四校联考 推冰块

2<=n,m<=10^9，0<=k<=50000。

我们发现有用的格子不是很多，经过详细的分类讨论，只有这些格子是有用的：

四个角，以及障碍物（或减速带）本身和上下左右四个方向，以及障碍物所在行列（及±1的）的头尾两个。

那么我们只要把所有 障碍 和 减速带 按x-y和y-x排序一下，对于每一个有用的格子二分一下找到往左和往右会推到哪里，连边完暴力bfs即可。

#include <iostream>
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <time.h>
#include <stdlib.h>
#include <string>
#include <bitset>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <algorithm>
#include <sstream>
#include <stack>
#include <iomanip>
using namespace std;
#define pb push_back
#define mp make_pair
typedef pair<int,int> pii;
typedef long long ll;
typedef double ld;
typedef vector<int> vi;
#define fi first
#define se second
#define fe first
#define FO(x) {freopen(#x".in","r",stdin);freopen(#x".out","w",stdout);}
#define Edg int M=0,fst[SZ],vb[SZ],nxt[SZ];void ad_de(int a,int b){++M;nxt[M]=fst[a];fst[a]=M;vb[M]=b;}void adde(int a,int b){ad_de(a,b);ad_de(b,a);}
#define Edgc int M=0,fst[SZ],vb[SZ],nxt[SZ],vc[SZ];void ad_de(int a,int b,int c){++M;nxt[M]=fst[a];fst[a]=M;vb[M]=b;vc[M]=c;}void adde(int a,int b,int c){ad_de(a,b,c);ad_de(b,a,c);}
#define es(x,e) (int e=fst[x];e;e=nxt[e])
#define VIZ {printf("digraph G{\n"); for(int i=1;i<=n;i++) for es(i,e) printf("%d->%d;\n",i,vb[e]); puts("}");}
#ifdef LOCAL
#define TIMER cerr<<clock()<<"ms\n"
#else
#define TIMER
#endif
#define SZ 1234567
int n,m,k,N=0;
int xs[SZ],ys[SZ],ts[SZ];
typedef pair<int,int> pii;
map<pii,int> sta;
bool cmp2(pii a,pii b)
{
    if(a.se!=b.se) return a.se<b.se;
    return a.fi<b.fi;
}
pii ps[SZ]; int pn=0;
pii ss[SZ],rs[SZ];
int dx[4]={1,-1,0,0},dy[4]={0,0,-1,1};
void rec(int a,int b)
{
    if(sta[pii(a,b)]==1) return;
    if(a<1||b<1||a>n||b>m) return;
    ps[++pn]=pii(a,b);
}
int ls(pii a) {return lower_bound(ps+1,ps+1+pn,a)-ps;}
int S,T;
int qs[SZ];
int dist[SZ];
#undef SZ
#define SZ 1234567
Edg
void conn(pii a,pii b)
{
    if(a==b) return;
    ad_de(ls(a),ls(b));
}
void spfa()
{
    int h=0,t=0;
    qs[t++]=S; dist[S]=1;
    while(h^t)
    {
        int x=qs[h++];
        for es(x,e)
        {
            int b=vb[e];
            if(dist[b]) continue;
            dist[b]=dist[x]+1;
            qs[t++]=b;
        }
    }
}
int main()
{
    FO(ice)
    scanf("%d%d%d",&n,&m,&k);
    for(int i=1;i<=k;i++)
    {
        scanf("%d%d%d",xs+i,ys+i,ts+i);
        sta[pii(xs[i],ys[i])]=ts[i]+1;
    }
    rec(1,1); rec(n,m);
    rec(1,m); rec(n,1);
    for(int i=1;i<=k;i++)
    {
        rec(xs[i],1); rec(xs[i],m);
        rec(1,ys[i]); rec(n,ys[i]);
        rec(xs[i]+1,1); rec(xs[i]+1,m);
        rec(xs[i]-1,1); rec(xs[i]-1,m);
        rec(1,ys[i]+1); rec(n,ys[i]+1);
        rec(1,ys[i]-1); rec(n,ys[i]-1);
        rec(xs[i],ys[i]);
        for(int j=0;j<4;j++)
        rec(xs[i]+dx[j],ys[i]+dy[j]);
    }
    sort(ps+1,ps+1+pn);
    pn=unique(ps+1,ps+1+pn)-ps-1;
    int sn=0,rn=0;
    for(int i=1;i<=k;i++)
    {
        if(ts[i]==0) ss[++sn]=pii(xs[i],ys[i]);
        else rs[++rn]=pii(xs[i],ys[i]);
    }
    ss[++sn]=pii(-2000000000,-2000000000);
    ss[++sn]=pii(2000000000,2000000000);
    rs[++rn]=pii(-2000000000,-2000000000);
    rs[++rn]=pii(2000000000,2000000000);
    sort(ss+1,ss+1+sn); sort(rs+1,rs+1+rn);
    //先处理左右
    for(int i=1;i<=pn;i++)
    {
        int x=ps[i].fi,y=ps[i].se;
        pii cur=pii(x,y);
        if(y!=1) //L
        {
        int maxn=1;
        int id=lower_bound(rs+1,rs+1+rn,cur)-rs-1;
        pii ns=rs[id];
        if(ns.fi==x) maxn=max(maxn,ns.se);
        id=lower_bound(ss+1,ss+1+sn,cur)-ss-1;
        ns=ss[id];
        if(ns.fi==x) maxn=max(maxn,ns.se+1);
        conn(cur,pii(x,maxn));
        }
        if(y!=m) //R
        {
        int minn=m;
        int id=upper_bound(rs+1,rs+1+rn,cur)-rs;
        pii ns=rs[id];
        if(ns.fi==x) minn=min(minn,ns.se);
        id=upper_bound(ss+1,ss+1+sn,cur)-ss;
        ns=ss[id];
        if(ns.fi==x) minn=min(minn,ns.se-1);
        conn(cur,pii(x,minn));
        }
    }
    sort(ss+1,ss+1+sn,cmp2); sort(rs+1,rs+1+rn,cmp2);
    for(int i=1;i<=pn;i++)
    {
        int x=ps[i].fi,y=ps[i].se;
        pii cur=pii(x,y);
        if(x!=1) //U
        {
        int maxn=1;
        int id=lower_bound(rs+1,rs+1+rn,cur,cmp2)-rs-1;
        pii ns=rs[id];
        if(ns.se==y) maxn=max(maxn,ns.fi);
        id=lower_bound(ss+1,ss+1+sn,cur,cmp2)-ss-1;
        ns=ss[id];
        if(ns.se==y) maxn=max(maxn,ns.fi+1);
        conn(cur,pii(maxn,y));
        }
        if(x!=n) //R
        {
        int minn=n;
        int id=upper_bound(rs+1,rs+1+rn,cur,cmp2)-rs;
        pii ns=rs[id];
        if(ns.se==y) minn=min(minn,ns.fi);
        id=upper_bound(ss+1,ss+1+sn,cur,cmp2)-ss;
        ns=ss[id];
        if(ns.se==y) minn=min(minn,ns.fi-1);
        conn(cur,pii(minn,y));
        }
    }
    S=ls(pii(1,1));T=ls(pii(n,m));
    spfa(); cout<<dist[T]-1<<"\n";
}