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a8aeabdf18
* [mypy] Annotate `graphs/finding_bridges.py` * Remove from excluded in `mypy.ini` * Add doctest.testmod() * psf/black formatting * Annotations for `graphs/random_graph_generator.py` * Remove from excluded in `mypy.ini` * Resolve merge conflict * Resolve merge conflict * Update mypy.ini * Update mypy.ini * Remove from excluded
107 lines
2.7 KiB
Python
107 lines
2.7 KiB
Python
"""
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An edge is a bridge if, after removing it count of connected components in graph will
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be increased by one. Bridges represent vulnerabilities in a connected network and are
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useful for designing reliable networks. For example, in a wired computer network, an
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articulation point indicates the critical computers and a bridge indicates the critical
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wires or connections.
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For more details, refer this article:
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https://www.geeksforgeeks.org/bridge-in-a-graph/
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"""
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def __get_demo_graph(index):
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return [
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{
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0: [1, 2],
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1: [0, 2],
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2: [0, 1, 3, 5],
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3: [2, 4],
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4: [3],
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5: [2, 6, 8],
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6: [5, 7],
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7: [6, 8],
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8: [5, 7],
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},
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{
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0: [6],
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1: [9],
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2: [4, 5],
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3: [4],
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4: [2, 3],
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5: [2],
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6: [0, 7],
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7: [6],
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8: [],
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9: [1],
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},
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{
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0: [4],
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1: [6],
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2: [],
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3: [5, 6, 7],
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4: [0, 6],
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5: [3, 8, 9],
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6: [1, 3, 4, 7],
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7: [3, 6, 8, 9],
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8: [5, 7],
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9: [5, 7],
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},
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{
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0: [1, 3],
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1: [0, 2, 4],
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2: [1, 3, 4],
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3: [0, 2, 4],
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4: [1, 2, 3],
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},
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][index]
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def compute_bridges(graph: dict[int, list[int]]) -> list[tuple[int, int]]:
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"""
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Return the list of undirected graph bridges [(a1, b1), ..., (ak, bk)]; ai <= bi
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>>> compute_bridges(__get_demo_graph(0))
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[(3, 4), (2, 3), (2, 5)]
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>>> compute_bridges(__get_demo_graph(1))
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[(6, 7), (0, 6), (1, 9), (3, 4), (2, 4), (2, 5)]
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>>> compute_bridges(__get_demo_graph(2))
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[(1, 6), (4, 6), (0, 4)]
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>>> compute_bridges(__get_demo_graph(3))
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[]
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>>> compute_bridges({})
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[]
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"""
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id = 0
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n = len(graph) # No of vertices in graph
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low = [0] * n
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visited = [False] * n
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def dfs(at, parent, bridges, id):
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visited[at] = True
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low[at] = id
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id += 1
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for to in graph[at]:
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if to == parent:
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pass
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elif not visited[to]:
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dfs(to, at, bridges, id)
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low[at] = min(low[at], low[to])
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if id <= low[to]:
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bridges.append((at, to) if at < to else (to, at))
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else:
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# This edge is a back edge and cannot be a bridge
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low[at] = min(low[at], low[to])
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bridges: list[tuple[int, int]] = []
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for i in range(n):
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if not visited[i]:
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dfs(i, -1, bridges, id)
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return bridges
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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