# 4672. Snags

Title Description

I did not learn again today. MDZ

No learning MDZ love to play all kinds of pinball games, so this is a pinball theme.

It has a grid line $ $ $ m $ n-columns, wherein the n-$ $ $ and $ m $ m $ coprime and an odd number. $ Bottom left coordinates (0,0) $, top right coordinates $ (m, n) $.

A negligibly small initial size of balls in $ (m / 2,0) $, the initial velocity vector is $ (- 1 / 2,1 / 2) $ (i.e., an initial down to the left).

There are certain grid block, when encountering a boundary or border grid box, mirror reflection will be issued. If the ball hit a box, the box will disappear.

After the location of each block has now been asked how long all square disappears.

data range

$1 \leq n, m, k \leq 10^{5}, \quad k \leq mn-1$

answer

Consider violence, each block is split into four sides, with the set maintenance and x + y equal xy edges.

If you hit a boundary to consider how to do, found that if the arrival of a boundary by a direction from a boundary, the boundary that the next direction by this time or will reach this boundary, then compressed with a disjoint-set about the path to .

Code

#include <bits/stdc++.h>
using namespace std;
const int N=4e5+5;
int m,n,k,t,f[N<<3];
struct P{int x,y;}p[N];
long long ans,g[N<<3];
struct O{
    int x,y,i;
    friend bool operator < (const O& A,const O& B){
        if (A.x==B.x){
            if (A.y==B.y) return A.i<B.i;
            return A.y<B.y;
        }
        return A.x<B.x;
    }
};
set<O>s[2][N];
set<O>::iterator it;
#define pi pair<int,int>
#define M make_pair
#define fi first
#define se second
map<pair<pi,pi>,int>mp;
pair<pi,pi>h[N<<3];
void ins(int x,int y,int i){
    s[0][x+y].insert((O){x,y,i});
    s[1][x-y+n].insert((O){x,y,i});
}
void era ( you get, you y, you i) {
    s [ 0 ] [x + y] .erase (s [ 0 ] [x + y] .find ((O) {x, y, i}));
    s [ 1 ] [x-y + n] .erase (s [ 1 ] [x-y + n] .find ((O) {x, y, i}));
}
void era(int i){
    int x=p[i].x,y=p[i].y;
    was (x - 2 , y - 1 , i) was (x- 1 , and, i);
    was (x - 1 , y - 2 , i) was (x, y- 1 , i); K-- ;
}
int get(int x){
    return f[x]==x?x:f[x]=get(f[x]);
}
int main () {
    cin>>m>>n>>k;m<<=1;n<<=1;
    for (int i=1,x,y;i<=k;i++){
        scanf("%d%d",&x,&y);
        x<<=1;y<<=1;p[i]=(P){x,y};
        ins(x-2,y-1,i);ins(x-1,y,i);
        ins(x-1,y-2,i);ins(x,y-1,i);
    }
    int x=m>>1,y=0,dx=-1,dy=1,o,v;
    if (!mp.count(M(M(x,y),M(dx,dy))))
        mp[M(M(x,y),M(dx,dy))]=++t,
        f[t]=t,h[t]=M(M(x,y),M(dx,dy));
    while(k){
        o=0;
        if (mp.count(M(M(x,y),M(dx,dy))))
            o=mp[M(M(x,y),M(dx,dy))];
        if (dx<0 && dy>0){
            it=s[0][x+y].lower_bound((O){x,0,0});
            if (it==s[0][x+y].begin()){
                if (x+y>n) g[get(o)]+=n-y,ans+=n-y,x=x+y-n,y=n,dy=-1;
                else g[get(o)]+=x,ans+=x,y=x+y,x=0,dx=1;
                if (!mp.count(M(M(x,y),M(dx,dy))))
                    mp[M(M(x,y),M(dx,dy))]=++t,
                    f[t]=t,h[t]=M(M(x,y),M(dx,dy));
                v=mp[M(M(x,y),M(dx,dy))];
                ans+=g[get(v)];
                x = h [ get (v)]. fi.fi, y = h [ get (v)]. fi.se,
                dx=h[get(v)].se.fi,dy=h[get(v)].se.se;
                if (!o) continue;
                g[get(v)]+=g[get(o)];
                f[get(o)]=get(v);
                continue;
            }
            it--;O u=*it;era(u.i);ans+=x-u.x;x=u.x;y=u.y;
            if (y&1) dx=1; else dy=-1; continue;
        }
        if (dx>0 && dy<0){
            it=s[0][x+y].upper_bound((O){x,0,0});
            if (it==s[0][x+y].end()){
                if (x+y-m>0) g[get(o)]+=m-x,ans+=m-x,y=x+y-m,x=m,dx=-1;
                else g[get(o)]+=y,ans+=y,x=x+y,y=0,dy=1;
                if (!mp.count(M(M(x,y),M(dx,dy))))
                    mp[M(M(x,y),M(dx,dy))]=++t,
                    f[t]=t,h[t]=M(M(x,y),M(dx,dy));
                v=mp[M(M(x,y),M(dx,dy))];
                ans+=g[get(v)];
                x = h [ get (v)]. fi.fi, y = h [ get (v)]. fi.se,
                dx=h[get(v)].se.fi,dy=h[get(v)].se.se;
                if (!o) continue;
                g[get(v)]+=g[get(o)];
                f[get(o)]=get(v);
                continue;
            }
            O u=*it;era(u.i);ans+=u.x-x;x=u.x;y=u.y;
            if (y&1) dx=-1; else dy=1; continue;
        }
        if (dx>0 && dy>0){
            it=s[1][x-y+n].upper_bound((O){x,0,0});
            if (it==s[1][x-y+n].end()){
                if (m-x+y<n) g[get(o)]+=m-x,ans+=m-x,y=m-x+y,x=m,dx=-1;
                else g[get(o)]+=n-y,ans+=n-y,x=x-y+n,y=n,dy=-1;
                if (!mp.count(M(M(x,y),M(dx,dy))))
                    mp[M(M(x,y),M(dx,dy))]=++t,
                    f[t]=t,h[t]=M(M(x,y),M(dx,dy));
                v=mp[M(M(x,y),M(dx,dy))];
                ans+=g[get(v)];
                x = h [ get (v)]. fi.fi, y = h [ get (v)]. fi.se,
                dx=h[get(v)].se.fi,dy=h[get(v)].se.se;
                if (!o) continue;
                g[get(v)]+=g[get(o)];
                f[get(o)]=get(v);
                continue;
            }
            O u=*it;era(u.i);ans+=u.x-x;x=u.x;y=u.y;
            if (y&1) dx=-1; else dy=-1; continue;
        }
        if (dx<0 && dy<0){
            it=s[1][x-y+n].lower_bound((O){x,0,0});
            if (it==s[1][x-y+n].begin()){
                if (y-x>0) g[get(o)]+=x,ans+=x,y=y-x,x=0,dx=1;
                else g[get(o)]+=y,ans+=y,x=x-y,y=0,dy=1;
                if (!mp.count(M(M(x,y),M(dx,dy))))
                    mp[M(M(x,y),M(dx,dy))]=++t,
                    f[t]=t,h[t]=M(M(x,y),M(dx,dy));
                v=mp[M(M(x,y),M(dx,dy))];
                ans+=g[get(v)];
                x = h [ get (v)]. fi.fi, y = h [ get (v)]. fi.se,
                dx=h[get(v)].se.fi,dy=h[get(v)].se.se;
                if (!o) continue;
                g[get(v)]+=g[get(o)];
                f[get(o)]=get(v);
                continue;
            }
            it--;O u=*it;era(u.i);ans+=x-u.x;x=u.x;y=u.y;
            if (y&1) dx=1; else dy=1; continue;
        }
    }
    cout<<ans<<endl; return 0;
}