Question

I have a bit of a problem with the algorithm proposed as homework by our teachers. It goes something like this:

Having a number of sticks like so:

4 (the number of piles to use)

11 7 5 4 (length of the sticks)

1 1 3 3 (how many sticks per length)

I have to figure out an algorithm that will form the minimal number of sticks by merging them. The solution for the previous example is this:

15 3 (15(optimal sum) * 3(minimal sticks) = 45 = 11*1 + 7*1 + 5*3 + 4*3)

11 4

7 4 4

5 5 5

Now I am not asking for you guys to solve this problem, but to give me a line to follow, I have tried to reduce it to a ‘Make Change’ problem, it went good until the part where I had to select from the remaining solutions the good ones.

The complexity desired is an exponential one and the restrictions are:

1. 0 < sticks < 100
2. 0 < max_sum_of_sticks < 1000

So do you guys have a second thought on this?

Thank you very much for your time.

Explanation on minimal number of sticks : if for instance i had a set of sticks. The sum to be formed is 80, i have a fair amount of solutions :

1 stick of length 80

2 sticks of length 40

4 sticks of length 20 so on.

The first one is trivial and we discard it,for the remaining solutions I have to test if I can build them with the sets of sticks I have because there is a possibility that the solution chosen, for example 2*40, isn’t a reliable one because we have sticks that were not used.

Answer 1

This looks a lot like the Knapsack problem.

You might also take a look at Branch and bound, which is a general algorithm for all kinds of optimization problems.