Possible combination of coins

Question

Hello, I'm just new here. I have some algorithm problem with algorithm that couldn't put it to a code. The problem is "For a given denomination of money (5, 10, 20, 50, 100), get all possible combinations that will not exceed 2000 and at least one of them is present".
I know this is easy for others but for me, it's quite difficult. I already searched but I can't find something that is similar with this problem.
Here's what I tried,
Given:
denominations = { 5, 10, 20, 50, 100};
total = 2000;
A=5, B=10, C=20, D=50, E=100
A' = counts of A // A' >= 1
B' = counts of B // B' >= 1
C' = counts of C // C' >= 1
D' = counts of D // D' >= 1
E' = counts of E // E' >= 1
A A' + BB' + C*C' + D*D' + E*E' <= total
The problem is I can't find a way for a possible counts of the denomination.
Any help is much appreciated.
Thanks.

Answer 1

For a brute force approach, consider a simpler problem:
Can you solve the problem if denominations = {5} and maxValue = 1820?
For each solution of the problem the above case, does it generate a smaller problem to be solved for the next higher denomination in {5, 10, 20, 50, 100}?
Can you see how to get a solution to the bigger problem from the smaller ones?
If you've done data structures in your course, you may also want to make it more efficient by memotisation so you don't recompute the combinations of 20,50,100 given 10 = 2 * 5 etc.