# Fraction to Recuring Decimal

String representation of a decimal comes from the quotient of to integer is either of finite length or has a recuring sequence in its fractional part. The ends of the recuring part is at the position we get a remain value twice and the begin of recuring starts at the position where the same remain first occurs. So we just preserve remain values we meet during division along with their position and every time we get a remain, we check if it has appeard. We will also end the loop when we get a remain of 0.

Although the basic idea to solve this problem is simple, we have a lot of things to pay attention on:

1. We uses numerator ^ donominator to decide if the result is negative. Note that if numerator = 0 and denominator < 0, the expression returns a negative value, but the result of division is neither positive nor negative --- it is zero. We should not add a negative sign to the string in this case.
2. If we divide Integer.MIN_VALUE by -1, we will get an integer that exceed the range of int. So at first we need to cast values to to long.
3. We use a HashSet<Long, Integer> to save the mapping from remain to the position it first appears. But set.get(i) returns an Integer object so that if we are using StringBuilder's insert function to insert a char, there will be an ambiguous error. We can use either sbd.insert((int)set.get(remain), '(') or sbd.insert(set.get(remain), "(")).
import java.util.*;

public class FractionToRecuringDecimal {
public String fractionToDecimal(int numerator, int denominator) {
StringBuilder sbd = new StringBuilder();

if ((numerator ^ denominator) < 0) sbd.append('-');

long n = numerator;
long d = denominator;

n = Math.abs(n);
d = Math.abs(d);

long res = n / d;
long remain = n % d;

sbd.append(res);
if (remain == 0) return sbd.toString();

sbd.append('.');
HashMap<Long, Integer> remainMap = new HashMap<Long, Integer>();
remainMap.put(remain, sbd.length());

do {
remain *= 10;
res = remain / d;
remain %= d;

sbd.append(res);

if (remain == 0) break;
if (remainMap.containsKey(remain)) {
sbd.insert((int)remainMap.get(remain), '(');
sbd.append(')');
break;
}

remainMap.put(remain, sbd.length());

} while (true);

return sbd.toString();
}
}