hdu 3480

斜率dp

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#define maxn 10005
#define maxm 5005
using namespace std;
int dp[maxn][maxm];
int q[maxn*];
int num[maxn];

bool check(int j,int tail,int i)
{
    int yk=dp[q[tail-]][j-]+num[q[tail-]+]*num[q[tail-]+];
    int yj=dp[q[tail]][j-]+num[q[tail]+]*num[q[tail]+];
    int yi=dp[i][j-]+num[i+]*num[i+];
    int xk=*num[q[tail-]+];
    int xj=*num[q[tail]+];
    int xi=*num[i+];
    if((yi-yk)*(xj-xk)<=(yj-yk)*(xi-xk))return ;
    return ;
}

bool get(int head,int j,int i)
{
    int y1=dp[q[head]][j-]+num[q[head]+]*num[q[head]+];
    int y2=dp[q[head+]][j-]+num[q[head+]+]*num[q[head+]+];
    int x1=num[q[head]+];
    int x2=num[q[head+]+];
    if((y2-y1)<=*num[i]*(x2-x1))return ;
    return ;
}

int main()
{
    int n,m,t;
    int ca=;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&n,&m);
        for(int i=;i<=n;i++)scanf("%d",&num[i]);
        sort(num+,num+n+);
        int tail,head;
        for(int i=;i<=n;i++)
            dp[i][]=(num[i]-num[])*(num[i]-num[]);
        for(int j=;j<=m;j++)
        {
            head=tail=;
            q[++tail]=j-;
            for(int i=j;i<=n;i++)
            {
                while(tail-head>&&check(j,tail,i))tail--;
                q[++tail]=i;
                while(tail-head>&&get(head+,j,i))head++;
                int best=q[head+];
                dp[i][j]=dp[best][j-]+(num[i]-num[best+])*(num[i]-num[best+]);

            }
        }
        printf("Case %d: %d\n",ca++,dp[n][m]);
    }
    return ;
}

四边形不等式优化：

#include<cstdio>
#include<cstring>
#include<algorithm>
#define maxn 10005
#define maxm 5005
#define inf 99999999
using namespace std;

int dp[maxn][maxm];
int s[maxn][maxm];
int num[maxn];

int main()
{
    int n,m;
    int t,ca=;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&n,&m);
        for(int i=; i<=n; i++)
            scanf("%d",&num[i]);
        sort(num+,num++n);
        dp[][]=;
        for(int i=; i<=n; i++)
        {
            dp[i][]=(num[i]-num[])*(num[i]-num[]);
        }
        for(int j=; j<=m; j++)
        {
            s[n+][j]=n-;
            for(int i=n; i>=j; i--)
            {
                dp[i][j]=inf;
                for(int k=s[i][j-]; k<=s[i+][j]; k++)
                {
                    int tmp=dp[k][j-]+(num[i]-num[k+])*(num[i]-num[k+]);
                    if(dp[i][j]>tmp)
                    {
                        s[i][j]=k;
                        dp[i][j]=tmp;
                    }
                }
            }
        }
        printf("Case %d: %d\n",ca++,dp[n][m]);
    }
    return ;
}