TikZ - Sudoku, circle and connect with lines some cells

Question

In the following code, I would like to have the possibility to draw some circles and lines on the grids from some cell to others like in the following picture. This is to illustrate advanced "chain" techniques.

Output expected

Code

\documentclass{article}
    \usepackage{tikz}
    \usetikzlibrary{backgrounds}
    \usepackage{graphicx}

% Some customizable styles
    \tikzset {
        highlight/.style = {yellow, opacity=0.3},
        digit/.style = {minimum height = 5mm, minimum width=5mm, anchor=center },
        circle/.style = {draw=green!80!black, dotted, very thick},
        cross/.style = {red, opacity=.5, shorten >=1mm, shorten <=1mm, very thick, line cap=round},
        hint/.style={blue, font=\sf, minimum width=3mm, minimum height=3mm}
    }

% Original code-----------------------------------------------------------
% Modified the \node to give a unique name to each one, which is the
% row number, a dash and the column number. E.g: 1-1, 4-5, etc.
    \newcounter{row}
    \newcounter{col}

    \newcommand\setrow[9]{
        \setcounter{col}{1}
        \foreach \n in {#1, #2, #3, #4, #5, #6, #7, #8, #9} {
            \edef\x{\value{col} - 0.5}
            \edef\y{9.5 - \value{row}}
            \node[digit,name={\arabic{row}-\arabic{col}}] at (\x, \y) {\n};
            \stepcounter{col}
        }
        \stepcounter{row}
    }

% New code -------------------------------------------------------------
    \def\highlightcell#1#2{
        \fill[highlight] (#1-#2.north west) rectangle (#1-#2.south east);
    }

    \def\circlecell#1#2{
        \draw[circle] (#1-#2) circle(4mm);
    }

    \def\crosscell#1#2{
        \draw[cross] (#1-#2.north west) -- (#1-#2.south east);
        \draw[cross] (#1-#2.north east) -- (#1-#2.south west);
    }

    \def\highlightrow#1{
       \fill[highlight] (#1-1.north west) rectangle (#1-9.south east);
    }

    \def\highlighcolumn#1{
        \fill[highlight] (1-#1.north west) rectangle (9-#1.south east);
    }

    \def\hintcell#1#2#3{
        \node at (#1-#2) {\hintbox{#3}};
    }

    \def\highlightrectangle#1#2#3#4{
        \begin{pgfonlayer}{background}
        \fill[highlight] (#1-#2.north west) rectangle (#3-#4.south east);
        \end{pgfonlayer}
    }

% UGLY code. Do not read :-)
\def\hintbox#1{
    \resizebox{4.5mm}{4.5mm}{%
        \tikz[scale=0.3]{%
            \def\auxc{0}
            \foreach \m in {1,...,9} {
                \pgfmathparse{mod(\auxc,3)}
                \xdef\x{\pgfmathresult}
                \pgfmathparse{-floor(\auxc/3)}
                \xdef\y{\pgfmathresult}
                \xdef\hintprinted{0}
                \foreach \n in {#1} {
                    \ifnum\n=\m
                        \node[hint] at (\x,\y) {\n};
                        \xdef\hintprinted{1}
                    \fi
                }
                \ifnum\hintprinted=0
                      \node[hint, opacity=0.1] at (\x,\y) {\m};
                \fi
                \pgfmathparse{\auxc+1}
                \xdef\auxc{\pgfmathresult}
            }
        }%
    }
}


\begin{document}

    \begin{tikzpicture}[scale=.5]
        \begin{scope}
            \draw (0, 0) grid (9, 9);
            \draw[very thick, scale=3] (0, 0) grid (3, 3);
            \setcounter{row}{1}

    % Single entries
            \setrow {7}{4}{ }  { }{8}{ }  { }{ }{5}
            \setrow { }{ }{ }  {4}{ }{6}  { }{ }{ }
            \setrow { }{ }{1}  { }{2}{ }  {4}{ }{ }

            \setrow { }{6}{ }  { }{ }{ }  { }{2}{ }
            \setrow {5}{ }{8}  { }{7}{ }  {1}{ }{3}
            \setrow { }{3}{ }  { }{ }{ }  { }{9}{ }

            \setrow { }{ }{4}  { }{5}{ }  {9}{ }{ }
            \setrow { }{ }{ }  {1}{ }{2}  { }{ }{ }
            \setrow {3}{ }{ }  { }{9}{ }  { }{ }{8}

    % Hints
    %  * Row 1
            \hintcell{1}{3}{2,3,6,9}
            \hintcell{1}{4}{3,9}
            \hintcell{1}{6}{1,3,9}
            \hintcell{1}{7}{2,3,6}
            \hintcell{1}{8}{1,3,6}
    %  * Row 2
            \hintcell{2}{1}{2,8,9}
            \hintcell{2}{2}{2,5,8,9}
            \hintcell{2}{3}{2,3,5,9}
            \hintcell{2}{5}{1,3}
            \hintcell{2}{7}{2,3,7,8}
            \hintcell{2}{8}{1,3,7,8}
            \hintcell{2}{9}{1,2,7,9}
    %  * Row 3
            \hintcell{3}{1}{6,8,9}
            \hintcell{3}{2}{5,8,9}
            \hintcell{3}{4}{3,5,7,9}
            \hintcell{3}{6}{3,5,7,9}
            \hintcell{3}{8}{3,6,7,8}
            \hintcell{3}{9}{6,7,9}
    %  * Row 4
            \hintcell{4}{1}{1,4,9}
            \hintcell{4}{3}{7,9}
            \hintcell{4}{4}{3,5,8,9}
            \hintcell{4}{5}{1,3,4}
            \hintcell{4}{6}{1,3,4,5,8,9}
            \hintcell{4}{7}{5,7,8}
            \hintcell{4}{9}{4,7}
    %  * Row 5
            \hintcell{5}{2}{2,9}
            \hintcell{5}{4}{2,6,9}
            \hintcell{5}{6}{4,9}
            \hintcell{5}{8}{4,6}
    %  * Row 6
            \hintcell{6}{1}{1,2,4}
            \hintcell{6}{3}{2,7}
            \hintcell{6}{4}{2,5,6,8}
            \hintcell{6}{5}{1,4,6}
            \hintcell{6}{6}{1,4,5,8}
            \hintcell{6}{7}{5,6,7,8}
            \hintcell{6}{9}{4,6,7}
    %  * Row 7
            \hintcell{7}{1}{1,2,6,8}
            \hintcell{7}{2}{1,2,7,8}
            \hintcell{7}{4}{3,6,7,8}
            \hintcell{7}{6}{3,7,8}
            \hintcell{7}{8}{1,3,6,7}
            \hintcell{7}{9}{1,2,6,7}
    %  * Row 8
            \hintcell{8}{1}{6,8,9}
            \hintcell{8}{2}{5,7,8,9}
            \hintcell{8}{3}{5,6,7,9}
            \hintcell{8}{5}{3,4,6}
            \hintcell{8}{7}{3,5,6,7}
            \hintcell{8}{8}{3,4,5,6,7}
            \hintcell{8}{9}{4,6,7}
    %  * Row 9
            \hintcell{9}{2}{1,2,5,7}
            \hintcell{9}{3}{2,5,6,7}
            \hintcell{9}{4}{6,7}
            \hintcell{9}{6}{4,7}
            \hintcell{9}{7}{2,5,6,7}
            \hintcell{9}{8}{1,4,5,6,7}
        \end{scope}
\end{tikzpicture}

\end{document}

The code comes from TikZ - Placing several numbers in one cell of a Sudoku grid.

Answer 1

Since in the code there's already a very well structure, this comes almost straightforward.

I defined, similarly to the existent \circlecell, a new command \circlenumber which draws a circle and place an empty node with a label:

% command to circle numbers:
% #1: optional -> circle color
% #2: mandatory -> cell identifier
% #3: mandatory -> name of the cell
\newcommand\circlenumber[3][red!80!black]{
        \draw[circle number=#1, radius=5mm] (#2) circle node[outer sep=1mm] (#3){};
}

Later on, using the labels provided by the user the connections will be drawn. Example:

% Circle some cell
\circlenumber{4-2}{start}
\circlenumber{3-6}{middle}
\circlenumber{7-4}{end}
% Connect
\foreach \source/\dest in {start/middle,middle/end}
    \draw[circle number=red!80!black] (\source)--(\dest);

The code (there's also an example in which the connections are drawn in the background layer):

\documentclass{article}
    \usepackage{tikz}
    \usetikzlibrary{backgrounds}
    \usepackage{graphicx}

% Some customizable styles
    \tikzset {
        highlight/.style = {yellow, opacity=0.3},
        digit/.style = {minimum height = 5mm, minimum width=5mm, anchor=center },
        circle/.style = {draw=green!80!black, dotted, very thick},
        circle number/.style = {draw=#1,very thick},
        cross/.style = {red, opacity=.5, shorten >=1mm, shorten <=1mm, very thick, line cap=round},
        hint/.style={blue, font=\sf, minimum width=3mm, minimum height=3mm}
    }

% Original code-----------------------------------------------------------
% Modified the \node to give a unique name to each one, which is the
% row number, a dash and the column number. E.g: 1-1, 4-5, etc.
    \newcounter{row}
    \newcounter{col}

    \newcommand\setrow[9]{
        \setcounter{col}{1}
        \foreach \n in {#1, #2, #3, #4, #5, #6, #7, #8, #9} {
            \edef\x{\value{col} - 0.5}
            \edef\y{9.5 - \value{row}}
            \node[digit,name={\arabic{row}-\arabic{col}}] at (\x, \y) {\n};
            \stepcounter{col}
        }
        \stepcounter{row}
    }

% New code -------------------------------------------------------------
    \def\highlightcell#1#2{
        \fill[highlight] (#1-#2.north west) rectangle (#1-#2.south east);
    }

    \def\circlecell#1#2{
        \draw[circle] (#1-#2) circle(4mm);
    }

    % command to circle numbers:
    % #1: optional -> circle color
    % #2: mandatory -> cell identifier
    % #3: mandatory -> name of the cell
    \newcommand\circlenumber[3][red!80!black]{
        \draw[circle number=#1, radius=5mm] (#2) circle node[outer sep=1mm] (#3){};
    }

    \def\crosscell#1#2{
        \draw[cross] (#1-#2.north west) -- (#1-#2.south east);
        \draw[cross] (#1-#2.north east) -- (#1-#2.south west);
    }

    \def\highlightrow#1{
       \fill[highlight] (#1-1.north west) rectangle (#1-9.south east);
    }

    \def\highlighcolumn#1{
        \fill[highlight] (1-#1.north west) rectangle (9-#1.south east);
    }

    \def\hintcell#1#2#3{
        \node at (#1-#2) {\hintbox{#3}};
    }

    \def\highlightrectangle#1#2#3#4{
        \begin{pgfonlayer}{background}
        \fill[highlight] (#1-#2.north west) rectangle (#3-#4.south east);
        \end{pgfonlayer}
    }

% UGLY code. Do not read :-)
\def\hintbox#1{
    \resizebox{4.5mm}{4.5mm}{%
        \tikz[scale=0.3]{%
            \def\auxc{0}
            \foreach \m in {1,...,9} {
                \pgfmathparse{mod(\auxc,3)}
                \xdef\x{\pgfmathresult}
                \pgfmathparse{-floor(\auxc/3)}
                \xdef\y{\pgfmathresult}
                \xdef\hintprinted{0}
                \foreach \n in {#1} {
                    \ifnum\n=\m
                        \node[hint] at (\x,\y) {\n};
                        \xdef\hintprinted{1}
                    \fi
                }
                \ifnum\hintprinted=0
                      \node[hint, opacity=0.1] at (\x,\y) {\m};
                \fi
                \pgfmathparse{\auxc+1}
                \xdef\auxc{\pgfmathresult}
            }
        }%
    }
}


\begin{document}

    \begin{tikzpicture}[scale=.5]
        \begin{scope}
            \draw (0, 0) grid (9, 9);
            \draw[very thick, scale=3] (0, 0) grid (3, 3);
            \setcounter{row}{1}

    % Single entries
            \setrow {7}{4}{ }  { }{8}{ }  { }{ }{5}
            \setrow { }{ }{ }  {4}{ }{6}  { }{ }{ }
            \setrow { }{ }{1}  { }{2}{ }  {4}{ }{ }

            \setrow { }{6}{ }  { }{ }{ }  { }{2}{ }
            \setrow {5}{ }{8}  { }{7}{ }  {1}{ }{3}
            \setrow { }{3}{ }  { }{ }{ }  { }{9}{ }

            \setrow { }{ }{4}  { }{5}{ }  {9}{ }{ }
            \setrow { }{ }{ }  {1}{ }{2}  { }{ }{ }
            \setrow {3}{ }{ }  { }{9}{ }  { }{ }{8}

    % Hints
    %  * Row 1
            \hintcell{1}{3}{2,3,6,9}
            \hintcell{1}{4}{3,9}
            \hintcell{1}{6}{1,3,9}
            \hintcell{1}{7}{2,3,6}
            \hintcell{1}{8}{1,3,6}
    %  * Row 2
            \hintcell{2}{1}{2,8,9}
            \hintcell{2}{2}{2,5,8,9}
            \hintcell{2}{3}{2,3,5,9}
            \hintcell{2}{5}{1,3}
            \hintcell{2}{7}{2,3,7,8}
            \hintcell{2}{8}{1,3,7,8}
            \hintcell{2}{9}{1,2,7,9}
    %  * Row 3
            \hintcell{3}{1}{6,8,9}
            \hintcell{3}{2}{5,8,9}
            \hintcell{3}{4}{3,5,7,9}
            \hintcell{3}{6}{3,5,7,9}
            \hintcell{3}{8}{3,6,7,8}
            \hintcell{3}{9}{6,7,9}
    %  * Row 4
            \hintcell{4}{1}{1,4,9}
            \hintcell{4}{3}{7,9}
            \hintcell{4}{4}{3,5,8,9}
            \hintcell{4}{5}{1,3,4}
            \hintcell{4}{6}{1,3,4,5,8,9}
            \hintcell{4}{7}{5,7,8}
            \hintcell{4}{9}{4,7}
    %  * Row 5
            \hintcell{5}{2}{2,9}
            \hintcell{5}{4}{2,6,9}
            \hintcell{5}{6}{4,9}
            \hintcell{5}{8}{4,6}
    %  * Row 6
            \hintcell{6}{1}{1,2,4}
            \hintcell{6}{3}{2,7}
            \hintcell{6}{4}{2,5,6,8}
            \hintcell{6}{5}{1,4,6}
            \hintcell{6}{6}{1,4,5,8}
            \hintcell{6}{7}{5,6,7,8}
            \hintcell{6}{9}{4,6,7}
    %  * Row 7
            \hintcell{7}{1}{1,2,6,8}
            \hintcell{7}{2}{1,2,7,8}
            \hintcell{7}{4}{3,6,7,8}
            \hintcell{7}{6}{3,7,8}
            \hintcell{7}{8}{1,3,6,7}
            \hintcell{7}{9}{1,2,6,7}
    %  * Row 8
            \hintcell{8}{1}{6,8,9}
            \hintcell{8}{2}{5,7,8,9}
            \hintcell{8}{3}{5,6,7,9}
            \hintcell{8}{5}{3,4,6}
            \hintcell{8}{7}{3,5,6,7}
            \hintcell{8}{8}{3,4,5,6,7}
            \hintcell{8}{9}{4,6,7}
    %  * Row 9
            \hintcell{9}{2}{1,2,5,7}
            \hintcell{9}{3}{2,5,6,7}
            \hintcell{9}{4}{6,7}
            \hintcell{9}{6}{4,7}
            \hintcell{9}{7}{2,5,6,7}
            \hintcell{9}{8}{1,4,5,6,7}
        \end{scope}
    % Circle some cell
    \circlenumber{4-2}{start}
    \circlenumber{3-6}{middle}
    \circlenumber{7-4}{end}
    % Connect
    \foreach \source/\dest in {start/middle,middle/end}
            \draw[circle number=red!80!black] (\source)--(\dest);

    % In background
    \circlenumber{5-9}{end 2}
    \begin{pgfonlayer}{background}
            \draw[circle number=red!80!black] (middle)--(end 2);
    \end{pgfonlayer}
\end{tikzpicture}

\end{document}

The result: