@@ -21,7 +21,7 @@ The pseudocode could be represented as such:
2121 - Select the edge with the min weight of an unvisited vertex from top of heap.
2222 - Add the selected vertex to the visited vertices.
2323 - Add selected vertex's neighboring edges of unvisited vertices into the heap.
24-
24+ 2525Since we are sorting based on vertices, the sorting will take log(V) run-time.
2626However, we have to sort this based on number of vertices or edges because we can be given a graph of islands or nodes that have edges to all nodes.
2727That is why its O((V+E) log(V)) run-time.
@@ -31,14 +31,14 @@ from collections import defaultdict
3131
3232class Solution:
3333 def minimumCost(self, N: int, connections: List[List[int]]) -> int:
34-
34+
3535 def create_adj_list(connections):
3636 adj_list = defaultdict(list)
3737 for city1, city2, cost in connections:
3838 adj_list[city1].append(Vertex(city2, cost))
3939 adj_list[city2].append(Vertex(city1, cost))
4040 return adj_list
41-
41+
4242 adj_list = create_adj_list(connections)
4343 visited = set([N])
4444 min_heap = list(adj_list[N] if N in adj_list else [])
@@ -51,18 +51,19 @@ class Solution:
5151 visited.add(vertex.to)
5252 min_cost += vertex.cost
5353 for vertex in adj_list[vertex.to]:
54- heapq.heappush(min_heap, vertex)
54+ if vertex.to not in visited:
55+ heapq.heappush(min_heap, vertex)
5556 return min_cost if len(visited) == N else -1
56-
57+
5758class Vertex(object):
58-
59+
5960 def __init__(self, to, cost):
6061 self.to = to
6162 self.cost = cost
62-
63+
6364 def __lt__(self, other):
6465 return self.cost < other.cost
65-
66+
6667 def __repr__(self):
6768 return 'To: {}, Cost: {}'.format(self.to, self.cost)
6869```
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