POJ 3614 Sunscreen

Posted 2020-06-10

网络流，Dinic G++ 964ms水过，SAP 620ms AC

源点到每一个防晒霜建边，容量为cover[i]；

每一个防晒霜与它能保护的奶牛之间连一条边，容量为1；

每一个奶牛连到汇点一条边，容量为1。

最大流就是答案。

Dinic模板：

#include<cstdio>
#include<cstring>
#include<string>
#include<cmath>
#include<vector>
#include<queue>
#include<algorithm>
using namespace std;

const int maxn = 6000 + 10;
const int INF = 0x7FFFFFFF;
struct Edge
{
    int from, to, cap, flow;
    Edge(int u, int v, int c, int f) :from(u), to(v), cap(c), flow(f) {}
};
vector<Edge>edges;
vector<int>G[maxn];
bool vis[maxn];
int d[maxn];
int cur[maxn];
int n, m, s, t;

void init()
{
    for (int i = 0; i < maxn; i++)
        G[i].clear();
    edges.clear();
}
void AddEdge(int from, int to, int cap)
{
    edges.push_back(Edge(from, to, cap, 0));
    edges.push_back(Edge(to, from, 0, 0));
    int w = edges.size();
    G[from].push_back(w - 2);
    G[to].push_back(w - 1);
}
bool BFS()
{
    memset(vis, 0, sizeof(vis));
    queue<int>Q;
    Q.push(s);
    d[s] = 0;
    vis[s] = 1;
    while (!Q.empty())
    {
        int x = Q.front();
        Q.pop();
        for (int i = 0; i<G[x].size(); i++)
        {
            Edge e = edges[G[x][i]];
            if (!vis[e.to] && e.cap>e.flow)
            {
                vis[e.to] = 1;
                d[e.to] = d[x] + 1;
                Q.push(e.to);
            }
        }
    }
    return vis[t];
}
int DFS(int x, int a)
{
    if (x == t || a == 0)
        return a;
    int flow = 0, f;
    for (int &i = cur[x]; i<G[x].size(); i++)
    {
        Edge e = edges[G[x][i]];
        if (d[x]+1 == d[e.to]&&(f=DFS(e.to,min(a,e.cap-e.flow)))>0)
        {
            edges[G[x][i]].flow+=f;
            edges[G[x][i] ^ 1].flow-=f;
            flow+=f;
            a-=f;
            if(a==0) break;
        }
    }
    if(!flow) d[x] = -1;
    return flow;
}
int dinic(int s, int t)
{
    int flow = 0;
    while (BFS())
    {
        memset(cur, 0, sizeof(cur));
        flow += DFS(s, INF);
    }
    return flow;
}

int C,L;
int minSPF[maxn],maxSPF[maxn];
int SPF[maxn];

bool judge(int a,int b)
{
    if(SPF[a]>=minSPF[b]&&SPF[a]<=maxSPF[b])
        return 1;
    return 0;
}

int main()
{
    //0 源点 C+L+1汇点 1--L 防晒霜，L+1--L+C奶牛
    scanf("%d%d",&C,&L);
    init();
    s=0;t=C+L+1;

    for(int i=1;i<=C;i++)
        scanf("%d%d",&minSPF[i],&maxSPF[i]);

    for(int i=1;i<=L;i++)
    {
        int x;
        scanf("%d%d",&SPF[i],&x);
        AddEdge(0,i,x);
    }

    for(int i=1;i<=L;i++)
        for(int j=1;j<=C;j++)
            if(judge(i,j))
                AddEdge(i,j+L,1);

    for(int i=L+1;i<=C+L;i++) AddEdge(i,t,1);

    printf("%d\n",dinic(s,t));
    return 0;
}

 

SAP模板：

#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn=500000,maxm=3000000,INF=1<<30;
int tot=0,S,T,n,m,cur[maxn],lay[maxn],gap[maxn],pre[maxn],V[maxm],Q[maxn],G[maxm],N[maxm],B[maxm],F[maxn];
bool dw(int &x,int y)
{
     if (y< x)
     {
       x=y;
       return 1;
      }
      return 0;
}
void add(int a,int b,int c)
{
     ++tot;V[tot]=b;G[tot]=c;N[tot]=F[a];F[a]=tot;
     ++tot;V[tot]=a;G[tot]=0;N[tot]=F[b];F[b]=tot;
     B[tot]=tot-1;B[tot-1]=tot;
}
void bfs(int n)
{
     int u,hd=0,tl=1,p;
     memset(lay,127,sizeof(lay));
     memset(gap,0,sizeof(gap));
     Q[1]=T;lay[T]=0;gap[0]=1;
     while (hd!=tl)
     {
       u=Q[++hd];
       for (p=F[u];p;p=N[p])
         if (G[B[p]]>0&&lay[V[p]]>=n)
         {
             lay[V[p]]=lay[u]+1;
             gap[lay[V[p]]]++;
             Q[++tl]=V[p];
             cur[V[p]]=B[p];
         }
     }
}
inline int sap(int n)
{
    int u=S,v,flow,ret=0,mL,cnt=0,x,y;
    memset(pre,0,sizeof(pre));bfs(n);
    u=S;
    while (lay[S]< n)
    {
        cnt++;
        for (int &p=cur[u];p;p=N[p])
          if (G[p]>0&&lay[u]==lay[V[p]]+1) break;
        if (cur[u])
        {
            v=V[cur[u]];
            pre[v]=u;
            u=v;
            if (v==T)
            {
                flow=INF;
                x=T;
                while (x!=S)
                {
                    x=pre[x];
                    dw(flow,G[cur[x]]);
                }
                ret+=flow;
                if (ret>=INF) return ret;
                x=T;
                while (x!=S)
                {
                    x=pre[x];
                    G[cur[x]]-=flow;
                    G[B[cur[x]]]+=flow;
                }
                u=S;
            }
        }else {
                  mL=n;
                  for (int p=F[u];p;p=N[p])
                    if (G[p]>0&&dw(mL,lay[V[p]]+1)) cur[u]=p;
                  gap[lay[u]]--;
                  if (gap[lay[u]]==0) return ret;
                  gap[mL]++;lay[u]=mL;
                  if (u!=S) u=pre[u];
              }

    }
    return ret;
}


int C,L;
int minSPF[maxn],maxSPF[maxn];
int SPF[maxn];

bool judge(int a,int b)
{
    if(SPF[a]>=minSPF[b]&&SPF[a]<=maxSPF[b])
        return 1;
    return 0;
}

int main()
{
    //0 源点 C+L+1汇点 1--L 防晒霜，L+1--L+C奶牛
    scanf("%d%d",&C,&L);
    S=0;T=C+L+1;

    for(int i=1;i<=C;i++)
        scanf("%d%d",&minSPF[i],&maxSPF[i]);

    for(int i=1;i<=L;i++)
    {
        int x;
        scanf("%d%d",&SPF[i],&x);
        add(0,i,x);
    }

    for(int i=1;i<=L;i++)
        for(int j=1;j<=C;j++)
            if(judge(i,j))
                add(i,j+L,1);

    for(int i=L+1;i<=C+L;i++) add(i,T,1);

    printf("%d\n",sap(C+L+1));
    return 0;
}