【最大流模板——Dinic算法】【有向图】

た入场券 2022-06-10 07:46 154阅读 0赞

#include <cstdio>
    #include <cstring>
    #include <algorithm>
    #include <queue>
    
    using namespace std;
    
    const int inf = 0x3f3f3f3f;
    const int N = 214;
    const int M = 214;
    
    struct Edge{
        int v;
        int cap;/*边的容量*/
        int next;
    }edge[M<<1];
    
    int cnt, head[N], level[N];
    
    void Init();
    void add_edge(int u, int v, int w);
    bool bfs(int s, int t);
    int dfs(int u, int t, int f);
    int max_flow(int s, int t);
    
    int main(){
        int n, m, i, u, v, w;
        while(~scanf("%d %d", &n, &m)){
            Init();
            for(i = 0; i < n; i++){
                scanf("%d %d %d", &u, &v, &w);
                add_edge(u, v, w);
            }
            printf("%d\n", max_flow(1, m));
        }
        return 0;
    }
    void Init(){
        cnt = 0;/*必须初始化为零-异或运算改变反向弧*/
        memset(head, -1, sizeof(head));
    }
    void add_edge(int u, int v, int w){
        edge[cnt].v = v;
        edge[cnt].cap = w;
        edge[cnt].next = head[u];
        head[u] = cnt++;
    
        edge[cnt].v = u;
        edge[cnt].cap = 0;/*有向图反向弧容量初始化为0*/
        edge[cnt].next = head[v];
        head[v] = cnt++;
    }
    bool bfs(int s, int t){
       /*bfs构造分层网络*/
        queue <int> q;
        memset(level, -1, sizeof(level));
        level[s] = 0;
        q.push(s);
        while(!q.empty()){
            int u = q.front();
            q.pop();
            for(int i = head[u]; ~i; i = edge[i].next){
                int v = edge[i].v;
                if(edge[i].cap > 0 && level[v] == -1){
                    level[v] = level[u] + 1;
                    q.push(v);
                }
            }
        }
        if(level[t] != -1)
            return true;
        else
            return false;
    }
    int dfs(int u, int t, int f){
       /*dfs沿阻塞流增广*/
        if(u == t)
            return f;
        int flow = 0, d;
        for(int i = head[u]; ~i; i = edge[i].next){
            int v = edge[i].v;
            if(edge[i].cap > 0 && level[u] < level[v] && (d = dfs(v, t, min(edge[i].cap, f)))){
                edge[i].cap -= d;
                edge[i^1].cap += d;
                flow += d;
                f -= d;
                if(!f)
                    break;
            }
        }
        if(flow == 0)
            level[u] = -1;
        return flow;
    }
    int max_flow(int s, int t){
        int flow = 0;
        while(bfs(s, t)){
            flow += dfs(s, t, inf);
        }
        return flow;
    }