Hdu 1532 Drainage Ditches【网络流】

网络流模板提

Sap模板：

const int N = 220 , M = 2020;#define inf (1<<29)int gap[N] , dis[N] , pre[N] , cur[N];int NV , n , m;struct Edge {    int v , w , next;    Edge () {}    Edge(int v,int w,int next):v(v),w(w),next(next) {}}edge[M];int maxflow;int E , head[N];void addedge(int u,int v,int w) {    edge[E] = Edge(v,w,head[u]);    head[u] = E ++;    edge[E] = Edge(u,0,head[v]);    head[v] = E++;}void init() {    E = 0;    memset(head,-1,sizeof(int)*(NV+1));}int sap(int st,int en) {    memset(dis,0,sizeof(int)*(NV+1));    memset(gap,0,sizeof(int)*(NV+1));    for(int i=0;i<NV;i++) cur[i] = head[i];    int u = pre[st] = st , maxflow = 0 , aug = inf;    gap[0] = NV;    while(dis[st] < NV) {loop:   for(int &i=cur[u];i!=-1;i=edge[i].next) {            int v = edge[i].v;            if(edge[i].w && dis[u] == dis[v] + 1) {                aug = aug<edge[i].w?aug:edge[i].w;                pre[v] = u;                u = v;                if(v == en) {                    maxflow += aug;                    for(u=pre[u];v!=st;v=u,u=pre[u]) {                        edge[cur[u]].w -= aug;                        edge[cur[u]^1].w += aug;                    }                    aug = inf;                }                goto loop;            }        }        int mindis = NV;        for(int i=head[u];i!=-1;i=edge[i].next) {            int v = edge[i].v;            if(edge[i].w && mindis > dis[v]) {                cur[u] = i;                mindis = dis[v];            }        }        if( --gap[dis[u]] == 0 ) break;        gap[ dis[u] = mindis+1 ] ++;        u = pre[u];    }    return maxflow;}int main() {    while(~scanf("%d%d",&m,&n)) {    NV = n + 1;    init();    for(int i=0;i<m;i++) {        int u , v , w;        scanf("%d%d%d",&u,&v,&w);        u -- ; v -- ;        addedge(u , v , w);    }    printf("%d\n",sap(0,n-1)); }    return 0;}

dinic算法

dinic算法不断重复一下过程：

首先从源点沿着可增广边做一遍广搜，给每个点标记一个距离。如果遍历不到汇点，既找不到增广路，算法结束。

在增广的时候，只选择距离恰好是自己距离加一的点扩展。这样保证了每次以最短路增广。其次在找到了一条增广路后，并不是立刻回退到源点，而是寻找到增光路上第一个满流的边的起点继续访问。

dinic模板：

#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#include <queue>using namespace std;#define inf (1<<29)const int N = 220 , M = 20200;struct Edge {    int v ,f , next;    Edge () {}    Edge (int v,int f,int next) :v(v),f(f),next(next) {};}edge[M];int E , head[N];void init() {    E = 0; memset(head,-1,sizeof(head));}void addedge(int u,int v,int f) {    edge[E] = Edge(v,f,head[u]); head[u] = E++;    edge[E] = Edge(u,0,head[v]); head[v] = E++;}int n , m , NV , st , ed;queue <int> q;bool vis[N];int dist[N];void bfs() {    memset(dist,0,sizeof(dist));    while(!q.empty()) q.pop();    vis[st] = true;    q.push(st);    while(!q.empty()) {        int u = q.front(); q.pop();        for(int i=head[u];i!=-1;i=edge[i].next) {            if(edge[i].f && !vis[edge[i].v]) {                q.push(edge[i].v);                dist[edge[i].v] = dist[u] + 1;                vis[edge[i].v] = true;            }        }    }}int dfs(int u,int delta) {    if(u == ed) return delta;    else {        int ret = 0;        for(int i=head[u];delta && i!=-1;i=edge[i].next) {            if(edge[i].f && dist[edge[i].v] == dist[u] + 1) {                int dd = dfs(edge[i].v ,min(edge[i].f,delta));                edge[i].f -= dd;                edge[i^1].f += dd;                delta -= dd;                ret += dd;            }        }        return ret;    }}int maxflow() {    int ret = 0;    while(true) {        memset(vis,0,sizeof(vis));        bfs();        if(!vis[ed]) return ret;        ret += dfs(st ,ed);    }}int main() {    while(~scanf("%d%d",&m,&n)) {        init();        st = 1; ed = n;        while(m--) {            int u , v , f;            scanf("%d%d%d",&u,&v,&f);            addedge(u,v,f);        }        int ans = maxflow();        printf("%d\n" , ans);    }    return 0;}