hdu 3045 斜率优化DP

思路：dp[i]=dp[j]+sum[i]-sum[j]-(i-j)*num[j+1];

然后就是比较斜率。

注意的时这里j+t<=i；

#include<iostream>

#include<cstdio>

#include<cstring>

#include<algorithm>

#include<cmath>

#define Maxn 400010

#define LL __int64

using namespace std;

LL num[Maxn],sum[Maxn],dp[Maxn];

int que[Maxn*10];

LL Getleft(int j,int k)

{

    return dp[j]-sum[j]+j*num[j+1]-(dp[k]-sum[k]+k*num[k+1]);

}

LL Getright(int j,int k)

{

    return num[j+1]-num[k+1];

}

int main()

{

    int n,t,head,rear;

    LL i,j;

    while(scanf("%d%d",&n,&t)!=EOF){

        memset(dp,0,sizeof(dp));

        for(i=1;i<=n;i++){

            scanf("%I64d",num+i);

        }

        sort(num+1,num+n+1);

        for(i=1;i<=n;i++){

            sum[i]=num[i]+sum[i-1];

        }

        head=1,rear=0;

        que[++rear]=0;

        for(i=t;i<=n;i++){

            j=i-t+1;

            while(head<rear&&Getleft(que[head+1],que[head])<=Getright(que[head+1],que[head])*i){

                head++;

            }

            dp[i]=dp[que[head]]+sum[i]-sum[que[head]]-(i-que[head])*num[que[head]+1];

            while(head<rear&&j>=t&&Getleft(j,que[rear])*Getright(que[rear],que[rear-1])<=Getleft(que[rear],que[rear-1])*Getright(j,que[rear])){

                rear--;

            }

            if(j>=t)

            que[++rear]=j;

        }

        printf("%I64d\n",dp[n]);

    }

    return 0;

}