bzoj2460 BeiJing2011—元素

Posted 2020-08-11 MashiroSky

www.lydsy.com/JudgeOnline/problem.php?id=2460 (题目链接)

题意：n个二元组(a,b)，求一个∑b最大，且所有子集XOR<>0的集合

Solution 
　　线性基的经典应用。具体证明好像要用到拟阵，不会，好像是很高深的东西。

代码：

// bzoj2460
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<cmath>
#define LL long long
#define inf 2147483640
#define Pi acos(-1.0)
#define free(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout);
using namespace std;

const int maxn=1010;
struct data {LL num;int x;}a[maxn];
LL bin[65];
int n,b[65];

bool cmp(data a,data b) {
    return a.x>b.x;
}
int main() {
    bin[0]=1;for (int i=1;i<=60;i++) bin[i]=bin[i-1]<<1;
    scanf("%d",&n);
    for (int i=1;i<=n;i++) scanf("%lld%d",&a[i].num,&a[i].x);
    sort(a+1,a+1+n,cmp);
    int ans=0;
    for (int i=1;i<=n;i++) {
        for (int j=60;j>=0;j--)
            if (a[i].num&bin[j]) {
                if (!b[j]) {b[j]=i;break;}
                else a[i].num^=a[b[j]].num;
            }
        if (a[i].num) ans+=a[i].x;
    }
    printf("%d\n",ans);
    return 0;
}