[BZOJ3262]陌上花开

题目大意：

\(n(n\le10^5)\)个三元组\((x,y,z)(x,y,z\le2\times10^6)\)，求三位偏序。

思路：

CDQ分分治套树状数组。需要注意相同的三元组会互相产生贡献。

源代码：

#include<cstdio>
#include<cctype>
#include<vector>
#include<climits>
#include<algorithm>
inline int getint() {register char ch;while(!isdigit(ch=getchar()));register int x=ch^'0';while(isdigit(ch=getchar())) x=(((x<<2)+x)<<1)+(ch^'0');return x;
}
const int N=1e5+1,M=2e5+1;
int n,m,c,ans[N],cnt[N],w[N];
struct Node {int x,y,z,id,w;bool operator == (const Node &rhs) const {return x==rhs.x&&y==rhs.y&&z==rhs.z;}bool operator != (const Node &rhs) const {return x!=rhs.x||y!=rhs.y||z!=rhs.z;}
};
Node a[N];
inline bool cmp1(const Node &p1,const Node &p2) {if(p1.x==p2.x) {if(p1.y==p2.y) return p1.z<p2.z;return p1.y<p2.y;}return p1.x<p2.x;
}
inline bool cmp2(const Node &p1,const Node &p2) {if(p1.y==p2.y) return p1.z<p2.z;return p1.y<p2.y;
}
class FenwickTree {private:int val[M];int lowbit(const int &x) const {return x&-x;}public:void modify(int p,const int &x) {for(;p<=m;p+=lowbit(p)) val[p]+=x;}int query(int p) const {int ret=0;for(;p;p-=lowbit(p)) ret+=val[p];return ret;}
};
FenwickTree t;
void cdq(const int &b,const int &e) {if(b==e) {ans[a[b].id]+=a[b].w-1;return;};const int mid=(b+e)>>1;cdq(b,mid);cdq(mid+1,e);int p=b,q=mid+1;for(;q<=e;q++) {for(;p<=mid&&a[p].y<=a[q].y;p++) {t.modify(a[p].z,a[p].w);}ans[a[q].id]+=t.query(a[q].z);}while(--p>=b) t.modify(a[p].z,-a[p].w);std::inplace_merge(&a[b],&a[mid]+1,&a[e]+1,cmp2);
}
int main() {n=getint(),m=getint();for(register int i=1;i<=n;i++) {const int x=getint(),y=getint(),z=getint();a[i]=(Node){x,y,z,i};}std::sort(&a[1],&a[n]+1,cmp1);for(register int i=1,tmp;i<=n;i++) {if(a[i-1]==a[i]) {a[i-1]=(Node){INT_MAX,INT_MAX,INT_MAX};} else tmp=0;a[i].w=++tmp;}std::sort(&a[1],&a[n]+1,cmp1);c=std::unique(&a[1],&a[n]+1)-&a[1];while(a[c]==(Node){INT_MAX,INT_MAX,INT_MAX}) c--;cdq(1,c);for(register int i=1;i<=c;i++) {cnt[ans[a[i].id]]+=a[i].w;}for(register int i=0;i<n;i++) {printf("%d\n",cnt[i]);}return 0;
}