Artwork Gym - 101550A 离线并查集

题目：题目链接

思路：每个空白区域当作一个并查集，因为正着使用并查集分割的话dfs会爆栈，判断过于复杂也会导致超时，我们采用离线反向操作，先全部涂好，然后把黑格子逐步涂白，我们把每个空白区域当作一个并查集，然后采用合并并查集的方法来做，好困啊，明天还有课，具体思路有空再写吧，先睡觉了。

AC代码：

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <vector>

 using namespace std;

 #define y1 yy1
 #define y2 _y2

 const int maxn =  + ;
 const int maxq =  + ;

 int grid[maxn][maxn], x1[maxq], y1[maxq], x2[maxq], y2[maxq], num[maxn * maxn], n, m, q, sum, ans[maxq];

 int cx[] = { -, , ,  };
 int cy[] = { , -, ,  };

 void init();
 int cal(int, int);
 bool judge(int, int);
 void unite(int, int);
 int _find(int);
 void solve();

 int main()
 {
     ios::sync_with_stdio();
     cin.tie();

     cin >> n >> m >> q;

     for (int i = ; i <= q; ++i) {
         cin >> x1[i] >> y1[i] >> x2[i] >> y2[i];
         if (x1[i] == x2[i])
             for (int j = y1[i]; j <= y2[i]; ++j)
                 ++grid[x1[i]][j];
         else
             for (int j = x1[i]; j <= x2[i]; ++j)
                 ++grid[j][y1[i]];
     }

     init();

     solve();

     for (int i = ; i <= q; ++i)
         cout << ans[i] << endl;

     return ;
 }

 void init() {
     for (int i = ; i <= n * m; ++i)
         num[i] = i;

     sum = n * m;

     for (int i = ; i <= n; ++i) {
         for (int j = ; j <= m; ++j) {
             if (!grid[i][j]) {
                 for (int k = ; k < ; ++k) {
                     if (judge(i + cx[k], j + cy[k]) && !grid[i + cx[k]][j + cy[k]]) {
                         unite(cal(i, j), cal(i + cx[k], j + cy[k]));
                     }
                 }
             }
             else
                 --sum;
         }
     }
 }

 int cal(int x, int y) {
     return (x - ) * m + y;
 }

 bool judge(int x, int y) {
     return x >  && x <= n && y >  && y <= m;
 }

 void unite(int x, int y) {
     int a = _find(x), b = _find(y);
     if (a == b)
         return;

     --sum;
     num[a] = b;
 }

 int _find(int x) {
     return x == num[x] ? x : num[x] = _find(num[x]);
 }

 void solve() {
     for (int i = q; i > ; --i) {
         ans[i] = sum;
         if (x1[i] == x2[i]) {
             for (int j = y1[i]; j <= y2[i]; ++j) {
                 --grid[x1[i]][j];
                 if (!grid[x1[i]][j]) {
                     ++sum;
                     for (int k = ; k < ; ++k) {
                         if (judge(x1[i] + cx[k], j + cy[k]) && !grid[x1[i] + cx[k]][j + cy[k]])
                             unite(cal(x1[i], j), cal(x1[i] + cx[k], j + cy[k]));
                     }
                 }
             }
         }
         else {
             for (int j = x1[i]; j <= x2[i]; ++j) {
                 --grid[j][y1[i]];
                 if (!grid[j][y1[i]]) {
                     ++sum;
                     for (int k = ; k < ; ++k)
                         if (judge(j + cx[k], y1[i] + cy[k]) && !grid[j + cx[k]][y1[i] + cy[k]])
                             unite(cal(j, y1[i]), cal(j + cx[k], y1[i] + cy[k]));
                 }
             }
         }
     }
 }