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G - Vitya and Strange Lesson
CodeForces - 842D
Today at the lesson Vitya learned a very interesting function — mex. Mex of a sequence of numbers is the minimum non-negative number that is not present in the sequence as element. For example, mex([4, 33, 0, 1, 1, 5]) = 2 and mex([1, 2, 3]) = 0.
Vitya quickly understood all tasks of the teacher, but can you do the same?
You are given an array consisting of n non-negative integers, and m queries. Each query is characterized by one number x and consists of the following consecutive steps:
- Perform the bitwise addition operation modulo 2 (xor) of each array element with the number x.
- Find mex of the resulting array.
Note that after each query the array changes.
Input
First line contains two integer numbers n and m (1 ≤ n, m ≤ 3·105) — number of elements in array and number of queries.
Next line contains n integer numbers ai (0 ≤ ai ≤ 3·105) — elements of then array.
Each of next m lines contains query — one integer number x (0 ≤ x ≤ 3·105).
Output
For each query print the answer on a separate line.
Examples
Input
2 2
1 3
1
3
Output
1
0
Input
4 3
0 1 5 6
1
2
4
Output
2
0
0
Input
5 4
0 1 5 6 7
1
1
4
5
Output
2
2
0
2
题意 + 思路：
这两篇博客解释的非常好，我就不多说了
https://blog.csdn.net/brazy/article/details/77841433
https://blog.csdn.net/xzzf1024/article/details/79181290
解释：
主函数里 再次求MEX的时候 和上次的MEX值异或
num^=x; //与上次得到的值异或
printf("%d\n",num^Find_Trie(num));这相当于再次输入的X与存在字典树的序列异或。（设存在字典树的序列a，则相当于a^x1^x2）;
个人理解+代码：
//MEX求数列中未出现过的最小自然数
//X异或任何一位结果不同
//与存在的数异或后 会再次成为这个N数组的数
//求MEX的值 会出现在 不在这N数组的数。
//再次求MEX的时候 和上次的MEX值异或 就可以了
//
#include <map>
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <vector>
#include <string>
#include <cstring>
using namespace std;
#define mem(a,b) memset(a,b,sizeof(a))
using namespace std;
const int maxn=1e6;
int trie[5*maxn][2];
int vis[5*maxn];
int rt,tot;
void init()
{mem(vis,0);mem(trie,0);tot=0;
}
void Build_Trie(int y)
{rt=0;for(int i=31; i>=0; i--){int x=(y>>i)&1;if(!trie[rt][x])trie[rt][x]=++tot;rt=trie[rt][x];}vis[rt]=y;
}
int Find_Trie(int y)
{rt=0;int ans=0;for(int i=31; i>=0; i--){int x=(y>>i)&1; //找到最小的异或值if(!trie[rt][x])rt=trie[rt][x^1];elsert=trie[rt][x];}return vis[rt];
}
map<int,int>mp;
int main()
{int n,m,y;while(~scanf("%d%d",&n,&m)){init();mp.clear();int x;for(int i=0; i<n; i++){scanf("%d",&x);mp[x]=1;}for(int i=0; i<=600005; i++){if(!mp[i])Build_Trie(i);}int num=0;for(int i=0; i<m; i++){scanf("%d",&x);num^=x; //与上次得到的值异或printf("%d\n",num^Find_Trie(num));}}return 0;
}
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