[BZOJ1563][NOI2009]诗人小G(决策单调性优化DP)

模板题。

每个决策点都有一个作用区间，后来的决策点可能会比先前的优。于是对于每个决策点二分到它会比谁在什么时候更优，得到新的决策点集合与区间。

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

 const int N=;
 const ll MAX=1e18;
 int T,n,l,p,top;
 ll sm[N],f[N];
 char ch[N][];
 struct P{ int l,r,p; }q[N];

 ll ksm(ll x){
     if (x<) x=-x;
     ll res=; rep(i,,p) res*=x; return res;
 }

 ll cal(int j,int i){ return f[j]+ksm(sm[i]-sm[j]+(i-j-)-l); }

 int find(P a,int b){
     int l=a.l,r=a.r;
     while (l<=r){
         int mid=(l+r)>>;
         if (cal(a.p,mid)<cal(b,mid)) l=mid+; else r=mid-;
     }
     return l;
 }

 void DP(){
     int st=,ed=; q[]=(P){,n,};
     rep(i,,n){
         if (st<=ed && i>q[st].r) st++;
         f[i]=cal(q[st].p,i);
         if (st>ed || cal(i,n)<=cal(q[ed].p,n)){
             while (st<=ed && cal(i,q[ed].l)<=cal(q[ed].p,q[ed].l)) ed--;
             if (st>ed) q[++ed]=(P){i,n,i};
             else{
                 int t=find(q[ed],i);
                 q[ed].r=t-; q[++ed]=(P){t,n,i};
             }
         }
     }
 }

 int main(){
     freopen("bzoj1563.in","r",stdin);
     freopen("bzoj1563.out","w",stdout);
     for (scanf("%d",&T); T--; ){
         scanf("%d%d%d",&n,&l,&p);
         rep(i,,n) scanf("%s",ch[i]);
         rep(i,,n) sm[i]=sm[i-]+strlen(ch[i]);
         DP();
         if (f[n]>MAX) printf("Too hard to arrange\n");
             else printf("%lld\n",(long long)(f[n]));
         puts("--------------------");
     }
     return ;
 }