bzoj2616: SPOJ PERIODNI——笛卡尔树+DP

#include<bits/stdc++.h>
#define reg register int
#define il inline
#define int long long
#define numb (ch^‘0‘)
using namespace std;
typedef long long ll;
il void rd(int &x){
    char ch;x=0;bool fl=false;
    while(!isdigit(ch=getchar()))(ch==‘-‘)&&(fl=true);
    for(x=numb;isdigit(ch=getchar());x=x*10+numb);
    (fl==true)&&(x=-x);
}
namespace Miracle{
const int N=505;
const int mod=1e9+7;
ll f[N][N];
ll tmp[N];
ll jie[1000000+5],inv[1000000+5];
int qm(int x,int y){
    int ret=1;
    while(y){
        if(y&1) ret=(ll)ret*x%mod;
        x=(ll)x*x%mod;
        y>>=1;
    }
    return ret;
}
int n,k;
int ch[N][2],sz[N],fa[N],h[N];
int sta[N],top;
int a[N];
int build(){
    top=0;
    int las=0;
    for(reg i=1;i<=n;++i){
        las=0;
        while(top&&a[i]<a[sta[top]]){
            las=sta[top];
            --top;
            if(top&&a[sta[top]]>a[i]) ch[sta[top]][1]=las,fa[las]=sta[top];
            else ch[i][0]=las,fa[las]=i;
        }
        sta[++top]=i;
    }
    while(top>1) ch[sta[top-1]][1]=sta[top],fa[sta[top]]=sta[top-1],--top;
    return sta[1];
}
int C(int n,int m){
    if(n<0||m<0||n<m) return 0;
    return (ll)jie[n]*inv[m]%mod*inv[n-m]%mod;
}
void dfs(int x){
//    cout<<" x ff "<<x<<" "<<ff<<endl;
    f[x][0]=1;
    if(!x) return;
    sz[x]=1;
    dfs(ch[x][0]);dfs(ch[x][1]);
    sz[x]+=sz[ch[x][0]]+sz[ch[x][1]];
    h[x]=a[x]-a[fa[x]];
    f[x][0]=1;
    for(reg s=0;s<=1;++s){
        if(!ch[x][s]) continue;
        int y=ch[x][s];
        for(reg j=k;j>=0;--j){
            for(reg t=1;t<=j;++t){
                f[x][j]=(f[x][j]+f[x][j-t]*f[y][t])%mod;
            }
        }
    }
    for(reg i=k;i>=0;--i){
        for(reg j=1;j<=min(min(i,sz[x]),h[x]);++j){
            f[x][i]=(f[x][i]+f[x][i-j]*C(h[x],j)%mod*C(sz[x]-(i-j),j)%mod*jie[j]%mod)%mod;
        }
    }
}
int main(){
    rd(n);rd(k);
    int m=0;
    for(reg i=1;i<=n;++i) rd(a[i]),m=max(m,a[i]);
    m=max(m,max(n,k));
    jie[0]=1;
    for(reg i=1;i<=m;++i) jie[i]=(ll)jie[i-1]*i%mod;
    inv[m]=qm(jie[m],mod-2);
    for(reg i=m-1;i>=0;--i) inv[i]=(ll)inv[i+1]*(i+1)%mod;
    
    int rt=build();
//    cout<<" rt "<<rt<<endl;
    f[0][0]=1;
    dfs(rt);
    printf("%lld",f[rt][k]);
    return 0;
}

}
signed main(){
//    freopen("data.in","r",stdin);
//    freopen("my.out","w",stdout);
    Miracle::main();
    return 0;
}