Strongly connected components #2114
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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: | ||
| """ | ||
| Use depth first search to sort graph | ||
| At this time graph is the same as input | ||
| >>> topology_sort(test_graph_1, 0, 5 * [False]) | ||
| [1, 2, 4, 3, 0] | ||
| >>> topology_sort(test_graph_2, 0, 6 * [False]) | ||
| [2, 1, 5, 4, 3, 0] | ||
| """ | ||
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| visited[vert] = True | ||
| order = [] | ||
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cclauss marked this conversation as resolved.
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| for neighbour in graph[vert]: | ||
| if not visited[neighbour]: | ||
| 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: | ||
| """ | ||
| Use depth first search to find strongliy connected | ||
| vertices. Now graph is reversed | ||
| >>> find_components({0: [1], 1: [2], 2: [0]}, 0, 5 * [False]) | ||
| [0, 1, 2] | ||
| >>> find_components({0: [2], 1: [0], 2: [0, 1]}, 0, 6 * [False]) | ||
| [0, 2, 1] | ||
| """ | ||
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| visited[vert] = True | ||
| component = [vert] | ||
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cclauss marked this conversation as resolved.
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| for neighbour in reversed_graph[vert]: | ||
| if not visited[neighbour]: | ||
| component += find_components(reversed_graph, neighbour, visited) | ||
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| return component | ||
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| def strongly_connected_components(graph: dict) -> list: | ||
| """ | ||
| This function takes graph as a parameter | ||
| and then returns the list of strongly connected components | ||
| >>> strongly_connected_components(test_graph_1) | ||
| [[0, 1, 2], [3], [4]] | ||
| >>> strongly_connected_components(test_graph_2) | ||
| [[0, 2, 1], [3, 5, 4]] | ||
| """ | ||
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| visited = len(graph) * [False] | ||
| reversed_graph = {vert: [] for vert in range(len(graph))} | ||
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Member
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| for vert, neighbours in graph.items(): | ||
| for neighbour in neighbours: | ||
| reversed_graph[neighbour].append(vert) | ||
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| order = [] | ||
| for i, was_visited in enumerate(visited): | ||
| if not was_visited: | ||
| order += topology_sort(graph, i, visited) | ||
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| components_list = [] | ||
| visited = len(graph) * [False] | ||
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Member
There was a problem hiding this comment. Remove comments, rename variables better. |
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| for i in range(len(graph)): | ||
| vert = order[len(graph) - i - 1] | ||
| if not visited[vert]: | ||
| component = find_components(reversed_graph, vert, visited) | ||
| components_list.append(component) | ||
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| return components_list | ||
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| if __name__ == "__main__": | ||
| import doctest | ||
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| doctest.testmod() | ||
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cclauss marked this conversation as resolved.
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@cclauss Do you have any idea how we can avoid declaring these variables here but keep current doctests?
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I think we are OK here. Naming helps a lot so when I see
test_graph_1, I immediately know that this data is for testing purposes. If I was going to move this algorithm to some larger program, I will need to do some level of refactoring. I might move all the doctests and the test data to a separate test_xyz.py file or I might remove them altogether. For our purposes in this repo, a single file that contains the algorithm, tests, and test data is good for learning purposes as long as we are diligent with our naming.