[hdu 3507]斜率优化dp

Posted 2020-10-04 ACMsong

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=3507

kuangbin大佬的博客讲的非常清楚orzhttp://www.cnblogs.com/kuangbin/archive/2012/08/26/2657650.html

#include<bits/stdc++.h>
using namespace std;

typedef long long ll;

deque<ll> q;
const int maxn=500005;
int a[maxn];
ll sum[maxn];
ll dp[maxn];

bool calc(int k,int j,int i)
{
    return dp[j]+sum[j]*sum[j]-dp[k]-sum[k]*sum[k]<=2ll*sum[i]*(sum[j]-sum[k]);
}

bool judge(int k,int j,int i)
{
    return (dp[j]+sum[j]*sum[j]-dp[k]-sum[k]*sum[k])*(sum[i]-sum[j])>=(dp[i]+sum[i]*sum[i]-dp[j]-sum[j]*sum[j])*(sum[j]-sum[k]);
}

int main()
{
    int n,m;
    while (~scanf("%d%d",&n,&m))
    {
        while (!q.empty()) q.pop_back();
        for (int i=1;i<=n;i++) scanf("%d",&a[i]);
        sum[0]=0;
        for (int i=1;i<=n;i++) sum[i]=sum[i-1]+a[i];
        dp[0]=0;
        q.push_back(0);
        for (int i=1;i<=n;i++)
        {
            while (q.size()>1)
            {
                auto it=q.begin();
                int k=*it;
                int j=*(++it);
                if (calc(k,j,i)) q.pop_front();
                else break;
            }
            int b=q.front();
            dp[i]=dp[b]+m+(sum[i]-sum[b])*(sum[i]-sum[b]);
            while (q.size()>1)
            {
                auto it=q.end();
                int j=*(--it);
                int k=*(--it);
                if (judge(k,j,i)) q.pop_back();
                else break;
            }
            q.push_back(i);
        }
        printf("%I64d\\n",dp[n]);
    }
    return 0;
}