[BZOJ4709][JSOI2011]柠檬(斜率优化DP)

显然选出的每一段首尾都是相同的，于是直接斜率优化，给每个颜色的数开一个单调栈即可。

#include<cstdio>
#include<vector>
#include<cstring>
#include<algorithm>
#define rep(i,l,r) for (int i=(l); i<=(r); i++)
typedef long long ll;
using namespace std;

const int N=100010;
ll n,ans,a[N],f[N],lst[N],top[N],cnt[N];
struct P{ ll x,y; };
vector<P>s[N];

bool Cmp(P a,P b,P c){ return (b.y-a.y)*(c.x-b.x)<=(c.y-b.y)*(b.x-a.x); }

int main(){
    freopen("bzoj4709.in","r",stdin);
    freopen("bzoj4709.out","w",stdout);
    scanf("%lld",&n);
    rep(i,1,n) scanf("%lld",&a[i]),cnt[i]=cnt[lst[a[i]]]+1,lst[a[i]]=i;
    rep(i,1,n) if (s[a[i]].size()==0) s[a[i]].push_back((P){0,0});
    rep(i,1,n){
        int p=a[i]; P tmp=(P){2*p*cnt[i],f[i-1]+p*cnt[i]*cnt[i]-2*p*cnt[i]};
        while (top[p]>1 && Cmp(s[p][top[p]-1],s[p][top[p]],tmp)) top[p]--,s[p].pop_back();
        top[p]++; s[p].push_back(tmp);
        while (top[p]>1 && (s[p][top[p]].x-s[p][top[p]-1].x)*cnt[i]>=s[p][top[p]].y-s[p][top[p]-1].y)
            top[p]--,s[p].pop_back();
        f[i]=s[p][top[p]].y-s[p][top[p]].x*cnt[i]+p+2*p*cnt[i]+p*cnt[i]*cnt[i]; ans=max(ans,f[i]);
    }
    printf("%lld
",ans);
    return 0;
}