topological sort Algorithm
In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge UV from vertex u to vertex V, u arrives before V in the ordering. For case, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one undertaking must be performed before another; in this application, a topological ordering is exactly a valid sequence for the tasks.
"""Topological Sort."""
# a
# / \
# b c
# / \
# d e
edges = {"a": ["c", "b"], "b": ["d", "e"], "c": [], "d": [], "e": []}
vertices = ["a", "b", "c", "d", "e"]
def topological_sort(start, visited, sort):
"""Perform topolical sort on a directed acyclic graph."""
current = start
# add current to visited
visited.append(current)
neighbors = edges[current]
for neighbor in neighbors:
# if neighbor not in visited, visit
if neighbor not in visited:
sort = topological_sort(neighbor, visited, sort)
# if all neighbors visited add current to sort
sort.append(current)
# if all vertices haven't been visited select a new one to visit
if len(visited) != len(vertices):
for vertice in vertices:
if vertice not in visited:
sort = topological_sort(vertice, visited, sort)
# return sort
return sort
if __name__ == "__main__":
sort = topological_sort("a", [], [])
print(sort)
