线性基学习

线性基学习

先膜一下mona，感谢他生动的讲解……Orz
然后
这哥们讲的不错

我的板子

第一个

luoguP3812模板

#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<iomanip>
#include<algorithm>
#include<ctime>
#include<queue>
#include<stack>
#include<vector>
#define rg register
#define il inline
#define lst long long
#define ldb long double
#define N 55
using namespace std;
const int Inf=1e9;

int n;
lst p[N];

il lst read()
{
    rg lst s=0,m=0;rg char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')m=1;ch=getchar();}
    while(ch>='0'&&ch<='9')s=(s<<3)+(s<<1)+(ch^48),ch=getchar();
    return m?-s:s;
}

il void Insert(rg lst x)
{
    for(rg int i=50;i>=0;--i)
    {
        if(!(x&(1ll<<i)))continue;
        if(!p[i])p[i]=x;
        x^=p[i];
    }
}

il lst Query(rg lst x)
{
    for(rg int i=50;i>=0;--i)
        x=max(x,x^p[i]);
    return x;
}

int main()
{
    n=read();
    for(rg int i=1;i<=n;++i)
        Insert(read());
    printf("%lld
",Query(0));
    return 0;
}

第二个……

luogu彩灯

#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<iomanip>
#include<algorithm>
#include<ctime>
#include<queue>
#include<stack>
#include<vector>
#define rg register
#define il inline
#define lst long long
#define ldb long double
#define N 55
#define mod 2008
using namespace std;
const int Inf=1e9;

int n,m,ans;
lst p[N];
char light[N];

il int read()
{
    rg int s=0,m=0;rg char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')m=1;ch=getchar();}
    while(ch>='0'&&ch<='9')s=(s<<3)+(s<<1)+(ch^48),ch=getchar();
    return m?-s:s;
}

il void Insert(rg lst x)
{
    for(rg int i=50;i>=0;--i)
    {
        if(!(x&(1ll<<i)))continue;
        if(!p[i])p[i]=x;
        x^=p[i];
    }
}

il lst qpow(rg int a,rg int b)
{
    rg lst base=a,res=1;
    while(b)
    {
        if(b&1)res=(res*base)%mod;
        base=(base*base)%mod;
        b>>=1;
    }
    return res;
}

int main()
{
    n=read(),m=read();
    for(rg int i=1;i<=m;++i)
    {
        scanf("%s",light);
        rg lst ss=0;
        for(rg int j=0;j<n;++j)
            ss=ss*2+(light[j]=='O'?1:0);
        Insert(ss);
    }
    for(rg int i=50;i>=0;--i)
        if(p[i])ans++;
    printf("%lld
",qpow(2,ans));
    return 0;
}

题单(没错，xzy的)

• [x] ※【模板】线性基 https://www.luogu.org/problemnew/show/P3812
• [ ] [BeiJing2011] 元素 http://www.lydsy.com/JudgeOnline/problem.php?id=2460
• [ ] [CQOI2013] 新Nim游戏 https://www.luogu.org/problemnew/show/P4301
• [ ] ※[WC2011] 最大XOR和路径 https://www.luogu.org/problemnew/show/P4151
• [ ] [SCOI2016] 幸运数字 https://www.luogu.org/problemnew/show/P3292
• [ ] [BZOJ3811] 玛里苟斯 http://www.lydsy.com/JudgeOnline/problem.php?id=3811
• [ ] [BZOJ2844] albus就是要第一个出场 http://www.lydsy.com/JudgeOnline/problem.php?id=2844
• [ ] ※[HDU2949] XOR https://vjudge.net/problem/HDU-3949