【NOI2015】小园丁与老司机

dp+有源汇上下界的最小流；
dp：按pair

#include
#define rep(i,k,n) for(int i=k;i<=(n);i++)
#define rep2(i,k,n) for(int i=k;i>=(n);i--)
using namespace std;
const int N=50305;
const int M=600005;
const int inf=0x3f3f3f3f;
struct node{
    int x,y,id;node(int x=0,int y=0,int id=0):x(x),y(y),id(id){}
}a[N];
bool cmp(node A,node B){
    return A.y==B.y ? A.xint n;
map<int,int> mp1,mp2,mp3;
int f[N],fa[N],from[N],mx[N],pos,tag[N],stk[N],top,f2[N],ans,in[N],out[N];
int S,T,SS,TT,cur[N],Sum=0;
void dp1(){
    memset(f,-0x7f,sizeof(f));
    memset(mx,-0x7f,sizeof(f));
    f[0]=0;
    int t=0;
    for(int i=0;i<=n;i=++t){
        while(t1].y==a[t].y)t++;
        rep(j,i,t){
            if(mp1.find(a[j].x+a[j].y)!=mp1.end()){
                int p=mp1[a[j].x+a[j].y];
                if(f[p]+1>f[j])f[j]=f[p]+1,fa[j]=p;
            }
            mp1[a[j].x+a[j].y]=j;

            if(mp2.find(a[j].x-a[j].y)!=mp2.end()){
                int p=mp2[a[j].x-a[j].y];
                if(f[p]+1>f[j])f[j]=f[p]+1,fa[j]=p;
            }
            mp2[a[j].x-a[j].y]=j;

            if(mp3.find(a[j].x)!=mp3.end()){
                int p=mp3[a[j].x];
                if(f[p]+1>f[j])f[j]=f[p]+1,fa[j]=p;
            }
            mp3[a[j].x]=j;
        }
        int now=-1;
        rep(j,i+1,t){
            if(now==-1||f[j-1]>f[now])now=j-1;
            if(f[now]+j-i>mx[j])mx[j]=f[now]+j-i,from[j]=now;
        }
        now=-1;
        rep2(j,t-1,i){
            if(now==-1||f[j+1]>f[now])now=j+1;
            if(f[now]+t-j>mx[j])mx[j]=f[now]+t-j,from[j]=now;
        }
        rep(j,i,t)if(mx[j]>f[j])f[j]=mx[j],tag[j]=1;    
    }
    pos=0;
    rep(i,1,n)if(!pos||f[i]>f[pos])pos=i;       
}
void dp2(){
    mp1.clear(),mp2.clear(),mp3.clear();
    memset(f2,-0x7f,sizeof(f2));
    memset(mx,-0x7f,sizeof(f));
    rep(i,1,n)if(f[i]==ans)f2[i]=1;
    int t=n;
    for(int i=n;i>=0;i=--t){
        while(t && a[t-1].y==a[t].y)t--;
        rep2(j,i,t){
            if(mp1.find(a[j].x+a[j].y)!=mp1.end()){
                int p=mp1[a[j].x+a[j].y];
                if(f2[p]+1>f2[j])f2[j]=f2[p]+1;
            }
            mp1[a[j].x+a[j].y]=j;

            if(mp2.find(a[j].x-a[j].y)!=mp2.end()){
                int p=mp2[a[j].x-a[j].y];
                if(f2[p]+1>f2[j])f2[j]=f2[p]+1; 
            }
            mp2[a[j].x-a[j].y]=j;

            if(mp3.find(a[j].x)!=mp3.end()){
                int p=mp3[a[j].x];
                if(f2[p]+1>f2[j])f2[j]=f2[p]+1;
            }
            mp3[a[j].x]=j;
        }
        int now=-1;
        rep(j,t+1,i){
            if(now==-1||f2[j-1]+i-j+1>f2[now]+i-now)now=j-1;
            if(f2[now]+i-now>mx[j])mx[j]=f2[now]+i-now;
        }
        now=-1;
        rep2(j,i-1,t){
            if(now==-1||f2[j+1]+j+1-t>f2[now]+now-t)now=j+1;
            if(f2[now]+now-t>mx[j])mx[j]=f2[now]+now-t;
        }
        rep(j,t,i)if(mx[j]>f2[j])f2[j]=mx[j];   
    }
}
void print(int x,int y){
    if(xint lx=x;
        while(lx>=0 && a[lx].y==a[y].y)printf("%d ",a[lx].id),lx--;
        int rx=x+1;
        while(rx<=y && a[rx].y==a[y].y)printf("%d ",a[rx].id),rx++;
    }else{
        int rx=x;
        while(rx<=n && a[rx].y==a[y].y)printf("%d ",a[rx].id),rx++;
        int lx=x-1;
        while(lx>=y && a[lx].y==a[y].y)printf("%d ",a[lx].id),lx--;
    }
}
void solve(){
    printf("%d\n",ans=f[pos]);
    top=0;
    int now=pos;
    while(now!=-1){
        if(now)stk[++top]=now;
        if(tag[now]){
        stk[++top]=from[now];
        now=fa[from[now]];
        }else now=fa[now];
    }
    while(top){
        if(a[stk[top]].y==a[stk[top-1]].y)print(stk[top],stk[top-1]),top--;
        else printf("%d ",a[stk[top]].id);
        top--;
    }
    printf("\n");
}
struct E{
    int to,next,cap;E(int to=0,int next=0,int cap=0):to(to),next(next),cap(cap){}
}edge[M];
int head[N],tot=1;
void add(int x,int y,int cap){
    edge[++tot]=E(y,head[x],cap);head[x]=tot;
    edge[++tot]=E(x,head[y],0);head[y]=tot;
}
void build(){
    mp1.clear(),mp2.clear(),mp3.clear();
    S=n+1,T=S+1,SS=T+1,TT=SS+1;
    rep(i,0,n){
        if(mp1.find(a[i].x+a[i].y)!=mp1.end()){
                int p=mp1[a[i].x+a[i].y];
                if(f[p]+f2[i]==ans){
                    add(p,i,inf);
                    out[p]++;
                    in[i]++;
                }
            }
            mp1[a[i].x+a[i].y]=i;

            if(mp2.find(a[i].x-a[i].y)!=mp2.end()){
                int p=mp2[a[i].x-a[i].y];
                if(f[p]+f2[i]==ans){
                    add(p,i,inf);
                    out[p]++;
                    in[i]++;
                }
            }
            mp2[a[i].x-a[i].y]=i;

            if(mp3.find(a[i].x)!=mp3.end()){
                int p=mp3[a[i].x];
                if(f[p]+f2[i]==ans){
                    add(p,i,inf);
                    out[p]++;
                    in[i]++;
                }
            }
            mp3[a[i].x]=i;
    }
    rep(i,0,n){
        add(S,i,inf),add(i,T,inf);
        if(in[i]>out[i]){
            add(SS,i,in[i]-out[i]);
            Sum+=in[i]-out[i];
        }else{
            add(i,TT,out[i]-in[i]);
            Sum+=out[i]-in[i];
        }
    }
}
queue<int> Q;
int d[N];
bool bfs(){
    memset(d,0x7f,sizeof(d));
    memcpy(cur,head,sizeof(head));
    Q.push(SS);d[SS]=0;
    while(!Q.empty()){
        int u=Q.front();Q.pop();
        for(int i=head[u];i;i=edge[i].next)if(edge[i].cap){
            int v=edge[i].to;
            if(d[v]>d[u]+1){
            d[v]=d[u]+1;Q.push(v);}
        }
    }return d[TT]int dfs(int u,int a){
    if(u==TT || !a)return a;
    int flow=0,f;
    for(int &i=cur[u];i;i=edge[i].next)if(edge[i].cap){
        int v=edge[i].to;
        if(d[v]==d[u]+1 && (f=dfs(v,min(a,edge[i].cap)))>0){
            edge[i].cap-=f;
            edge[i^1].cap+=f;
            flow+=f;
            a-=f;
            if(!a)return flow;
        }
    }
    return flow;
}
void dinic(){
    while(bfs()){
        dfs(SS,inf);
    }
}
int main(){
//  freopen("in.in","r",stdin);
//  freopen("out.out","w",stdout);
    scanf("%d",&n);
    int x,y;
    rep(i,1,n){
        scanf("%d%d",&x,&y);
        a[i]=node(x,y,i);
    }sort(a+1,a+n+1,cmp);
    memset(fa,-1,sizeof(fa));
    if(n==1){printf("0\n\n0\n");return 0;}
    dp1();
    solve();
    dp2();
    build();
    dinic();
    add(T,S,inf);
    dinic();
    printf("%d\n",edge[tot].cap);
}