We are given a set of denominations and a total amount.
We have to find the minimum number of coins needed to make the total.
I wish to know the logic behind the solution. Thanks in advance.
If we denote the denominations as [w1, w2 ... wn], such that wi = 5 × wi+1, then the denominations forms a superincreasing sequence. The page lists a general greedy algorithm if the denominations are powers of K, where K ≥ 2.
The proof is simple, if you remove a single coin of denomination wi, you would need at least 5 coins of lower denomination to get the same sum.
