[BZOJ2253][2010 Beijing wc]纸箱堆叠（dp+bit+cdq分治）

题目描述

传送门

题解

最长上升子序列+三维偏序问题
裸的dp人人会对吧 O(n2)
考虑对序列进行cdq分治，每一次用左边的区间来更新右边的区间
按照x分治，每一次按照y排序，然后z用树状数组查询
需要注意的是，这里全部都是严格大于，也就是说分治的时候划分到左右两边的点不能出现x相等的情况，这样的话就预处理一下然后在选中点的时候搞一搞就行了
并且更新的顺序必须是：递归左区间，处理左区间对右区间的影响，递归右区间

代码

#include
#include
#include
#include
#include
using namespace std;
#define N 300005

int A,Mod,n,LSH,ans;
int lsh[N],L[N],R[N],C[N],f[N],ch[N];
struct data{int x,y,z,id;}q[N],a[N],b[N];

int cmp(data a,data b)
{
    return a.xx||(a.x==b.x&&a.yy)||(a.x==b.x&&a.y==b.y&&a.zint cmpy(data a,data b)
{
    return a.yy;
}
void cover(int loc)
{
    for (int i=loc;i<=LSH;i+=i&-i)
        C[i]=0;
}
void add(int loc,int val)
{
    for (int i=loc;i<=LSH;i+=i&-i)
        C[i]=max(C[i],val);
}
int query(int loc)
{
    int ans=0;
    for (int i=loc;i>=1;i-=i&-i)
        ans=max(ans,C[i]);
    return ans;
}
void cdq(int l,int r)
{
    if (q[l].x==q[r].x) return;
    int mid=(l+r)>>1;
    if (L[mid]!=l) mid=L[mid]-1;
    else mid=R[mid];
    cdq(l,mid);

    int tot=0;
    int pa=1,pb=1,acnt=0,bcnt=0;
    for (int i=l;i<=mid;++i) a[++acnt]=q[i];
    for (int i=mid+1;i<=r;++i) b[++bcnt]=q[i];
    sort(a+1,a+acnt+1,cmpy);sort(b+1,b+bcnt+1,cmpy);
    while (pb<=bcnt)
    {
        while (pa<=acnt&&a[pa].yy)
        {
            add(a[pa].z,f[a[pa].id]);
            ch[++tot]=a[pa].z;
            ++pa;
        }
        f[b[pb].id]=max(f[b[pb].id],query(b[pb].z-1)+1);
        ++pb;
    }
    for (int i=1;i<=tot;++i) cover(ch[i]);

    cdq(mid+1,r);
}
int main()
{
    scanf("%d%d%d",&A,&Mod,&n);q[0].z=1;
    for (int i=1;i<=n;++i)
    {
        q[i].x=(long long)q[i-1].z*A%Mod,q[i].y=(long long)q[i].x*A%Mod;
        q[i].z=(long long)q[i].y*A%Mod;
        lsh[++LSH]=q[i].x,lsh[++LSH]=q[i].y,lsh[++LSH]=q[i].z;
    }
    for (int i=1;i<=n;++i)
    {
        if (q[i].x>q[i].y) swap(q[i].x,q[i].y); 
        if (q[i].y>q[i].z) swap(q[i].y,q[i].z);
        if (q[i].x>q[i].y) swap(q[i].x,q[i].y);
    }
    sort(lsh+1,lsh+LSH+1);LSH=unique(lsh+1,lsh+LSH+1)-lsh-1;
    for (int i=1;i<=n;++i)
        q[i].x=lower_bound(lsh+1,lsh+LSH+1,q[i].x)-lsh,
        q[i].y=lower_bound(lsh+1,lsh+LSH+1,q[i].y)-lsh,
        q[i].z=lower_bound(lsh+1,lsh+LSH+1,q[i].z)-lsh;
    sort(q+1,q+n+1,cmp);
    for (int i=1;i<=n;++i) q[i].id=i;

    for (int i=1;i<=n;++i)
        if (i==1||q[i].x!=q[i-1].x) L[i]=i;
        else L[i]=L[i-1];
    for (int i=n;i>=1;--i)
        if (i==n||q[i].x!=q[i+1].x) R[i]=i;
        else R[i]=R[i+1];
    f[q[1].id]=1;
    cdq(1,n);
    for (int i=1;i<=n;++i) ans=max(ans,f[i]);
    printf("%d\n",ans);
}