def prim(graph: UndirectedGraph) -> UndirectedGraph:
"""
Prim's algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph.
This means it finds a subset of the edges that forms a tree that includes every vertex
O(E + V log V)
"""
current_vertex = graph.get_vertices()[0]
new_graph = UndirectedGraph()
heap = FibonacciHeap(map(lambda x: (x, current_vertex), graph.get_outgoing_edges(current_vertex)))
vertices = {current_vertex}
while not heap.is_empty():
edge, current_vertex = heap.pop()
next_vertex = edge.a if edge.a != current_vertex else edge.b
if next_vertex in vertices:
continue
# Add edge to the minimum spanning tree
vertices.add(next_vertex)
new_graph.add_edge(current_vertex, next_vertex, edge.weight)
# Add all edges from this new point to the heap
[heap.insert((edge, next_vertex)) for edge in graph.get_outgoing_edges(next_vertex)]
return new_graph
def setUp(self):
self.undirected = UndirectedGraph()
self.undirected.add_edge(1, 2, 2)
self.undirected.add_edge(1, 3, 6)
self.undirected.add_edge(2, 4, 1)
self.undirected.add_edge(3, 5, 4)
def setUp(self):
g = UndirectedGraph()
g.add_edge(1, 2, 2)
g.add_edge(1, 3, 6)
g.add_edge(2, 3, 3)
g.add_edge(2, 4, 9)
g.add_edge(3, 4, 1)
g.add_edge(3, 5, 4)
g.add_edge(4, 5, 6)
self.graph = g
def kruskal(graph: UndirectedGraph) -> UndirectedGraph:
"""
Kruskal's algorithm is a minimum-spanning-tree algorithm which finds an edge of the least possible weight
that connects any two trees in the forest. It is a greedy algorithm in graph theory as it finds a minimum
spanning tree for a connected weighted undirected graph adding increasing cost arcs at each step.
Time complexity: O(E log V)
"""
spanning_tree = UndirectedGraph()
union_find = UnionFind(max(graph.get_vertices()) + 1)
heap = FibonacciHeap(graph.get_all_edges())
while not heap.is_empty():
edge = heap.pop()
# Only add the edge if it will not create a cycle
if union_find.find(edge.a) != union_find.find(edge.b):
spanning_tree.add_edge(edge.a, edge.b, edge.weight)
union_find.union(edge.a, edge.b)
return spanning_tree
def test_undirected_graph(self):
g = UndirectedGraph()
