CodeForces - 165E Compatible Numbers(SOSdp)

Posted 2021-06-26 Frozen_Guardian

题目链接：点击查看

题目大意：给出 $n$ 个数，问能否在数列中找到一个数，满足 $a_i\&a_j=0$

题目分析：题目中的式子可以转换为，$a_i$ 是 $a_j$ 补集的子集，然后就是 $SOSdp$ 的模板题了，因为输出的答案涉及到了 $-1$，所以可以将 $dp$ 初始化为 $-1$，然后直接维护每个超集的最大可行答案就好啦

转移的话就是子集向超集转移

代码：

// Problem: E. Compatible Numbers
// Contest: Codeforces - Codeforces Round #112 (Div. 2)
// URL: https://codeforces.com/contest/165/problem/E
// Memory Limit: 256 MB
// Time Limit: 4000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

// #pragma GCC optimize(2)
// #pragma GCC optimize("Ofast","inline","-ffast-math")
// #pragma GCC target("avx,sse2,sse3,sse4,mmx")
#include<iostream>
#include<cstdio>
#include<string>
#include<ctime>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<stack>
#include<climits>
#include<queue>
#include<map>
#include<set>
#include<sstream>
#include<cassert>
#include<bitset>
#include<list>
#include<unordered_map>
#define lowbit(x) x&-x
using namespace std;
typedef long long LL;
typedef unsigned long long ull;
template<typename T>
inline void read(T &x)
{
	T f=1;x=0;
	char ch=getchar();
	while(0==isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}
	while(0!=isdigit(ch)) x=(x<<1)+(x<<3)+ch-'0',ch=getchar();
	x*=f;
}
template<typename T>
inline void write(T x)
{
	if(x<0){x=~(x-1);putchar('-');}
    if(x>9)write(x/10);
    putchar(x%10+'0');
}
const int inf=0x3f3f3f3f;
const int N=1<<22;
int a[N],dp[N];
int main()
{
#ifndef ONLINE_JUDGE
//	freopen("data.in.txt","r",stdin);
//	freopen("data.out.txt","w",stdout);
#endif
//	ios::sync_with_stdio(false);
	memset(dp,-1,sizeof(dp));
	int n;
	read(n);
	for(int i=1;i<=n;i++) {
		read(a[i]);
		dp[a[i]]=a[i];
	}
	for(int j=0;j<22;j++) {
		for(int i=0;i<1<<22;i++) {//子集向超集转移
			if((i>>j)&1) {
				dp[i]=max(dp[i],dp[i^(1<<j)]);
			}
		}
	}
	for(int i=1;i<=n;i++) {
		printf("%d ",dp[(N-1)^a[i]]);
	}
	return 0;
}