最大流拆点——hdu2732，poj3436

一种很普遍的做法就是把一个带有容量的点拆成两个点，一个入点一个出点，链接两个点的边的权值为这个点的容量

hdu3732

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#include<vector>
#include<string>
#include<iostream>
#define INF 1e9
using namespace std;
const int maxn =+;

struct Edge
{
    int from,to,cap,flow;
    Edge(){}
    Edge(int f,int t,int c,int fl):from(f),to(t),cap(c),flow(fl){}
};

struct Dinic
{
    int n,m,s,t;
    vector<Edge> edges;
    vector<int> G[maxn];
    int cur[maxn];
    int d[maxn];
    bool vis[maxn];

    void init(int n,int s,int t)
    {
        this->n=n, this->s=s, this->t=t;
        edges.clear();
        for(int i=;i<n;i++) G[i].clear();
    }

    void AddEdge(int from,int to,int cap)
    {
        edges.push_back( Edge(from,to,cap,) );
        edges.push_back( Edge(to,from,,) );
        m = edges.size();
        G[from].push_back(m-);
        G[to].push_back(m-);
    }

    bool BFS()
    {
        queue<int> Q;
        Q.push(s);
        memset(vis,,sizeof(vis));
        d[s]=;
        vis[s]=true;
        while(!Q.empty())
        {
            int x=Q.front(); Q.pop();
            for(int i=;i<G[x].size();++i)
            {
                Edge& e=edges[G[x][i]];
                if(!vis[e.to] && e.cap>e.flow)
                {
                    d[e.to]=+d[x];
                    vis[e.to]=true;
                    Q.push(e.to);
                }
            }
        }
        return vis[t];
    }

    int DFS(int x,int a)
    {
        if(x==t || a==) return a;
        int flow=,f;
        for(int& i=cur[x];i<G[x].size();++i)
        {
            Edge& e=edges[G[x][i]];
            if(d[e.to]==d[x]+ && (f=DFS(e.to,min(a,e.cap-e.flow) ) )>)
            {
                e.flow +=f;
                edges[G[x][i]^].flow -=f;
                flow +=f;
                a-=f;
                if(a==) break;
            }
        }
        return flow;
    }

    int max_flow()
    {
        int ans=;
        while(BFS())
        {
            memset(cur,,sizeof(cur));
            ans += DFS(s,INF);
        }
        return ans;
    }
}DC;

int main()
{
    int T; scanf("%d",&T);
    for(int kase=;kase<=T;++kase)
    {
        int n,m,d,src,dst;
        int sum=;//蜥蜴数
        scanf("%d%d",&n,&d);
        for(int i=;i<=n;i++)
        {
            string s;
            cin>>s;
            if(i==)//第一次
            {
                m = s.size();
                src=, dst=*n*m+;
                DC.init(*n*m+,src,dst);
            }
            for(int j=;j<s.size();++j)if(s[j]-''>)
            {
                int id = (i-)*m+j+;//当前点编号
                DC.AddEdge(id, id+n*m, s[j]-'');
                if(i<=d || i+d>n || j<d || j+d>=m)//当前格子能直接跳出棋盘
                {
                    DC.AddEdge(id+n*m,dst,INF);
                }
                else //不能直接跳出去
                {
                    for(int k=;k<=n;k++)
                    for(int h=;h<m;h++)
                    {
                        int id2= (k-)*m+h+;
                        if(id==id2) continue;
                        if(abs(i-k)+abs(j-h)<= d) DC.AddEdge(id+n*m,id2,INF);
                    }
                }
            }
        }
        for(int i=;i<=n;++i)
        {
            string s;
            cin>>s;
            for(int j=;j<s.size();++j)
            {
                int id = (i-)*m+j+;//当前点编号
                if(s[j]=='L')
                {
                    ++sum;
                    DC.AddEdge(src,id,);
                }
            }
        }
        int ans = sum-DC.max_flow();
        if(ans==) printf("Case #%d: no lizard was left behind.\n",kase);
        else if(ans==) printf("Case #%d: 1 lizard was left behind.\n",kase);
        else printf("Case #%d: %d lizards were left behind.\n",kase,ans);
    }
    return ;
}

poj3436

#include<cstdio>
#include<iostream>
#include<cstring>
#define Maxn 110
using namespace std;

const int inf=0x3f3f3f3f;
struct line{
    int to,next,cap;
}p[Maxn*Maxn*];
int head[Maxn];
int q[Maxn];
int d[Maxn];
int cur[Maxn];
int tot;
int src,t;
int n,m;
void addedge(int a,int b,int c){
    p[tot].to=b;
    p[tot].next=head[a];
    p[tot].cap=c;
    head[a]=tot++;
}
void insert(int a,int b,int c){
    addedge(a,b,c);
    addedge(b,a,);
}
bool bfs(){
    memset(d,-,sizeof d);
    int s=,e=-;
    q[++e]=src;
    d[src]=;
    while(s<=e){
        int u=q[s++];
        for(int i=head[u];i!=-;i=p[i].next){
            int v=p[i].to;
            if(d[v]==-&&p[i].cap){
                d[v]=d[u]+;
                q[++e]=v;
            }
        }
    }
    return d[t]!=-;
}
int dfs(int u,int alpha){
    if(u==t) return alpha;
    int w,used=;
    for(int i=cur[u];i!=-&&used<alpha;i=p[i].next){
        int v=p[i].to;
        if(p[i].cap&&d[v]==d[u]+){
            w=dfs(v,min(alpha-used,p[i].cap));
            used+=w;
            p[i].cap-=w;
            p[i^].cap+=w;
            cur[u]=i;
        }
    }
    if(!used) d[u]=-;
    return used;
}
int dinic(){
    int ans=;
    src=,t=*m+;
    while(bfs()){
        for(int i=src;i<=t;i++) cur[i]=head[i];
        ans+=dfs(src,inf);
    }
    return ans;
}
int num[Maxn];
int input[Maxn][],output[Maxn][];
int vis[Maxn][Maxn];
bool check(int x,int y){
    return x==y||y==;
}
bool ck1(int d){ //没有1
    for(int i=;i<n;i++)
        if(input[d][i]==) return false;
    return true;
}
bool ck2(int d){ //全1
    for(int i=;i<n;i++)
        if(output[d][i]!=) return false;
    return true;
}
int main()
{
    while(~scanf("%d%d",&n,&m)){
        for(int i=;i<=m;i++){
            scanf("%d",num+i);
            for(int j=;j<n;j++)
                scanf("%d",&input[i][j]);
            for(int j=;j<n;j++)
                scanf("%d",&output[i][j]);
        }
        memset(head,-,sizeof head);
        memset(vis,,sizeof vis);
        tot=;
        for(int i=;i<=m;i++)
            for(int j=;j<=m;j++){
                if(i==j) continue;
                bool flag=true;
                for(int k=;k<n;k++)
                    if(!check(output[i][k],input[j][k])){
                        flag=false;
                        break;
                    }
                if(flag){
                    insert(i+m,j,num[i]);
                    vis[i+m][j]=;
                }
            }
        for(int i=;i<=m;i++){
            insert(i,i+m,num[i]); //拆点
            if(ck1(i)) insert(,i,num[i]);
            if(ck2(i)) insert(i+m,*m+,num[i]);
        }
        printf("%d",dinic());
        int cnt=;
        for(int i=;i<=m;i++){
            for(int j=head[i+m];j!=-;j=p[j].next)
                if(vis[i+m][p[j].to]&&p[j].cap<num[i]) cnt++;
        }
        printf(" %d\n",cnt);
        for(int i=;i<=m;i++){
            for(int j=head[i+m];j!=-;j=p[j].next)
                if(vis[i+m][p[j].to]&&p[j].cap<num[i]){
                    printf("%d %d %d\n",i,p[j].to,num[i]-p[j].cap);
                }
        }
    }
    return ;
}