Java小例子：求素數<br />素數（質數）指的是不能被分解的數，除了1 和它本身之外就沒有其它數能夠整除。這裡是一個小例子，說明如何求取十萬以內的所有素數。
素數的分佈沒有規律可言，所以要檢驗一個數是不是素數，就必須將它同所有小於它的數作除法。不過有一個簡便的方法，就是不需要檢驗所有小於它的數，而只要檢驗所有小於它的素數。如果所有小於它的素數都不能將其整除，那麼它就是素數。
public class Primes { public static void main(String[] args) { // 求素數List<Integer> primes = getPrimes(100000); // 輸出結果for (int i = 0; i < primes.size(); i++ ) { Integer prime = primes.get(i); System.out.printf("%8d", prime); if (i % 10 == 9) { System.out.println(); } } } /** * 求n 以內的所有素數* * @param n 範圍* * @return n 以內的所有素數*/ private static List<Integer> getPrimes(int n) { List<Integer> result = new ArrayList<Integer>(); result.add(2); for (int i = 3; i <= n; i += 2) { if (!divisible(i, result)) { result.add(i); } } return result; } / ** * 判斷n 是否能被整除* * @param n 要判斷的數字* @param primes 包含素數的列表* * @return 如果n 能被primes 中任何一個整除，則返回true。 */ private static boolean divisible(int n, List<Integer> primes) { for (Integer prime : primes) { if (n % prime == 0) { return true; } } return false; } }
Java小例子：模擬分數的類Fraction
這裡是一個模擬分數運算的例子：Fraction 類。分數運算完後要用最大公約數除分子分母。所以這裡也有個用輾轉相除法求最大公約數的例子。另外在構造Fraction 對象時如果分母為零將會拋出異常，這也是必要的檢查。
public class FractionTest { public static void main(String[] args) { Fraction a = new Fraction(7, 32); Fraction b = new Fraction(13, 32); System.out.println(a + " + " + b + " = " + a.add(b) + "(" + a.add(b).doubleValue() + ")"); System.out.println(a + " - " + b + " = " + a.minus(b) + "(" + a.minus(b).doubleValue() + ")"); System.out.println(a + " * " + b + " = " + a.multiply(b ) + "(" + a.multiply(b).doubleValue() + ")"); System.out.println(a + " / " + b + " = " + a.devide(b) + "(" + a.devide(b).doubleValue() + ")"); } } // 分數class Fraction { private int numerator; // 分子private int denominator; // 分母Fraction(int numerator, int denominator) { if ( denominator == 0) { throw new IllegalArgumentException("分母不能為0"); } this.numerator = numerator; this.denominator = denominator; shrink(); } Fraction() { this(0, 1); } public int getNumerator() { return numerator; } public void setNumerator(int numerator) { this.numerator = numerator; } public int getDenominator() { return denominator; } public void setDenominator(int denominator) { this.denominator = denominator; } //分子分母同除以最大公約數private Fraction shrink() { int maxCommonDivisor = getMaxCommonDivisor(this.denominator, this.numerator); this.numerator /= maxCommonDivisor; this.denominator /= maxCommonDivisor; return this; } // 輾轉相除法求最大公約數private int getMaxCommonDivisor(int a, int b) { int mod = a % b; if (mod == 0) { return b; } else { return getMaxCommonDivisor(b, mod); } } // 分數加法public Fraction add(Fraction that) { return new Fraction(this.numerator * that.denominator + this.denominator * that.numerator, this.denominator * that.denominator); } // 分數減法public Fraction minus(Fraction that) { return new Fraction(this.numerator * that.denominator - this.denominator * that.numerator, this.denominator * that.denominator); } // 分數乘法public Fraction multiply(Fraction that) { return new Fraction(this.numerator * that.numerator, this.denominator * that.denominator); } // 分數除法public Fraction devide(Fraction that) { return new Fraction(this.numerator * that.denominator, this.denominator * that.numerator); } public double doubleValue() { return (double) numerator / denominator; } @Override public String toString() { return String.format("{%d/%d}", this.numerator, this.denominator); } }
運行輸出：
{7/32} + {13/32} = {5/8}(0.625){7/32} - {13/32} = {-3/16}(-0.1875){7/32} * {13 /32} = {91/1024}(0.0888671875){7/32} / {13/32} = {7/13}(0.5384615384615384)