matlab最小费用最大流代码例子
时间: 2023-09-12 17:08:42 浏览: 48
以下是一个使用Matlab实现最小费用最大流算法的示例代码:
```matlab
function [max_flow, min_cost] = min_cost_max_flow(capacity, cost, source, sink)
% capacity: 流量限制矩阵,capacity(i,j)表示从节点i到节点j的流量上限
% cost: 每单位流量的花费矩阵,cost(i,j)表示从节点i到节点j的每单位流量花费
% source: 源点
% sink: 汇点
n = size(capacity, 1);
% 计算残量矩阵
residual = capacity;
% 初始化流量和费用
max_flow = 0;
min_cost = 0;
while true
[augment, path, cost] = bellman_ford(residual, cost, source, sink);
if augment == 0
break; % 不存在增广路,结束
end
max_flow = max_flow + augment;
min_cost = min_cost + augment * cost(path(end-1), path(end));
for i = 1:length(path)-1
residual(path(i), path(i+1)) = residual(path(i), path(i+1)) - augment;
residual(path(i+1), path(i)) = residual(path(i+1), path(i)) + augment;
end
end
end
function [augment, path, cost] = bellman_ford(residual, cost, source, sink)
n = size(residual, 1);
% 初始化距离和前驱节点
dist = inf(1, n);
prev = zeros(1, n);
% 起点到自身的距离为0
dist(source) = 0;
% 进行n-1轮松弛操作
for i = 1:n-1
for u = 1:n
for v = 1:n
if residual(u, v) > 0 && dist(u) + cost(u, v) < dist(v)
dist(v) = dist(u) + cost(u, v);
prev(v) = u;
end
end
end
end
% 判断是否存在增广路
if dist(sink) == inf
augment = 0;
path = [];
cost = 0;
return;
end
% 寻找增广路
augment = inf;
u = sink;
path = u;
while u ~= source
v = prev(u);
augment = min(augment, residual(v, u));
path = [v, path];
u = v;
end
% 计算增广路的花费
cost = 0;
for i = 1:length(path)-1
cost = cost + cost(path(i), path(i+1));
end
end
```
该代码实现了基于Bellman-Ford算法的最小费用最大流算法。在实际应用中,还需要考虑如何构造流量限制矩阵和每单位流量的花费矩阵,以及如何处理无解情况等问题。