# Bin packing algorithm

## Bin packing algorithm

24   14   8   x   19   25   6   17   9

The numbers in the list represent the exact weights, in kilograms, of 9 suitcases. One suitcase is weighed inaccurately and the only information known about the unknown weight, x kg, of this suitcase is that $\inline&space;19<&space;x\leqslant&space;23$. The suitcases are to be transported in containers that can hold a maximum of 50 kilograms.

(a) Use the first-fit bin packing algorithm, on the list provided, to allocate the suitcases to containers.

(b) Using the list provided, carry out a quick sort to produce a list of the weights in descending order. Show the result of each pass and identify your pivots clearly.

(c) Apply the first-fit decreasing bin packing algorithm to the ordered list to determine the 2 possible allocations of suitcases to containers.

After the first-fit decreasing bin packing algorithm has been applied to the ordered list, one of the containers is full.

(d) Calculate the possible integer values of x. You must show your working.

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