BZOJ 1954 The xor-longest Path

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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…

BZOJ 1954: Pku3764 The xor-longest Path(贪心+trie)

传送门解题思路 \(trie\)的一个比较经典的应用,首先把每个点到根的异或和算出,然后建一棵\(trie\)把所有权值插入到\(Trie\)中,之后枚举所有结点,在\(Trie\)上贪心的跑统计答案,时间复杂度\(O(nlogn)\) 代码 #include<iostream> #include<cstdio> #include<cstring> using namespace std; const int N=100005; inline int rd(){ in…

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…

【BZOJ】1954: Pku3764 The xor-longest Path

[算法]trie树+xor路径 [题解] 套路1:统计从根到每个点的xor路径和,由于xor的自反性,两个点到根的xor路径和异或起来就得到两点间路径和. 然后问题就是找到n个值中异或值最大的两个值,考虑枚举每个数字,对于一个数找到与其异或和最大的数. 套路2:对所有数值二进制建01-trie,对于一个已知数字在trie上每一层尽量往另一端走,O(log n)得到与其异或和最大的数. 复杂度O(n log n). 另一种做法,用两个指针从根往下,尽量分叉走,查询总复杂度O(log n),但是建树…