最小费用最大流模板

流量网络最大流算法实现

最新推荐文章于 2023-12-31 19:44:50 发布

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本文详细阐述了最大流量最小费用流（MCMF）算法的实现过程，包括初始化、边添加、SPFA查找最短路径及费用优化等关键步骤。通过实例分析，展示了如何在给定网络中求解最大流量并最小化总费用。

const int MAXN = 1010;
const int MAXM = 504000;

struct Edge
{
    int to,next,cap,flow,cost;
}edge[MAXM];

int head[MAXM],tol;
int pre[MAXN],dis[MAXN];
bool vis[MAXN];
int N;

void Init(int n)
{
    N = n;
    tol = 0;
    memset(head,-1,sizeof(head));
}

void addedge(int u,int v,int cap,int cost)
{
    edge[tol].to = v;
    edge[tol].cap = cap;
    edge[tol].cost = cost;
    edge[tol].flow = 0;
    edge[tol].next = head[u];
    head[u] = tol++;
    edge[tol].to = u;
    edge[tol].cap = 0;
    edge[tol].cost = -cost;
    edge[tol].flow = 0;
    edge[tol].next = head[v];
    head[v] = tol++;
}

bool spfa(int s,int t)
{
    queue<int> q;
    for(int i = 0;i < N; ++i)
    {
        dis[i] = INF;
        vis[i] = false;
        pre[i] = -1;
    }
    dis[s] = 0;
    vis[s] = true;
    q.push(s);

    while(q.empty() == false)
    {
        int u = q.front();
        q.pop();
        vis[u] = false;
        for(int i = head[u];i != -1;i = edge[i].next)
        {
            int v = edge[i].to;
            if(edge[i].cap > edge[i].flow && dis[v] > dis[u] + edge[i].cost)
            {
                dis[v] = dis[u] + edge[i].cost;
                pre[v] = i;
                if(vis[v] == false)
                {
                    vis[v] = true;
                    q.push(v);
                }
            }
        }
    }
    if(pre[t] == -1)
        return false;
    return true;
}

int MCMF(int s,int t,int &cost)
{
    int flow = 0;
    cost = 0;
    while(spfa(s,t))
    {
        int Min = INF;
        for(int i = pre[t];i != -1;i = pre[edge[i^1].to])
            Min = min(Min,edge[i].cap - edge[i].flow);

        for(int i = pre[t];i != -1;i = pre[edge[i^1].to])
        {
            edge[i].flow += Min;
            edge[i^1].flow -= Min;
            cost += edge[i].cost*Min;
        }
        flow += Min;
    }
    return flow;
}