Bzoj 1041: [haoi2008] the entire point primitive stock group on the circle

1041: [haoi2008] full point time limit: 10 sec memory limit: 162 MB
Submit: 2027 solved: 853
[Submit] [Status] Description

Returns the number of points in the circumference of a given circle (x ^ 2 + y ^ 2 = R ^ 2.

Input

R

Output

Number of points

Sample input4sample output4hint

 

N <= 2000 000

 

Source

This topic can be understood by the primitive stock groups (x, y, z), x ^ 2 + y ^ 2 = Z, and gcd (X, y) = gcd (x, z) = gcd (y, z) = 1 can be expressed

X = a ^ 2-B ^ 2

Y = 2 * a * B

Z = a ^ 2 + B ^ 2

This topic is known as Z, so we can first SQRT (n) n's factor Z, and then SQRT (z) won't a, just for statistics.

#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 1100#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,nn;qword gcd(qword x,qword y){        return (x%y==0)?y:gcd(y,x%y);}int count(qword n){        qword x,y;        if (n==1)        {        //        cout<<"0 "<<nn<<endl;                return 4;        }        qword l=ceil(sqrt(n));        int ans=0;        for (x=1;x<l;x++)        {                y=sqrt(n-x*x);                if (x*x+y*y!=n)continue;                if (x>=y)break;                if (gcd(y*y-x*x,2*y*y)!=1)continue;        //        cout<<(y*y-x*x)*(nn/n)<<" "<<2*x*y*(nn/n)<<endl;        //        cout<<2*x*y*(nn/n)<<" "<<(y*y-x*x)*(nn/n)<<endl;                ans+=1+(x&&y);        }        return ans*4;}int main(){        freopen("input.txt","r",stdin);        //freopen("output.txt","w",stdout);        int i,j,k;        int x,y,z;        scanf(LL,&n);        nn=n;        qword ans=0;        qword l=ceil(sqrt(n));        for (i=1;i<l;i++)        {                if (n%i==0)                {                        ans+=count(i);                        ans+=count(n/i);                }        }        if (l*l==n)ans+=count(l);        printf(LL"\n",ans);        return 0;}

 

 

Bzoj 1041: [haoi2008] the entire point primitive stock group on the circle