POJ3764 The xor-longest Path

【POJ3764 The xor-longest Path】的更多相关文章

poj3764 The XOR Longest Path【dfs】【Trie树】

The xor-longest Path Time Limit: 2000MS Memory Limit: 65536K Total Submissions: 10038 Accepted: 2040 Description In an edge-weighted tree, the xor-length of a path p is defined as the xor sum of the weights of edges on p: ⊕ is the xor operator. W…

题解 bzoj1954【Pku3764 The xor – longest Path】

做该题之前,至少要先会做这道题. 记 $d[u]$ 表示 $1$ 到 $u$ 简单路径的异或和,该数组可以通过一次遍历求得. $~$ 考虑 $u$ 到 $v$ 简单路径的异或和该怎么求? 令 $z=\operatorname{lca}(u,v)$ ,则 $u$ 到 $v$ 简单路径的异或和可以分成两段求解:一段是 $z$ 到 $u$ 简单路径的异或和,一段是 $z$ 到 $v$ 简单路径的异或和,二者异或一下即为 $u$ 到 $v$ 简…

Solve Longest Path Problem in linear time

We know that the longest path problem for general case belongs to the NP-hard category, so there is no known polynomial time solution for it. However, for a special case which is directed acyclic graph, we can solve this problem in linear time. First…

Why longest path problem doesn't have optimal substructure?

We all know that the shortest path problem has optimal substructure. The reasoning is like below: Supppose we have a path p from node u to v, another node t lies on path p: u->t->v ("->" means a path). We claim that u->t is also a sh…

【poj3764】 The xor-longest Path

http://poj.org/problem?id=3764 (题目链接) 今天的考试题,看到异或就有点虚,根本没往正解上想.. 题意给出一棵带权树,请找出树上的一条路径,使其边上权值的异或和最大. solution 首先我们考虑从根向下dfs,记录下每个点i到根上权值的异或和${val[i]}$.根据异或和的性质:${x~Xor~y~Xor~y=x}$.所以我们可以由${val}$数组两两组合得出树上任意两点之间路径的异或和.(不理解请自己脑补OvO) 然而这样对于时间复杂度并没有提高,仍然…

POJ3764,BZOJ1954 The xor-longest Path

题意 In an edge-weighted tree, the xor-length of a path p is defined as the xor sum of the weights of edges on p: \[ _{xor}length(p)=\oplus_{e \in p}w(e) \] $⊕$ is the xor operator. We say a path the xor-longest path if it has the largest xor-length.…

【poj3764】The xor-longest Path

The xor-longest Path Description In an edge-weighted tree, the xor-length of a path p is defined as the xor sum of the weights of edges on p: ⊕ is the xor operator. We say a path the xor-longest path if it has the largest xor-length. Given an edge-we…