1 #include<cstdio> 2 #include<iostream> 3 #include<algorithm> 4 #define M 200009 5 //#define N 100000 6 using namespace std; 7 struct data 8 { 9 int x,y,a1,yy; 10 }a[M]; 11 struct dat 12 { 13 int F,id; 14 }b[M]; 15 int n,mo[M],zhan[M],tnt,sum[M],st=1,ans[M],N; 16 bool mark[M]; 17 bool cmp(data b1,data b2) 18 { 19 return b1.a1<b2.a1; 20 } 21 bool cmp1(dat b1,dat b2) 22 { 23 return b1.F<b2.F; 24 } 25 void jia(int a1,int a2) 26 { 27 for(;a1<=N;a1+=a1&-a1) 28 sum[a1]+=a2; 29 return; 30 } 31 void mobiwus() 32 { 33 mo[1]=1; 34 for(int i=2;i<=N;i++) 35 { 36 if(!mark[i]) 37 { 38 zhan[++tnt]=i; 39 mo[i]=-1; 40 } 41 for(int j=1;i*zhan[j]<=N&&j<=tnt;j++) 42 { 43 mark[i*zhan[j]]=1; 44 if(i%zhan[j]) 45 mo[i*zhan[j]]=mo[i]*mo[zhan[j]]; 46 else 47 mo[i*zhan[j]]=0; 48 } 49 } 50 return; 51 } 52 int query(int a1) 53 { 54 int ss=0; 55 for(;a1;a1-=a1&-a1) 56 ss+=sum[a1]; 57 return ss; 58 } 59 void su(int n,int m,int j) 60 { 61 if(n>m) 62 swap(n,m); 63 int last=0,re=0; 64 for(int i=1;i<=n;i=last+1) 65 { 66 last=min(n/(n/i),m/(m/i)); 67 re+=(n/i)*(m/i)*(query(last)-query(i-1)); 68 } 69 ans[j]=re; 70 return; 71 } 72 int main() 73 { 74 scanf("%d",&n); 75 for(int i=1;i<=n;i++) 76 { 77 scanf("%d%d%d",&a[i].x,&a[i].y,&a[i].a1); 78 a[i].yy=i; 79 N=max(N,a[i].x); 80 N=max(N,a[i].y); 81 } 82 sort(a+1,a+n+1,cmp); 83 mobiwus(); 84 for(int i=1;i<=N;i++) 85 { 86 b[i].F=1; 87 b[i].id=i; 88 } 89 for(int i=2;i<=N;i++) 90 for(int j=1;j*i<=N;j++) 91 b[i*j].F+=i; 92 sort(b+1,b+N+1,cmp1); 93 for(int i=1;i<=n;i++) 94 { 95 for(;b[st].F<=a[i].a1&&st<=N;st++) 96 for(int j=1;j*b[st].id<=N;j++) 97 jia(j*b[st].id,b[st].F*mo[j]); 98 su(a[i].x,a[i].y,a[i].yy); 99 } 100 for(int i=1;i<=n;i++) 101 printf("%d ",ans[i]&0x7fffffff); 102 return 0; 103 }
莫比乌斯反演