hdu 3507 斜率dp优化

#include <iostream>
#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
const int maxn=500000+10;
int dp[maxn],q[maxn],sum[maxn];
int n,m;
int getdp(int i,int j)
{
    return dp[j]+m+(sum[i]-sum[j])*(sum[i]-sum[j]);
}
int getup(int j,int k)
{
    return dp[j]+sum[j]*sum[j]-(dp[k]+sum[k]*sum[k]);
}
int getdown(int j,int k)
{
     return 2*(sum[j]-sum[k]);
}
int main()
{
    while(~scanf("%d%d",&n,&m))
    {
        for(int i=1;i<=n;i++)
        {
            scanf("%d",&sum[i]);
        }
        sum[0]=dp[0]=0;
        for(int i=1;i<=n;i++)
            sum[i]=sum[i]+sum[i-1];
        int head,tail;
        head=tail=0;
        q[tail++]=0;
        for(int i=1;i<=n;i++)
        {
            while(head+1<tail && getup(q[head+1],q[head])<=sum[i]*getdown(q[head+1],q[head]))//sum[i]单调递增注意是<=
                 head++;
            dp[i]=getdp(i,q[head]);
            while(head+1<tail && getup(i,q[tail-1])*getdown(q[tail-1],q[tail-2])<=getup(q[tail-1],q[tail-2])*getdown(i,q[tail-1]))//维护斜率单调递增队列
                tail--;
            q[tail++]=i;
        }
        printf("%d\n",dp[n]);
    }
}