CODEWITHSUNDEEP
python-3.x
user10301542
user10301542

Reputation:

Understanding factorials and alternate code

Python newbie here. I am trying to understand the following code to calculate Euler's number:

import math

num(i=10):
   sum([1 / math.factorial(z) for z in range(0, i)])

I would really like to get a better grasp on how equations are done in code. I have read many tutorials, but I don't understand them well enough to apply a concept to unique situations like in the above code. Can someone just explain to me what is happening in this code step by step? Additionally, I have not been able to figure out how to do factorials, and it would be very helpful to me if someone would explain how input a factorial in a function (the hard way) without imports.

Upvotes: 1

Views: 57

Answers (1)

Onyambu
Onyambu

Reputation: 79208

for you to understand the above code, you first must understand the language itself. e=1/0!+1/1!+1/2!+1/3!+1/4!+..., so you need to do:

total=0
for i in range(100):
  total +=1/math.factorial(i)

print(total)
2.7182818284590455

in case you understand what a for loop is and how it runs. This is much faster compared to what you wrote above.

Now in python there is something called list comprehension. That is, creating a list from a for-loop without necessarily pre-defining the list. so you can do `[i for i in range(10)] which will create a list of 10 elements. You can therefore manipulate each element as you create the list ie

 [i**2 for i in range(10)]

 [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

so in your case you are doing [1/math.factorial(i) for i in range(100)]. This creates the list [1.0, 1.0, 0.5, 0.16666666666666666, 0.041666666666666664,...] which you then add the list by calling sum on this list. ie sum([1/math.factorial(i) for i in range(100)])

Defining your own factorial

factorial is a function that multiplies all numbers from 1 to the specified value. with factorial(0) set at 1

factorial(3)= 1*2*3.

thus you can define it as:

def factorial(x):
    if x == 0: return 1
    val = 1
    for i in range(1,x+1):
        val *=i
    return val


factorial(3)
Out[40]: 6

factorial(4)
Out[41]: 24

You can also use recursiveness to define factorial:

def factorial(x):
    if x==0: return 1
    else: return x * factorial(x-1)

Upvotes: 1

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