划分树

1.模板

const int N(1e5+5), H(log2(N)+2);
int a[H][N], toleft[H][N], sorted[N];

void build(int h, int L, int R){
    if(L==R) return;
    int mid=(L+R)>>1, nl=mid-L+1;
    for(int i=L; i<=R; i++) nl-=a[h][i]<sorted[mid];
    for(int i=L, lp=L, rp=mid+1; i<=R; i++){
        if(a[h][i]<sorted[mid]) a[h+1][lp++]=a[h][i];
        else if(a[h][i]>sorted[mid]) a[h+1][rp++]=a[h][i];
        else nl? a[h+1][lp++]=a[h][i], --nl: a[h+1][rp++]=a[h][i];
        toleft[h][i]=toleft[h][L-1]+lp-L;
    }
    build(h+1, L, mid), build(h+1, mid+1, R);
}

int query(int h, int L, int R, int l, int r, int k){
    if(L==R) return a[h][L];
    int nl=toleft[h][r]-a[h][l-1], nr=r-l+1-nl, mid=(L+R)>>1;
    if(nl>=k){
        l=L+toleft[h][l-1]-toleft[h][L-1], r=l+nl-1;
        return query(h+1, L, mid, l, r, k);
    }
    r+=toleft[h][R]-toleft[h][r], l=r-nr+1;
    return query(h+1, mid+1, R, l, r, k-nl);
}

int Rank(int h, int L, int R, int l, int r, int v){
    if(L==R) return a[h][L]<v;
    int nl=toleft[h][r]-a[h][l-1], nr=r-l+1-nl, mid=(L+R)>>1;
    if(sorted[mid]>=v){
        l=L+toleft[h][l-1]-toleft[h][L-1], r=l+nl-1;
        return Rank(h+1, L, mid, l, r, v);
    }
    r+=toleft[h][R]-toleft[h][r], l=r-nr+1;
    return nl+Rank(h+1, mid+1, R, l, r, v);
}

2.实现细节