欧拉工程第73题：Counting fractions in a range

题目链接：https://projecteuler.net/problem=73

n/d的真分数 ，当d《=12000时 在 1/3 and 1/2 之间的有多少个

public class P73{
    void run(){
        
        FareySequences();
    }
    void FareySequences(){
        int limit = 12000;
        int a = 1;
        int b = 3;
        int c = 4000;
        int d = 11999;
        int count=0;
        while(!(c==1 && d==2)){
            count ++;
            int k = (limit+b)/d;
            int e = k*c -a;
            int f = k*d -b;
            a = c;
            b = d;
            c = e;
            d = f;
        }
        System.out.println(count);        
    }
//    7295372
//    117ms
    void BruteForce2(){
        int max_n = 12000+1;

        int result=0;
        for(int i=5;i<max_n;i++){
            for(int j=i/3+1;j<(i-1)/2+1;j++){
                if(gcd(i,j)==1){
                        result++;
                }
            }
        }
        System.out.println(result);
    }
//    7295372
//    1923ms
    void BruteForce(){
        int max_n = 12000+1;
        double target2=0.5;
        double target1=1/3.0;
        int result=0;
        for(int i=5;i<max_n;i++){
            for(int j=i+1;j<max_n;j++){
                if(gcd(i,j)==1){
                    double tmp = i/(j*1.0);
                    if(tmp>target1 && tmp<target2)
                        result++;
                }
            }
        }
        System.out.println(result);
    }
//    7295372
//    8877ms

    int gcd(int a,int b){
        int temp;
        if(a<b){
            temp =a;
            a = b ;
            b = temp;
        }
        while(b!=0){
            temp = a%b;
            a = b;
            b = temp;
        }
        return a;
    }
    void calculate(){
        int max_n = 1000000;
        long a = 3;
        long b = 7;
        long r = 0;
        long s = 1;
        int q = 0;
        long p = 0;
        for( q = max_n;q>2;q--){
             p = (a*q-1)/b;
            if(p*s>r*q){
                s = q;
                r = p;
            }
        }
        System.out.println(r+"/"+s);
    }
    boolean isPrime(int num){
        if(num==2||num==3) return true;
        if(num<2) return false;
        for(int i=5;i<Math.sqrt(num)+1;i++)
            if(num%i==0) return false;
        return true;
    }
    long[] cal_phi(int max_n){
        long[] phi = new long[max_n+1];
        for(int i=1;i<max_n;i++){
            phi[i] += i;
            for(int j =2*i;j<max_n;j+=i)
                phi[j]-=phi[i];
        }
        return phi;
    }
    public static void main(String[] args){
        long t0 = System.currentTimeMillis();
        new P73().run();
        long t1= System.currentTimeMillis();
        System.out.println((t1-t0)+"ms");
    }
}