P3657 [USACO17FEB]Why Did the Cow Cross the Road II P

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  • 题目提供者 FarmerJohn2
  • 评测方式 云端评测
  • 标签 枚举,暴力 树状数组 离散化 USACO 2017 高性能
  • 难度 提高+/省选-
  • 时空限制 1000ms / 128MB

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    题目描述

    Farmer John is continuing to ponder the issue of cows crossing the road through his farm, introduced in the preceding problem. He realizes that interaction between some pairs of breeds is actually acceptable if the breeds are friendly, a property that turns out to be easily characterized in terms of breed ID: breeds $a$ and $b$ are friendly if $|a - b| \leq 4$ , and unfriendly otherwise. It is ok for cows to wander into fields designated for other breeds, as long as they are friendly. Given the ordering of $N$ fields on both sides of the road through FJ's farm (again, with exactly one field for each breed on each side), please help FJ determine the maximum number of crosswalks he can draw over his road, such that no two intersect, and such that each crosswalk joins a pair of fields containing two breeds that are friendly. Each field can be accessible via at most one crosswalk (so crosswalks don't meet at their endpoints).

    题意简述:

    给你两条由n个点组成的一条直链,点带有点权且每条直链的点权为1-n的排列,你可以随意设置每个链中点排列的顺序,现在要求你在两个链中连线

    两个点能连线需满足:

    1. 在不同的链上

    2. 不与前面的线交叉

    3. 点权差值小于等于4

    4. 一个点只能连一条线

    求最大可能连线数

    输入输出格式

    输入格式:

    The first line of input contains $N$ ( $1 \leq N \leq 100,000$ ). The next $N$ lines describe the order, by breed ID, of fields on one side of the road; each breed ID is an integer in the range $1 \ldots N$ . The last $N$ lines describe the order, by breed ID, of the fields on the other side of the road. Each breed ID appears exactly once in each ordering.

    输出格式:

    Please output the maximum number of disjoint "friendly crosswalks" Farmer John can draw across the road.

    输入输出样例

    输入样例#1: 复制
    6
    1
    2
    3
    4
    5
    6
    6
    5
    4
    3
    2
    1
    输出样例#1: 复制
    5
    

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    感谢@Adscn提供题意简述

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