HDU 6619 Horse 斜率优化dp

Posted 2022-06-10 profish

http://acm.hdu.edu.cn/showproblem.php?pid=6619

#include<bits/stdc++.h>
#define fi first
#define se second
#define INF 0x3f3f3f3f
#define LNF 0x3f3f3f3f3f3f3f3f
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pqueue priority_queue
#define NEW(a,b) memset(a,b,sizeof(a))
const double pi=4.0*atan(1.0);
const double e=exp(1.0);
const int maxn=1e4+8;
typedef long long LL;
typedef unsigned long long ULL;
const LL mod=1e9+7;
const ULL base=1e7+7;
const int maxp=26+5;
using namespace std;
LL a[maxn],f[maxn];
LL g[maxn],gg[maxn];
LL dp[maxn][58];
LL q[58][maxn];
LL l[58],r[58];
LL gdp(int i,int j,int k) return dp[j][k]-gg[j]-g[j]*(i-j)+gg[i];
LL gfz(int j,int h,int k) return dp[j][k]-gg[j]+g[j]*(j)-(dp[h][k]-gg[h]+g[h]*(h));
LL gfm(int j,int h) return g[j]-g[h];
int main()
    int t;
    scanf("%d",&t);
    int n,m,k;
    while(t--)
        scanf("%d%d%d",&n,&k,&m);
        for(int i=1;i<=n;i++)
            scanf("%lld",&a[i]);
            g[i]=g[i-1]+a[i];
            gg[i]=g[i]+gg[i-1];
        
        for(int i=1;i<=k;i++)
            l[i]=r[i]=1;
            q[i][l[i]]=0;
        
        for(int i=1;i<=n;i++)
            for(int j=1;j<=i&&j<=k+1;j++)
                while(l[j-1]<r[j-1]&&gfz(q[j-1][l[j-1]+1],q[j-1][l[j-1]],j-1)<=i*gfm(q[j-1][l[j-1]+1],q[j-1][l[j-1]])) l[j-1]++;
                dp[i][j]=gdp(i,q[j-1][l[j-1]],j-1);
                while(l[j]<r[j]&&gfz(i,q[j][r[j]],j)*gfm(q[j][r[j]],q[j][r[j]-1])<=gfm(i,q[j][r[j]])*gfz(q[j][r[j]],q[j][r[j]-1],j)) r[j]--;
                q[j][++r[j]]=i;
            
        
        for(int i=1;i<=n;i++)
            f[i]=a[i]*(n-i+1);
        
        sort(f+1,f+1+n);
        LL ans=0;
        for(int i=n;i>=n-m+1;i--)
            ans+=f[i];
        
        ans-=dp[n][k+1];
        printf("%lld\n",ans);