2019牛客暑期多校训练营（第一场） H XOR

思想：

线性基和快速幂

代码：

#include<iostream>
#include<stdio.h>
#include<cstring>
#include<vector>
using namespace std;
typedef long long ll;
const int mod = 1e9+7;
ll base[62],rem[100005],baser[62],num[100005];
int n;
bool insert(ll t,ll *base){
    int i;
    for(int i= 60;i>=0;i--){
        if(t&(1ll<<i)){
            if(!base[i]){
                base[i] =t;
                return true;
            }
            else t = t^base[i];
        }
    }
    return false;
}
ll qpow(ll x,ll pow){
    ll sum = 1;
    while(pow){
        if(pow%2==1) sum=sum*x%mod;
        x=x*x%mod;
        pow>>=1;
    }
    return sum;
}
bool check(ll t,ll *base){
    for(int i=60;i>=0;i--){
        if(t&(1ll<<i))
            t^=base[i];
    }
    return t ==0;
}
int main(){
    while(~scanf("%d",&n)){
        int i,j,flag = 0;
        ll ans = 0;
        vector<ll> index;
        memset(base,0,sizeof(base));
        memset(rem,0,sizeof(rem));
        memset(baser,0,sizeof(baser));
        for(i=1;i<=n;i++){
            scanf("%lld",&num[i]);
            if(!insert(num[i],base))
                rem[++flag] = num[i];
            else 
                index.push_back(i);
        }
        if(flag==0){
            cout<<"0"<<endl;
            return 0;
        }
        ans = (ans+(ll)flag*qpow(2,flag-1)%mod)%mod;
        for(int i=1;i<=flag;i++) 
            insert(rem[i],baser);
        for(i=0;i<index.size();i++){
            ll basedr[62],x = num[index[i]];
            for(j=0;j<=60;j++)
                basedr[j] = baser[j];
            for(j=0;j<index.size();j++){
                if(j!=i) 
                    insert(num[index[j]],basedr);
            }
            if(check(x,basedr)) ans = (ans+qpow(2,flag-1))%mod;
        }
        cout<<ans<<endl;
    }
    return 0;
} 

借鉴博客：

https://blog.csdn.net/liufengwei1/article/details/96571038

https://blog.csdn.net/weixin_43702895/article/details/97683338