3. $\quad \begin{array} { l l l l l l l l l l } 42 & 21 & 15 & 16 & 35 & 10 & 31 & 11 & 27 & 39 \end{array}$
\begin{enumerate}[label=(\alph*)]
\item Use the first-fit bin packing algorithm to determine how the numbers listed above can be packed into bins of size 65
\item The list of numbers is to be sorted into descending order. Use a quick sort to obtain the sorted list. You should show the result of each pass and identify your pivots clearly.
\item Use the first-fit decreasing bin packing algorithm on your ordered list to pack the numbers into bins of size 65

The nine distinct numbers below are to be sorted into descending order

$$\begin{array} { l l l l l l l l l } 
23 & 14 & 17 & \boldsymbol { x } & 21 & 18 & 8 & 20 & 11
\end{array}$$

A bubble sort, starting at the left-hand end of the list, is to be used to obtain the sorted list. After the first complete pass, the list is

$$\begin{array} { l l l l l l l l l } 
23 & 17 & \boldsymbol { x } & 21 & 18 & 14 & 20 & 11 & 8
\end{array}$$

After the second complete pass, the list is

$$\begin{array} { l l l l l l l l l } 
23 & 17 & 21 & 18 & \boldsymbol { x } & 20 & 14 & 11 & 8
\end{array}$$
\item Using this information, write down the smallest interval that must contain $\boldsymbol { x }$. Give your answer as an inequality.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2017 Q3 [13]}}