smooth-numbers

A friend of mine is interviewing for a job. One of the interview questions got me thinking, just wanted some feedback. There are 2 non-negative integers: i and j. Given the following equation, find an (optimal) solution to iterate over i and j in such a way that the output is sorted. 2^i * 5^j So the first few rounds would look like this: 2^0 * 5^0 = 1 2^1 * 5^0 = 2 2^2 * 5^0 = 4 2^0 * 5^1 = 5 2^3 * 5^0 = 8 2^1 * 5^1 = 10 2^4 * 5^0 = 16 2^2 * 5^1 = 20 2^0 * 5^2 = 25 Try as I might, I can't see a pattern. Your thoughts? user515430 Dijkstra derives an eloquent solution in "A Discipline of

I have a set of prime numbers and I have to generate integers using only those prime factors in increasing order. For example, if the set is p = {2, 5} then my integers should be 1, 2, 4, 5, 8, 10, 16, 20, 25, … Is there any efficient algorithm to solve this problem? The basic idea is that 1 is a member of the set, and for each member of the set n so also 2 n and 5 n are members of the set. Thus, you begin by outputting 1, and push 2 and 5 onto a priority queue. Then, you repeatedly pop the front item of the priority queue, output it if it is different from the previous output, and push 2