蓝桥杯：有理数

如果求 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + … + 1/100 = ?

要求绝对精确，不能有误差。

思路：使用double计算会丢失精度，需要自己创建有理数类

public class Rati {
	private BigInteger zi = BigInteger.ZERO;
	private BigInteger mu = BigInteger.ONE;
	
	static BigInteger gcd(BigInteger a, BigInteger b) {
		if(b.equals(b.ZERO)) return a;
		return gcd(b, a.mod(b));
	}
	
	public Rati(long x) {
		this(BigInteger.valueOf(x), BigInteger.ONE);
	}
	
	public Rati(long x, long y) {
		this(BigInteger.valueOf(x), BigInteger.valueOf(y));
	}
	
	public Rati(BigInteger x) {
		this(x, BigInteger.ONE);
	}
	
	public Rati(BigInteger x, BigInteger y) {
		zi = x;
		mu = y;
		BigInteger g = gcd(x, y);
		zi = zi.divide(g);
		mu = mu.divide(g);
	}
	
	public Rati add(Rati ra) {
		return new Rati(zi.multiply(ra.mu).add(mu.multiply(ra.zi)), mu.multiply(ra.mu));
	}
	
	public Rati mul(Rati ra) {
		return new Rati(zi.multiply(ra.zi), mu.multiply(ra.mu));
	}
	
	public String toString() {
		String s = zi.toString();
		if(mu.equals(BigInteger.ONE) == false) s+="/"+mu;
		return s;
	}
	
	public static void main(String[] args) {
		Rati sum = new Rati(0);
		for(int i = 1; i<=100; i++) {
			sum = sum.add(new Rati(1,i));
		}
		System.out.println(sum.toString());
	}
}