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* ci(pre-commit): Add pep8-naming to `pre-commit` hooks (#7038) * refactor: Fix naming conventions (#7038) * Update arithmetic_analysis/lu_decomposition.py Co-authored-by: Christian Clauss <cclauss@me.com> * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * refactor(lu_decomposition): Replace `NDArray` with `ArrayLike` (#7038) * chore: Fix naming conventions in doctests (#7038) * fix: Temporarily disable project euler problem 104 (#7069) * chore: Fix naming conventions in doctests (#7038) Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
62 lines
1.5 KiB
Python
62 lines
1.5 KiB
Python
# Ford-Fulkerson Algorithm for Maximum Flow Problem
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"""
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Description:
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(1) Start with initial flow as 0;
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(2) Choose augmenting path from source to sink and add path to flow;
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"""
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def bfs(graph, s, t, parent):
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# Return True if there is node that has not iterated.
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visited = [False] * len(graph)
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queue = []
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queue.append(s)
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visited[s] = True
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while queue:
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u = queue.pop(0)
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for ind in range(len(graph[u])):
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if visited[ind] is False and graph[u][ind] > 0:
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queue.append(ind)
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visited[ind] = True
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parent[ind] = u
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return True if visited[t] else False
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def ford_fulkerson(graph, source, sink):
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# This array is filled by BFS and to store path
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parent = [-1] * (len(graph))
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max_flow = 0
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while bfs(graph, source, sink, parent):
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path_flow = float("Inf")
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s = sink
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while s != source:
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# Find the minimum value in select path
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path_flow = min(path_flow, graph[parent[s]][s])
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s = parent[s]
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max_flow += path_flow
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v = sink
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while v != source:
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u = parent[v]
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graph[u][v] -= path_flow
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graph[v][u] += path_flow
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v = parent[v]
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return max_flow
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graph = [
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[0, 16, 13, 0, 0, 0],
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[0, 0, 10, 12, 0, 0],
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[0, 4, 0, 0, 14, 0],
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[0, 0, 9, 0, 0, 20],
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[0, 0, 0, 7, 0, 4],
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[0, 0, 0, 0, 0, 0],
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]
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source, sink = 0, 5
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print(ford_fulkerson(graph, source, sink))
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