Java小例子：求素数
素数(质数)指的是不能被分解的数，除了 1 和它本身之外就没有其它数能够整除。这里是一个小例子，说明如何求取十万以内的所有素数。
素数的分布没有规律可言，所以要检验一个数是不是素数，就必须将它同所有小于它的数作除法。不过有一个简便的方法，就是不需要检验所有小于它的数，而只要检验所有小于它的素数。如果所有小于它的素数都不能将其整除，那么它就是素数。
public class Primes {
public static void main(String[] args) {
// 求素数
List primes = getPrimes(100000);
// 输出结果
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：模拟分数的类 Fraction
这里是一个模拟分数运算的例子：Fraction 类。分数运算完后要用最大公约数除分子分母。所以这里也有个用辗转相除法求最大公约数的例子。另外在构造 Fraction 对象时如果分母为零将会抛出异常，这也是必要的检查。
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() + ")");
}
}
// 分数
class Fraction {
private int numerator; // 分子
private int denominator; // 分母
Fraction(int numerator, int denominator) {
if (denominator == 0) {
throw new IllegalArgumentException("分母不能为 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约数
private Fraction shrink() {
int maxCommonDivisor = getMaxCommonDivisor(this.denominator, this.numerator);
this.numerator /= maxCommonDivisor;
this.denominator /= maxCommonDivisor;
return this;
}
// 辗转相除法求最大公约数
private int getMaxCommonDivisor(int a, int b) {
int mod = a % b;
if (mod == 0) {
return b;
} else {
return getMaxCommonDivisor(b, mod);
}
}
// 分数加法
public Fraction add(Fraction that) {
return new Fraction(this.numerator * that.denominator + this.denominator * that.numerator,
this.denominator * that.denominator);
}
// 分数减法
public Fraction minus(Fraction that) {
return new Fraction(this.numerator * that.denominator - this.denominator * that.numerator,
this.denominator * that.denominator);
}
// 分数乘法
public Fraction multiply(Fraction that) {
return new Fraction(this.numerator * that.numerator,
this.denominator * that.denominator);
}
// 分数除法
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);
}
}
运行输出：
{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)