XOR Clique

https://pintia.cn/problem-sets/1036903825309761536/problems/1041156503909756928

K XOR Clique

BaoBao has a sequence a​1​​,a​2​​,...,a​n​​. He would like to find a subset S of {1,2,...,n} such that ∀i,j∈S, a​i​​⊕a​j​​<min(a​i​​,a​j​​) and ∣S∣ is maximum, where ⊕ means bitwise exclusive or.

Input

There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:

The first line contains an integer n (1≤n≤10​5​​), indicating the length of the sequence.

The second line contains n integers: a​1​​,a​2​​,...,a​n​​ (1≤a​i​​≤10​9​​), indicating the sequence.

It is guaranteed that the sum of n in all cases does not exceed 10​5​​.

Output

For each test case, output an integer denoting the maximum size of S.

Sample Input

3
3
1 2 3
3
1 1 1
5
1 2323 534 534 5

Sample Output

2
3
2

作者: 浙江大学竞赛命题组

单位: ACMICPC

时间限制: 500 ms

内存限制: 64 MB

代码长度限制: 32 KB

#include<stdio.h>
#include<algorithm>
using namespace std;
int main()
{
	int i,j;
	for(i=0;i<=16;i++)
	{
		for(j=0;j<=100;j++)
		{
			if((i^j)<min(i,j))
			printf("%d %d
",i,j);
		
		}
	}
	return 0;
}

可以看出规律，符合条件的在2^n与2^(n+1)之间，所以只要求在哪个阶段中的数最多即可。

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#include<algorithm>
using namespace std;
#define N 120
int a[N];
int main()
{
	int n,i,j,t,maxn,x;
	scanf("%d",&t);
	while(t--)
	{    
		maxn=0;
		memset(a,0,sizeof(a));
		scanf("%d",&n);
		for(i=1;i<=n;i++)
		{
			scanf("%d",&x);
			for(j=0;;j++)
			{
				if(x>=pow(2,j)&&x<pow(2,j+1))
				{
					a[j]++;	
					maxn=max(a[j],maxn);
					break;
				}
			}
		}
		printf("%d
",maxn);
	}
	return 0;
}