算法精粹(algorithm-essentials)

感谢soulmachine@github提供内容
## Fraction to Recurring Decimal

### 描述

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)".


### 分析

这题的难点是如何找到无限循环的那一段。仔细回想一下人脑进行除法的过程,会发现,当一个余数第二次重复出现时,就说明小数点后开始无限循环了。


### 代码

{% if book.java %}
```java
// Fraction to Recurring Decimal
// Time Complexity: ?, Space Complexity: ?
public class Solution {
public String fractionToDecimal(int numerator, int denominator) {
if (numerator == 0) return "0";

final StringBuilder result = new StringBuilder();
// determine the sign
if ((numerator < 0) ^ (denominator < 0)) result.append('-');

// Integer.MIN_VALUE will overflow, so use long
// Math.abs(MIN_VALUE) will overflow
long n = numerator;
n = Math.abs(n);
long d = denominator;
d = Math.abs(d);

// append integral part
result.append(String.valueOf(n / d));
if (n % d == 0) return result.toString();
result.append('.');

final Map map = new HashMap<>();
// simulate the division process
for (long r = n % d; r != 0; r %= d) {
// find a existed remainder, so we reach
// the end of the repeating part
if (map.containsKey(r)) {
result.insert(map.get(r), "(");
result.append(')');
break;
}

map.put(r, result.length());

r *= 10;
result.append(Character.forDigit((int)(r/d), 10));
}

return result.toString();
}
}
```
{% endif%}