[BZOJ2502]清理雪道（有源汇有上下界的最小流）

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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<algorithm>#include<iostream>#include<cstring>#include<cstdio>#include<cmath>#include<queue>using namespace std;#define N 110#define E 30005#define inf 1000000000int 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]<t)    {        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]);}

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