The example will work faster: I have some numbers (ie: 2, 3 and 7) and must combine them with any operations (+, -, * and /), so I approximate as much as possible to a given number.
So, for a target number 21, it would find that 3 x 7 is the best option.
For a target of 19, it would find (3 x 7) - 2.
For a target of 16, it would find (2 x 7) + 3 = 17 (best approximation, as exact number couldn't be computed).
If you know of any existing algorithm, it would be highly appreciated some clue ;-)
The target number can be any (let's say up to 100,000) and the operands no more than 10 (you can use each of them just one time).
I know I can use a brute-force algorithm (backtracking), taking out illegal operations (ie, negative numbers), but I need the operation done in less than a second or so, using Javascript, and doesn't look like feasible far away from 6 digits (too much permutations & operations).