mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 01:00:15 +00:00
dbddac74d3
* Fix finding_bridges algorithms + tests * update type hints * Better, more obvious condition fix * fix prev commit + more tests * Short explanation + url * Update finding_bridges.py Co-authored-by: Christian Clauss <cclauss@me.com>
101 lines
2.6 KiB
Python
101 lines
2.6 KiB
Python
"""
|
|
An edge is a bridge if, after removing it count of connected components in graph will
|
|
be increased by one. Bridges represent vulnerabilities in a connected network and are
|
|
useful for designing reliable networks. For example, in a wired computer network, an
|
|
articulation point indicates the critical computers and a bridge indicates the critical
|
|
wires or connections.
|
|
|
|
For more details, refer this article:
|
|
https://www.geeksforgeeks.org/bridge-in-a-graph/
|
|
"""
|
|
|
|
|
|
def __get_demo_graph(index):
|
|
return [
|
|
{
|
|
0: [1, 2],
|
|
1: [0, 2],
|
|
2: [0, 1, 3, 5],
|
|
3: [2, 4],
|
|
4: [3],
|
|
5: [2, 6, 8],
|
|
6: [5, 7],
|
|
7: [6, 8],
|
|
8: [5, 7],
|
|
},
|
|
{
|
|
0: [6],
|
|
1: [9],
|
|
2: [4, 5],
|
|
3: [4],
|
|
4: [2, 3],
|
|
5: [2],
|
|
6: [0, 7],
|
|
7: [6],
|
|
8: [],
|
|
9: [1],
|
|
},
|
|
{
|
|
0: [4],
|
|
1: [6],
|
|
2: [],
|
|
3: [5, 6, 7],
|
|
4: [0, 6],
|
|
5: [3, 8, 9],
|
|
6: [1, 3, 4, 7],
|
|
7: [3, 6, 8, 9],
|
|
8: [5, 7],
|
|
9: [5, 7],
|
|
},
|
|
{
|
|
0: [1, 3],
|
|
1: [0, 2, 4],
|
|
2: [1, 3, 4],
|
|
3: [0, 2, 4],
|
|
4: [1, 2, 3],
|
|
},
|
|
][index]
|
|
|
|
|
|
def compute_bridges(graph: dict[int, list[int]]) -> list[tuple[int, int]]:
|
|
"""
|
|
Return the list of undirected graph bridges [(a1, b1), ..., (ak, bk)]; ai <= bi
|
|
>>> compute_bridges(__get_demo_graph(0))
|
|
[(3, 4), (2, 3), (2, 5)]
|
|
>>> compute_bridges(__get_demo_graph(1))
|
|
[(6, 7), (0, 6), (1, 9), (3, 4), (2, 4), (2, 5)]
|
|
>>> compute_bridges(__get_demo_graph(2))
|
|
[(1, 6), (4, 6), (0, 4)]
|
|
>>> compute_bridges(__get_demo_graph(3))
|
|
[]
|
|
>>> compute_bridges({})
|
|
[]
|
|
"""
|
|
|
|
id = 0
|
|
n = len(graph) # No of vertices in graph
|
|
low = [0] * n
|
|
visited = [False] * n
|
|
|
|
def dfs(at, parent, bridges, id):
|
|
visited[at] = True
|
|
low[at] = id
|
|
id += 1
|
|
for to in graph[at]:
|
|
if to == parent:
|
|
pass
|
|
elif not visited[to]:
|
|
dfs(to, at, bridges, id)
|
|
low[at] = min(low[at], low[to])
|
|
if id <= low[to]:
|
|
bridges.append((at, to) if at < to else (to, at))
|
|
else:
|
|
# This edge is a back edge and cannot be a bridge
|
|
low[at] = min(low[at], low[to])
|
|
|
|
bridges = []
|
|
for i in range(n):
|
|
if not visited[i]:
|
|
dfs(i, -1, bridges, id)
|
|
return bridges
|