108 lines
2.8 KiB
Python
108 lines
2.8 KiB
Python
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# https://en.wikipedia.org/wiki/Minimum-cost_flow_problem in O(V^2 * E)
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from heapq import *
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class Edge:
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def __init__(self, to, cap, cost, rev):
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self.to = to
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self.cap = cap
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self.cost = cost
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self.rev = rev
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self.f = 0
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def add_edge(graph, s, t, cap, cost):
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graph[s].append(Edge(t, cap, cost, len(graph[t])))
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graph[t].append(Edge(s, 0, -cost, len(graph[s]) - 1))
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def bellman_ford(graph, s, dist):
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n = len(graph)
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dist[:] = [float('inf')] * n
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dist[s] = 0
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inqueue = [False] * n
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q = [0] * n
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qt = 0
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q[qt] = s
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qt += 1
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qh = 0
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while (qh - qt) % n != 0:
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u = q[qh % n]
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inqueue[u] = False
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for i in range(len(graph[u])):
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e = graph[u][i]
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if e.cap <= e.f:
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continue
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v = e.to
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ndist = dist[u] + e.cost
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if dist[v] > ndist:
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dist[v] = ndist
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if not inqueue[v]:
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inqueue[v] = True
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q[qt % n] = v
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qt += 1
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qh += 1
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def min_cost_flow(graph, s, t, maxf):
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n = len(graph)
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prio = [0] * n
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curflow = [0] * n
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prevedge = [0] * n
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prevnode = [0] * n
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pot = [0] * n
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bellman_ford(graph, s, pot) # bellmanFord invocation can be skipped if edges costs are non-negative
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flow = 0
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flow_cost = 0
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while flow < maxf:
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q = [(0, s)]
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prio[:] = [float('inf')] * n
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prio[s] = 0
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finished = [False] * n
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curflow[s] = float('inf')
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while not finished[t] and q:
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(prio_u, u) = heappop(q)
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if prio_u != prio[u]:
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continue
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finished[u] = True
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for i in range(len(graph[u])):
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e = graph[u][i]
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if e.f >= e.cap:
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continue
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v = e.to
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nprio = prio[u] + e.cost + pot[u] - pot[v]
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if prio[v] > nprio:
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prio[v] = nprio
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heappush(q, (nprio, v))
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prevnode[v] = u
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prevedge[v] = i
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curflow[v] = min(curflow[u], e.cap - e.f)
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if prio[t] == float('inf'):
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break
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for i in range(n):
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if finished[i]:
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pot[i] += prio[i] - prio[t]
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df = min(curflow[t], maxf - flow)
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flow += df
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v = t
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while v != s:
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e = graph[prevnode[v]][prevedge[v]]
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e.f += df
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graph[v][e.rev].f -= df
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flow_cost += df * e.cost
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v = prevnode[v]
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return flow, flow_cost
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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, 1)
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add_edge(graph, 0, 2, 2, 1)
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add_edge(graph, 1, 2, 2, 1)
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assert (4, 6) == min_cost_flow(graph, 0, 2, float('inf'))
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test()
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