Algorithme Dijkstra
"""
The below code provides an implementation
for the dijkstra's shortest path algorithm
(https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm).
Let v be the number of vertices of graph and e number of
edges in the input graph.
Time complexity: O(v^2 + e)
Space complexity: O(v)
"""
class Graph:
def __init__(self, vertices, edges):
self.V = vertices # nb of vertices
self.E = edges # adjacency list
# Print the lengths of shortest paths from
# src to all the other nodes. If no path
# is found, output would be -1.
def print_min_dists(self, src, min_dist_list):
print("Min distance from " + str(src) + ":")
for vertex in range(self.V):
print(vertex, "\t", min_dist_list[vertex])
# Below function computes lengths of shortest paths
# between src and all other vertices in the graph
# using the Dijkstra's algorithm. Element at index i
# in output list represents length of shortest path
# from src to vertex i.
def dijkstra(self, src):
# Initially all distances are initialized to infinity
min_dist_list = [float("inf")] * self.V
min_dist_list[src] = 0
# List of already visited nodes
visited = set()
# Loop until all nodes are processed
while len(visited) != self.V:
# The entire graph is searched for vertex having
# min distance to source node.
vertex, current_min_dist = self.get_vertex_min_dist(
min_dist_list, visited)
# If remaining nodes are not reachable, abort
if current_min_dist == float("inf"):
break
# Mark current vertex as visited
visited.add(vertex)
# Update distances of nodes adjacent to current vertex
for edge in self.E[vertex]:
destination, dist_to_destination = edge
if destination in visited:
continue
new_path_dist = current_min_dist + dist_to_destination
current_destination_dist = min_dist_list[destination]
if new_path_dist < current_destination_dist:
min_dist_list[destination] = new_path_dist
return list(map(lambda x: -1 if x == float("inf") else x, min_dist_list))
# Get next vertex with min distance to source
def get_vertex_min_dist(self, distances, visited):
current_min_dist = float("inf")
vertex = -1
for vertex_idx, distance in enumerate(distances):
if vertex_idx in visited:
continue
if distance <= current_min_dist:
vertex = vertex_idx
current_min_dist = distance
return vertex, current_min_dist
vertices = 4
edges = {
0: [(1, 2), (3, 6)],
1: [(0, 2), (2, 2)],
2: [(1, 2), (3, 1)],
3: [(0, 6), (2, 1)]
}
graph = Graph(vertices, edges)
graph.print_min_dists(0, graph.dijkstra(0))
"""
Above outputs:
Min distance from 0:
0 0
1 2
2 4
3 5
"""
Wissam