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72 lines
1.7 KiB
Python
72 lines
1.7 KiB
Python
# https://en.wikipedia.org/wiki/Dinic%27s_algorithm in O(V^2 * E)
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class Edge:
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def __init__(self, t, rev, cap):
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self.t = t
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self.rev = rev
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self.cap = cap
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self.f = 0
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def add_edge(graph, s, t, cap):
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graph[s].append(Edge(t, len(graph[t]), cap))
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graph[t].append(Edge(s, len(graph[s]) - 1, 0))
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def dinic_bfs(graph, src, dest, dist):
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dist[:] = [-1] * len(dist)
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dist[src] = 0
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Q = [0] * len(graph)
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size_q = 0
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Q[size_q] = src
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size_q += 1
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i = 0
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while i < size_q:
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u = Q[i]
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for e in graph[u]:
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if dist[e.t] < 0 and e.f < e.cap:
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dist[e.t] = dist[u] + 1
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Q[size_q] = e.t
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size_q += 1
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i += 1
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return dist[dest] >= 0
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def dinic_dfs(graph, ptr, dist, dest, u, f):
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if u == dest:
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return f
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while ptr[u] < len(graph[u]):
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e = graph[u][ptr[u]]
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if dist[e.t] == dist[u] + 1 and e.f < e.cap:
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df = dinic_dfs(graph, ptr, dist, dest, e.t, min(f, e.cap - e.f))
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if df > 0:
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e.f += df
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graph[e.t][e.rev].f -= df
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return df
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ptr[u] += 1
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return 0
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def max_flow(graph, src, dest):
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flow = 0
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dist = [0] * len(graph)
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while dinic_bfs(graph, src, dest, dist):
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ptr = [0] * len(graph)
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while True:
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df = dinic_dfs(graph, ptr, dist, dest, src, float('inf'))
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if df == 0:
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break
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flow += df
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return flow
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def test():
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graph = [[] for _ in range(3)]
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add_edge(graph, 0, 1, 3)
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add_edge(graph, 0, 2, 2)
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add_edge(graph, 1, 2, 2)
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assert 4 == max_flow(graph, 0, 2)
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test()
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