Given an integer n, find the number of digits that appear in its factorial, where factorial is defined as, factorial(n) = 1*2*3*4……..*n and factorial(0) = 1
Input : n = 1 Output : 1 1! = 1 , hence number of digits is 1 Input : 5 Output : 3 5! = 120, i.e., 3 digits Input : 10 Output : 7 10! = 3628800, i.e., 7 digits
A naive solution would be to calculate the n! first and then calculate the number of digits present in it. However as the value for n! can be very large, it would become cumbersome to store them in a variable (Unless you’re working in python!) .
A better solution would be to use the useful property of logarithms to calculate the required answer.
We know, log(a*b) = log(a) + log(b) Therefore log( n! ) = log(1*2*3....... * n) = log(1) + log(2) + ........ +log(n) Now, observe that the floor value of log base 10 increased by 1, of any number, gives the number of digits present in that number. Hence, output would be : floor(log(n!)) + 1.
Below is a the implementation of the same.
1 3 7 199
In the next set, we’d see how to further optimize our approach and reduce the time complexity for the same program.
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- Count digits in a factorial | Set 2
- Number of digits in N factorial to the power N
- Smallest number with at least n digits in factorial
- Find sum of digits in factorial of a number
- Count of numbers between range having only non-zero digits whose sum of digits is N and number is divisible by M
- Count Divisors of Factorial
- Count numbers in given range such that sum of even digits is greater than sum of odd digits
- Count factorial numbers in a given range
- Count trailing zeroes in factorial of a number
- Find the last digit when factorial of A divides factorial of B
- Count even and odd digits in an Integer
- Count numbers with same first and last digits
- Count total number of digits from 1 to n
- Count digits in given number N which divide N
- Count of integers of length N and value less than K such that they contain digits only from the given set