I have a very long "list" of numbers ( maybe thousands ) which may be grouped, by sum into "n" groups. The number of groups and values are given. For example:
I need to find a summary of which numbers in the "list" will crate given "groups".
Ideas?
On
This looks like a variation of The Subset Sum Problem Given a list of numbers, does some subset's sum equal 0? The complexity remains the same if the target isn't zero.
A brute force algorithm is loop through the desired targets generating subsets, then add each subset's terms. There are $2^N-1$ possible subsets if you ignore the empty set. You can generate the subsets by generating the first $2^N-1$ binary numbers, and have a routine that can convert the number into its corresponding sum. $1$ means include, $0$ means exclude.
You probably don't want to use this method for 1000 data points. That article has some alternatives.
You can solve the problem via integer linear programming as follows. Let binary decision variable $x_{i,g}$ indicate whether item $i$ (with value $v_i$) appears in group $g$. Let $s_g$ be the target sum for group $g$. The problem is to find a feasible solution to the linear constraints \begin{align} \sum_g x_{i,g} &= 1 &&\text{for all $i$} \\ \sum_i v_i x_{i,g} &= s_g &&\text{for all $g$} \end{align}