How to measure the minimum width or height of several boxes?

I know we can get the maximum width or height of several boxes via:

\setbox0=\vbox{\hbox{a}\hbox{b}\hbox{c}}
The maximum width is \the\wd0

\setbox0=\hbox{\hbox{a}\hbox{b}\hbox{c}}
The maximum height is \the\ht0


But how to get the minimum width or height?

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The idea is simple: set the boxes and measure them.

\documentclass{article}

\makeatletter
\newcommand{\settominwidth}[1]{\saltyegg@settomin{\wd}{#1}}
\newcommand{\settominheight}[1]{\saltyegg@settomin{\ht}{#1}}
\newcommand{\settomindepth}[1]{\saltyegg@settomin{\dp}{#1}}

\newcommand{\saltyegg@settomin}[3]{%
#2\maxdimen
\@for\next:=#3\do{%
\sbox\z@{\next}%
\ifdim#1\z@<#2%
#2=#1\z@
\fi}%
}
\makeatother

\newlength{\saltyeggtest}

\begin{document}

\settominwidth{\saltyeggtest}{a,b,c,f}
\the\saltyeggtest

\settominheight{\saltyeggtest}{a,b,c,f}
\the\saltyeggtest

\settomindepth{\saltyeggtest}{a,b,c,f}
\the\saltyeggtest

\end{document}


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Here is at least one straight-forward way without abstraction into a macro:

\newdimen\minwd

% what needs to happen in order to find the minimum width inner hbox in:
% \hbox{\hbox{first}\hbox{second}\hbox{third}}

\leavevmode % otherwise hboxes stack
\setbox0\hbox{first}%
\minwd=\wd0
\box0
\setbox0\hbox{second}%
\ifdim\wd0<\minwd \minwd=\wd0 \fi
\box0
\setbox0\hbox{third}%
\ifdim\wd0<\minwd \minwd=\wd0 \fi
\box0

minwd = \the\minwd

\bye


In another answer I have a made a macro for a similar thing.

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If you need an expandable solution, and the boxes are already there (thus avoiding the non-expandable step of putting some material into boxes), and use a tex engine with e-TeX extensions enabled:

% compile with etex (or pdftex, etc...) as this requires e-TeX extensions
%
\input xint.sty

\def\minimalwidthofboxes #1{%
\dimexpr\xintiMinof {\xintApply{\number\wd\firstofone}{#1}}sp\relax }

\long\def\firstofone #1{#1}% \long in case \firstofone already exists and was
% declared long

% why \firstofone? because \xintApply\macro{{item1}..{item2}} does
% \macro{item1}, hence here this would give \number\wd{\bA} which is illicit, we
% want \number\wd\bA without braces (besides, on the other hand, it doesn't
% matter if the list contains the single token \bA or the braced token {\bA})

%% EXAMPLES

\newbox\bA
\newbox\bB
\newbox\bC

\setbox\bA\hbox{Aah}

\setbox\bB\hbox{BB}

\setbox\bC\hbox{CCC}

\the\minimalwidthofboxes {\bA\bB\bC}\ % or equivalently {{\bA}{\bB}{\bC}}
is the minimal width among \the\wd\bA, \the\wd\bB, \the\wd\bC.

\newbox\bD \setbox\bD\hbox{bb}

\the\minimalwidthofboxes {{\bA}{\bB}{\bC}{\bD}}
is the minimal width among \the\wd\bA, \the\wd\bB, \the\wd\bC\ and \the\wd\bD.

\bye

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