Exercise 7.1-1

Using figure 7.1 as a model, illustrate the operation of PARTITION on the array $A = \{13, 19, 9, 5, 12, 8, 7, 4, 21, 2, 6, 11\}$.
$7.1-1 Partition Operation$
Mathjax was not up to the challenge for building this table. I used https://www.tablesgenerator.com/ to build the foundation of this table and then expanded upon it with various techniques in order to get the look just right. Here is the final LaTeX code in all its awkward glory:
\documentclass{article}
\usepackage{array}
\usepackage{xcolor}
\usepackage{colortbl}
\usepackage{multirow,hhline}
\newcolumntype{?}{!{\vrule width 1.5pt}}
\begin{document}

\begin{table}[]
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\rule{0pt}{4ex}  

\multicolumn{1}{c}{\multirow{2}{*}{b.}} & i & p & j & & & & & & & & & & r \\ \hhline{~~------------~} 
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\rule{0pt}{4ex}  

\multicolumn{1}{c}{\multirow{2}{*}{c.}} & i & p & & j & & & & & & & & & r \\ \hhline{~~------------~} 
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\multicolumn{1}{c}{\multirow{2}{*}{e.}} & & p & i & & & j & & & & & & & r \\ \hhline{~~------------~} 
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\rule{0pt}{4ex}  

\multicolumn{1}{c}{\multirow{2}{*}{f.}} & & p & i & & & & j & & & & & & r \\ \hhline{~~------------~} 
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\rule{0pt}{4ex}  

\multicolumn{1}{c}{\multirow{2}{*}{g.}} & & p & & i & & & & j & & & & & r \\ \hhline{~~------------~} 
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\rule{0pt}{4ex}  

\multicolumn{1}{c}{\multirow{2}{*}{h.}} & & p & & & i & & & & j & & & & r \\ \hhline{~~------------~} 
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\rule{0pt}{4ex}  

\multicolumn{1}{c}{\multirow{2}{*}{i.}} & & p & & & & i & & & & j & & & r \\ \hhline{~~------------~} 
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\rule{0pt}{4ex}  

\multicolumn{1}{c}{\multirow{2}{*}{j.}} & & p & & & & i & & & & & j & & r \\ \hhline{~~------------~} 
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\rule{0pt}{4ex}  

\multicolumn{1}{c}{\multirow{2}{*}{k.}} & & p & & & & & i & & & & & j & r \\ \hhline{~~------------~} 
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\rule{0pt}{4ex}  

\multicolumn{1}{c}{\multirow{2}{*}{l.}} & & p & & & & & & i & & & & & r \\ \hhline{~~------------~} 
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\rule{0pt}{4ex}  
\end{tabular}
\end{table}
\end{document}