Luogu2161 [SHOI2009]会场预约-线段树

Solution

线段树维护 sum 表示区间内预约个数， L 表示区间最左边的预约， R 表示区间最右边的预约。

$pushup$ 就是这样 ：

 void up(int nd) {
         sum[nd] = sum[lson] + sum[rson] - (R[lson] == L[rson] && R[lson]);
         L[nd] = L[lson]; R[nd] = R[rson];
 }

每次查询答案类似于$pushup$。

考虑把旧预约删去 ：

若该次新预约 开始时间为$l$， 结束时间为$r$，是第$i$ 个预约， 则将 与该区间在右边 和 在左边相交的 旧预约的区间都用0覆盖。

然后再把新预约的区间都用 $i$覆盖。

$pushdown$ 和 $laz$ 数组也有些细节

Code

 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #define rd read()
 using namespace std;

 const int N = 2e5 + ;
 const int end = 1e5;

 struct met {
     int L, R;
 }in[N];

 int read() {
     int X = , p = ; char c = getchar();
     for (; c > '' || c < ''; c = getchar())
         if (c == '-') p = -;
     for (; c >= '' && c <= ''; c = getchar())
         X = X *  + c - '';
     return X * p;
 }

 namespace SegT {
     int sum[N << ], L[N << ], R[N << ], laz[N << ];
     struct node {
         int sum, L, R;
     };
 #define lson nd << 1
 #define rson nd << 1 | 1
 #define mid ((l + r) >> 1)
     void up(int nd) {
         sum[nd] = sum[lson] + sum[rson] - (R[lson] == L[rson] && R[lson]);
         L[nd] = L[lson]; R[nd] = R[rson];
     }

     void make(int nd, int x) {
         sum[nd] = x ?  : ; L[nd] = R[nd] = laz[nd] = x;
     }

     void down(int nd) {
         if (~laz[nd]) {
             make(lson, laz[nd]); make(rson, laz[nd]);
             laz[nd] = -;
         }
     }

     void modify(int cl, int cr, int c, int l, int r, int nd) {
         if (cl <= l && r <= cr) {
             make(nd, c); return;
         }
         down(nd);
         if (mid >= cl)
             modify(cl, cr, c, l, mid, lson);
         if (mid < cr)
             modify(cl, cr, c, mid + , r, rson);
         up(nd);
     }

     node query(int cl, int cr ,int l, int r, int nd) {
         if (cl <= l && r <= cr) {
             node tmp;
             tmp.sum = sum[nd]; tmp.L = L[nd]; tmp.R = R[nd];
             return tmp;
         }
         node tmp, ls, rs;
         down(nd);
         if (mid >= cl && !(mid < cr))
             return query(cl, cr, l, mid, lson);
         else if (!(mid >= cl) && mid < cr)
             return query(cl, cr, mid + , r, rson);
         ls = query(cl, cr, l, mid, lson);
         rs = query(cl, cr, mid + , r, rson);
         tmp.sum = ls.sum + rs.sum - (ls.R == rs.L && ls.R);
         tmp.L = ls.L; tmp.R = rs.R;
         return tmp;
     }
 }using namespace SegT;

 int main()
 {
     int n = rd;
     memset(laz, -, sizeof(laz));
     for (int i = ; i <= n; ++i) {
         char ch = getchar();
         while (ch > 'Z' || ch < 'A') ch = getchar();
         if (ch == 'A') {
             int l = rd, r = rd;
             in[i].L = l; in[i].R = r;
             node ans = query(l, r, , end, );
             printf("%d\n", ans.sum);
             if (ans.L) modify(in[ans.L].L, in[ans.L].R, , , end, );
             if (ans.R) modify(in[ans.R].L, in[ans.R].R, , , end, );
             modify(l, r, i, , end, );
         }
         else {
             node ans = query(, end, , end, );
             printf("%d\n", ans.sum);
         }
     }
 }