【CF1027C】Minimum Value Rectangle（贪心，数学）

题意：给定n根木棍，不允许拼接或折断，选择四根组成矩形，求所有合法矩形中周长平方与面积比最小的一个，输出拼成这个矩形的四根木棍

n<=1e6

思路：猜结论：答案必定从相邻的4根中产生

证明见https://www.luogu.org/blog/78371/so1ution-cf1027c

 #include<cstdio>
 #include<cstring>
 #include<string>
 #include<cmath>
 #include<iostream>
 #include<algorithm>
 #include<map>
 #include<set>
 #include<queue>
 #include<vector>
 using namespace std;
 typedef long long ll;
 typedef unsigned int uint;
 typedef unsigned long long ull;
 typedef pair<int,int> PII;
 typedef vector<int> VI;
 #define fi first
 #define se second
 #define MP make_pair
 #define N   1100000
 #define MOD 1000000007
 #define eps 1e-8
 #define pi acos(-1)
 #define oo 110000000000000

 int a[N],b[N];

 int read()
 {
    int v=,f=;
    char c=getchar();
    while(c<||<c) {if(c=='-') f=-; c=getchar();}
    while(<=c&&c<=) v=(v<<)+v+v+c-,c=getchar();
    return v*f;
 }

 void swap(int &x,int &y)
 {
     int t=x;x=y;y=t;
 }

 int main()
 {
     //freopen("1.in","r",stdin);
     //freopen("1.out","w",stdout);
     int cas;
     scanf("%d",&cas);
     while(cas--)
     {
         int n;
         scanf("%d",&n);
         for(int i=;i<=n;i++) scanf("%d",&a[i]);
         sort(a+,a+n+);
         int m=;
         int i=;
         while(i<n)
         {
             i++;
             if(i+<=n&&a[i]==a[i+]) {b[++m]=a[i]; i++;}
         }
         ll c=*(b[]+b[]);
         ll s=b[]*b[];
         ll ans1=c;
         ll ans2=s;
         int k=;
         for(int i=;i<=m-;i++)
         {
             c=*(b[i]+b[i+]);
             s=b[i]*b[i+];
             if(s*ans1*ans1>ans2*c*c) {ans1=c; ans2=s; k=i;}
         }
         printf("%d %d %d %d\n",b[k],b[k],b[k+],b[k+]);
     }
     return ;
 }