大数的 Java 数据类型 [重复]

Question

我需要计算一个最大为 130 的不同大小的阶乘程序的运行时间！。但是，该程序当前使用的是长数据类型，并且不足以容纳输出。在 20 阶乘之后，它变为负数并出现故障。如何存储更大的数字，以便计算多达 130 个阶乘？以下是完成这项工作的方法：

public class FactorialCalculation {
    long startTime = System.nanoTime();

    //recursive Factorial method
    public long factorial(long number) {
        if (number <= 1)
            return 1;
        else
            return number * factorial(number - 1);
    }

    //Now output the factorials of 0 through 15
    public void displayFactorials() {
        // Calculate the factorial of o through 15
        for (int counter = 0; counter <= 130; counter++)
            System.out.print("Factorial of:" + counter + " " + factorial(counter) + " \n");

        long estimatedTime = System.nanoTime() - startTime;
        System.out.println(estimatedTime);

    } // end of the method displayFactorials


}  // end of class FactorialCalculation 

这是显示它变为负数然后变为 0 的输出。

Factorial of:0 1 
Factorial of:1 1 
Factorial of:2 2 
Factorial of:3 6 
Factorial of:4 24 
Factorial of:5 120 
Factorial of:6 720 
Factorial of:7 5040 
Factorial of:8 40320 
Factorial of:9 362880 
Factorial of:10 3628800 
Factorial of:11 39916800 
Factorial of:12 479001600 
Factorial of:13 6227020800 
Factorial of:14 87178291200 
Factorial of:15 1307674368000 
Factorial of:16 20922789888000 
Factorial of:17 355687428096000 
Factorial of:18 6402373705728000 
Factorial of:19 121645100408832000 
Factorial of:20 2432902008176640000 
Factorial of:21 -4249290049419214848 
Factorial of:22 -1250660718674968576 
Factorial of:23 8128291617894825984 
Factorial of:24 -7835185981329244160 
Factorial of:25 7034535277573963776 
Factorial of:26 -1569523520172457984 
Factorial of:27 -5483646897237262336 
Factorial of:28 -5968160532966932480 
Factorial of:29 -7055958792655077376 
Factorial of:30 -8764578968847253504 
Factorial of:31 4999213071378415616 
Factorial of:32 -6045878379276664832 
Factorial of:33 3400198294675128320 
Factorial of:34 4926277576697053184 
Factorial of:35 6399018521010896896 
Factorial of:36 9003737871877668864 
Factorial of:37 1096907932701818880 
Factorial of:38 4789013295250014208 
Factorial of:39 2304077777655037952 
Factorial of:40 -70609262346240000 
Factorial of:41 -2894979756195840000 
Factorial of:42 7538058755741581312 
Factorial of:43 -7904866829883932672 
Factorial of:44 2673996885588443136 
Factorial of:45 -8797348664486920192 
Factorial of:46 1150331055211806720 
Factorial of:47 -1274672626173739008 
Factorial of:48 -5844053835210817536 
Factorial of:49 8789267254022766592 
Factorial of:50 -3258495067890909184 
Factorial of:51 -162551799050403840 
Factorial of:52 -8452693550620999680 
Factorial of:53 -5270900413883744256 
Factorial of:54 -7927461244078915584 
Factorial of:55 6711489344688881664 
Factorial of:56 6908521828386340864 
Factorial of:57 6404118670120845312 
Factorial of:58 2504001392817995776 
Factorial of:59 162129586585337856 
Factorial of:60 -8718968878589280256 
Factorial of:61 3098476543630901248 
Factorial of:62 7638104968020361216 
Factorial of:63 1585267068834414592 
Factorial of:64 -9223372036854775808 
Factorial of:65 -9223372036854775808 
Factorial of:66 0 
Factorial of:67 0 
Factorial of:68 0 
Factorial of:69 0 
Factorial of:70 0 
Factorial of:71 0 
Factorial of:72 0 
Factorial of:73 0 
Factorial of:74 0 
Factorial of:75 0 
Factorial of:76 0 
Factorial of:77 0 
Factorial of:78 0 
Factorial of:79 0 
Factorial of:80 0 
Factorial of:81 0 
Factorial of:82 0 
Factorial of:83 0 
Factorial of:84 0 
Factorial of:85 0 
Factorial of:86 0 
Factorial of:87 0 
Factorial of:88 0 
Factorial of:89 0 
Factorial of:90 0 
Factorial of:91 0 
Factorial of:92 0 
Factorial of:93 0 
Factorial of:94 0 
Factorial of:95 0 
Factorial of:96 0 
Factorial of:97 0 
Factorial of:98 0 
Factorial of:99 0 
Factorial of:100 0 
Factorial of:101 0 
Factorial of:102 0 
Factorial of:103 0 
Factorial of:104 0 
Factorial of:105 0 
Factorial of:106 0 
Factorial of:107 0 
Factorial of:108 0 
Factorial of:109 0 
Factorial of:110 0 
Factorial of:111 0 
Factorial of:112 0 
Factorial of:113 0 
Factorial of:114 0 
Factorial of:115 0 
Factorial of:116 0 
Factorial of:117 0 
Factorial of:118 0 
Factorial of:119 0 
Factorial of:120 0 
Factorial of:121 0 
Factorial of:122 0 
Factorial of:123 0 
Factorial of:124 0 
Factorial of:125 0 
Factorial of:126 0 
Factorial of:127 0 
Factorial of:128 0 
Factorial of:129 0 
Factorial of:130 0 

Answer 1

BigInteger 可以很好地用于此应用程序。

如果您阅读了 javadoc，可以保证*BigInteger 能够支持最多 2 个^MAXINT 的数字；即 2^2147483647。即（非常粗略）7.9 * 10^646456992。

130！大约是 6.466855489220473e+219 或 6.46 * 10²¹⁹。如您所见，与保证可表示的最大值相比，这是微不足道的。

---

* - 当然，这个保证假设你有足够的堆空间。但我们谈论的是 (MAXINT / 8 ) 字节...... 0.25 GB......这在现代 64 位计算机上并不是一个巨大的数字。

Answer 2

看看BigInteger。这可以存储非常大的值，大小不确定，但由于它被实现为int[]，它应该可能如this question. 中所解释的那样

Answer 3

查看以下代码 sn-p，这将满足要求。
您可以通过使用 BigInteger/BigDecimal 而不是 long 数据类型来实现此目的。

long startTime = System.nanoTime();

public static void main(String[] args) {

    Test t  =   new Test();
    t.displayFactorials();
}


     //recursive Factorial method
public BigDecimal factorial(BigDecimal number)
{
      if (number.intValue()  <= 1)
    return BigDecimal.ONE;
      else
    return number.multiply( factorial ( number.subtract(BigDecimal.ONE) ) );
}

 //Now output the factorials of 0 through 15
public void displayFactorials()
{
        // Calculate the factorial of o through 15
           for ( int counter = 0; counter <= 130; counter++ )
               System.out.print ( "Factorial of:" + counter + " " + 
               factorial ( new BigDecimal(counter+"") ) + " \n");

         long estimatedTime = System.nanoTime() - startTime;
         System.out.println(estimatedTime);

} // end of the method displayFactorials

您也可以将BigDecimal 更改为BigInteger。