hdu 6191--Query on A Tree（持久化字典树）

题目链接

[align=left]Problem Description[/align]
Monkey A lives on a tree, he always plays on this tree.

One day, monkey A learned about one of the bit-operations, xor. He was keen of this interesting operation and wanted to practise it at once.

Monkey A gave a value to each node on the tree. And he was curious about a problem.

The problem is how large the xor result of number x and one node value of label y can be, when giving you a non-negative integer x and a node label u indicates that node y is in the subtree whose root is u(y can be equal to u).

Can you help him?

[align=left]Input[/align]
There are no more than 6 test cases.

For each test case there are two positive integers n and q, indicate that the tree has n nodes and you need to answer q queries.

Then two lines follow.

The first line contains n non-negative integers V1,V2,⋯,Vn, indicating the value of node i.

The second line contains n-1 non-negative integers F1,F2,⋯Fn−1, Fi means the father of node i+1.

And then q lines follow.

In the i-th line, there are two integers u and x, indicating that the node you pick should be in the subtree of u, and x has been described in the problem.

2≤n,q≤105

0≤Vi≤109

1≤Fi≤n, the root of the tree is node 1.

1≤u≤n,0≤x≤109

[align=left]Output[/align]
For each query, just print an integer in a line indicating the largest result.

[align=left]Sample Input[/align]

2 2
1 2
1

1 3
2 1

[align=left]Sample Output[/align]

2

3

题意：有一棵由n个节点构成的树，每个点上有一个权值，现在q次询问，每次输入u，x 表示以u为根节点的子树上 以某个节点上的权值异或x得到的最大值？

思路：持久化 trie 树，感觉和主席树差不多，是有 n 个版本的字典树，在遍历树的过程中经过点时，建立新的字典树，但实际上与旧的相比每次只是增加了log2（1e9）个节点，另外是在子树 u 上求最大异或值，所以需要保存 u 子树之前节点号和 u 子树中的最后一个节点的编号，作差即可得到相应的数据；

代码如下：

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <vector>
using namespace std;
const int N=1e5+5;
int a
;
struct Node
{
int son[2];
int sum[2];
}node[35*N];
vector<int>G
;
int la
,to
,root
;
int tot1,tot2;

void init()
{
node[0].son[0]=node[0].son[1]=0;
node[0].sum[0]=node[0].sum[1]=0;
root[0]=0;
tot1=tot2=0;
for(int i=1;i<N;i++) G[i].clear();
}
void build(int pre,int now,int x,int deep)
{
if(deep<0) return ;
int tmp=!!(x&(1<<deep));
node[now]=node[pre];
node[now].sum[tmp]++;
build(node[pre].son[tmp],node[now].son[tmp]=++tot2,x,deep-1);
}
void dfs(int now)
{
la[now]=++tot1;
build(root[la[now]-1],root[la[now]]=++tot2,a[now],30);
for(int i=0;i<G[now].size();i++)
{
int v=G[now][i];
dfs(v);
}
to[now]=tot1;
}
int query(int pre,int now,int sum,int x,int deep)
{
if(deep<0) return sum;
int tmp=!!(x&(1<<deep));
if(node[now].sum[tmp^1]>node[pre].sum[tmp^1])
return query(node[pre].son[tmp^1],node[now].son[tmp^1],sum|(1<<deep),x,deep-1);
return query(node[pre].son[tmp],node[now].son[tmp],sum,x,deep-1);
}
int main()
{
int n,q;
while(scanf("%d%d",&n,&q)!=EOF)
{
init();
for(int i=1;i<=n;i++) scanf("%d",&a[i]);
for(int i=2;i<=n;i++)
{
int x; scanf("%d",&x);
G[x].push_back(i);
}
dfs(1);
while(q--)
{
int u,x; scanf("%d%d",&u,&x);
printf("%d\n",query(root[la[u]-1],root[to[u]],0,x,30));
}
}
return 0;
}