converting Integer to String process ("under the hood")

Question

I'm new to Python and face a real problem in understanding the way how str(123) or int('123') functions work.

I tried to check builtins.py but there's kinda a mess of functions and methods that I can't understand. Is it all about binary conversion?

As a wrong example:

1. str(123) => bin(123) -> 1111011 -> 1100101 + 1111011 + 1010101 -> compare with some-table -> '123'

Are there any simple explanations or articles that can help? How do str(), int() do their "conversion magic"? Would be perfect if you answer me in Python-like style but it's not nessescary...

Articles in C++ that are beyond my experience:

1. Easiest way to convert int to string in C++

2. http://we.easyelectronics.ru/Soft/preobrazuem-v-stroku-chast-1-celye-chisla.html

Article that is trying to explain this process by dividing number number / 10 and number % 10:

1. How are integers converted to strings under the hood?

Answer 1

String to integer

Let's start with converting a string to an int, as I think it's a bit simpler to think through. I'll make a few assumptions to start:

1. our int method will only deal with int inputs, no floats, complex numbers, etc. for now.
2. we will only deal with positive numbers for now as well.
3. I won't be dealing with intentionally wrong inputs, like int("Wassup")

The implementation will go through the string input from right to left, and build up the integer number by number.

def custom_int(input):
    # Your intuition is right that we will need some kind of look up! this matches a character to a number
    s_to_i_dict= {'0': 0, '1': 1, '2': 2, '3': 3, '4': 4, '5': 5, '6': 6, '7': 7, '8': 8, '9': 9}
    
    # imagine our input is the string "123", we want to build up the number 123 
    # one digit at a time. If you break it down, 123 is equal to 100 + 20 + 3
    # Thinking it through further, that's the same as 1*100 + 2*10 + 3*1

    # So for each digit going right to left, we'll multiply it by some multiplier
    # add it to our result, theb change that multiplier to handle the next digit.
    
    multiplier = 1
    output = 0

    # This is a little shortcut to get you looping through a list or a string from the last element to the first:
    for digit in input[::-1]:
        # digit is a character, we find the corresponding number, multiply it by the multiplier, then add it to the old version of output
        output = output + ( s_to_i_dict[digit] * multiplier)

        # we are done with this digit, so the next multiplier should be 10 times the last (going from digits to tens to hundreds etc.)
        multiplier = multiplier * 10
    return output

Running this you'd get:

s_to_i("123")

123

type(s_to_i("123"))

<class 'int'>

For the "123" input, our loop will run 3 times. the first time around output will just be the rightmost digit 3, the next time around, we will add 2*10 to output, giving us 23.

The final time through the loop we will get 23 + 1*100, or 123.

Integer to string

We can apply the exact same pattern to the int to string conversion. The same assumptions apply as I won't cover all edge cases, but fundamentally we will do the same thing: go through the numbers from right to left, then build up a string representation of the number.

Now we can't loop over numbers as easily as we loop over strings, but with some good use of mod and division we can get a similar pattern. say n = 123, how do we get just the rightmost digit from the number? Well the rightmost digit is the remainder of dividing n by 10, or in code rightmost_digit = n % 10.

Once we have the rightmost digit, the next step is to try to extract the second rightmost digit, 2 in this case. There are a few ways to do that but my favorite is to recognize that we have already grabbed the rightmost digit, so we don't need it anymore

We can update our number n as follows: n = n // 10 which will give n the value of 12 instead of 123. This is called integer division, and is basically primary school division before you discovered floats :P

How does this help? well notice that 2 is the rightmost digit of 12 and we already know how to grab that! Let's put this all together in a function.

def i_to_s(input):
  # Notice that this is the opposite dictionary than before. ints are the key, and they give us the character we need.
  i_to_s_dict={0: '0', 1: '1', 2: '2', 3: '3', 4: '4', 5: '5', 6: '6', 7: '7', 8: '8', 9: '9'}
  
  # This time we want our output to be a string so we initialize an empty string
  output = ""
  
  # There are more precise ways to set up this loop, as this one creates an edge case I'll leave up to you to find, but works with _almost_ every integer :P
  while(input != 0):

    rightmost_digit = input % 10
    
    # We concatenate the new character we found with the output we've accumulated so far
    output = i_to_s(rightmost_digit) + output
    
    # Change the initial number for the next iteration
    input = input // 10
  
  return output

i_to_s(123)

'123'

type(i_to_s(123))

<class 'str'>