[BZOJ2502]清理雪道（有源汇有上下界的最小流）

题目描述

传送门

题解

建原图很简单：
对于能到达的点x,y，x->y,[1,inf]
s->i,[0,inf]；i->t,[0,inf]

将原图进行改造
建立附加源汇ss,tt
对于原图中有的边x->y,[b,c]，连边x->y,c-b
记某一个点的权d(i)为所有流入这个点的边的下界和-所有流出这个点的边的下界和
若d(i)>0，连边ss->i,d(i)
若d(i)<0，连边i->tt,-d(i)
然后对ss->tt跑最大流
然后连边t->s,inf
再对ss->tt跑最大流
此时t->s,inf这条边的实际流量就是原图中的最小流

代码

#include
#include
#include
#include
#include
#include
using namespace std;
#define N 110
#define E 30005
#define inf 1000000000

int n,m,x,s,t,ss,tt,maxflow;
int tot,point[N],nxt[E],v[E],remain[E];
int d[N],deep[N],num[N],last[N],cur[N];
queue <int> q;

void addedge(int x,int y,int cap)
{
    ++tot; nxt[tot]=point[x]; point[x]=tot; v[tot]=y; remain[tot]=cap;
    ++tot; nxt[tot]=point[y]; point[y]=tot; v[tot]=x; remain[tot]=0;
}
void bfs(int t)
{
    for (int i=1;i<=t;++i) deep[i]=t;
    deep[t]=0;
    for (int i=1;i<=t;++i) cur[i]=point[i];
    while (!q.empty()) q.pop();
    q.push(t);
    while (!q.empty())
    {
        int now=q.front();q.pop();
        for (int i=point[now];i!=-1;i=nxt[i])
            if (deep[v[i]]==t&&remain[i^1])
            {
                deep[v[i]]=deep[now]+1;
                q.push(v[i]);
            }
    }
}
int addflow(int s,int t)
{
    int now=t,ans=inf;
    while (now!=s)
    {
        ans=min(ans,remain[last[now]]);
        now=v[last[now]^1];
    }
    now=t;
    while (now!=s)
    {
        remain[last[now]]-=ans;
        remain[last[now]^1]+=ans;
        now=v[last[now]^1];
    }
    return ans;
}
void isap(int s,int t)
{
    bfs(t);
    for (int i=1;i<=t;++i) ++num[deep[i]];

    int now=s;
    while (deep[s]if (now==t)
        {
            maxflow+=addflow(s,t);
            now=s;
        }

        bool has_find=false;
        for (int i=cur[now];i!=-1;i=nxt[i])
            if (deep[v[i]]+1==deep[now]&&remain[i])
            {
                has_find=true;
                cur[now]=i;
                last[v[i]]=i;
                now=v[i];
                break;
            }

        if (!has_find)
        {
            int minn=t-1;
            for (int i=point[now];i!=-1;i=nxt[i])
                if (remain[i]) minn=min(minn,deep[v[i]]);
            if (!(--num[deep[now]])) break;
            ++num[deep[now]=minn+1];
            cur[now]=point[now];
            if (now!=s) now=v[last[now]^1];
        }
    }
}
int main()
{
    tot=-1;memset(point,-1,sizeof(point));
    scanf("%d",&n);
    s=n+1,t=s+1,ss=t+1,tt=ss+1;
    for (int i=1;i<=n;++i)
    {
        scanf("%d",&m);
        while (m--)
        {
            scanf("%d",&x);
            addedge(i,x,inf);
            --d[i],++d[x];
        }
        addedge(s,i,inf);
        addedge(i,t,inf);
    }
    for (int i=1;i<=t;++i)
    {
        if (d[i]>0) addedge(ss,i,d[i]);
        if (d[i]<0) addedge(i,tt,-d[i]);
    }
    isap(ss,tt);
    addedge(t,s,inf);
    isap(ss,tt);
    printf("%d\n",remain[tot]);
}