FAQ: Dijkstra's Algorithm: Python - Dijkstra's Algorithm in Python: Review

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This community-built FAQ covers the “Dijkstra’s Algorithm in Python: Review” exercise from the lesson “Dijkstra’s Algorithm: Python”.

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In the instruction video, there is an “unvisited” list containing all the unvisited vertices, and it contains every vertex at first. In each iteration, the smallest one will be popped out using a min heap. However, in the python implementation, this list, vertices_to_explore, does not contain all vertices at first; it only has the start vertex at first, and other vertices are added to the list during the iteration. What are the differences?

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In the code implementation we are storing two values: the vertex itself and its relative cost
ex (“A”, 0) in the video explanation the list only contains a visual reference of the “unvisited” vertices
The practical implementation is correct because we are not just popping off the cheapest vertices but we are updating and pushing back with the updated cost.
By the way in the code I see that the unvisited_vertex variable is initialized: [(0, start)] wich could stay the same as they are in the relative graph: [(start, 0)] wich will cause less confusion in the code implementation.

def dijkstra(graph, start):
    distances = {}
    for vertex in graph:
        distances[vertex] = inf
    distances[start] = 0
    unvisited_vertex = [(start, 0)]
    while unvisited_vertex:
        current_vertex, distance = heappop(unvisited_vertex)
        for neighbor, weight in graph[current_vertex]:
            new_distance = distance + weight
            if new_distance < distances[neighbor]:
                distances[neighbor] = new_distance
                heappush(unvisited_vertex, (neighbor, new_distance))
    return distances