Group values up to a threshold and minimize groups

Question

Given a threshold $t$ and a list of numbers $N$. $\forall n \in N: n \leq t$ Now group the numbers so that the sum of the numbers $s$ is lower or equal $t$. Minimize the amount of groups.

Example: $N={20,19,18,17,14,12,9,5,4}$ and $t = 40$

Possible Grouping: ${(20,19),(18,17,4),(14,12,9,5)}$ (Greedy)

Is greedy a strategy/algorithm, that will lead to the optimal solution? If not, are there other algorithms to solve this problem?

https://cs.stackexchange.com/q/59964/755 – D.W. Dec 10 '17 at 20:23 — D.W., Dec 10 '17 at 20:23

score 1 · Answer 1 · answered Dec 11 '17 at 16:39

1

I just learned that this is the bin packing problem with goal of minimizing the bins. This problem is NP hard. So the greedy strategy wont guarantee an optimal solution.

answered Dec 11 '17 at 16:39

Bernd Strehl

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Group values up to a threshold and minimize groups

1 Answers1