I'm currently learning C++.
I am looking for Hamming numbers (numbers whose prime divisors are less or equal to 5).
When I input a number n, the program should output the n-th Hamming number.
Following numbers are input, and output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ...
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 ...
Finding Hamming numbers looks easy, but increasing the input number increases run time cost exponentially.
If I input over 1000
, it almost costs over 1
second,
and over 1200
, it almost costs over 5
seconds.
This is the code I wrote:
while (th > 1)
{
h++;
x = h;
while (x % 2 == 0)
x /= 2;
while (x % 3 == 0)
x /= 3;
while (x % 5 == 0)
x /= 5;
if (x == 1)
th--;
}
So I would like to know how I can find the answer faster. This algorithm doesn't seem to be very good.
Thanks in advance.
In this link you can find two different solutions for finding the nth hamming number. The second method is the optimized one which can get the result in a few seconds.