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* Implement strongly connected components for graph algorithms
* fixup! Format Python code with psf/black push
* Delete trailing whitespace
* updating DIRECTORY.md
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* fixup! Format Python code with psf/black push
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Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
106 lines
2.4 KiB
Python
106 lines
2.4 KiB
Python
"""
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https://en.wikipedia.org/wiki/Strongly_connected_component
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Finding strongly connected components in directed graph
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"""
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test_graph_1 = {
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0: [2, 3],
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1: [0],
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2: [1],
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3: [4],
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4: [],
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}
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test_graph_2 = {
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0: [1, 2, 3],
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1: [2],
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2: [0],
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3: [4],
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4: [5],
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5: [3],
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}
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def topology_sort(graph: dict, vert: int, visited: list) -> list:
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"""
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Use depth first search to sort graph
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At this time graph is the same as input
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>>> topology_sort(test_graph_1, 0, 5 * [False])
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[1, 2, 4, 3, 0]
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>>> topology_sort(test_graph_2, 0, 6 * [False])
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[2, 1, 5, 4, 3, 0]
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"""
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visited[vert] = True
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order = []
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for neighbour in graph[vert]:
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if not visited[neighbour]:
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order += topology_sort(graph, neighbour, visited)
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order.append(vert)
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return order
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def find_components(reversed_graph: dict, vert: int, visited: list) -> list:
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"""
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Use depth first search to find strongliy connected
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vertices. Now graph is reversed
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>>> find_components({0: [1], 1: [2], 2: [0]}, 0, 5 * [False])
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[0, 1, 2]
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>>> find_components({0: [2], 1: [0], 2: [0, 1]}, 0, 6 * [False])
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[0, 2, 1]
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"""
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visited[vert] = True
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component = [vert]
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for neighbour in reversed_graph[vert]:
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if not visited[neighbour]:
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component += find_components(reversed_graph, neighbour, visited)
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return component
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def strongly_connected_components(graph: dict) -> list:
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"""
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This function takes graph as a parameter
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and then returns the list of strongly connected components
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>>> strongly_connected_components(test_graph_1)
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[[0, 1, 2], [3], [4]]
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>>> strongly_connected_components(test_graph_2)
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[[0, 2, 1], [3, 5, 4]]
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"""
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visited = len(graph) * [False]
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reversed_graph = {vert: [] for vert in range(len(graph))}
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for vert, neighbours in graph.items():
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for neighbour in neighbours:
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reversed_graph[neighbour].append(vert)
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order = []
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for i, was_visited in enumerate(visited):
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if not was_visited:
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order += topology_sort(graph, i, visited)
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components_list = []
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visited = len(graph) * [False]
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for i in range(len(graph)):
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vert = order[len(graph) - i - 1]
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if not visited[vert]:
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component = find_components(reversed_graph, vert, visited)
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components_list.append(component)
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return components_list
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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