[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=100010;
const ll MAX=1e18;
int T,n,l,p,top;
ll sm[N],f[N];
char ch[N][35];
struct P{ int l,r,p; }q[N];

ll ksm(ll x){
    if (x<0) x=-x;
    ll res=1; rep(i,1,p) res*=x; return res;
}

ll cal(int j,int i){ return f[j]+ksm(sm[i]-sm[j]+(i-j-1)-l); }

int find(P a,int b){
    int l=a.l,r=a.r;
    while (l<=r){
        int mid=(l+r)>>1;
        if (cal(a.p,mid)<cal(b,mid)) l=mid+1; else r=mid-1;
    }
    return l;
}

void DP(){
    int st=1,ed=1; q[1]=(P){0,n,0};
    rep(i,1,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-1; 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,1,n) scanf("%s",ch[i]);
        rep(i,1,n) sm[i]=sm[i-1]+strlen(ch[i]);
        DP();
        if (f[n]>MAX) printf("Too hard to arrange
");
            else printf("%lld
",(long long)(f[n]));
        puts("--------------------");
    }
    return 0;
}