[luogu2501 HAOI2006] 数字序列 (递推LIS)

//By Menteur_Hxy
#include <map>
#include <set>
#include <cmath>
#include <queue>
#include <cstdio>
#include <string>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define LL long long
#define M(a,b) memset(a,(b),sizeof(a))
#define F(i,a,b) for(register int i=(a);i<=(b);i++)
#define C(i,a,b) for(register int i=(b);i>=(a);i--)
#define E(i,u) for(register int i=head[u];i;i=nex[i])
using namespace std;

inline LL rd() {
    LL x=0,fla=1; char c=‘ ‘;
    while(c>‘9‘|| c<‘0‘) {if(c==‘-‘) fla=-fla; c=getchar();}
    while(c<=‘9‘ && c>=‘0‘) x=x*10+c-‘0‘,c=getchar();
    return x*fla;
}

inline void out(LL x){
    int a[30],wei=0;
    if(x<0) putchar(‘-‘),x=-x;
    for(;x;x/=10) a[++wei]=x%10;
    if(wei==0){ puts("0"); return;}
    for(int j=wei;j>=1;--j) putchar(‘0‘+a[j]);
    putchar(‘\n‘);
}

const int N=35010;
const int INF=0x3f3f3f3f;
int n,tp,cnt,L;
int b[N],f[N],head[N],to[N],nex[N],mn[N];
LL g[N],s1[N],s2[N];

void add(int x,int y) {
    nex[++cnt]=head[x],to[cnt]=y,head[x]=cnt;
}

int find(int x) { int l=1,r=L,t=0;
    while(l<=r) { int mid=(l+r)>>1;
        if(mn[mid]<=x) t=mid,l=mid+1;
        else r=mid-1;
    }
    return t;
}

void dp() {
    M(mn,127);
    mn[0]=-INF;
    F(i,1,n) { int t=find(b[i]);
        f[i]=t+1;
        L=max(L,t+1);
        mn[t+1]=min(mn[t+1],b[i]);
    }
}

int main() {
    n=rd();
    F(i,1,n) b[i]=rd()-i; b[++n]=INF;
    dp();
    C(i,0,n) add(f[i],i),g[i]=(LL)INF;
    g[0]=0;b[0]=-INF;
    F(x,1,n) E(i,f[x]-1) { int p=to[i];
        if(p>x) break;
        if(b[p]>b[x]) continue;
        F(j,p,x) s1[j]=abs(b[p]-b[j]),s2[j]=abs(b[x]-b[j]);
        F(j,p+1,x) s1[j]+=s1[j-1],s2[j]+=s2[j-1];
        F(j,p,x-1) g[x]=min(g[x],g[p]+s1[j]-s1[p]+s2[x]-s2[j]);
    }
    out(n-f[n]);out(g[n]);
    return 0;
}