6. The twelve numbers in the list below are to be packed into bins of size \(n\), where \(n\) is a positive integer.
When the first-fit bin packing algorithm is applied to the list, the following allocation is obtained.
Bin 1: 28315
Bin 2: 25161811
Bin 3: 352215
Bin 4: 2713
- Based on the packing shown above, determine the possible values of \(n\). You must give reasons for your answer.
- The original list of twelve numbers is to be sorted into ascending order. Use a quick sort to obtain the sorted list. You should show the result of each pass and identify your pivots clearly.
When the first-fit decreasing bin packing algorithm is applied to the list, the following allocation is obtained.
Bin 1: 35315
Bin 2: 282716
Bin 3: 252218
Bin 4: 151311 - Determine the value of \(n\). You must give a reason for your answer.