Find vector elements that sum up to specific number in MATLAB

Question

Let us consider that we have a vector VEC.

Is ther a way to find which vector elements can be grouped so as they sum up to a given number NUM in MATLAB?

Answer 1

If I'm not mistaken this problem is NP-hard.
But an interesting approach might be using bintprog:

n = numel( VEC );
x0 = zeros( 1, n ); % one possible init guess
x = bintprog( zeros( n, 1 ), ...  % objective function meaningless, we look for feasibility
              [], [], ... % no inequality constraints
              VEC(:)', NUM, ... %' we want the sum of selected elements to equal NUM
              x0 ); % changing init x0 might result with different solutions
find( x ) 

the binary vector x (the solution of the optimization in bintprog) selects the relevant elements that sum to NUM