Problem

The numbers in the list shown above are the weights, in kilograms, of ten boxes. The boxes are to be transported in containers that will each hold a maximum weight of 40 kilograms.

$17 \quad 9 \quad 15 \quad 8 \quad 20 \quad 13 \quad 28 \quad 4 \quad 12 \quad 5$

(a) Calculate a lower bound for the number of containers that will be needed to transport the boxes. You must show your working.

(b) Use the first-fit bin packing algorithm to allocate the boxes to the containers.

(c) Using the list provided, carry out a quick sort to produce a list of the weights in ascending order. You must make your pivots clear.

(d) Use the binary search algorithm to try to locate the weight of 9 in the sorted list. Clearly indicate how you choose your pivots and which part of the list is being rejected at each stage.