1.1. $3.56.32.95.43.12.83.71.74.13.32.2$

The numbers listed above are to be sorted into descending order.

(i) Perform one pass of a bubble sort, starting at the left-hand end of the list. You must write down the list that results at the end of this first pass.

(ii) Write down the number of comparisons and the number of swaps performed during this first pass.

1.2. After a second pass using this bubble sort, the updated list is

$6.35.43.53.13.72.94.13.32.82.21.7$

Use a quick sort on this updated list to obtain the fully sorted list. You should show the result of each pass and identify your pivots clearly.

1.3. Apply the first-fit decreasing bin packing algorithm to the fully sorted list to pack the numbers into bins of size 11.5

1.4. Determine whether your answer to part (c) uses the minimum number of bins. You must justify your answer.