import heapq

def dijkstra(graph, start):
    distances = {vertex: float('inf') for vertex in graph}
    distances[start] = 0

    pq = [(0, start)]

    while pq:
        current_distance, current_vertex = heapq.heappop(pq)

        if current_distance > distances[current_vertex]:
            continue

        for neighbor, weight in graph[current_vertex].items():
            distance = current_distance + weight

            if distance < distances[neighbor]:
                distances[neighbor] = distance
                heapq.heappush(pq, (distance, neighbor))

    return distances

graph = {
         'A' : {'B' : 4, 'C' : 2},
         'B' : {'A' : 4, 'C' : 1, 'D' : 5},
         'C' : {'A' : 2, 'B' : 1, 'D' : 8, 'E' : 10},
         'D' : {'B' : 5, 'C' : 8, 'E' : 2},
         'E' : {'C' : 10, 'D' : 2}
}

print(dijkstra(graph, 'A'))