LA3905 Meteor

https://vjudge.net/problem/UVALive-3905

计算出每个点在相框中的时间段，扫描线做即可

关键在如何快速计算每个点在相框中的时间段。对每个点进行运动分解，进入的时间L是x进入和y进入的最大，退出时间R是x退出和y退出的最小，画图看一下即可

画图同时可以发现不经过相框的时候会导致L >= R

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <cstdlib>
 #include <algorithm>
 #include <queue>
 #include <vector>
 #define min(a, b) ((a) < (b) ? (a) : (b))
 #define max(a, b) ((a) > (b) ? (a) : (b))
 #define abs(a) ((a) < 0 ? (-1 * (a)) : (a))
 inline void swap(int &a, int &b)
 {
     int tmp = a;a = b;b = tmp;
 }
 inline void read(int &x)
 {
     x = ;char ch = getchar(), c = ch;
     while(ch < '' || ch > '') c = ch, ch = getchar();
     while(ch <= '' && ch >= '') x = x *  + ch - '', ch = getchar();
     if(c == '-') x = -x;
 }

 const int INF = 0x3f3f3f3f;
 const int MAXN =  + ;

 int tt,w,h,n,x[MAXN],y[MAXN],a[MAXN],b[MAXN],flag[MAXN << ], cnt[MAXN << ], tot, t[MAXN << ], ans, tag;

 bool cmp(int a, int b)
 {
     return t[a] == t[b] ? flag[a] > flag[b] : t[a] < t[b];
 }

 inline void update(int x, int a, int w, int &L, int &R)
 {
     if(a == )
     {
         if(x <=  || x >= w) R = L - ;
     }
     else if(a > )
     {
         L = max(L, -x *  / a);
         R = min(R, (w - x) *  / a);
     }
     else
     {
         L = max(L, (w - x) *  / a);
         R = min(R, -x *  / a);
     }
 }

 int main()
 {
     read(tt);
     for(;tt;--tt)
     {
         read(w), read(h), read(n);
         for(register int i = ;i <= n;++ i) read(x[i]), read(y[i]), read(a[i]), read(b[i]);
         tot = ;
         for(register int i = ;i <= n;++ i)
         {
             int L = , R = INF;
             update(x[i], a[i], w, L, R);
             update(y[i], b[i], h, L, R);
             if(L < R)
             {
                 t[++tot] = L;flag[tot] = ;cnt[tot] = tot;
                 t[++tot] = R;flag[tot] = ;cnt[tot] = tot;
             }
         }
         std::sort(cnt + , cnt +  + tot, cmp);
         ans = tag = ;
         for(register int i = ;i <= tot;++ i)
         {
             if(flag[cnt[i]]) -- tag;
             else ++ tag;
             ans = max(ans, tag);
         }
         printf("%d\n", ans);
     }
     return ;
 } 

LA3905