hdu 3480 Division(四边形不等式优化)

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<string>
#include<vector>
#include<stack>
#include<bitset>
#include<cstdlib>
#include<cmath>
#include<set>
#include<list>
#include<deque>
#include<map>
#include<queue>
#define ll long long int
using namespace std;
inline ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
inline ll lcm(ll a,ll b){return a/gcd(a,b)*b;}
int moth[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
int dir[4][2]={1,0 ,0,1 ,-1,0 ,0,-1};
int dirs[8][2]={1,0 ,0,1 ,-1,0 ,0,-1, -1,-1 ,-1,1 ,1,-1 ,1,1};
const int inf=0x3f3f3f3f;
const ll mod=1e9+7;
int dp[10007][5007]; //dp[i][j] 表示前i个人 分组成j组 
int s[10007][5007]; //决策数组 
int a[10007];
int main(){
    ios::sync_with_stdio(false);
    int t;
    cin>>t;
    int w=0;
    while(t--){
        int n,m;
        cin>>n>>m;
        for(int i=1;i<=n;i++){
            cin>>a[i];
        }
        sort(a+1,a+1+n); //排序后满足一个区间内的值是首尾的差平方 
        for(int i=1;i<=n;i++){ //初始化边界 
            dp[i][1]=(a[i]-a[1])*(a[i]-a[1]); //前i个人分成1组 
            s[i][1]=1; //初始化决策数组的左边界 
        }
        for(int j=2;j<=m;j++){
            s[n+1][j]=n-1; //初始化决策数组的右边界 
            for(int i=n;i>=j;i--){
                dp[i][j]=inf;
                for(int k=s[i][j-1];k<=s[i+1][j];k++){ //四边形不等式优化 
                    if(dp[i][j]>dp[k][j-1]+(a[i]-a[k+1])*(a[i]-a[k+1])){
                        dp[i][j]=dp[k][j-1]+(a[i]-a[k+1])*(a[i]-a[k+1]);
                        s[i][j]=k;
                    }
                }
            }
        }    
        cout<<"Case "<<++w<<": ";
        cout<<dp[n][m]<<endl;
    }
    return 0;
}