[flow, cost_flow] = min_cost_max_flow(c, u, s, t)的代码
时间: 2024-06-08 08:10:32 浏览: 57
这个函数是用来求解最小费用最大流问题的。下面是代码和参数说明:
```python
def min_cost_max_flow(c, u, s, t):
"""
求解最小费用最大流问题
:param c: 二维数组,表示各个边的费用,c[i][j]表示从节点i到节点j的费用,如果没有边,则为float('inf')
:param u: 二维数组,表示各个边的容量,u[i][j]表示从节点i到节点j的最大容量,如果没有边,则为0
:param s: 源节点
:param t: 汇节点
:return: (max_flow, min_cost),其中max_flow表示最大流量,min_cost表示最小费用
"""
n = len(c)
flow = 0
cost = 0
while True:
# 使用Bellman-Ford算法求解最短路
dist = [float('inf')] * n
dist[s] = 0
prev = [-1] * n
q = [s]
inqueue = [False] * n
inqueue[s] = True
while len(q) > 0:
u = q.pop(0)
inqueue[u] = False
for v in range(n):
if u == v or u == -1 or v == -1:
continue
if u != s and prev[u] != v:
continue
if u == s and v == t:
continue
if u == s and c[u][v] == float('inf'):
continue
if u != s and u != t and v != t and prev[u] != v:
continue
if u != s and u != t and v == t and prev[u] != v:
continue
if u == s and u != t and v != t and c[u][v] <= 0:
continue
if u != s and u != t and v != t and (c[u][v] <= 0 or prev[u] == v):
continue
new_dist = dist[u] + c[u][v]
if new_dist < dist[v]:
dist[v] = new_dist
prev[v] = u
if not inqueue[v]:
q.append(v)
inqueue[v] = True
if prev[t] == -1:
break
# 计算最大流量
f = float('inf')
v = t
while v != s:
u = prev[v]
f = min(f, u[v])
v = u
flow += f
# 计算最小费用
v = t
while v != s:
u = prev[v]
cost += f * c[u][v]
u[v] -= f
v = u
return flow, cost
```
其中,参数c和u分别表示费用和容量的二维数组,s和t分别表示源节点和汇节点。函数返回两个值,第一个值是最大流量,第二个值是最小费用。
Bellman-Ford算法是用来求解最短路径的算法,这里用来求解费用的最短路径。在这个函数中,我们使用Bellman-Ford算法来求解从源节点到汇节点的最短路径,然后根据这个最短路径来更新流量和费用。循环直到没有增广路为止,此时就得到了最小费用最大流。
阅读全文