hdu_4742_Pinball Game 3D(cdq分治+树状数组)

题目链接：hdu_4742_Pinball Game 3D

题意：

给你n个点，让你求三维的LIS，并且求出有多少种组合能达到LIS。

题解：

求三维的LIS，典型的三维偏序问题，x排序,解决一维，cdq分治y，解决一维，树状数组维护z，解决一维。

注意，cdq中sort不要调用太多，不然会被卡常。

 #include<bits/stdc++.h>
 #define F(i,a,b) for(int i=a;i<=b;i++)
 using namespace std;
 typedef pair<int,int>P;

 const int N=1e5+,mod=<<;
 int t,n,hsh_ed,hsh[N];
 P sum[N],dp[N];

 struct node
 {
     int x,y,z,id;
     bool operator <(const node & b)const{return x<b.x||(x==b.x&&y<b.y)||(x==b.x&&y==b.y&&z<b.z);}
 }a[N],b[N];

 inline void up(P &a,P b)
 {
     if(a.first==b.first)a.second+=b.second;
     else if(a.first<b.first)a=b;
 }
 inline void add(int x,P c){while(x<=hsh_ed)up(sum[x],c),x+=x&-x;}
 inline P ask(int x){P an=P(,);while(x)up(an,sum[x]),x-=x&-x;return an;}
 inline void back(int x){while(x<=hsh_ed)sum[x]=P(,),x+=x&-x;}

 void cdq(int l,int r)
 {
     if(l==r)return;
     int mid=l+r>>;
     cdq(l,mid);
     F(i,l,r)b[i]=a[i],b[i].x=;
     sort(b+l,b++r);
     F(i,l,r)
     {
         if(b[i].id<=mid)add(b[i].z,dp[b[i].id]);
         else
         {
             P now=ask(b[i].z);
             if(now.first+>dp[b[i].id].first)dp[b[i].id]=P(now.first+,now.second);
             else if(now.first+==dp[b[i].id].first)dp[b[i].id].second+=now.second;
         }
     }
     F(i,l,r)if(b[i].id<=mid)back(b[i].z);
     cdq(mid+,r);
 }

 int main()
 {
     scanf("%d",&t);
     while(t--)
     {
         scanf("%d",&n),hsh_ed=;
         F(i,,n)
         {
             scanf("%d%d%d",&a[i].x,&a[i].y,&a[i].z);
             hsh[i]=a[i].z;
         }
         sort(a+,a++n);
         sort(hsh+,hsh++n),hsh_ed=unique(hsh+,hsh++n)-hsh;
         F(i,,n)
         {
             dp[i]=P(,),a[i].id=i;
             a[i].z=lower_bound(hsh+,hsh++hsh_ed,a[i].z)-hsh;
         }
         cdq(,n);
         P ans=P(,);
         F(i,,n)up(ans,dp[i]);
         printf("%d %d\n",ans.first,ans.second%mod);
     }
     return ;
 }