python-dijkstra

Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a weighted graph.

Contents

• How to use dijksta module?
  • Find all distances and paths
  • Find the shortest path
  • Find the shortest distance
• Drawing graphs

How to use dijksta module?

You must show your graph as an adjacency matrix. For example, notice this graph with its adjacency matrix:

Notice that using python's indexing you get a = 0, b = 1 ... g = 6, z = 7

Download dijkstra.py module and copy this in your workspace

Find all distances and paths

dijkstra.find_all(wmat, start, end=-1):

Returns a tuple with a distances' list and paths' list of all remaining vertices with the same indexing.

    (distances, paths)

For example, distances[x] are the shortest distances from x vertex which shortest path is paths[x]. x is an element of {0, 1, ..., n-1} where n is the number of vertices

Args:
wmat    --  weighted graph's adjacency matrix
start   --  paths' first vertex
end     --  (optional) path's end vertex. Return just the 
            distance and its path

Exceptions:
Index out of range, Be careful with start and end vertices.

Example code

import dijkstra # Import the module

# Weighted adjacency matrix
wmat = [[0, 2, 0, 0, 0, 1, 0, 0],
        [2, 0, 2, 2, 4, 0, 0, 0],
        [0, 2, 0, 0, 3, 0, 0, 1],
        [0, 2, 0, 0, 4, 3, 0, 0],
        [0, 4, 3, 4, 0, 0, 7, 0],
        [1, 0, 0, 3, 0, 0, 5, 0],
        [0, 0, 0, 0, 7, 5, 0, 6],
        [0, 0, 1, 0, 0, 0, 6, 0]]

print(dijkstra.find_all(wmat, 0))

Output:

([0, 2, 4, 4, 6, 1, 6, 5], [[0], [0, 1], [0, 1, 2], [0, 5, 3], [0, 1, 4], [0, 5], [0, 5, 6], [0, 1, 2, 7]])

Find the shortest path

dijkstra.find_shortest_path(wmat, start, end=-1):

Returns paths' list of all remaining vertices.

Args:
wmat    --  weighted graph's adjacency matrix
start   --  paths' first vertex
end     --  (optional) path's end vertex. Return just
            the path

Exceptions:
Index out of range, Be careful with start and end vertices.

Example code with final vertex

import dijkstra # Import the module

# Weighted adjacency matrix
wmat = [[0, 2, 0, 0, 0, 1, 0, 0],
        [2, 0, 2, 2, 4, 0, 0, 0],
        [0, 2, 0, 0, 3, 0, 0, 1],
        [0, 2, 0, 0, 4, 3, 0, 0],
        [0, 4, 3, 4, 0, 0, 7, 0],
        [1, 0, 0, 3, 0, 0, 5, 0],
        [0, 0, 0, 0, 7, 5, 0, 6],
        [0, 0, 1, 0, 0, 0, 6, 0]]

print(dijkstra.find_shortest_path(wmat, 0, 7))

Output:

[0, 1, 2, 7]

Example code without final vertex

import dijkstra # Import the module

# Weighted adjacency matrix
wmat = [[0, 2, 0, 0, 0, 1, 0, 0],
        [2, 0, 2, 2, 4, 0, 0, 0],
        [0, 2, 0, 0, 3, 0, 0, 1],
        [0, 2, 0, 0, 4, 3, 0, 0],
        [0, 4, 3, 4, 0, 0, 7, 0],
        [1, 0, 0, 3, 0, 0, 5, 0],
        [0, 0, 0, 0, 7, 5, 0, 6],
        [0, 0, 1, 0, 0, 0, 6, 0]]

print(dijkstra.find_shortest_path(wmat, 0))

Output:

[[0], [0, 1], [0, 1, 2], [0, 5, 3], [0, 1, 4], [0, 5], [0, 5, 6], [0, 1, 2, 7]]

Find the shortest distance

dijkstra.find_shortest_distance(wmat, start, end=-1):

Returns distances' list of all remaining vertices.

Args:
wmat    --  weighted graph's adjacency matrix
start   --  paths' first vertex
end     --  (optional) path's end vertex. Return just
            the distance

Exceptions:
Index out of range, Be careful with start and end vertices.

Example code with final vertex

import dijkstra # Import the module

# Weighted adjacency matrix
wmat = [[0, 2, 0, 0, 0, 1, 0, 0],
        [2, 0, 2, 2, 4, 0, 0, 0],
        [0, 2, 0, 0, 3, 0, 0, 1],
        [0, 2, 0, 0, 4, 3, 0, 0],
        [0, 4, 3, 4, 0, 0, 7, 0],
        [1, 0, 0, 3, 0, 0, 5, 0],
        [0, 0, 0, 0, 7, 5, 0, 6],
        [0, 0, 1, 0, 0, 0, 6, 0]]

print(dijkstra.find_shortest_distance(wmat, 0, 7))

Output:

5

Example code without final vertex

import dijkstra # Import the module

# Weighted adjacency matrix
wmat = [[0, 2, 0, 0, 0, 1, 0, 0],
        [2, 0, 2, 2, 4, 0, 0, 0],
        [0, 2, 0, 0, 3, 0, 0, 1],
        [0, 2, 0, 0, 4, 3, 0, 0],
        [0, 4, 3, 4, 0, 0, 7, 0],
        [1, 0, 0, 3, 0, 0, 5, 0],
        [0, 0, 0, 0, 7, 5, 0, 6],
        [0, 0, 1, 0, 0, 0, 6, 0]]

print(dijkstra.find_shortest_distance(wmat, 0))

Output:

[0, 2, 4, 4, 6, 1, 6, 5]

Drawing graphs

To get a visual representation using the adjacency matrix, you can use the next module draw_graph.py

draw_graph.undirected_graph(wmat, name="weighted_undirected_graph")

Creates a pdf file with the weigthted graph's visualization. You must have installed graphviz (Python conector and OS compilation)

OS: https://www.graphviz.org/

Python module: https://graphviz.readthedocs.io/en/stable/index.html

Args:
wmat  --  weigthted graph's adjacency matrix
name  --  (optional) graph's filenma

Example code

import draw_graph # Import the module

# Weighted adjacency matrix
wmat = [[0, 2, 0, 0, 0, 1, 0, 0],
        [2, 0, 2, 2, 4, 0, 0, 0],
        [0, 2, 0, 0, 3, 0, 0, 1],
        [0, 2, 0, 0, 4, 3, 0, 0],
        [0, 4, 3, 4, 0, 0, 7, 0],
        [1, 0, 0, 3, 0, 0, 5, 0],
        [0, 0, 0, 0, 7, 5, 0, 6],
        [0, 0, 1, 0, 0, 0, 6, 0]]

print(draw_graph.undirected_graph(wmat))

Output file: wmat.pdf