poj 3709 K-Anonymous Sequence 斜率優化dp

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int maxn=5e5+9;
long long a[maxn];
long long dp[maxn],sum[maxn];
int que[maxn];

bool chk1(int k,int j,int i)
{
    long long s1=(dp[j]-sum[j]+a[j+1]*j)-(dp[k]-sum[k]+a[k+1]*k);
    s1*=(a[i+1]-a[j+1]);
    long long s2=(dp[i]-sum[i]+a[i+1]*i)-(dp[j]-sum[j]+a[j+1]*j);
    s2*=(a[j+1]-a[k+1]);
    return s1>s2;
}

bool chk2(int k,int j,int i)
{
    long long s=(dp[j]-sum[j]+a[j+1]*j)-(dp[k]-sum[k]+a[k+1]*k);
    return s<=(a[j+1]-a[k+1])*i;
}

int main()
{
//    freopen("in.txt","r",stdin);
    int T;
    scanf("%d",&T);
    while(T--)
    {
        int n,m;
        scanf("%d %d",&n,&m);
        sum[0]=0;
        for(int i=1;i<=n;i++)
        {
            scanf("%lld",&a[i]);
            a[i]++;
            sum[i]=sum[i-1]+a[i];
        }
        int front=1,end=0;
        dp[m]=sum[m]-a[1]*m;
        que[++end]=0;
        dp[0]=0;
        for(int i=1;i+m<=n;i++)
        {
            if(i>=m)
            {
                if(a[i+1]==a[que[end]+1])
                {
                    if(dp[i]<dp[que[end]])
                    {
                        end--;
                        while(front<end&&chk1(que[end-1],que[end],i))
                        end--;
                        que[++end]=i;
                    }
                }
                else
                {
                    while(front<end&&chk1(que[end-1],que[end],i))
                    end--;
                    que[++end]=i;
                }
            }
            while(front<end&&chk2(que[front],que[front+1],i+m))
            front++;
            int u=que[front];
            dp[i+m]=dp[u]+sum[i+m]-sum[u]-a[u+1]*(i+m-u);
        }
        printf("%lld\n",dp[n]);
    }
    return 0;
}