最小费用最大流具体例子代码
时间: 2023-11-12 14:04:34 浏览: 28
以下是最小费用最大流的具体例子代码,使用了Dijkstra算法来求解最短路:
```python
from collections import deque
import heapq
class Edge:
def __init__(self, capacity, cost, from_vertex, to_vertex):
self.capacity = capacity
self.cost = cost
self.from_vertex = from_vertex
self.to_vertex = to_vertex
class Graph:
def __init__(self, num_vertices):
self.num_vertices = num_vertices
self.adjacency_list = [[] for _ in range(num_vertices)]
self.edges = []
def add_edge(self, from_vertex, to_vertex, capacity, cost):
forward_edge = Edge(capacity, cost, from_vertex, to_vertex)
backward_edge = Edge(0, -cost, to_vertex, from_vertex)
forward_edge.backward_edge = backward_edge
backward_edge.backward_edge = forward_edge
self.adjacency_list[from_vertex].append(forward_edge)
self.adjacency_list[to_vertex].append(backward_edge)
self.edges.append(forward_edge)
self.edges.append(backward_edge)
def minimum_cost_maximum_flow(self, source, sink):
total_flow = 0
total_cost = 0
while True:
dist = [float('inf')] * self.num_vertices
prev_edge = [None] * self.num_vertices
visited = [False] * self.num_vertices
dist[source] = 0
# Dijkstra's algorithm
pq = [(0, source)]
while pq:
(d, u) = heapq.heappop(pq)
if visited[u]:
continue
visited[u] = True
for edge in self.adjacency_list[u]:
v = edge.to_vertex
if edge.capacity > 0 and dist[u] + edge.cost < dist[v]:
dist[v] = dist[u] + edge.cost
prev_edge[v] = edge
heapq.heappush(pq, (dist[v], v))
if not visited[sink]:
break
# Augment the flow along the path found by Dijkstra's algorithm
path_flow = float('inf')
v = sink
while v != source:
edge = prev_edge[v]
path_flow = min(path_flow, edge.capacity)
v = edge.from_vertex
total_flow += path_flow
total_cost += dist[sink] * path_flow
v = sink
while v != source:
edge = prev_edge[v]
edge.capacity -= path_flow
edge.backward_edge.capacity += path_flow
v = edge.from_vertex
return (total_flow, total_cost)
```
在上述代码中,我们实现了 `Edge` 类来表示图的边。每个边都有容量和费用。我们还实现了 `Graph` 类来表示图。我们在这个类中实现了 `add_edge()` 方法来添加新的边到图中。我们还实现了 `minimum_cost_maximum_flow()` 方法来求解最小费用最大流。在该方法中,我们采用了Dijkstra算法来求解最短路,并使用堆来优化算法的效率。在找到一条增广路径后,我们通过该路径来增加最大流,并更新总费用。