Question

我正在尝试实施EEA。我发现了这种模式，我也用它。

extended_euclid(a,b)
1  if b = 0
2      than return (a,1,0)
3  (d',s',t') <-- extended_euclid(b, a mod b)
4  (d,s,t) <--- (d',t',s' - (a div b)t')
5  return (d,s,t)

我的代码看起来像这样：

public static Triple extendedEuclid(BigInteger a, BigInteger b) {
    if (b.equals(new BigInteger("0"))) {
        return new Triple(a, new BigInteger("1"), new BigInteger("0"));
    } else {
       Triple i = extendedEuclid(b, a.mod(b));
       return new Triple(i.getA(), i.getB(), (i.getC().divide(i.getB()).multiply(i.getC())));
    }
}

我不太确定我的代码是否正确。我查了很多页面，比如20左右，但我仍然没有得到它。我精神错乱了。感谢。

Answer 1

看起来您在最终退货时无法进行操作。您还错误地实现了Triple的第三个值。这是我的实施。（为了清楚起见，我还使用了BigInteger的辅助常量/方法+重命名的变量。）

public class ExtendedEuclidAlgorithm {
    public static void main(final String[] args) {
        System.out.println("eea(240, 46) = " + apply(BigInteger.valueOf(240), BigInteger.valueOf(46)));
        System.out.println("eea(65, 40) = " + apply(BigInteger.valueOf(65), BigInteger.valueOf(40)));
        System.out.println("eea(1239, 735) = " + apply(BigInteger.valueOf(1239), BigInteger.valueOf(735)));
    }

    /*
     * extended_euclid(d,s)
          if s = 0
              than return (d,1,0)
          (d',s',t') <-- extended_euclid(s, d mod s)
          return (d',t',s' - (d div s)t')
     */
    public static Triple apply(final BigInteger a, final BigInteger b) {
        if (b.equals(BigInteger.ZERO)) {
            return new Triple(a, BigInteger.ONE, BigInteger.ZERO);
        } else {
            final Triple extension = apply(b, a.mod(b));
            return new Triple(extension.d, extension.t, extension.s.subtract(a.divide(b).multiply(extension.t)));
        }
    }


    private static class Triple {
        public final BigInteger d;
        public final BigInteger s;
        public final BigInteger t;
        private Triple(final BigInteger d, final BigInteger s, final BigInteger t) {
            this.d = d;
            this.s = s;
            this.t = t;
        }
        @Override
        public String toString() {
            return "Triple{" +
                    "d=" + d +
                    ", s=" + s +
                    ", t=" + t +
                    '}';
        }
    }
}

eea（240,46）= Triple {d = 2，s = -9，t = 47}
      eea（65,40）= Triple {d = 5，s = -3，t = 5}
      eea（1239,735）=三倍{d = 21，s = -16，t = 27}

我验证了Wikipedia和here的响应值。

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