How many pages in a book?

Description:

Every book has n pages with page numbers 1 to n. The summary is made by adding up the number of digits of all page numbers.

Task: Given the summary, find the number of pages n the book has.

Example

If the input is summary=25, then the output must be n=17: The numbers 1 to 17 have 25 digits in total: 1234567891011121314151617.

Be aware that you'll get enormous books having up to 100.000 pages.

All inputs will be valid.

Here's the opposite kata, which is more complex (Paginating a huge book)

 

 

 

Solution:

1. Get as many numbers as the summary.
2. Convert the numbers into a string.
3. If the length of the string matches the summary, the last number is returned.

 

 

def amount_of_pages(summary):
    a = ''
    for i in range(1, summary+1):
        a += str(i)
        if len(a) == summary:
            return i
            
            
>>> Time: 4235ms

 

 

 

 

Best Practices:

 

def amount_of_pages(summary):
    # 1-9:          9       = 9 * 1 * 10**0
    # 10-99:        180     = 9 * 2 * 10**1
    # 100-999:      2700    = 9 * 3 * 10**2
    # 1000-9999:    36000   = 9 * 4 * 10**3
    # 10000-99999:  450000  = 9 * 5 * 10**4
    res = 0
    for x in range(1, 6):
        y = 9 * x * 10**(x-1)
        if summary <= y:
            return res + summary//x
        res += y//x
        summary -= y
        
        
>>> Time: 476ms