YBTOJ最大异或对

Posted 2021-05-15 Jayun

题目大意：

在给定的 \\(N\\) 个整数 \\(A_1，A_2……A_N\\) 中选出两个进行 \\(xor\\)（异或）运算，得到的结果最大是多少？

正文：

01trie 板子。

代码：

const int N = 2e6 + 10;

inline ll READ()
{
	ll x = 0, f = 1;
	char c = getchar();
	while (c != \'-\' && (c < \'0\' || c > \'9\')) c = getchar();
	if (c == \'-\') f = -f, c = getchar();
	while (c >= \'0\' && c <= \'9\') x = (x << 3) + (x << 1) + c - \'0\', c = getchar();
	return x * f;
}

int n, k;
ll a[N];

struct Trie
{
	int ch[N][2];
	ll siz[N], tot;
	Trie(){tot = 1;} 
	void ins(ll val) 
	{
		int u = 1;
		for (ll i = 31ll; ~i; --i)
		{
			bool k = (val >> i) & 1; siz[u]++;
			if (!ch[u][k]) ch[u][k] = ++tot;
			u = ch[u][k];
		}
		siz[u] ++;
		return;
	}
	
	ll query(ll val, int n) 
	{
		int u = 1;ll tmp = 0;
		for (int i = 31; ~i; --i)
		{
			bool k = (val >> i) & 1;
			if(!ch[u][k ^ 1]) u = ch[u][k];
			else if (n <= siz[ch[u][k ^ 1]]) u = ch[u][k ^ 1], tmp |= 1ll << i;
			else n -= siz[ch[u][k ^ 1]], u = ch[u][k];
//			if (val == 1036879) printf ("%lld, %d, t[][]={%d, %d}\\n", tmp, u, ch[u][0], ch[u][1]);
		}
		return tmp;
	}
}t;
ll ans = 0;

int main()
{
	n = READ();
//	t.ins(0);
	for (int i = 1; i <= n; i++)
		a[i] = READ(), t.ins(a[i]);
	for (ll i = 1, x; i <= n; i++)
		ans = max(ans, x = t.query(a[i], 1));
	printf ("%lld\\n", ans);
	return 0;
}