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

  1. // Fraction to Recurring Decimal
  2. // Time Complexity: ?, Space Complexity: ?
  3. public class Solution {
  4.     public String fractionToDecimal(int numerator, int denominator) {
  5.         if (numerator == 0) return "0";
  7.         final StringBuilder result = new StringBuilder();
  8.         // determine the sign
  9.         if ((numerator < 0) ^ (denominator < 0)) result.append('-');
  11.         // Integer.MIN_VALUE will overflow, so use long
  12.         // Math.abs(MIN_VALUE) will overflow
  13.         long n = numerator;
  14.         n = Math.abs(n);
  15.         long d = denominator;
  16.         d = Math.abs(d);
  18.         // append integral part
  19.         result.append(String.valueOf(n / d));
  20.         if (n % d == 0) return result.toString();
  21.         result.append('.');
  23.         final Map<Long, Integer> map = new HashMap<>();
  24.         // simulate the division process
  25.         for (long r = n % d; r != 0; r %= d) {
  26.             // find a existed remainder, so we reach
  27.             // the end of the repeating part
  28.             if (map.containsKey(r)) {
  29.                 result.insert(map.get(r), "(");
  30.                 result.append(')');
  31.                 break;
  32.             }
  34.             map.put(r, result.length());
  36.             r *= 10;
  37.             result.append(Character.forDigit((int)(r/d), 10));
  38.         }
  40.         return result.toString();
  41.     }
  42. }

原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/java/number-theory/fraction-to-recurring-decimal.html