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 setUp(self):
self.uf = UnionFind(12)
