[英]Project Euler 233
Let f(N) be the number of points with integer coordinates that are on a circle passing through (0,0), (N,0), (0,N), and (N,N).
令f(N)为通过(0,0),(N,0),(0,N)和(N,N)的圆上具有整数坐标的点数。
It can be shown that f(10000) = 36.
可以证明f(10000)= 36。
What is the sum of all positive integers N 1011 such that f(N) = 420 ?
使f(N)= 420的所有正整数N 1011的总和是多少?
Alright, so I think that I have the basic idea for Project Euler number 233. Here is my code: 好吧,所以我认为我对233号欧拉计划有基本的了解。这是我的代码:
/*
* Andrew Koroluk
*/
public class euler233 {
public static void main(String[] args) {
System.out.println(f(10000));
System.out.println(f(1328125));
System.out.println(f(84246500));
System.out.println(f(248431625));
//if(true) return;
double ans = 0;
for(double N=10000; N<=(Math.pow(10, 11)); N++) {
//System.out.println(N);
if( f(N)==420 ) {
ans+= N;
System.out.println(N);
}
}
System.out.println(ans);
}
static double f(double N) {
double ans = 0;
double r = Math.sqrt(2*N*N)/2;
//System.out.println(r*r);
double r2 = r*r;
for(int x=1; x<=r; x++) {
for(int y=1; y<=r; y++) {
if( x*x + y*y == r2 ) {
ans+=4;
break;
}
}
}
return ans;
}
static boolean isInt(double a) {
if(a==(int)a) return true;
return false;
}
}
Basically what I am doing is finding solutions for right triangles inscribed inside the circle, having a hypotenuse the length of the circles diameter. 基本上,我正在做的事情是找到圆形内刻直角三角形的解决方案,这些直角三角形的斜边为圆形直径的长度。 I am not positive that my code is correct.
我不能肯定我的代码是正确的。
If it is correct, then my problem is optimizing the f(N) function and optimizing the loop to find numbers for f(N) = 420. 如果正确,那么我的问题是优化f(N)函数并优化循环以找到f(N)= 420的数字。
New Code: 新代码:
public class euler233 {
static long[] primes;
public static void main(String[] args) {
System.out.println(r(1328125));
Clock c = new Clock();
System.out.println(f2(10000));
c.getTimeSeconds();
c.reset();
System.out.println(f2(1328125));
c.getTimeSeconds();
}
static long f2(long N) {
return SquaresR2(N*N);
}
static boolean isInt(long a) {
if(a==(int)a) return true;
return false;
}
static int SquaresR2(long n) {
//System.out.println("start");
int sum = 0;
outer:
for(int a=0; a<Math.sqrt(n)-1; a++) {
for(int b=0; b<Math.sqrt(n)-1; b++) {
if( a*a + b*b == n ) {
if(a>b) break outer;
sum+=4;
System.out.println(n+" = "+a+"^2 + "+b+"^2");
}
}
}
sum*=2;
if(Math.sqrt(n)==(int)Math.sqrt(n)) sum+=4;
return sum;
}
static int r(int n) {
return 4*(d1(n) - d3(n));
}
private static int d1(int n) {
int k=1, sum=0;
while(true) {
int d = 4*k+1;
if(d>n) break;
if(n%d==0) sum++;
k++;
}
return sum;
}
private static int d3(int n) {
int k=1, sum=0;
while(true) {
int d = 4*k+3;
if(d>n) break;
if(n%d==0) sum++;
k++;
}
return sum;
}
}
A few points: 几点:
You have to find a much better approach, a few hints: 您必须找到一种更好的方法,有一些提示:
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