莫比乌斯反演
1 #include<cstdio> 2 #include<cstdlib> 3 #include<algorithm> 4 #include<cstring> 5 #include<vector> 6 #include<cmath> 7 #include<queue> 8 #define MAXN 50000+10 9 #define INF 0x7f7f7f7f 10 #define LINF 0x7f7f7f7f7f7f7f7f 11 #define ll long long 12 #define pb push_back 13 #define ft first 14 #define sc second 15 #define mp make_pair 16 #define pil pair<int,ll> 17 #define pll pair<ll,ll> 18 using namespace std; 19 int isp[MAXN]; 20 int mu[MAXN],s[MAXN]; 21 vector<int> p; 22 void getmu(){ 23 s[1]=mu[1]=1; 24 for(int i=2;i<MAXN;i++){ 25 if(!isp[i]){ 26 p.pb(i); 27 mu[i]=-1; 28 } 29 for(int j=0;j<p.size()&&i*p[j]<MAXN;j++){ 30 isp[i*p[j]]=1; 31 if(i%p[j]==0){ 32 mu[i*p[j]]=0; 33 break; 34 } 35 mu[i*p[j]]=-mu[i]; 36 } 37 s[i]=s[i-1]+mu[i]; 38 } 39 } 40 int calc(int n,int m,int k){ 41 if(n>m)swap(n,m); 42 n/=k,m/=k; 43 int ret=0,lst; 44 for(int i=1;i<=n;i=lst+1){ 45 lst=min(n/(n/i),m/(m/i)); 46 ret+=((s[lst]-s[i-1])*(n/lst)*(m/lst)); 47 } 48 return ret; 49 } 50 int a,b,c,d,k; 51 int main() 52 { 53 //freopen("data.in","r",stdin); 54 getmu(); 55 int T; 56 scanf("%d",&T); 57 while(T--){ 58 scanf("%d%d%d%d%d",&a,&b,&c,&d,&k);a--,c--; 59 int ans=calc(b,d,k)-calc(a,d,k)-calc(b,c,k)+calc(a,c,k); 60 printf("%d ",ans); 61 } 62 return 0; 63 }