原始ピタゴラス数探索ロジック：一般項導出編

PythagoraSwitch2.java

import java.util.ArrayList;
import java.util.List;

public class PythagoraSwitch2 {

    /**
     * @param args
     */
    public static void main(String[] args) {
        final int MAX = Integer.parseInt(args[0]);
        long start = System.nanoTime();
        List<PythagorasNum> result = new ArrayList<>();
        work:
        for (int m = 1; m <= (int) Math.sqrt(MAX); m++) {
            int m2 = m * m;
            for (int n = m % 2 + 1; n < m; n += 2) {
                if (isRelativelyPrime(m, n)) {
                    int n2 = n * n;
                    int c = m2 + n2;
                    if (c > MAX)
                        continue work;
                    int a = m2 - n2;
                    int b = 2 * m * n;
                    if (a > b) {
                        int tmp = a;
                        a = b;
                        b = tmp;
                    }
                    result.add(new PythagorasNum(a, b, c));
                }
            }
        }
        long end = System.nanoTime();
        System.out.println(result);
        System.out.println("count:" + result.size());
        System.out.println("time:" + (end - start) / 1000000);
    }

    private static boolean isRelativelyPrime(int m, int n) {
        return gcd(m, n) == 1;
    }

    private static int gcd(int max, int min) {
        int residue = max % min;
        return (residue == 0) ? min : gcd(min, residue);
    }

    private static class PythagorasNum {
        final int a;
        final int b;
        final int c;
        PythagorasNum(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }
        @Override public String toString() {
            return "(" + a + ", " + b + ", " + c + ")";
        }
    }
}