BZOJ 1041: [HAOI2008]圆上的整点

Sol

$x^2+y^2=r^2$

$y^2=r^2-x^2$

$y^2=(r-x)(r+x)$

$r-x=du^2,r+x=dv^2$

$2r=d(u^2+v^2),(v,u)==1$

$y^2=d^2u^2v^2$

Code

/**************************************************************
Problem: 1041
User: BeiYu
Language: C++
Result: Accepted
Time:80 ms
Memory:1300 kb
****************************************************************/

#include<cstdio>
#include<cmath>
#include<algorithm>
#include<iostream>
using namespace std;

typedef long long LL;

LL r,n,ans;

inline LL in(LL x=0,char ch=getchar()){ while(ch>'9'||ch<'0') ch=getchar();
while(ch>='0'&&ch<='9') x=(x<<3)+(x<<1)+ch-'0',ch=getchar();return x; }

LL calc(LL d){
LL res=0,m=n/d;
for(LL u=1,v;2*u*u<=m;u++){
v=sqrt(m-u*u)+0.5;
if(v<=u) break;
if(v*v+u*u==m&&__gcd(u,v)==1) res++;
}return res;
}
int main(){
//  freopen("in.in","r",stdin);
r=in(),n=r<<1;
for(LL d=1;d*d<=n;d++) if(n%d==0){
if(d*d==n) ans+=calc(d);
else ans+=calc(d)+calc(n/d);
}
cout<<ans*4+4<<endl;
return 0;
}


posted @ 2016-09-08 20:24  北北北北屿  阅读(69)  评论(0编辑  收藏