166. Fraction to Recurring Decimal (M)

Fraction to Recurring Decimal (M)

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.

Example 1:

Input: numerator = 1, denominator = 2
Output: "0.5"

Example 2:

Input: numerator = 2, denominator = 1
Output: "2"

Example 3:

Input: numerator = 2, denominator = 3
Output: "0.(6)"

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题意

计算一个分数表示的有理数的小数形式，若为无限循环小数，则将循环部分用括号标记。

思路

直接按照小学除法步骤进行模拟，判断出现循环的依据是计算过程中有余数出现了两次，利用Hash进行标记。

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代码实现

class Solution {
    public String fractionToDecimal(int numerator, int denominator) {
        Map<Long, Integer> map = new HashMap<>();	// key为余数值，value为对应的小数位
        StringBuilder sb = new StringBuilder();
        
        // 先将分子分母全部转化为正数，并记录符号信息
        // 因为最小负int取绝对值后会溢出，所以全用long来计算
        boolean negative = numerator < 0 && denominator > 0 || numerator > 0 && denominator < 0;
        long dividend = Math.abs((long) numerator), divisor = Math.abs((long) denominator);
        long remainder = dividend % divisor, quotient = dividend / divisor;

        sb.append(quotient);			// 将整数部分存入
        // 仍有余数，说明存在小数部分
        if (remainder != 0) {
            sb.append(".");
            // 余数最终为0，说明是有限小数，不为0则需要找到无限循环小数的循环部分
            while (remainder != 0) {
                if (!map.containsKey(remainder)) {
                    map.put(remainder, sb.length());
                    quotient = remainder * 10 / divisor;
                    remainder = remainder * 10 % divisor;
                    sb.append(quotient);
                } else {
                    sb.insert(map.get(remainder), "(");
                    sb.append(')');
                    break;
                }
            }
        }
        
        return (negative ? "-" : "") + sb.toString();
    }
}