分式化简。设计算法将一个给定的真分数化简为最简分数形式,例如将6/8化简为3/4,给出其伪代码和代码。
时间: 2024-09-28 20:14:22 浏览: 54
《数据结构与算法设计课程设计》(12级6班)实验报告册(2014-9-2)[1].pdf
分式化简通常涉及找到分子和分母的最大公约数(GCD),然后用这个数同时除以分子和分母。以下是简单的算法描述:
**伪代码:**
```
function simplify_fraction(numerator, denominator):
gcd = find_gcd(numerator, denominator)
simplified_numerator = numerator // gcd
simplified_denominator = denominator // gcd
if simplified_numerator == simplified_denominator:
return simplified_numerator, simplified_denominator # 如果结果为整数,则无需简化
else:
return simplified_numerator, simplified_denominator
function find_gcd(a, b):
while b != 0:
a, b = b, a % b
return a
```
**Python 代码实现:**
```python
def gcd(a, b):
while b:
a, b = b, a % b
return a
def simplify_fraction(numerator, denominator):
gcd_value = gcd(numerator, denominator)
simplified_numerator = numerator // gcd_value
simplified_denominator = denominator // gcd_value
return simplified_numerator, simplified_denominator
# 示例
original_fraction = 6, 8
simplified_fraction = simplify_fraction(*original_fraction)
print(f"原始分数 {original_fraction[0]}/{original_fraction[1]} 化简后为 {simplified_fraction[0]}/{simplified_fraction[1]}")
```
在这个例子中,`find_gcd`函数计算两个数的最大公约数,而`simplify_fraction`函数则根据最大公约数对原分数进行化简。
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