Define the problem PARTITION as follows:

PARTITION

Input: A collection of integers.

Output: YES if the collection can be split into two such that the sum of the integers in each partition sums to the same amount. NO otherwise.

(a) Assuming that PARTITION is \(\mathcal{N} \mathcal{P}\)-complete, prove that BIN PACKING is \(\mathcal{N} \mathcal{P}\)-complete.

(b) Assuming that PARTITION is \(\mathcal{N} \mathcal{P}\)-complete, prove that KNAPSACK is \(\mathcal{N} \mathcal{P}\)-complete.