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1f8a21d727
* Tighten up psf/black and flake8
* Fix some tests
* Fix some E741
* Fix some E741
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
95 lines
3.0 KiB
Python
95 lines
3.0 KiB
Python
INF = float("inf")
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class Dinic:
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def __init__(self, n):
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self.lvl = [0] * n
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self.ptr = [0] * n
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self.q = [0] * n
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self.adj = [[] for _ in range(n)]
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"""
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Here we will add our edges containing with the following parameters:
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vertex closest to source, vertex closest to sink and flow capacity
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through that edge ...
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"""
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def add_edge(self, a, b, c, rcap=0):
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self.adj[a].append([b, len(self.adj[b]), c, 0])
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self.adj[b].append([a, len(self.adj[a]) - 1, rcap, 0])
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# This is a sample depth first search to be used at max_flow
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def depth_first_search(self, vertex, sink, flow):
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if vertex == sink or not flow:
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return flow
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for i in range(self.ptr[vertex], len(self.adj[vertex])):
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e = self.adj[vertex][i]
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if self.lvl[e[0]] == self.lvl[vertex] + 1:
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p = self.depth_first_search(e[0], sink, min(flow, e[2] - e[3]))
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if p:
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self.adj[vertex][i][3] += p
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self.adj[e[0]][e[1]][3] -= p
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return p
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self.ptr[vertex] = self.ptr[vertex] + 1
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return 0
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# Here we calculate the flow that reaches the sink
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def max_flow(self, source, sink):
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flow, self.q[0] = 0, source
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for l in range(31): # noqa: E741 l = 30 maybe faster for random data
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while True:
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self.lvl, self.ptr = [0] * len(self.q), [0] * len(self.q)
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qi, qe, self.lvl[source] = 0, 1, 1
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while qi < qe and not self.lvl[sink]:
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v = self.q[qi]
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qi += 1
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for e in self.adj[v]:
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if not self.lvl[e[0]] and (e[2] - e[3]) >> (30 - l):
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self.q[qe] = e[0]
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qe += 1
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self.lvl[e[0]] = self.lvl[v] + 1
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p = self.depth_first_search(source, sink, INF)
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while p:
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flow += p
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p = self.depth_first_search(source, sink, INF)
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if not self.lvl[sink]:
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break
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return flow
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# Example to use
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"""
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Will be a bipartite graph, than it has the vertices near the source(4)
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and the vertices near the sink(4)
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"""
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# Here we make a graphs with 10 vertex(source and sink includes)
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graph = Dinic(10)
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source = 0
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sink = 9
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"""
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Now we add the vertices next to the font in the font with 1 capacity in this edge
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(source -> source vertices)
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"""
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for vertex in range(1, 5):
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graph.add_edge(source, vertex, 1)
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"""
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We will do the same thing for the vertices near the sink, but from vertex to sink
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(sink vertices -> sink)
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"""
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for vertex in range(5, 9):
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graph.add_edge(vertex, sink, 1)
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"""
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Finally we add the verices near the sink to the vertices near the source.
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(source vertices -> sink vertices)
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"""
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for vertex in range(1, 5):
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graph.add_edge(vertex, vertex + 4, 1)
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# Now we can know that is the maximum flow(source -> sink)
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print(graph.max_flow(source, sink))
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