USACO 1.3Ski Course Design

Posted 2020-08-11 水郁

n个点（n<=1000）大小范围[0,100]，改变一些点的值，使得极差不超过17，代价为改变值的平方。

枚举修改后的最低高度low，维护最小代价。

/*
TASK: skidesign
LANG:C++
URL:http://train.usaco.org/usacoprob2?a=LxVrSLLAzuR&S=skidesign
*/
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#define ll long long
#define N 1005
using namespace std;
int n,h[N];
int tol=0x3f3f3f3f;
int sqr(int x){
    return x*x;
}
int main() {
    freopen("skidesign.in","r",stdin);
    freopen("skidesign.out","w",stdout);
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%d",&h[i]);
    }
    sort(h+1,h+1+n);
    for(int low=h[1];low<=h[n]-17;low++){
        int ans=0;
        for(int i=1;i<=n;i++){
            if(h[i]<low)ans+=sqr(low-h[i]);
            else if(h[i]>low+17)ans+=sqr(h[i]-low-17);
        }
        tol=min(tol,ans);
    }
    printf("%d\n",tol);
}