按不同顺序求值时表达式的差异

Question

我们都知道数学函数(PEMDAS)的标准操作顺序，但是如果我们用从左到右的表达式来计算呢？

挑战

通过标准输入或命令行args给出一个字符串，找出该表达式的传统计算(PEMDAS)和顺序(从左到右)计算之间的区别。

详细信息

• 您将获得如下格式的字符串："1 +2*3^2- 11 /2+ 16“
• 为了简化事情，将有：
  • 每个数和每个运算符之间的空格
  • 无前导或尾随舱位
  • 没有十进制数或负数(只有非负整数)
  • 除+(加号)、-(减号)、*(乘)、/(除)、^(指数)外没有任何运算符
  • 没有父母需要担心
  • 如果更容易处理，您可以删除空格，但不允许对输入格式进行其他修改。

• 必须提供字符串的两个计算值之间差额的绝对值。
• 您的除法可以是浮点数除法，也可以是整数除法，两者都将被接受。
• 您的程序不能使用任何类型的表达式计算库。为了澄清-任何一种内置的eval函数，在这些函数中，您的语言计算同一语言的有效代码的字符串是可以接受的。
• 最好解释您的代码。
• 按字节数计算最短代码获胜
• 获胜者将於星期六(2014年7月19日)获选。

示例：

A: 1+2*3^2-11/2+ 16 (使用浮点除法)

• 按传统操作顺序:1+2*3^2- 11 /2+ 16 ->1+2*9- 11 /2+ 16 ->1+ 18 - 5.5 + 16 -> 29.5
• 有序遍历产率:1+2*3^2-11/2+ 16 ->3^2^2-11/2+ 16 ->9^2-11/2+ 16 ->81-11/2+ 16 -> 70 /2+ 16 -> 35 + 16 -> 51
• 结果差异:51-29.5= 21.5

B: 7-1*3^2+ 41 /3+2*9*2(使用整数除法)

• 按传统操作顺序:7-1*3^2+ 41 /3+2*9*2->7-1*9+ 41 /3+2*9*2->7-9+ 13 + 18 *2->7-9+ 13 + 36 -> 47
• 有序遍历产率:7-1*3^2+ 41 /3+2*9*2->6*3^2+ 41 /3+2*9*2-> 18 ^2+ 41 /3+2*9*2-> 324 + 41 /3+2*9*2-> 365 /3+2*9*2-> 121 +2*9*2->121+2*9*2-> 123 *9*2-> 1107 *2-> 2214
• 结果差异: 2214 - 47 = 2167

Answer 1

Python208

d=x=input();z=2;u='('*(((len(x)-len(x.replace(' ','')))/2)+1);d=x=d.replace(r'^','**');x=x.split();p=u+''.join(")".join(x[i:i+z]) for i in range(0,len(x),z))+")";m=eval(p)-eval(d);m=m*-1 if 0>m else m;print m;

卡尔文的霍布斯评论：

import re;e=input().replace('^','**');print abs(eval(e)-eval(e.count(' ')/2*'('+re.sub('(\d) ',r'\1)',e)))

解释：

# variable d  =  x, and x  =  user input

d = x = input() 

# variable z = 2

z = 2

# I take the length of the string 'x' (aka the equation we're solving) with 
# *all* whitespaces removed (it's the 'len(x.replace(' ', '')...' part) and 
# subtract that from 'len(x)' which is the vanilla length of our equation
# I divide the total by two and add one for reasons I'll explain in a minute
# the '(' * part means to make a string with as many '(' as I get from multiplying
# so '(' * 5 = '(((((', '(' * 3 = '((('

u = '(' * (((len(x) - len(x.replace(' ', ''))) / 2) + 1)

# Here I replace the caret with **, because in Python ^ == **
# I also split the string by whitespaces, but only for x;

d = x = d.replace(r'^','**'); x = x.split();

# I set the variable p = to the result of joining the list (aka array) that
# I just made with the .split() in the above section first with a ')' on every
# second character (e.g. [1,2,3,4,5,6] would be 1,2),3,4),... etc. I do it like
# this because in our math equation we'll (hopefully) follow the pattern of
# num op num op num op... etc. I insert parenthases because I'm using PEMDAS
# to my advantage by grouping each set of numbers in the order I want them
# to be completed. The initial ''.join simply rejoins all elements into a
# complete string (basically removes the commas that are left over from
# converting a list -> string). I add a '(' to the end because every 2nd
# character would skip the final one

p = u + ''.join(")".join(x[i:i + z]) for i in range(0, len(x), z)) + ")"

# I eval() both p and d. eval() will run arbitrary code, so you can pass it a
# string and it will act as if the string is code, so while print '1+1' would
# usually result in TypeError (or Value? I forget), print eval('1+1') would
# print '2', I have to do them separately because eval() thinks I wanna
# subtract two string for whatever reason

m = eval(p) - eval(d)

# Here I make use of Python's ternary operators by saying this:
# if 0 > m:
#   m = m * -1
# else:
#   m
# which means that if m is negative, multiply it by -1 to make it
# a positive number so we can get the absolute value. If it's not negative
# then we can just have m and not do anything with it

m = m * -1 if 0 > m else m

# Print m :)

print m