def demoPrim():
'''
Example code for the Prim's algorithm.
'''
# Define the vertices and edges of the graph, in the structure
# the class Graph expects them
vertices = ['A', 'B', 'C', 'D', 'E', 'F']
edges_with_lengths = {
'A': [('B', 5), ('C', 6), ('D', 4)],
'B': [('A', 5), ('C', 1), ('D', 2)],
'C': [('A', 6), ('B', 1), ('D', 2), ('F', 3), ('E', 5)],
'D': [('A', 4), ('B', 2), ('C', 2), ('F', 4)],
'E': [('C', 5), ('F', 4)],
'F': [('D', 4), ('C', 3), ('E', 4)]
}
# Create the graph object G = (V, E) given the V and E
g = ga.Graph(vertices, edges_with_lengths)
# Run Prim's algorithm for the defined graph
mst, total_weight = ga.MST().prim(G=(g.getVertices(), g.getEdges()),
w=g.getLengths())
print('Prim\'s Minimum Spanning Tree, for the given graph:')
print('MST:', mst)
print('MST total weight:', total_weight)
def demoBellmanFord():
'''
Example code for the Bellman-Ford algorithm.
'''
# Define the vertices and edges of the graph, in the structure
# the class Graph expects them
vertices = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'S']
edges_with_lengths = {
'A': [('E', 2)],
'B': [('A', 1), ('C', 1)],
'C': [('D', 3)],
'D': [('E', -1)],
'E': [('B', -2)],
'F': [('A', -4), ('E', -1)],
'G': [('F', 1)],
'S': [('A', 10), ('G', 8)]
}
# Create the graph object G = (V, E) given the V and E
g = ga.Graph(vertices, edges_with_lengths)
# Run Bellman-Ford algorithm for the defined graph
paths, cost = ga.GraphAlgorithms().bellmanFord(G=(g.getVertices(),
g.getEdges()),
l=g.getLengths(),
s='S')
# Back tracking the paths, we can get the shortest path for any destination node
print(
'Bellman-Ford shortest paths for the given graph, where starting node is \'S\':'
)
start_node = 'S'
for end_node in ['A', 'B', 'C', 'D', 'E', 'F', 'G']:
done = False
shortest_path = [end_node]
current = end_node
while not done:
shortest_path.insert(0, paths[current])
current = shortest_path[0]
if current == start_node:
done = True
print('Shortest path from \'',
start_node,
'\' to \'',
end_node,
'\' is: ',
shortest_path,
' with cost ',
cost[end_node],
sep='')
def demoBfs():
'''
Example code for the BFS algorithm.
'''
# Define the vertices and edges of the graph, in the structure
# the class Graph expects them
vertices = ['A', 'B', 'C', 'D', 'E', 'S']
edges_with_lengths = {
'A': [('S', 1), ('B', 1)],
'B': [('A', 1), ('C', 1)],
'C': [('B', 1), ('S', 1)],
'D': [('E', 1), ('S', 1)],
'E': [('D', 1), ('S', 1)],
'S': [('E', 1), ('D', 1), ('C', 1), ('A', 1)]
}
# Create the graph object G = (V, E) given the V and E
g = ga.Graph(vertices, edges_with_lengths)
# Run BFS algorithm for the defined graph
paths, cost = ga.GraphAlgorithms().bfs(G=(g.getVertices(), g.getEdges()),
s='B')
print(
'BFS shortest paths for the given graph, where starting node is \'B\':'
)
start_node = 'B'
for end_node in ['A', 'C', 'D', 'E', 'S']:
done = False
shortest_path = [end_node]
current = end_node
while not done:
shortest_path.insert(0, paths[current])
current = shortest_path[0]
if current == start_node:
done = True
print('Shortest path from \'',
start_node,
'\' to \'',
end_node,
'\' is: ',
shortest_path,
' with cost ',
cost[end_node],
sep='')
def demoDfs():
'''
Example code for the DFS algorithm.
'''
# Define the vertices and edges of the graph, in the structure
# the class Graph expects them
vertices = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L']
edges_with_lengths = {
'A': [('B', 1), ('E', 1)],
'B': [('A', 1)],
'C': [('D', 1), ('G', 1), ('H', 1)],
'D': [('C', 1), ('H', 1)],
'E': [('A', 1), ('I', 1), ('J', 1)],
'F': [],
'G': [('C', 1), ('H', 1), ('K', 1)],
'H': [('D', 1), ('L', 1), ('C', 1), ('G', 1), ('K', 1)],
'I': [('E', 1), ('J', 1)],
'J': [('E', 1), ('I', 1)],
'K': [('G', 1), ('H', 1)],
'L': [('H', 1)]
}
# Create the graph object G = (V, E) given the V and E
g = ga.Graph(vertices, edges_with_lengths)
# Run DFS algorithm for the defined graph
previsit, postvisit, ccnum = ga.GraphAlgorithms().dfs(G=(g.getVertices(),
g.getEdges()))
print('DFS output for the given graph:')
for node in vertices:
print('node \'{:1}\': first_discovery_time = {:2},last_departure_time = {:2}, connected_component = {:2}'.\
format(node, previsit[node], postvisit[node], ccnum[node]))
for i in range(1, max(ccnum.values()) + 1):
print('connected component ',
i,
': ', [k for k, v in ccnum.items() if v == i],
sep='')