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166. 分数到小数

English Version

题目描述

给定两个整数，分别表示分数的分子 numerator 和分母 denominator，以 字符串形式返回小数 。

如果小数部分为循环小数，则将循环的部分括在括号内。

如果存在多个答案，只需返回 任意一个 。

对于所有给定的输入，保证 答案字符串的长度小于 104 。

 

示例 1：

输入：numerator = 1, denominator = 2
输出："0.5"

示例 2：

输入：numerator = 2, denominator = 1
输出："2"

示例 3：

输入：numerator = 4, denominator = 333
输出："0.(012)"

 

提示：

  • -231 <= numerator, denominator <= 231 - 1
  • denominator != 0

解法

在进行除法时使用 HashMap 存储余数及其关联的索引，这样每当出现相同的余数时，我们就知道有一个重复的小数部分。

Python3

class Solution:
    def fractionToDecimal(self, numerator: int, denominator: int) -> str:
        if numerator == 0:
            return '0'
        res = []
        neg = (numerator > 0) ^ (denominator > 0)
        if neg:
            res.append('-')
        num, d = abs(numerator), abs(denominator)
        res.append(str(num // d))
        num %= d
        if num == 0:
            return ''.join(res)
        res.append('.')
        mp = {}
        while num != 0:
            mp[num] = len(res)
            num *= 10
            res.append(str(num // d))
            num %= d
            if num in mp:
                idx = mp[num]
                res.insert(idx, '(')
                res.append(')')
                break
        return ''.join(res)

Java

class Solution {
    public String fractionToDecimal(int numerator, int denominator) {
        if (numerator == 0) {
            return "0";
        }
        StringBuilder sb = new StringBuilder();
        boolean neg = (numerator > 0) ^ (denominator > 0);
        sb.append(neg ? "-" : "");
        long num = Math.abs((long) numerator);
        long d = Math.abs((long) denominator);
        sb.append(num / d);
        num %= d;
        if (num == 0) {
            return sb.toString();
        }
        sb.append(".");
        Map<Long, Integer> mp = new HashMap<>();
        while (num != 0) {
            mp.put(num, sb.length());
            num *= 10;
            sb.append(num / d);
            num %= d;
            if (mp.containsKey(num)) {
                int idx = mp.get(num);
                sb.insert(idx, "(");
                sb.append(")");
                break;
            }
        }
        return sb.toString();
    }
}

C++

using LL = long long;

class Solution {
public:
    string fractionToDecimal(int numerator, int denominator) {
        if (numerator == 0) return "0";
        string res = "";
        bool neg = (numerator > 0) ^ (denominator > 0);
        if (neg) res += "-";
        LL num = abs(numerator);
        LL d = abs(denominator);
        res += to_string(num / d);
        num %= d;
        if (num == 0) return res;
        res += ".";
        unordered_map<LL, int> mp;
        while (num) {
            mp[num] = res.size();
            num *= 10;
            res += to_string(num / d);
            num %= d;
            if (mp.count(num)) {
                int idx = mp[num];
                res.insert(idx, "(");
                res += ")";
                break;
            }
        }
        return res;
    }
};

Go

func fractionToDecimal(numerator int, denominator int) string {
	if numerator == 0 {
		return "0"
	}
	res := []byte{}
	neg := numerator*denominator < 0
	if neg {
		res = append(res, '-')
	}
	num := abs(numerator)
	d := abs(denominator)
	res = append(res, strconv.Itoa(num/d)...)
	num %= d
	if num == 0 {
		return string(res)
	}
	mp := make(map[int]int)
	res = append(res, '.')
	for num != 0 {
		mp[num] = len(res)
		num *= 10
		res = append(res, strconv.Itoa(num/d)...)
		num %= d
		if mp[num] > 0 {
			idx := mp[num]
			res = append(res[:idx], append([]byte{'('}, res[idx:]...)...)
			res = append(res, ')')
			break
		}
	}

	return string(res)
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

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