Provided that all of the vertices are reachable from the source vertex; Dijkstra’s algorithm can be used to find the shortest distance from the source vertex to all other vertices in a weighted graph. The graph can be directed or undirected, cyclic or acyclic, but the weights on all edges need to be nonnegative.
The following illustration shows the algorithm in action. Note that:
import sys # Function to find out which of the unvisited node # needs to be visited next def to_be_visited(): global visited_and_distance v = -10 # Choosing the vertex with the minimum distance for index in range(number_of_vertices): if visited_and_distance[index] == 0 \ and (v < 0 or visited_and_distance[index] <= \ visited_and_distance[v]): v = index return v # Creating the graph as an adjacency matrix vertices = [[0, 1, 1, 0], [0, 0, 1, 0], [0, 0, 0, 1], [0, 0, 0, 0]] edges = [[0, 3, 4, 0], [0, 0, 0.5, 0], [0, 0, 0, 1], [0, 0, 0, 0]] number_of_vertices = len(vertices) # The first element of the lists inside visited_and_distance # denotes if the vertex has been visited. # The second element of the lists inside the visited_and_distance # denotes the distance from the source. visited_and_distance = [[0, 0]] for i in range(number_of_vertices-1): visited_and_distance.append([0, sys.maxsize]) for vertex in range(number_of_vertices): # Finding the next vertex to be visited. to_visit = to_be_visited() for neighbor_index in range(number_of_vertices): # Calculating the new distance for all unvisited neighbours # of the chosen vertex. if vertices[to_visit][neighbor_index] == 1 and \ visited_and_distance[neighbor_index] == 0: new_distance = visited_and_distance[to_visit] \ + edges[to_visit][neighbor_index] # Updating the distance of the neighbor if its current distance # is greater than the distance that has just been calculated if visited_and_distance[neighbor_index] > new_distance: visited_and_distance[neighbor_index] = new_distance # Visiting the vertex found earlier visited_and_distance[to_visit] = 1 i = 0 # Printing out the shortest distance from the source to each vertex for distance in visited_and_distance: print("The shortest distance of ",chr(ord('a') + i),\ " from the source vertex a is:",distance) i = i + 1
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