【bzoj2442】修剪草坪

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f[i]=max{f[j]+sum[i]-sum[j+1]} (i-j-1<=k)

这个式子可以用单调性来优化

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#include<bits/stdc++.h>
#define FILE "read"
#define MAXN 100010
using namespace std;
typedef long long ll;
ll n,k,head,tail,a[MAXN],sum[MAXN],f[MAXN],q[MAXN];
inline int read(){
int x=0,f=1; char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1; ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0'; ch=getchar();}
return x*f;
}
int main(){
freopen(FILE".in","r",stdin);
freopen(FILE".out","w",stdout);
n=read(); k=read();
for(int i=1;i<=n;++i) a[i]=read(),sum[i]=sum[i-1]+a[i];
for(int i=1;i<=n;++i){
while(head<tail&&i-q[head]-1>k) ++head;
if(i<=k) f[i]=sum[i];
else f[i]=f[q[head]]+sum[i]-sum[q[head]+1];
while(head<tail&&f[i]-sum[i+1]>=f[q[tail]]-sum[q[tail]+1]) --tail;
q[++tail]=i;
}
printf("%lld\n",f[n]);
return 0;
}
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