\n",
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"assert_equal(result, ['a', 'c', 'd', 'g', 'i'])\n",
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"assert_equal(shortest_path.path_weight['i'], 8)\n",
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"</pre>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"Refer to the [Solution Notebook](https://github.com/donnemartin/interactive-coding-challenges/graphs_trees/graph_shortest_path/graph_shortest_path_solution.ipynb). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"%run ../../arrays_strings/priority_queue/priority_queue.py\n",
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"%load ../../arrays_strings/priority_queue/priority_queue.py"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"%run ../graph/graph.py\n",
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"%load ../graph/graph.py"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class ShortestPath(object):\n",
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"\n",
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" def __init__(self, graph):\n",
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" # TODO: Implement me\n",
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" pass\n",
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"\n",
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" def find_shortest_path(self, start_node_key, end_node_key):\n",
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" # TODO: Implement me\n",
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" pass"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**The following unit test is expected to fail until you solve the challenge.**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# %load test_shortest_path.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestShortestPath(object):\n",
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"\n",
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" def test_shortest_path(self):\n",
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" graph = Graph()\n",
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" graph.add_edge('a', 'b', weight=5)\n",
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" graph.add_edge('a', 'c', weight=3)\n",
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" graph.add_edge('a', 'e', weight=2)\n",
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" graph.add_edge('b', 'd', weight=2)\n",
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" graph.add_edge('c', 'b', weight=1)\n",
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" graph.add_edge('c', 'd', weight=1)\n",
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" graph.add_edge('d', 'a', weight=1)\n",
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" graph.add_edge('d', 'g', weight=2)\n",
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" graph.add_edge('d', 'h', weight=1)\n",
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" graph.add_edge('e', 'a', weight=1)\n",
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" graph.add_edge('e', 'h', weight=4)\n",
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" graph.add_edge('e', 'i', weight=7)\n",
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" graph.add_edge('f', 'b', weight=3)\n",
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" graph.add_edge('f', 'g', weight=1)\n",
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" graph.add_edge('g', 'c', weight=3)\n",
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" graph.add_edge('g', 'i', weight=2)\n",
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" graph.add_edge('h', 'c', weight=2)\n",
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" graph.add_edge('h', 'f', weight=2)\n",
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" graph.add_edge('h', 'g', weight=2)\n",
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" shortest_path = ShortestPath(graph)\n",
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" result = shortest_path.find_shortest_path('a', 'i')\n",
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" assert_equal(result, ['a', 'c', 'd', 'g', 'i'])\n",
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" assert_equal(shortest_path.path_weight['i'], 8)\n",
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"\n",
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" print('Success: test_shortest_path')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestShortestPath()\n",
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" test.test_shortest_path()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Solution Notebook\n",
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"\n",
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"Review the [Solution Notebook](https://github.com/donnemartin/interactive-coding-challenges/graphs_trees/graph_shortest_path/graph_shortest_path_solution.ipynb) for a discussion on algorithms and code solutions."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.4.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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@ -0,0 +1,355 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Solution Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Find the shortest path between two nodes in a graph.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
|
||||||
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"* [Test Cases](#Test-Cases)\n",
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||||||
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
|
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"* Is this a directional graph?\n",
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" * Yes\n",
|
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"* Could the graph have cycles?\n",
|
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" * Yes\n",
|
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|
" * Note: If the answer were no, this would be a DAG. \n",
|
||||||
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" * DAGs can be solved with a [topological sort](http://www.geeksforgeeks.org/shortest-path-for-directed-acyclic-graphs/)\n",
|
||||||
|
"* Are the edges weighted?\n",
|
||||||
|
" * Yes\n",
|
||||||
|
" * Note: If the edges were not weighted, we could do a BFS\n",
|
||||||
|
"* Are the edges all non-negative numbers?\n",
|
||||||
|
" * Yes\n",
|
||||||
|
" * Note: Graphs with negative edges can be done with Bellman-Ford\n",
|
||||||
|
" * Graphs with negative cost cycles do not have a defined shortest path\n",
|
||||||
|
"* Do we have to check for non-negative edges?\n",
|
||||||
|
" * No\n",
|
||||||
|
"* Can we assume this is a connected graph?\n",
|
||||||
|
" * Yes\n",
|
||||||
|
"* Can we assume the inputs are valid?\n",
|
||||||
|
" * No\n",
|
||||||
|
"* Can we assume we already have a graph class?\n",
|
||||||
|
" * Yes\n",
|
||||||
|
"* Can we assume we already have a priority queue class?\n",
|
||||||
|
" * Yes\n",
|
||||||
|
"* Can we assume this fits memory?\n",
|
||||||
|
" * Yes"
|
||||||
|
]
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|
},
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{
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||||||
|
"cell_type": "markdown",
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|
"metadata": {},
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||||||
|
"source": [
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||||||
|
"## Test Cases\n",
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|
"\n",
|
||||||
|
"The constaints state we don't have to check for negative edges, so we test with the general case.\n",
|
||||||
|
"\n",
|
||||||
|
"<pre>\n",
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|
"graph.add_edge('a', 'b', weight=5)\n",
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"graph.add_edge('a', 'c', weight=3)\n",
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"graph.add_edge('a', 'e', weight=2)\n",
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"graph.add_edge('b', 'd', weight=2)\n",
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"graph.add_edge('c', 'b', weight=1)\n",
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"graph.add_edge('c', 'd', weight=1)\n",
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"graph.add_edge('d', 'a', weight=1)\n",
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"graph.add_edge('d', 'g', weight=2)\n",
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"graph.add_edge('d', 'h', weight=1)\n",
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"graph.add_edge('e', 'a', weight=1)\n",
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"graph.add_edge('e', 'h', weight=4)\n",
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"graph.add_edge('e', 'i', weight=7)\n",
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"graph.add_edge('f', 'b', weight=3)\n",
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"graph.add_edge('f', 'g', weight=1)\n",
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"graph.add_edge('g', 'c', weight=3)\n",
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"graph.add_edge('g', 'i', weight=2)\n",
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"graph.add_edge('h', 'c', weight=2)\n",
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"graph.add_edge('h', 'f', weight=2)\n",
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"graph.add_edge('h', 'g', weight=2)\n",
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"shortest_path = ShortestPath(graph)\n",
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"result = shortest_path.find_shortest_path('a', 'i')\n",
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"assert_equal(result, ['a', 'c', 'd', 'g', 'i'])\n",
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"assert_equal(shortest_path.path_weight['i'], 8)\n",
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"</pre>"
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]
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},
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{
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"cell_type": "markdown",
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|
"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
|
||||||
|
"Wikipedia's animation:\n",
|
||||||
|
"\n",
|
||||||
|
"\n",
|
||||||
|
"\n",
|
||||||
|
"Initialize the following:\n",
|
||||||
|
"\n",
|
||||||
|
"* previous = {} # Key: node key, val: prev node key, shortest path\n",
|
||||||
|
" * Set each node's previous node key to None\n",
|
||||||
|
"* path_weight = {} # Key: node key, val: weight, shortest path\n",
|
||||||
|
" * Set each node's shortest path weight to infinity\n",
|
||||||
|
"* remaining = PriorityQueue() # Queue of node key, path weight\n",
|
||||||
|
" * Add each node's shortest path weight to the priority queue\n",
|
||||||
|
"\n",
|
||||||
|
"* Set the start node's path_weight to 0 and update the value in remaining\n",
|
||||||
|
"* Loop while remaining still has items\n",
|
||||||
|
" * Extract the min node (node with minimum path weight) from remaining\n",
|
||||||
|
" * Loop through each adjacent node in the min node\n",
|
||||||
|
" * Calculate the new weight:\n",
|
||||||
|
" * Adjacent node's edge weight + the min node's path_weight \n",
|
||||||
|
" * If the newly calculated path is less than the adjacent node's current path_weight:\n",
|
||||||
|
" * Set the node's previous node key leading to the shortest path\n",
|
||||||
|
" * Update the adjacent node's shortest path and update the value in the priority queue\n",
|
||||||
|
"* Walk backwards to determine the shortest path:\n",
|
||||||
|
" * Start at the end node, walk the previous dict to get to the start node\n",
|
||||||
|
"* Reverse the list and return it\n",
|
||||||
|
"\n",
|
||||||
|
"### Complexity for array-based priority queue:\n",
|
||||||
|
"\n",
|
||||||
|
"* Time: O(v^2), where v is the number of vertices\n",
|
||||||
|
"* Space: O(v^2)\n",
|
||||||
|
"\n",
|
||||||
|
"This might be better than the min-heap-based variant if the graph has a lot of edges.\n",
|
||||||
|
"\n",
|
||||||
|
"O(v^2) is better than O((v + v^2) log v).\n",
|
||||||
|
"\n",
|
||||||
|
"### Complexity for min-heap-based priority queue:\n",
|
||||||
|
"\n",
|
||||||
|
"* Time: O((v + e) log v), where v is the number of vertices, e is the number of edges\n",
|
||||||
|
"* Space: O((v + e) log v)\n",
|
||||||
|
"\n",
|
||||||
|
"This might be better than the array-based variant if the graph is sparse."
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"## Code"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 1,
|
||||||
|
"metadata": {
|
||||||
|
"collapsed": true
|
||||||
|
},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"%run ../../arrays_strings/priority_queue/priority_queue.py"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 2,
|
||||||
|
"metadata": {
|
||||||
|
"collapsed": true
|
||||||
|
},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"%run ../graph/graph.py"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 3,
|
||||||
|
"metadata": {
|
||||||
|
"collapsed": false
|
||||||
|
},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"import sys\n",
|
||||||
|
"\n",
|
||||||
|
"\n",
|
||||||
|
"class ShortestPath(object):\n",
|
||||||
|
"\n",
|
||||||
|
" def __init__(self, graph):\n",
|
||||||
|
" if graph is None:\n",
|
||||||
|
" raise TypeError('graph cannot be None')\n",
|
||||||
|
" self.graph = graph\n",
|
||||||
|
" self.previous = {} # Key: node key, val: prev node key, shortest path\n",
|
||||||
|
" self.path_weight = {} # Key: node key, val: weight, shortest path\n",
|
||||||
|
" self.remaining = PriorityQueue() # Queue of node key, path weight\n",
|
||||||
|
" for key in self.graph.nodes.keys():\n",
|
||||||
|
" # Set each node's previous node key to None\n",
|
||||||
|
" # Set each node's shortest path weight to infinity\n",
|
||||||
|
" # Add each node's shortest path weight to the priority queue\n",
|
||||||
|
" self.previous[key] = None\n",
|
||||||
|
" self.path_weight[key] = sys.maxsize\n",
|
||||||
|
" self.remaining.insert(\n",
|
||||||
|
" PriorityQueueNode(key, self.path_weight[key]))\n",
|
||||||
|
"\n",
|
||||||
|
" def find_shortest_path(self, start_node_key, end_node_key):\n",
|
||||||
|
" if start_node_key is None or end_node_key is None:\n",
|
||||||
|
" raise TypeError('Input node keys cannot be None')\n",
|
||||||
|
" if (start_node_key not in self.graph.nodes or\n",
|
||||||
|
" end_node_key not in self.graph.nodes):\n",
|
||||||
|
" raise ValueError('Invalid start or end node key')\n",
|
||||||
|
" # Set the start node's shortest path weight to 0\n",
|
||||||
|
" # and update the value in the priority queue\n",
|
||||||
|
" self.path_weight[start_node_key] = 0\n",
|
||||||
|
" self.remaining.decrease_key(start_node_key, 0)\n",
|
||||||
|
" while self.remaining:\n",
|
||||||
|
" # Extract the min node (node with minimum path weight)\n",
|
||||||
|
" # from the priority queue\n",
|
||||||
|
" min_node_key = self.remaining.extract_min().obj\n",
|
||||||
|
" min_node = self.graph.nodes[min_node_key]\n",
|
||||||
|
" # Loop through each adjacent node in the min node\n",
|
||||||
|
" for adj_key in min_node.adj_nodes.keys():\n",
|
||||||
|
" # Node's path:\n",
|
||||||
|
" # Adjacent node's edge weight + the min node's\n",
|
||||||
|
" # shortest path weight\n",
|
||||||
|
" new_weight = (min_node.adj_weights[adj_key] +\n",
|
||||||
|
" self.path_weight[min_node_key])\n",
|
||||||
|
" # Only update if the newly calculated path is\n",
|
||||||
|
" # less than the existing node's shortest path\n",
|
||||||
|
" if self.path_weight[adj_key] > new_weight:\n",
|
||||||
|
" # Set the node's previous node key leading to the shortest path\n",
|
||||||
|
" # Update the adjacent node's shortest path and\n",
|
||||||
|
" # update the value in the priority queue\n",
|
||||||
|
" self.previous[adj_key] = min_node_key\n",
|
||||||
|
" self.path_weight[adj_key] = new_weight\n",
|
||||||
|
" self.remaining.decrease_key(adj_key, new_weight)\n",
|
||||||
|
" # Walk backwards to determine the shortest path:\n",
|
||||||
|
" # Start at the end node, walk the previous dict to get to the start node\n",
|
||||||
|
" result = []\n",
|
||||||
|
" current_node_key = end_node_key\n",
|
||||||
|
" while current_node_key is not None:\n",
|
||||||
|
" result.append(current_node_key)\n",
|
||||||
|
" current_node_key = self.previous[current_node_key]\n",
|
||||||
|
" # Reverse the list\n",
|
||||||
|
" return result[::-1]"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"## Unit Test"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 4,
|
||||||
|
"metadata": {
|
||||||
|
"collapsed": false
|
||||||
|
},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"name": "stdout",
|
||||||
|
"output_type": "stream",
|
||||||
|
"text": [
|
||||||
|
"Overwriting test_shortest_path.py\n"
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"%%writefile test_shortest_path.py\n",
|
||||||
|
"from nose.tools import assert_equal\n",
|
||||||
|
"\n",
|
||||||
|
"\n",
|
||||||
|
"class TestShortestPath(object):\n",
|
||||||
|
"\n",
|
||||||
|
" def test_shortest_path(self):\n",
|
||||||
|
" graph = Graph()\n",
|
||||||
|
" graph.add_edge('a', 'b', weight=5)\n",
|
||||||
|
" graph.add_edge('a', 'c', weight=3)\n",
|
||||||
|
" graph.add_edge('a', 'e', weight=2)\n",
|
||||||
|
" graph.add_edge('b', 'd', weight=2)\n",
|
||||||
|
" graph.add_edge('c', 'b', weight=1)\n",
|
||||||
|
" graph.add_edge('c', 'd', weight=1)\n",
|
||||||
|
" graph.add_edge('d', 'a', weight=1)\n",
|
||||||
|
" graph.add_edge('d', 'g', weight=2)\n",
|
||||||
|
" graph.add_edge('d', 'h', weight=1)\n",
|
||||||
|
" graph.add_edge('e', 'a', weight=1)\n",
|
||||||
|
" graph.add_edge('e', 'h', weight=4)\n",
|
||||||
|
" graph.add_edge('e', 'i', weight=7)\n",
|
||||||
|
" graph.add_edge('f', 'b', weight=3)\n",
|
||||||
|
" graph.add_edge('f', 'g', weight=1)\n",
|
||||||
|
" graph.add_edge('g', 'c', weight=3)\n",
|
||||||
|
" graph.add_edge('g', 'i', weight=2)\n",
|
||||||
|
" graph.add_edge('h', 'c', weight=2)\n",
|
||||||
|
" graph.add_edge('h', 'f', weight=2)\n",
|
||||||
|
" graph.add_edge('h', 'g', weight=2)\n",
|
||||||
|
" shortest_path = ShortestPath(graph)\n",
|
||||||
|
" result = shortest_path.find_shortest_path('a', 'i')\n",
|
||||||
|
" assert_equal(result, ['a', 'c', 'd', 'g', 'i'])\n",
|
||||||
|
" assert_equal(shortest_path.path_weight['i'], 8)\n",
|
||||||
|
"\n",
|
||||||
|
" print('Success: test_shortest_path')\n",
|
||||||
|
"\n",
|
||||||
|
"\n",
|
||||||
|
"def main():\n",
|
||||||
|
" test = TestShortestPath()\n",
|
||||||
|
" test.test_shortest_path()\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_shortest_path\n"
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"%run -i test_shortest_path.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": "3.4.3"
|
||||||
|
}
|
||||||
|
},
|
||||||
|
"nbformat": 4,
|
||||||
|
"nbformat_minor": 0
|
||||||
|
}
|
||||||
41
graphs_trees/graph_shortest_path/priority_queue.py
Normal file
41
graphs_trees/graph_shortest_path/priority_queue.py
Normal file
|
|
@ -0,0 +1,41 @@
|
||||||
|
import sys
|
||||||
|
|
||||||
|
|
||||||
|
class PriorityQueueNode(object):
|
||||||
|
|
||||||
|
def __init__(self, obj, key):
|
||||||
|
self.obj = obj
|
||||||
|
self.key = key
|
||||||
|
|
||||||
|
def __repr__(self):
|
||||||
|
return str(self.obj) + ': ' + str(self.key)
|
||||||
|
|
||||||
|
|
||||||
|
class PriorityQueue(object):
|
||||||
|
|
||||||
|
def __init__(self):
|
||||||
|
self.queue = []
|
||||||
|
|
||||||
|
def insert(self, node):
|
||||||
|
if node is not None:
|
||||||
|
self.queue.append(node)
|
||||||
|
return self.queue[-1]
|
||||||
|
return None
|
||||||
|
|
||||||
|
def extract_min(self):
|
||||||
|
if not self.queue:
|
||||||
|
return None
|
||||||
|
minimum = sys.maxsize
|
||||||
|
for index, node in enumerate(self.queue):
|
||||||
|
if node.key < minimum:
|
||||||
|
minimum = node.key
|
||||||
|
minimum_index = index
|
||||||
|
node = self.queue.pop(minimum_index)
|
||||||
|
return node.obj
|
||||||
|
|
||||||
|
def decrease_key(self, obj, new_key):
|
||||||
|
for node in self.queue:
|
||||||
|
if node.obj is obj:
|
||||||
|
node.key = new_key
|
||||||
|
return node
|
||||||
|
return None
|
||||||
41
graphs_trees/graph_shortest_path/test_shortest_path.py
Normal file
41
graphs_trees/graph_shortest_path/test_shortest_path.py
Normal file
|
|
@ -0,0 +1,41 @@
|
||||||
|
from nose.tools import assert_equal
|
||||||
|
|
||||||
|
|
||||||
|
class TestShortestPath(object):
|
||||||
|
|
||||||
|
def test_shortest_path(self):
|
||||||
|
graph = Graph()
|
||||||
|
graph.add_edge('a', 'b', weight=5)
|
||||||
|
graph.add_edge('a', 'c', weight=3)
|
||||||
|
graph.add_edge('a', 'e', weight=2)
|
||||||
|
graph.add_edge('b', 'd', weight=2)
|
||||||
|
graph.add_edge('c', 'b', weight=1)
|
||||||
|
graph.add_edge('c', 'd', weight=1)
|
||||||
|
graph.add_edge('d', 'a', weight=1)
|
||||||
|
graph.add_edge('d', 'g', weight=2)
|
||||||
|
graph.add_edge('d', 'h', weight=1)
|
||||||
|
graph.add_edge('e', 'a', weight=1)
|
||||||
|
graph.add_edge('e', 'h', weight=4)
|
||||||
|
graph.add_edge('e', 'i', weight=7)
|
||||||
|
graph.add_edge('f', 'b', weight=3)
|
||||||
|
graph.add_edge('f', 'g', weight=1)
|
||||||
|
graph.add_edge('g', 'c', weight=3)
|
||||||
|
graph.add_edge('g', 'i', weight=2)
|
||||||
|
graph.add_edge('h', 'c', weight=2)
|
||||||
|
graph.add_edge('h', 'f', weight=2)
|
||||||
|
graph.add_edge('h', 'g', weight=2)
|
||||||
|
shortest_path = ShortestPath(graph)
|
||||||
|
result = shortest_path.find_shortest_path('a', 'i')
|
||||||
|
assert_equal(result, ['a', 'c', 'd', 'g', 'i'])
|
||||||
|
assert_equal(shortest_path.path_weight['i'], 8)
|
||||||
|
|
||||||
|
print('Success: test_shortest_path')
|
||||||
|
|
||||||
|
|
||||||
|
def main():
|
||||||
|
test = TestShortestPath()
|
||||||
|
test.test_shortest_path()
|
||||||
|
|
||||||
|
|
||||||
|
if __name__ == '__main__':
|
||||||
|
main()
|
||||||
Loading…
Reference in New Issue
Block a user