PyAlgDat 1.0.2

Various data structures and algorithms.

• ABOUT PYALGDAT

• FEATURES

• REQUIREMENTS

• INSTALLATION

• EXAMPLES

• DOCUMENTATION

• LICENSE

• AUTHOR

• CHANGELOG

ABOUT PYALGDAT

PyAlgDat is a collection of data structures and algorithms written in Python. The purpose of the code is to show how many of the abstract data types (ADTs) and algorithms being thought in Computer Science courses can be realised in Python.

My primary focus has been to write a library which presents a clear implementation of the various data structures and algorithms and how they can be used. This means that I have made a conscious tradeoff where clarity of the code outweighs subtle and exotic implementation constructs.

The library has mostly been implemented as a recreational project and should as such not be used in production code, since most of the data structures and algorithms are already available in the standard Python library. However, writing software that is robust, performs well, and is easy to maintain requires knowledge of data structures and algorithms. Therefore, implementing and experimenting with these provides valuable knowledge about the inner workings and implementation details found in such standard libraries.

FEATURES

Data structures included in the library

• Dynamic array

• Stack

• Queue

• BinaryHeap

  • MinHeap

  • MaxHeap

• LinkedList

  • Singly linked list

  • Doubly linked list

• Partition/Union-Find

• Graph

  • Directed

  • Undirected

  • Directed weighted

  • Undirected weighted

Additionally, the library contains the most common algorithms and operations needed when working with these data structures.

REQUIREMENTS

The library is selfcontained and does not have any external dependencies. PyAlgDat should run on any platform with Python 2.7 or above.

INSTALLATION

The package can be installed using pip

$ pip install PyAlgDat

EXAMPLES

PyAlgDat has a collection of functional test examples which shows how the library can be used from a client’s perspective.

Shortest path using Dijkstra’s algorithm

Below is a simple example showing howto create a directed weighted graph using PyAlgDat and how the shortest path in this graph can be found using Dijkstra’s algorithm.

#!/usr/bin/env python

"""
Test of Dijkstra's algorithm for a Directed Weighted Graph.
"""

def create_graph():
     """
     Creates a Directed Weighted Graph
     """
     # Create an empty directed weighted graph
     graph = DirectedWeightedGraph(7)

     # Create vertices
     vertex0 = UnWeightedGraphVertex(graph, "A")
     vertex1 = UnWeightedGraphVertex(graph, "B")
     vertex2 = UnWeightedGraphVertex(graph, "C")
     vertex3 = UnWeightedGraphVertex(graph, "D")
     vertex4 = UnWeightedGraphVertex(graph, "E")
     vertex5 = UnWeightedGraphVertex(graph, "F")
     vertex6 = UnWeightedGraphVertex(graph, "G")

     # Add vertices
     graph.add_vertex(vertex0)
     graph.add_vertex(vertex1)
     graph.add_vertex(vertex2)
     graph.add_vertex(vertex3)
     graph.add_vertex(vertex4)
     graph.add_vertex(vertex5)
     graph.add_vertex(vertex6)

     # Add edges
     graph.add_edge(vertex0, vertex1, 7)   # ( A <- B, 7 )
     graph.add_edge(vertex1, vertex2, 2)   # ( B <- C, 2 )
     graph.add_edge(vertex1, vertex6, 3)   # ( B -> G, 3 )
     graph.add_edge(vertex2, vertex3, 2)   # ( C -> D, 2 )
     graph.add_edge(vertex2, vertex6, 4)   # ( C -> G, 4 )
     graph.add_edge(vertex3, vertex4, 5)   # ( D -> E, 5 )
     graph.add_edge(vertex3, vertex6, 1)   # ( D -> G, 1 )
     graph.add_edge(vertex4, vertex5, 6)   # ( E -> F, 6 )
     graph.add_edge(vertex5, vertex0, 1)   # ( F <- A, 1 )
     graph.add_edge(vertex5, vertex6, 4)   # ( F <- G, 4 )
     graph.add_edge(vertex6, vertex0, 7)   # ( G -> A, 7 )
     graph.add_edge(vertex6, vertex4, 1)   # ( G -> E, 1 )

     #       B--<--7--<--A
     #      / \         / \
     #     /   \       /   \
     #    2     3     7     1
     #   /       \   /       \
     #  /         \ /         \
     # C-->--4-->--G--<--4--<--F
     #  \         / \         /
     #   \       /   \       /
     #    2     1     1     6
     #     \   /       \   /
     #      \ /         \ /
     #       D-->--5-->--E

     return graph

if __name__ == "__main__":

   # Make it possible to use py_alg_dat without performing
   # an installation. This is needed in order to be able
   # to run: python dijkstra_test.py, without having
   # performed an installation of the package. The is
   # neccessary due to Python's handling of relative
   # imports.
   if __package__ is None:
     import sys
     from os import path
     sys.path.append(path.dirname(path.dirname(path.abspath(__file__))))
     from py_alg_dat.graph import DirectedWeightedGraph
     from py_alg_dat.graph_vertex import UnWeightedGraphVertex
     from py_alg_dat.graph_algorithms import GraphAlgorithms
   else:
     from ..py_alg_dat.graph import DirectedWeightedGraph
     from ..py_alg_dat.graph_vertex import UnWeightedGraphVertex
     from ..py_alg_dat.graph_algorithms import GraphAlgorithms

   # Create the graph
   GRAPH = create_graph()
   # Run Dijkstra starting at vertex "A"
   TABLE = GraphAlgorithms.dijkstras_algorithm(GRAPH, GRAPH[0])
   # Find the edges in the Spanning Tree and its total weight
   SPANNING_TREE_EDGES = set()
   SPANNING_TREE_WEIGHT = 0
   for i in xrange(len(TABLE)):
     entry = TABLE[i]
     if entry.predecessor != None:
         edge = entry.edge
         SPANNING_TREE_EDGES.add(edge)
         SPANNING_TREE_WEIGHT += edge.get_weight()
   print "Edges in Spanning Tree: " + str(SPANNING_TREE_EDGES)
   print "Weight of Spanning Tree: " + str(SPANNING_TREE_WEIGHT)

Minimum spanning tree using Kruskal’s algorithm

Below is a simple example showing howto create an un-directed weighted graph using PyAlgDat and how the minimum spanning tree of this graph can be found using Kruskal’s algorithm.

#!/usr/bin/env python

"""
Test of Kruskal's algorithm for a UnDirected Weighted Graph.
"""

def create_graph():
    """
    Creates an UnDirected Weighted Graph
    """
    # Create an empty undirected weighted graph
    graph = UnDirectedWeightedGraph(7)

    # Create vertices
    vertex1 = UnWeightedGraphVertex(graph, "A")
    vertex2 = UnWeightedGraphVertex(graph, "B")
    vertex3 = UnWeightedGraphVertex(graph, "C")
    vertex4 = UnWeightedGraphVertex(graph, "D")
    vertex5 = UnWeightedGraphVertex(graph, "E")
    vertex6 = UnWeightedGraphVertex(graph, "F")
    vertex7 = UnWeightedGraphVertex(graph, "G")

    # Add vertices
    graph.add_vertex(vertex1)
    graph.add_vertex(vertex2)
    graph.add_vertex(vertex3)
    graph.add_vertex(vertex4)
    graph.add_vertex(vertex5)
    graph.add_vertex(vertex6)
    graph.add_vertex(vertex7)

    # Add edges
    graph.add_edge(vertex1, vertex2, 7)    # (A - B, 7)
    graph.add_edge(vertex1, vertex4, 5)    # (A - D, 5)
    graph.add_edge(vertex2, vertex3, 8)    # (B - C, 8)
    graph.add_edge(vertex2, vertex4, 9)    # (B - D, 9)
    graph.add_edge(vertex2, vertex5, 7)    # (B - E, 7)
    graph.add_edge(vertex3, vertex5, 5)    # (C - E, 5)
    graph.add_edge(vertex4, vertex5, 15)   # (D - E, 1)
    graph.add_edge(vertex4, vertex6, 6)    # (D - F, 6)
    graph.add_edge(vertex5, vertex6, 8)    # (E - F, 8)
    graph.add_edge(vertex5, vertex7, 9)    # (E - G, 9)
    graph.add_edge(vertex6, vertex7, 11)   # (F - G, 11)
    return graph

if __name__ == "__main__":
    # Make it possible to use py_alg_dat without performing
    # an installation. This is needed in order to be able
    # to run: python kruskal_test.py, without having
    # performed an installation of the package. The is
    # neccessary due to Python's handling of relative
    # imports.
    if __package__ is None:
       import sys
       from os import path
       sys.path.append(path.dirname(path.dirname(path.abspath(__file__))))
       from py_alg_dat.graph import UnDirectedWeightedGraph
       from py_alg_dat.graph_vertex import UnWeightedGraphVertex
       from py_alg_dat.graph_algorithms import GraphAlgorithms
    else:
       from ..py_alg_dat.graph import UnDirectedWeightedGraph
       from ..py_alg_dat.graph_vertex import UnWeightedGraphVertex
       from ..py_alg_dat.graph_algorithms import GraphAlgorithms

    # Create the graph
    GRAPH = create_graph()
    # Run Kruskal's algorithm
    MST = GraphAlgorithms.kruskals_algorithm(GRAPH)
    print MST

The above examples -and others can be found in the ‘examples’ folder in the PyAlgDat directory.

DOCUMENTATION

The PyAlgDat API contains Docstrings for all classes and methods. Additional documentation about the library can be found in the ‘docs’ folder in the PyAlgDat directory.

The full documentation is at http://pyalgdat.readthedocs.org/en/latest/.

LICENSE

PyAlgDat is published under the MIT License. The copyright and license are specified in the file “LICENSE.txt” in the PyAlgDat directory and shown below.

AUTHOR

Brian Horn, [e-mail]

CHANGELOG

1.0.2 (2016-09-01)

• Added Bellman-Ford graph algorithm

• Made unit tests part of the distribution

1.0.1 (2015-07-19)

• First release on PyPi

• Fixed a problem in singly linked list when inserting an element at a specific index, causing the reference to the tail element to be wrong.

• Fixed a problem in singly linked list when removing the last element.

• Implemented functionality to remove a vertex from a graph.

• Implemented functionality to remove an edge from a graph.

• Implemented shallow copy functionality in array_list.py.

• Implemented support for slicing in array_list.py.

• Implemented equal -and not equal operators in class UnDirectedGraph.

• Implemented equal -and not equal operators in singly_linked_list.py.

• Implemented equal -and not equal operators in doubly_linked_list.py.

• Implemented shallow copy functionality in singly_linked_list.py.

• Implemented shallow copy functionality in doubly_linked_list.py.

• Library has now changed name to PyAlgDat.

• Removed attribute ‘numberOfVertices’ in graph.py.

• Removed attribute ‘numberOfEdges’ in graph.py.

• Renamed attribute ‘vertexName’ in graph_vertex.py to ‘vertex_name’

• Renamed attribute ‘vertexNumber’ in graph_vertex.py to ‘vertex_number’

• Renamed attribute ‘vertexWeight’ in graph_vertex.py to ‘vertex_weight’

• PyAlgDat is licensed under The MIT License (MIT)

• Made PyAlgDat pylint compliant

• Added content to README.rst

• Added examples folder containing test programs showing API usage

1.0.0 (2014-02-09)

• First public release