ICPCCamp 2016 Day 6 - Spb SU and Spb AU Contest(Set intersection-随机)

题意：给n＋1个01串，每个串长度为 2n ，从中找出2个01串，它们前2n位里同一位上出现相同0，1的次数 ≥n/2
保证有解，输出任意解。

随机试即可，求证明

#include <iostream>
#include <cmath>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <string>
#include <vector>
#include <map>
#include <functional>
#include <cstdlib>
#include <queue>
#include <stack>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=Pre[x];p;p=Next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=Next[p]) 
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (500000000000LL)
#define F (100000007)
#define pb push_back
#define mp make_pair 
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
typedef long long ll;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int read()
{
    int x=0,f=1; char ch=getchar();
    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
    return x*f;
} 
#define MAXN (6000+10)
int n,m;
int a[MAXN][1000];
char s[MAXN];


int check(int i,int j) {
    int ans=0;
    Rep(k,m) 
        ans+=__builtin_popcount(a[i][k]&a[j][k]);
    return ans;
}


int main() {
    n=read();
    For(i,n+1) {
        scanf("%s",s);
        m=strlen(s);
        Rep(j,m)
            a[i][j]=s[j]-33;
    }


    srand(time(NULL));
    while(1) {
        int i=rand()%(n+1)+1;
        int j=rand()%(n+1)+1;
        if (i!=j && check(i,j)>=n/2) {
            if (i<j) swap(i,j);
            cout<<i << ' '<<j<<endl;
            return 0;
        }
    }



    return 0;
}