Java语言程序设计基础篇（第10版）编程练习题13.18(使用 Rational 类)

第十三章第十八题(使用 Rational 类)

题目要求：

编写程序，使用 Rational 类计算下面的求和数列:

你将会发现输出是不正确的，因为整数溢出(太大了)。为了解决这个问题，参见编程练习題13.15。
代码参考：

package chapter_13;import java.math.BigInteger;public class 编程练习题13_18RationalSum {public static void main(String[] args) {Rational2 resultRational2 = new Rational2();for (long i = 2; i <= 100; i++) {Rational2 rational2 = new Rational2(BigInteger.valueOf(i-1), BigInteger.valueOf(i));System.out.print(rational2.toString());if (i == 100) System.out.print(" = ");else if (i % 10 == 0) System.out.println(" + ");else System.out.print(" + ");resultRational2 = resultRational2.add(rational2);}//System.out.println(resultRational2);System.out.println(resultRational2.simplify());}
}class Rational2 extends Number implements Comparable<Rational2> {private BigInteger numerator = BigInteger.ZERO;private BigInteger denominator = BigInteger.ONE;public Rational2() {this(BigInteger.ZERO, BigInteger.ONE);}public Rational2(BigInteger numerator, BigInteger denominator) {BigInteger gcd = numerator.gcd(denominator);this.numerator = numerator.divide(gcd);this.denominator = denominator.divide(gcd);if (this.denominator.compareTo(BigInteger.ZERO) < 0) { // 确保分母为正this.numerator = this.numerator.negate();this.denominator = this.denominator.negate();}}private static BigInteger gcd(BigInteger n, BigInteger d) {return n.gcd(d);}public BigInteger getNumerator() {return numerator;}public BigInteger getDenominator() {return denominator;}public Rational2 add(Rational2 secondRational) {BigInteger n = numerator.multiply(secondRational.getDenominator()).add(denominator.multiply(secondRational.getNumerator()));BigInteger d = denominator.multiply(secondRational.getDenominator());return new Rational2(n, d);}public Rational2 subtract(Rational2 secondRational) {BigInteger n = numerator.multiply(secondRational.getDenominator()).subtract(denominator.multiply(secondRational.getNumerator()));BigInteger d = denominator.multiply(secondRational.getDenominator());return new Rational2(n, d);}public Rational2 multiply(Rational2 secondRational) {BigInteger n = numerator.multiply(secondRational.getNumerator());BigInteger d = denominator.multiply(secondRational.getDenominator());return new Rational2(n, d);}public Rational2 divide(Rational2 secondRational) {if (secondRational.getNumerator().equals(BigInteger.ZERO)) {throw new ArithmeticException("Division by zero");}BigInteger n = numerator.multiply(secondRational.getDenominator());BigInteger d = denominator.multiply(secondRational.getNumerator());return new Rational2(n, d);}@Overridepublic String toString() {return denominator.equals(BigInteger.ONE) ? numerator.toString() : numerator + "/" + denominator;}@Overridepublic boolean equals(Object other) {if (other instanceof Rational2) {Rational2 that = (Rational2) other;return this.subtract(that).getNumerator().equals(BigInteger.ZERO);}return false;}@Overridepublic int intValue() {return numerator.intValue() / denominator.intValue(); // 注意：这可能会损失精度}@Overridepublic float floatValue() {return (float)doubleValue();}@Overridepublic double doubleValue() {return numerator.doubleValue() / denominator.doubleValue();}@Overridepublic long longValue() {return numerator.longValue() / denominator.longValue(); // 同样注意精度损失}@Overridepublic int compareTo(Rational2 o) {return this.subtract(o).getNumerator().signum();}public Rational2 simplify() {BigInteger gcd = numerator.gcd(denominator);return new Rational2(numerator.divide(gcd), denominator.divide(gcd));}
}

输出结果：

1/2 + 2/3 + 3/4 + 4/5 + 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 
10/11 + 11/12 + 12/13 + 13/14 + 14/15 + 15/16 + 16/17 + 17/18 + 18/19 + 19/20 + 
20/21 + 21/22 + 22/23 + 23/24 + 24/25 + 25/26 + 26/27 + 27/28 + 28/29 + 29/30 + 
30/31 + 31/32 + 32/33 + 33/34 + 34/35 + 35/36 + 36/37 + 37/38 + 38/39 + 39/40 + 
40/41 + 41/42 + 42/43 + 43/44 + 44/45 + 45/46 + 46/47 + 47/48 + 48/49 + 49/50 + 
50/51 + 51/52 + 52/53 + 53/54 + 54/55 + 55/56 + 56/57 + 57/58 + 58/59 + 59/60 + 
60/61 + 61/62 + 62/63 + 63/64 + 64/65 + 65/66 + 66/67 + 67/68 + 68/69 + 69/70 + 
70/71 + 71/72 + 72/73 + 73/74 + 74/75 + 75/76 + 76/77 + 77/78 + 78/79 + 79/80 + 
80/81 + 81/82 + 82/83 + 83/84 + 84/85 + 85/86 + 86/87 + 87/88 + 88/89 + 89/90 + 
90/91 + 91/92 + 92/93 + 93/94 + 94/95 + 95/96 + 96/97 + 97/98 + 98/99 + 99/100 = 264414864639329557497913717698145082779489/2788815009188499086581352357412492142272

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