CF529B Group Photo 2 (online mirror version)

Posted 2020-12-05 ivanovcraft

贪心
枚举最后方案中最大的h，设为maxh
若某个人i的wi与hi均大于maxh，则此方案不可行
若某个人恰有一个属性大于maxh，则可确定他是否换属性
剩下的人按wi-hi从大到小排序后贪心选择
O(nlogn+n2)

#include<iostream>
#include<cstdio>
#include<vector>
#include<algorithm>
using namespace std;
const int maxn=1010;
int n,w[maxn],h[maxn],hh,ans=1e9,sw;
bool cmp(const int &a,const int &b)
{
    return w[a]-h[a]>w[b]-h[b];        //按wi-hi排序
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
    {
        scanf("%d%d",&w[i],&h[i]);
        hh=max(w[i],max(hh,h[i])),sw+=w[i];
    }
    for(int maxh=1;maxh<=hh;maxh++)
    {
        int cnt=0,rs=sw;
        vector<int>v;
        for(int i=1;i<=n;i++)    //分类讨论
        {
            if(w[i]>maxh&&h[i]>maxh)
            {
                cnt=1e9;
                break;
            }
            else if(w[i]>maxh&&h[i]<=maxh)
                continue;
            else if(w[i]<=maxh&&h[i]>maxh)
            {
                rs+=h[i]-w[i];
                cnt++;
            }
            else if(w[i]>h[i])
                v.push_back(i);        //把待处理元素放入vector
        }
        if(cnt>n/2)
            continue;
        sort(v.begin(),v.end(),cmp);
        for(int i=0;i<v.size()&&cnt+i<n/2;i++)
            rs+=h[v[i]]-w[v[i]];
        ans=min(ans,rs*maxh);
    }
    printf("%d
",ans);
    return 0;
}