Hi,
How can I find the sum of digits in a factorial of a number N, where N can be in range [1, 2000]? Can it be done without resorting to BigNum libraries?
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Think of logarithms.
Can you please elaborate. I am looking for a Log(N) complexity. The algorithm given below by sbakic uses string multiplication, which won't be Log(N).
-deleted-
Why did you delete your answer? I think it can actually work: if we know the number D of digits of the factorial F = N! and its log L = log(F), we can do some binary search in the factorial digits since log(x) is unique. For example, to find the most significant digit of the factorial we will try every 0 ≤ i ≤ 9; when we know that the most significant digit is i - 1. After that, we store the "current log" and do it again for the second most significant digit and for the third and so on... Overall complexity would be .
This is the algorithm for factorial of a number. Next step is trivial.
You're using a bignum library...
Can you give problem link, please?