TikZ: redefine/update node label

Question

I need to draw many nodes with labels that I can calculate from their indices. However, a small amount of them do not follow the rule, thus I need to assign their labels manually. Can I do that somehow?

MWE:

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}
    \foreach \i in {1,...,30}
    {
        \node at (\i,0) [rectangle,label=above:\i] (v\i) {$i$};
    }
    % here I want to make the label of node v7 to become $\varnothing$
\end{tikzpicture}
\end{document}

Note: this has nothing to do with animation, I just want to create the nodes in a loop and then change labels for some of them.

UPD: I corrected MWE, as the original one was not exactly what I implied.

Answer 1

You can use \node also, which is described on p. 250 of the pgfmanual, for that.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}
    \foreach \i in {1,...,10}
    {
        \node at (\i,0) [rectangle,label={above:$ \i $}] (v\i) {$i$};
    }
    \foreach \i in {3,6,8}{
        \node also [label={[fill=white]above:$ \varnothing $}] (v\i);
    }
\end{tikzpicture}
\end{document}

BIG THANKS TO MAX for the edit.

Just in case you ever have wider labels: give the labels names and use their width for Max' fill=white trick.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{calc}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}
    \foreach \i in {1,2,...,10}
    {
        \node at (\i,0) [rectangle,label={[name=lab\i]above:$\i\i$}] (v\i) {$i$};
    }
    \foreach \i in {3,6,10}{
        \path let \p1=($(lab\i.north east)-(lab\i.south west)$) in node also 
        [label={[fill=white,minimum width=\x1,minimum height=\y1]above:$ \varnothing $}] (v\i);
    }
\end{tikzpicture}
\end{document}

ADDENDUM: Just for curiosity I was wondering if there is a simple way to make Max' nice answer work with lists. I am sure there is and leave it to others to use some xparse or other magic. Here I just want to report an irony of fate. If one goes for the built-in LaTeX check whether or not something is an element of a list, then my naive attempt fails for two digits, precisely where the simplest version of the above also starts to go wrong. Rather funny and ironic, I'd say. ;-)

\documentclass[tikz]{standalone}
\makeatletter
% https://tex.stackexchange.com/a/260921/121799 and https://tex.stackexchange.com/a/287094/121799
\newcommand\ifmember[2]{% 
\in@{#1}{#2}%
\ifin@
\expandafter\@firstoftwo
\else
\expandafter\@secondoftwo
\fi
}
\makeatother
\usepackage{amssymb}

\begin{document}

\begin{tikzpicture}
    \foreach \i in {1,...,10}
    {   
        \edef\temp{\noexpand\ifmember{\i}{3,6,9}{\varnothing}{\i}}
        \node at (\i,0) [rectangle,label=above:$\temp$] (v\i) {$ i $};
    }
\end{tikzpicture}
\end{document}

Answer 2

You can use conditionals inside the \foreach loop:

\documentclass[tikz]{standalone}

\usepackage{amssymb}

\begin{document}
\begin{tikzpicture}
    \foreach \i in {1,...,10}
    {
        \ifnum\i=7
            \node at (\i,0) [rectangle,label=above:$ \varnothing $] (v\i) {$ i $};
        \else
            \node at (\i,0) [rectangle,label=above:$ \i $] (v\i) {$ i $};
        \fi
    }
    % here I want to make the label of node v7 to become $\varnothing$
\end{tikzpicture}
\end{document}

If you have more labels that should be different, the code stays more readable if you use \pgfmathparse to do check the conditional:

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}
    \foreach \i in {1,2,...,10}
    {
        \pgfmathparse{
            ifthenelse(\i==3,
                "varnothing",
                ifthenelse(\i==7,
                    "varnothing",
                    ifthenelse(\i==10,
                        "varnothing",
                        "i"
                    )
                )
            )
        }
        \def\myLabel{\csname\pgfmathresult\endcsname}
        \node at (\i,0) [rectangle,label={above:$ \myLabel $}] (v\i) {$i$};
    }
\end{tikzpicture}
\end{document}