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我正在尝试使用 BigInteger 制作扩展的欧几里得算法。但我不断收到错误消息

线程“主”java.lang.ArithmeticException 中的异常：BigInteger 除以零

我在谷歌上搜索，它说我可能会因为非整数除法而出错

我应该如何解决这个问题？

public static void main(String[] args) throws Exception{

    BigInteger ex1 = new BigInteger("9");
    BigInteger ex2 = new BigInteger("13");
    //if(eA.gcd(eB).equals(BigInteger.ONE))
//  {
        BigInteger[] val = gcd(ex1,ex2);
        
        System.out.println(val[1]);
        System.out.println(val[2]);
//  }
}

   // Returns a triple {d, a, b} such that d = a*p + b*q

   static BigInteger[] gcd(BigInteger p, BigInteger q) {
          if (p.equals(BigInteger.ZERO))
             return new BigInteger[] { p, BigInteger.valueOf(1), BigInteger.valueOf(0) };

          BigInteger[] vals = gcd(q, p.remainder(q));
          BigInteger d = vals[0];
          BigInteger a = vals[2];
          BigInteger b = vals[1].subtract((p.divide(q)).multiply(vals[2]));
          return new BigInteger[] { d, a, b };
       }
}
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1 回答 1

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这是由 Github Copilot 制作的工作变体（由我验证）：

// Returns a triple {d, a, b} such that d = a*p + b*q
static BigInteger[] extendedEuclidean(BigInteger p, BigInteger q) {
    BigInteger[] val = new BigInteger[3];

    if (q.equals(BigInteger.ZERO)) {
        val[0] = p;
        val[1] = BigInteger.ONE;
        val[2] = BigInteger.ZERO;
    } else {
        BigInteger[] val2 = extendedEuclidean(q, p.mod(q));
        val[0] = val2[0];
        val[1] = val2[2];
        val[2] = val2[1].subtract(p.divide(q).multiply(val2[2]));
    }

    return val;
}

注意：当p=0它返回时q，反之亦然。

与您的代码的不同之处在于，它检查的是q != 0（在某些时候肯定会变为 0），而不是p != 0.

测试：

input: 9, 13
d = 1, a = 3, b = -2

input: 2, 15
d = 1, a = -7, b = 1

input: 9, 12
d = 3, a = -1, b = 1

input: 0, 10
d = 10, a = 0, b = 1

input: 0, 0
d = 0, a = 1, b = 0

input: 1, 1
d = 1, a = 0, b = 1

input: 3, 0
d = 3, a = 1, b = 0
于 2021-11-01T20:36:15.703 回答