Java中的 BigInteger 类
BigInteger 类用于涉及非常大的整数计算的数学运算，这些计算超出了所有可用原始数据类型的限制。
这样一来，BigInteger 类由于其庞大的方法库而使用起来非常方便，并且在竞争性编程中也被大量使用。
下面给出了原始算术中的简单语句列表及其在 BigInteger 对象方面的类似语句。
例子：
int a, b;
BigInteger A, B; 初始化如下 如下：
a = 54;
b = 23;A = BigInteger.valueOf(54);
B = BigInteger.valueOf(37); 对于可用作字符串的整数，您可以按如下方式对其进行初始化：
A = new BigInteger(“54”);
B = new BigInteger(“123456789123456789”); 为了便于初始化，BigInteger 类中还定义了一些常量，如下所示：
A = BigInteger.ONE;
// Other than this, available constant are BigInteger.ZERO
// and BigInteger.TEN 数学运算如下：
int c = a + b;
BigInteger C = A.add(B); 其他类似的函数是减法（），乘法（），除法（），余数（），但所有这些函数都将 BigInteger 作为其参数，因此如果我们希望对整数或字符串进行此操作，请在将它们传递给函数之前将它们转换为 BigInteger，如下所示以下：
String str = “123456789”;
BigInteger C = A.add(new BigInteger(str));
int val = 123456789;
BigInteger C = A.add(BigInteger.valueOf(val)); 从 BigInteger 中提取值如下：
int x = A.intValue(); // value should be in limit of int x
long y = A.longValue(); // value should be in limit of long y
String z = A.toString(); 比较
if (a < b) {} // For primitive int
if (A.compareTo(B) < 0) {} // For BigInteger 实际上 compareTo 根据值返回 -1（小于）、0（等于）、1（大于）。对于平等，我们还可以使用：
if (A.equals(B)) {} // A is equal to B BigInteger 类的方法
| Method | Action Performed |
|---|---|
| add(BigInteger val) | Returns a BigInteger whose value is (this + val). |
| abs() | Returns a BigInteger whose value is the absolute value of this BigInteger. |
| and(BigInteger val) | Returns a BigInteger whose value is (this & val). |
| andNot(BigInteger val) | Returns a BigInteger whose value is (this & ~val). |
| bitCount() | Returns the number of bits in the two’s complement representation of this BigInteger that differ from its sign bit. |
| bitLength() | Returns the number of bits in the minimal two’s-complement representation of this BigInteger, excluding a sign bit. |
| byteValueExact() | Converts this BigInteger to a byte, checking for lost information. |
| clearBit(int n) | Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit cleared. |
| compareTo(BigInteger val) | Compares this BigInteger with the specified BigInteger. |
| divide(BigInteger val) | Returns a BigInteger whose value is (this / val). |
| divideAndRemainder(BigInteger val) | Returns an array of two BigIntegers containing (this / val) followed by (this % val). |
| doubleValue() | Converts this BigInteger to a double. |
| equals(Object x) | Compares this BigInteger with the specified Object for equality. |
| flipBit(int n) | Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit flipped. |
| floatValue() | Converts this BigInteger to a float. |
| gcd(BigInteger val) | Returns a BigInteger whose value is the greatest common divisor of abs(this) and abs(val). |
| getLowestSetBit() | Returns the index of the rightmost (lowest-order) one bit in this BigInteger (the number of zero bits to the right of the rightmost one bit). |
| hashCode() | Returns the hash code for this BigInteger. |
| intValue() | Converts this BigInteger to an int. |
| intValueExact() | Converts this BigInteger to an int, checking for lost information. |
| isProbablePrime(int certainty) | Returns true if this BigInteger is probably prime, false if it’s definitely composite. |
| longValue() | Converts this BigInteger to a long. |
| longValueExact() | Converts this BigInteger to a long, checking for lost information. |
| max(BigInteger val) | Returns the maximum of this BigInteger and val. |
| min(BigInteger val) | Returns the minimum of this BigInteger and val. |
| mod(BigInteger m | Returns a BigInteger whose value is (this mod m). |
| modInverse(BigInteger m) | Returns a BigInteger whose value is (this-1 mod m). |
| modPow(BigInteger exponent, BigInteger m | Returns a BigInteger whose value is (thisexponent mod m). |
| multiply(BigInteger val) | Returns a BigInteger whose value is (this * val). |
| negate() | Returns a BigInteger whose value is (-this). |
| nextProbablePrime() | Returns the first integer greater than this BigInteger that is probably prime. |
| not() | Returns a BigInteger whose value is (~this). |
| or(BigInteger val) | Returns a BigInteger whose value is (this | val). |
| pow(int exponent) | Returns a BigInteger whose value is (thisexponent). |
| probablePrime(int bitLength, Random rnd) | Returns a positive BigInteger that is probably prime, with the specified bitLength. |
| remainder(BigInteger val) | Returns a BigInteger whose value is (this % val). |
| setBit(int n) | Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit set. |
| shiftLeft(int n) | Returns a BigInteger whose value is (this << n). |
| shiftRight(int n) | Returns a BigInteger whose value is (this >> n). |
| shortValueExact() | Converts this BigInteger to a short, checking for lost information. |
| signum() | Returns the signum function of this BigInteger. |
| sqrt() | Returns the integer square root of this BigInteger. |
| sqrtAndRemainder() | Returns an array of two BigIntegers containing the integer square root s of this and its remainder this – s*s, respectively. |
| subtract(BigInteger val) | Returns a BigInteger whose value is (this – val). |
| testBit(int n) | Returns true if and only if the designated bit is set. |
| toByteArray() | Returns a byte array containing the two’s-complement representation of this BigInteger. |
| toString() | Returns the decimal String representation of this BigInteger. |
| toString(int radix) | Returns the string representation of this BigInteger in the given radix. |
| valueOf(long val) | Returns a BigInteger whose value is equal to that of the specified long. |
| xor(BigInteger val) | Returns a BigInteger whose value is (this ^ val). |
插图：
100 的阶乘包含 158 位数字，因此我们无法将其存储为任何可用的原始数据类型。我们可以在其中存储任意大小的 Integer。范围的上限没有理论上的限制，因为内存是动态分配的，但实际上由于内存有限，您可以存储一个具有 Integer.MAX_VALUE 位数的数字，这应该足以存储几乎所有大值。
例子：
Java
// Java program to find large factorials using BigInteger
import java.math.BigInteger;
import java.util.Scanner;
public class Example
{
// Returns Factorial of N
static BigInteger factorial(int N)
{
// Initialize result
BigInteger f = new BigInteger("1"); // Or BigInteger.ONE
// Multiply f with 2, 3, ...N
for (int i = 2; i <= N; i++)
f = f.multiply(BigInteger.valueOf(i));
return f;
}
// Driver method
public static void main(String args[]) throws Exception
{
int N = 20;
System.out.println(factorial(N));
}
}输出：
2432902008176640000Tip: If we have to write above program in C++, that would be too large and complex, we can look at Factorial of Large Number.
所以在了解了 BigInteger 类的函数之后，我们可以轻松解决许多复杂的问题，但是请记住，由于 BigInteger 类内部使用整数数组进行处理，所以对 BigInteger 对象的操作不如对原语的操作快。 BigIntgers 上的 add函数不会占用与 BigInteger 长度成正比的恒定时间，因此程序的复杂性会相应改变。
必读：
- Java中的大斐波那契数
- BigInteger 类还提供素数的快速方法。