def MSTPrim(graph: WeightedGraph, root: Any) -> WeightedGraph:
"""
Prim's algorithm to creating an MST from a weighted graph - a greedy algorithm taking all accessible edges from
the currently considered vertices into account
:param graph: a weighted graph of which we extract an MST from
:param root: the first node to consider
:return: an MST of the graph
"""
vertices = graph.adjacency_list.keys()
mst = WeightedGraph()
priority = {}
parent = {}
for vertex in vertices:
priority[vertex] = max(graph.weights.values()) # Acts as infinity
parent[vertex] = None
priority[root] = 0
q = MinPriorityQueue()
for vertex in vertices:
q.insert(vertex, priority[vertex])
while not q.is_empty():
node = q.extract_min()
u = node.value
u_weight = node.priority
mst.add_vertex(u)
if parent[u] is not None:
mst.add_weighted_edge(u, parent[u], u_weight)
for v in graph.adjacency_list[u]:
if v in q and graph.weights[(u, v)] < priority[v]:
priority[v] = graph.weights[(
u, v)] # update to the correct weight
q.update_priority(v,
priority[v]) # update to the correct weight
parent[v] = u
return mst
