Java小例子：求素數
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内的所有素數。
素數的分布沒有規律可言，是以要檢驗一個數是不是素數，就必須将它同所有小于它的數作除法。不過有一個簡便的方法，就是不需要檢驗所有小于它的數，而隻要檢驗所有小于它的素數。如果所有小于它的素數都不能将其整除，那麼它就是素數。
public class Primes {
public static void main(String[] args) {
// 求素數
List 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();
}
}
}
private static List getPrimes(int n) {
List result = new ArrayList();
result.add(2);
for (int i = 3; i <= n; i += 2) {
if (!divisible(i, result)) {
result.add(i);
}
}
return result;
}
private static boolean divisible(int n, List primes) {
for (Integer prime : primes) {
if (n % prime == 0) {
return true;
}
}
return false;
}
}
Java小例子：模拟分數的類 Fraction
這裡是一個模拟分數運算的例子：Fraction 類。分數運算完後要用最大公約數除分子分母。是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将會抛出異常，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);
}
}
運作輸出：
{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)