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* Improve comments, add doctests for kahns_algorithm_topo.py * Improve function docstring * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Rename variables, remove print --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
62 lines
1.8 KiB
Python
62 lines
1.8 KiB
Python
def topological_sort(graph: dict[int, list[int]]) -> list[int] | None:
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"""
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Perform topological sorting of a Directed Acyclic Graph (DAG)
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using Kahn's Algorithm via Breadth-First Search (BFS).
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Topological sorting is a linear ordering of vertices in a graph such that for
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every directed edge u → v, vertex u comes before vertex v in the ordering.
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Parameters:
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graph: Adjacency list representing the directed graph where keys are
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vertices, and values are lists of adjacent vertices.
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Returns:
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The topologically sorted order of vertices if the graph is a DAG.
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Returns None if the graph contains a cycle.
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Example:
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>>> graph = {0: [1, 2], 1: [3], 2: [3], 3: [4, 5], 4: [], 5: []}
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>>> topological_sort(graph)
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[0, 1, 2, 3, 4, 5]
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>>> graph_with_cycle = {0: [1], 1: [2], 2: [0]}
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>>> topological_sort(graph_with_cycle)
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"""
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indegree = [0] * len(graph)
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queue = []
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topo_order = []
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processed_vertices_count = 0
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# Calculate the indegree of each vertex
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for values in graph.values():
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for i in values:
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indegree[i] += 1
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# Add all vertices with 0 indegree to the queue
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for i in range(len(indegree)):
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if indegree[i] == 0:
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queue.append(i)
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# Perform BFS
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while queue:
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vertex = queue.pop(0)
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processed_vertices_count += 1
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topo_order.append(vertex)
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# Traverse neighbors
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for neighbor in graph[vertex]:
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indegree[neighbor] -= 1
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if indegree[neighbor] == 0:
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queue.append(neighbor)
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if processed_vertices_count != len(graph):
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return None # no topological ordering exists due to cycle
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return topo_order # valid topological ordering
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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