Bzoj 2705: [sdoi2012] longge issue pull data

2705: [sdoi2012] longge issue time limit: 3 sec memory limit: 128 MB
Submit: 1035 solved: 669
[Submit] [Status] Descriptionlongge has excellent scores in mathematics and is very happy to challenge difficult mathematical problems. Now the question is: given an integer N, you need to find Sigma gcd (I, n) (1 <= I <= N ). Input is an integer (n. Output is an integer. Sample input6
Sample output15
Hint

 

[Data Scope]

For 60% of the data, 0 <n <= 2 ^ 16.

For 100% of the data, 0 <n <= 2 ^ 32.

 

 

Source

 

Calculate the number of gcd (I, n) = K, that is, the number of gcd (I/k, n/K) = 1, that is, Phi (N/K ).

This topic makes me realize whether I think about it or not. I always think about it first, and there is no way to change my mind. Taking this question as an example, at first glance, I decided that it was the subject of the mobyus inversion and there was no other way to think about it.

#include<iostream>#include<cstdio>#include<cstdlib>#include<cstring>#include<ctime>#include<cmath>#include<algorithm>#include<set>#include<map>#include<vector>#include<string>#include<queue>using namespace std;#ifdef WIN32#define LL "%I64d"#else#define LL "%lld"#endif#define MAXN 1100000#define MAXV MAXN*2#define MAXE MAXV*2#define INF 0x3f3f3f3f#define INFL 0x3f3f3f3f3f3f3f3fLLtypedef long long qword;inline int nextInt(){        char ch;        int x=0;        bool flag=false;        do                ch=getchar(),flag=(ch==‘-‘)?true:flag;        while(ch<‘0‘||ch>‘9‘);        do x=x*10+ch-‘0‘;        while (ch=getchar(),ch<=‘9‘ && ch>=‘0‘);        return x*(flag?-1:1);}qword n,m;qword prime[MAXN],topp=-1;bool pflag[MAXN];int gcd(int x,int y){        return (x%y==0) ? y : gcd(y,x%y);}void init(){        int i,j;        for (i=2;i<MAXN;i++)        {                if (!pflag[i])                {                        prime[++topp]=i;                }                for (j=0;j<=topp && i*prime[j]<MAXN;j++)                {                        pflag[i*prime[j]]=true;                        if (i%prime[j]==0)                        {                                break;                        }                }        }}qword phi(qword x){        int i;        qword ret=1;        for (i=0;i<=topp && prime[i]*prime[i]<=x;i++)        {                if(x%prime[i]==0)                {                        ret*=prime[i]-1;                        x/=prime[i];                        while (x%prime[i]==0)                        {                                ret*=prime[i];                                x/=prime[i];                        }                }        }        if (x>1)        {                ret*=x-1;        }        return ret;}int main(){        freopen("input.txt","r",stdin);        //freopen("output.txt","w",stdout);        qword i;        scanf("%d",&n);        qword ans1=0,ans2=0;    //    for (i=1;i<=n;i++)    //            ans1+=gcd(i,n);    //    printf("%d\n",ans1);        init();        qword l=ceil(sqrt(n));        for (i=1;i*i<n;i++)        {                if (n%i==0)                {                        ans2+=(qword)i*phi(n/i);                        ans2+=(qword)(n/i)*phi(i);                }        }        if (l*l==n)        {                ans2+=(qword)(n/l)*phi(l);        }        printf(LL"\n",ans2);        return 0;}

 

 

Bzoj 2705: [sdoi2012] longge issue pull data