Training 1: (Persistent) Segment Tree

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Problem A

Solved by Weaver_zhu.

Problem from HDU4578.

Problem B

Solved by Xiejiadong.

Problem form BZOJ1818.

题意:如果一个点位于四个黑点之间,那么他可以变成白点,求最后有多少个白点。

题解:对于行和列分别求出 max 和 min ,就可以得到行和列的作用域。

于是就是求行和列两两之间的交点个数。

我们用线段树维护列,用扫描线扫描行,遇到左端点的时候对那一列 +1 ,遇到右端点的时候,对那一列 -1 。每次询问一个区间和就行了。

Problem C

Solved by Xiejiadong.

Problem from SPOJCOT.

题意:求树链上 $k$ 大数。

树链剖分以后主席树维护即可。

Problem D

Solved by Xiejiadong.

Problem from BZOJ3261.

可持久化字典树。

[题解]

Problem E

Solved by Xiejiadong.

主席树。

[题解]

Problem F

Solved by Xiejiadong.

Problem from Codeforces1080F.

主席树。

[题解]

Problem G

Unsolved.

Problem H

Solved by Xiejiadong.

Problem from BZOJ3551.

主席树。

BZOJ3545和BZOJ3551题目一样,只不过3551要求强制在线。

因为我的做法BZOJ3545也是支持在线的,所以就无所谓了。

[题解]

Problem I

Solved by Xiejiadong.

Problem from Codeforces242E.

看到异或,考虑拆位。

维护 $20$ 棵线段树,对于每一位需要维护一个 tag 表示当前有没有置反,维护区间和即可。

Problem J

Solved by Xiejiadong.

Problem from POJ2777.

题意:支持两个操作:

  • 给一个区间涂色
  • 询问一个区间里面有多少颜色

题解:颜色很少,状压。

线段树维护区间状态即可。

Problem K

Solved by Xiejiadong.

主席树。

求区间第$k$小数,权值线段树,差分维护。

在线段树上二分即可。