CodeForces - 1285D （2020.3.19训练F题）

Today, as a friendship gift, Bakry gave Badawy n integers a1,a2,…,an and challenged him to choose an integer X such that the value max1≤i≤n(ai⊕X) is minimum possible, where ⊕ denotes the bitwise XOR operation.

As always, Badawy is too lazy, so you decided to help him and find the minimum possible value of max1≤i≤n(ai⊕X).

Input
The first line contains integer n (1≤n≤105).

The second line contains n integers a1,a2,…,an (0≤ai≤230−1).

Output
Print one integer — the minimum possible value of max1≤i≤n(ai⊕X).

题意：给定n个数，求数X，使得X与这n个数相异或的最大值最小

我们可以创建一个异或字典树，每条路径只有0或1，从结点1开始创建第29位到第0位，如果只有0或1，则该位不贡献，01都有则要加上1<<num

ac代码

#include<iostream>

using namespace std;
typedef long long ll;
ll ch[1 << 21][2];
ll a;
ll cnt = 1;
void insert(ll x)
{
	ll p = 1;
	for (ll i = 29; i >= 0; i--)
	{
		ll pos = (x >> i) & 1;
		if (!ch[p][pos])
		{
			ch[p][pos] = ++cnt;
		}
		p = ch[p][pos];
	}
}
ll solve(ll num, ll pos)
{
	if (num == -1)
		return 0;
	if (ch[pos][0] == 0)
		return solve(num - 1, ch[pos][1]);
	else if (ch[pos][1] == 0)
		return solve(num - 1, ch[pos][0]);
	else
		return (1 << num) + min(solve(num - 1, ch[pos][0]), solve(num - 1, ch[pos][1]));

}
int main()
{
	ll n;
	cin >> n;
	for (ll i = 1; i <= n; i++)
	{
		cin >> a;
		insert(a);
	}
	cout << solve(29, 1) << endl;
}