166. Fraction to Recurring Decimal

Given two integers representing the numerator and denominator of a fraction, return the fraction in string format.

If the fractional part is repeating, enclose the repeating part in parentheses.

For example,

• Given numerator = 1, denominator = 2, return "0.5".
• Given numerator = 2, denominator = 1, return "2".
• Given numerator = 2, denominator = 3, return "0.(6)".

Hint:

1. No scary math, just apply elementary math knowledge. Still remember how to perform a long division?
2. Try a long division on 4/9, the repeating part is obvious. Now try 4/333. Do you see a pattern?
3. Be wary of edge cases! List out as many test cases as you can think of and test your code thoroughly.

public class Solution {    public String fractionToDecimal(int numerator, int denominator) {        //Test Cases: 1,6; -50,8; -1,-2147483648;         // convert int to long, in the case of -2147483648,-1, A will leak        long numeratorLong = Long.valueOf(numerator);         long denominatorLong = Long.valueOf(denominator);        long A = Math.abs(numeratorLong/denominatorLong);        //numeratorLong/denominatorLong could be 0, but the sign can be '-', for example: -1,6        String sign = numeratorLong*denominatorLong<0?"-":"";        // to calculate tail (the part after '.'), both numerator and denominator need to be positive.        String tail = helper(Math.abs(numeratorLong%denominatorLong),Math.abs(denominatorLong));        // in the case of 10,5, it should not return 2. but 2.        return tail.equals("")? sign+Long.toString(A) : sign+Long.toString(A)+"."+tail;    }    String helper(long numerator,long denominator){        StringBuilder result= new StringBuilder();        //repeat part can be longer than 1, for example 1/7=0.(428571), so need a ArrayList to save all previous numerators        ArrayList<Long> newNumerators = new ArrayList<Long>();        while(numerator!=0){            //in case of 7/180, result is 0, but numerator is 70 not 0, so while keep going;             newNumerators.add(numerator);            result.append(Long.toString(numerator*10/denominator));            numerator = (numerator*10)%denominator;            for(int i=0; i<newNumerators.size(); i++){                //when find repeat numerator, means result also will repeat, no need to calculate, just add () and return                if(numerator==newNumerators.get(i)){                    result.insert(i,"(");                    result.append(")");                    return result.toString();                }            }        }        return result.toString();    }}