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Rational.java Rational.java Below is the syntax highlighted version of Rational.java from §9.2 Floating Point. /****************************************************************************** * Compilation: javac Rational.java * Execution: java Rational * * Immutable ADT for Rational numbers. * * Invariants * ----------- * - gcd(num, den) = 1, i.e, the rational number is in reduced form * - den >= 1, the denominator is always a positive integer * - 0/1 is the unique representation of 0 * * We employ some tricks to stave of overflow, but if you * need arbitrary precision rationals, use BigRational.java. * ******************************************************************************/ public class Rational implements Comparable { private static Rational zero = new Rational(0, 1); private int num; // the numerator private int den; // the denominator // create and initialize a new Rational object public Rational(int numerator, int denominator) { if (denominator == 0) { throw new ArithmeticException("denominator is zero"); } // reduce fraction int g = gcd(numerator, denominator); num = numerator / g; den = denominator / g; // needed only for negative numbers if (den < 0) { den = -den; num = -num; } } // return the numerator and denominator of (this) public int numerator() { return num; } public int denominator() { return den; } // return double precision representation of (this) public double toDouble() { return (double) num / den; } // return string representation of (this) public String toString() { if (den == 1) return num + ""; else return num + "/" + den; } // return { -1, 0, +1 } if a < b, a = b, or a > b public int compareTo(Rational b) { Rational a = this; int lhs = a.num * b.den; int rhs = a.den * b.num; if (lhs < rhs) return -1; if (lhs > rhs) return +1; return 0; } // is this Rational object equal to y? public boolean equals(Object y) { if (y == null) return false; if (y.getClass() != this.getClass()) return false; Rational b = (Rational) y; return compareTo(b) == 0; } // hashCode consistent with equals() and compareTo() // (better to hash the numerator and denominator and combine) public int hashCode() { return this.toString().hashCode(); } // create and return a new rational (r.num + s.num) / (r.den + s.den) public static Rational mediant(Rational r, Rational s) { return new Rational(r.num + s.num, r.den + s.den); } // return gcd(|m|, |n|) private static int gcd(int m, int n) { if (m < 0) m = -m; if (n < 0) n = -n; if (0 == n) return m; else return gcd(n, m % n); } // return lcm(|m|, |n|) private static int lcm(int m, int n) { if (m < 0) m = -m; if (n < 0) n = -n; return m * (n / gcd(m, n)); // parentheses important to avoid overflow } // return a * b, staving off overflow as much as possible by cross-cancellation public Rational times(Rational b) { Rational a = this; // reduce p1/q2 and p2/q1, then multiply, where a = p1/q1 and b = p2/q2 Rational c = new Rational(a.num, b.den); Rational d = new Rational(b.num, a.den); return new Rational(c.num * d.num, c.den * d.den); } // return a + b, staving off overflow public Rational plus(Rational b) { Rational a = this; // special cases if (a.compareTo(zero) == 0) return b; if (b.compareTo(zero) == 0) return a; // Find gcd of numerators and denominators int f = gcd(a.num, b.num); int g = gcd(a.den, b.den); // add cross-product terms for numerator Rational s = new Rational((a.num / f) * (b.den / g) + (b.num / f) * (a.den / g), lcm(a.den, b.den)); // multiply back in s.num *= f; return s; } // return -a public Rational negate() { return new Rational(-num, den); } // return |a| public Rational abs() { if (num >= 0) return this; else return negate(); } // return a - b public Rational minus(Rational b) { Rational a = this; return a.plus(b.negate()); } public Rational reciprocal() { return new Rational(den, num); } // return a / b public Rational divides(Rational b) { Rational a = this; return a.times(b.reciprocal()); } // test client public static void main(String[] args) { Rational x, y, z; // 1/2 + 1/3 = 5/6 x = new Rational(1, 2); y = new Rational(1, 3); z = x.plus(y); StdOut.println(z); // 8/9 + 1/9 = 1 x = new Rational(8, 9); y = new Rational(1, 9); z = x.plus(y); StdOut.println(z); // 1/200000000 + 1/300000000 = 1/120000000 x = new Rational(1, 200000000); y = new Rational(1, 300000000); z = x.plus(y); StdOut.println(z); // 1073741789/20 + 1073741789/30 = 1073741789/12 x = new Rational(1073741789, 20); y = new Rational(1073741789, 30); z = x.plus(y); StdOut.println(z); // 4/17 * 17/4 = 1 x = new Rational(4, 17); y = new Rational(17, 4); z = x.times(y); StdOut.println(z); // 3037141/3247033 * 3037547/3246599 = 841/961 x = new Rational(3037141, 3247033); y = new Rational(3037547, 3246599); z = x.times(y); StdOut.println(z); // 1/6 - -4/-8 = -1/3 x = new Rational( 1, 6); y = new Rational(-4, -8); z = x.minus(y); StdOut.println(z); } } Copyright © 2000–2017, Robert Sedgewick and Kevin Wayne. Last updated: Fri Oct 20 14:12:12 EDT 2017.