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93 lines
2.4 KiB
Python
93 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 = {0: [2, 3], 1: [0], 2: [1], 3: [4], 4: []}
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test_graph_2 = {0: [1, 2, 3], 1: [2], 2: [0], 3: [4], 4: [5], 5: [3]}
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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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