(Apologies since this was likely asked before, but I cannot find it. )
Is there a way to find the shortest path from some value V to some destination value D using only addition of values from a given set of numbers S?
For example, starting value V = 0. Destination value D=5.
Allowed operation is only addition (+) and only values from the following set: S={4,-3}
The solution is 0+4+4-3=D (or any other ordering of these numbers), but nevertheless, requires at least 3 operations.
Another example, starting value V = 0. Destination value D=4.
Allowed operation is only addition (+) and only values from the following set: S={3,-7}
D=0+3+3+3+3+3+3-7-7=4. It requires at least 8 operations.
Finally, starting value V = 0. Destination value D=2.
Allowed operation is only addition (+) and only values from the following set: S={3,-6, -9}
Is impossible to complete.
So the question is: How to find the shortest path to get from starting value V to destination value D, by only adding numbers from set S?
How is this called? How can this be figured out? Many thanks!