hihocoder1860 最大异或和

思路：

把N个前缀异或和插入一棵trie树中，然后对每个前缀异或和x计算能使x ^ y最大的前缀异或和y。利用了异或运算的a ^ b ^ a = b的性质。

参考了https://cloud.tencent.com/developer/article/1343206

实现：

#include <iostream>
using namespace std;

const int INF = 0x3f3f3f3f;
const int N = 100005;
int a[N], cnt = 0;

struct trieNode
{
    trieNode * next[2];
}; 

trieNode pool[N * 32];

trieNode * createTrie()
{
    trieNode * root = &pool[cnt++];
    for (int i = 0; i < 2; i++)
    {
        root->next[i] = NULL;    
    }
    return root;
} 

void insert(trieNode * root, int x)
{
    trieNode * tmp = root;
    int index;
    for (int i = 31; i >= 0; i--)
    {
        int msk = (1 << i);
        if (msk & x) index = 1;
        else index = 0;
        if (tmp->next[index] == NULL)
        {
            tmp->next[index] = createTrie();
        }
        tmp = tmp->next[index];
    }
}

int search(trieNode * root, int x)
{
    trieNode * tmp = root;
    int res = 0;
    for (int i = 31; i >= 0; i--)
    {
        int msk = 1 << i;
        int need;
        if (msk & x) need = 0;
        else need = 1;
        if (i == 31) need = 1 - need;
        if (tmp->next[need])
        {
            res += (need << i);
            tmp = tmp->next[need];
        }
        else
        {
            res += (1 - need << i);
            tmp = tmp->next[1 - need];
        }
    }
    return x ^ res;
}

int main()
{
    int n;
    while (cin >> n)
    {
        cnt = 0;
        trieNode * root = createTrie();
        for (int i = 1; i <= n; i++)
        {
            cin >> a[i];
            a[i] = a[i - 1] ^ a[i];
            insert(root, a[i]);
        }
        insert(root, 0);
        int ans = -INF;
        for (int i = 1; i <= n; i++)
        {
            ans = max(ans, search(root, a[i]));
        }
        cout << ans << endl;
    }
    return 0;
}