xtuoj Fraction
时间: 2025-01-09 15:39:09 AIGC 浏览: 62
针对 XTUOJ 平台上的 Fraction 问题,虽然提供的参考资料并未直接涉及此具体编程竞赛题目[^1],可以基于一般性的分数处理方法提供指导。
对于解决此类问题的关键在于如何高效地表示和操作分数。通常情况下,在程序设计竞赛中遇到的分数运算主要包括但不限于:
- 分数相加减
- 分数乘除法
- 化简分数
### 实现分数类
创建一个 `Fraction` 类来封装这些基本功能是一个不错的选择。下面展示了一个简单的 Python 版本实现方式:
```python
from math import gcd
class Fraction:
def __init__(self, numerator=0, denominator=1):
common_divisor = gcd(numerator, denominator)
self.numerator = int(numerator / common_divisor)
self.denominator = int(denominator / common_divisor)
def add(self, other_fraction):
new_numerator = self.numerator * other_fraction.denominator + \
self.denominator * other_fraction.numerator
new_denominator = self.denominator * other_fraction.denominator
return Fraction(new_numerator, new_denominator)
def subtract(self, other_fraction):
new_numerator = self.numerator * other_fraction.denominator - \
self.denominator * other_fraction.numerator
new_denominator = self.denominator * other_fraction.denominator
return Fraction(new_numerator, new_denominator)
def multiply(self, other_fraction):
new_numerator = self.numerator * other_fraction.numerator
new_denominator = self.denominator * other_fraction.denominator
return Fraction(new_numerator, new_denominator)
def divide(self, other_fraction):
inverted_other = Fraction(other_fraction.denominator, other_fraction.numerator)
return self.multiply(inverted_other)
def simplify(self):
divisor = gcd(self.numerator, self.denominator)
simplified_num = int(self.numerator / divisor)
simplified_deno = int(self.denominator / divisor)
return f"{simplified_num}/{simplified_deno}"
```
上述代码定义了用于执行常见算术运算的方法,并通过最大公约数(`gcd`)函数简化最终的结果。这有助于保持计算过程中的准确性并减少误差累积的可能性。
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