# # 【LeetCode】592. Fraction Addition and Subtraction 解题报告（Python）

## # 题目描述：

Given a string representing an expression of fraction addition and subtraction, you need to return the calculation result in string format. The final result should be irreducible fraction. If your final result is an integer, say 2, you need to change it to the format of fraction that has denominator 1. So in this case, 2 should be converted to 2/1.

Example 1:

``````Input:"-1/2+1/2"
Output: "0/1"
``````

Example 2:

``````Input:"-1/2+1/2+1/3"
Output: "1/3"
``````

Example 3:

``````Input:"1/3-1/2"
Output: "-1/6"
``````

Example 4:

``````Input:"5/3+1/3"
Output: "2/1"
``````

Note:

1. The input string only contains '0' to '9', '/', '+' and '-'. So does the output.
2. Each fraction (input and output) has format ±numerator/denominator. If the first input fraction or the output is positive, then '+' will be omitted.
3. The input only contains valid irreducible fractions, where the numerator and denominator of each fraction will always be in the range [1,10]. If the denominator is 1, it means this fraction is actually an integer in a fraction format defined above.
4. The number of given fractions will be in the range [1,10].
5. The numerator and denominator of the final result are guaranteed to be valid and in the range of 32-bit int.

## # 解题方法

1. 同分母分式相加减，只把分子相加减，分母不变；
2. 异分母分式相加减，先通分变为同分母分式，再按同分母分式相加减的法则运算；
3. 完成分式的加减运算后，若所得分式不是既约分式应约分化为既约分式。

``````class Solution(object):
"""
:type expression: str
:rtype: str
"""
if expression[0] == '-':
expression = '0/1' + expression
expression = expression.replace('-', '+-')
son_moms = []
for fractions in expression.split('+'):
son_moms.append(map(int, fractions.split('/')))
ans = [0, 1]
for son_mom in son_moms:
ans[0] = ans[0] * son_mom[1] + son_mom[0] * ans[1]
ans[1] = ans[1] * son_mom[1]
for div in range(2, abs(min(ans))):
while (ans[0] % div == 0) and (ans[1] % div == 0):
ans[0] /= div
ans[1] /= div
if ans[0] == 0:
return '0/1'
return str(ans[0]) + "/" + str(ans[1])
``````

## # 日期

2018 年 6 月 11 日 ———— 今天学科三在路上跑的飞快～