Algorithmic thinking - Living quality diagram

matrix.pdf

matrix.tex

% https://tex.stackexchange.com/questions/376528/how-to-shade-or-highlight-the-lower-triangular-part-in-a-matrix-with-tikzpicture
% https://www.bu.edu/math/files/2013/08/tikzpgfmanual.pdf
\documentclass{article}

\usepackage{tikz}
\usepackage{amsmath,amsthm,amssymb}

\usetikzlibrary{backgrounds, matrix}
\usetikzlibrary{patterns}

\begin{document}

\begin{figure}[htb]
    \centering
    \resizebox{0.5\textwidth}{!}{%
    \begin{tikzpicture}
        \matrix (m) [matrix of math nodes,
                     left delimiter = |,
                     right delimiter = |,
                     nodes={minimum size=2em},
                     ampersand replacement=\&]
        {
        *   \&   *   \&   *\\
        *   \&   C   \&   B \\
        *   \&   A   \&   ? \\
        };
        \begin{pgfonlayer}{background}
        \begin{scope}[blend group = soft light]
        \draw[rounded corners, pattern=north east lines, opacity=.2]
            (m-1-1.north) -| (m-1-2.east) -| (m-3-2.east) |- (m-3-1.south) -| (m-3-1.west) |- (m-1-1.north);

        %\draw[rounded corners, dotted, fill=red!10!white, opacity=0.8]
        %    (m-1-1.north) -| (m-1-2.east) -| (m-2-2.east) |- (m-2-1.south) -| (m-2-1.west) |- (m-1-1.north);

        \draw[rounded corners, pattern=north west lines, opacity=.2]
            (m-1-1.north) -| (m-1-3.east) -| (m-2-3.east) |- (m-2-1.south) -| (m-2-1.west) |- (m-1-1.north);
        \end{scope}
        \end{pgfonlayer}
    \end{tikzpicture}
    }
\end{figure}

Let $\Delta$ be the sum of the values in the last row of interest, i.e.

\newcommand{\boxA}{%
    \begin{tikzpicture}[scale=0.5]\node[rectangle,draw, pattern=north east lines] (r) at (0,0) {}; \end{tikzpicture}%
}

% https://tex.stackexchange.com/questions/569100/how-can-i-overlap-patterns-in-a-venn-diagram-legend
\newcommand{\boxC}{%
    \begin{tikzpicture}[scale=0.5]\node[rectangle,draw, pattern=north west lines,postaction={pattern=north east lines}] (r) at (0,0) {}; \end{tikzpicture}%
}

\begin{align}
\Delta &=\boxA - \boxC \cr
&= A - C \cr
\end{align}

we have for the final value in the entry $?$

\begin{align}
? &= B + \Delta + v \cr
  &= B + A - C + v \cr
\end{align}

where $v$ is the value from table 6.2

\end{document}