Prune a branch in a tree

Question

I would like to prune (for indication) some branches of this minimax tree. I'd like to have a cross line over each branch that would be pruned in the final tree. I cannot seem to be able to do it with synttree package in an obvious way. Can somebody suggest an elegant way to do that?

A minimal working example of the tree that I'd like some of its leaves pruned is the following:

\documentclass[10pt,a4paper]{article}

\usepackage[T1]{fontenc}
\usepackage[bitstream-charter]{mathdesign}
\usepackage{subfig}
\usepackage[latin1]{inputenc}                           % Input encoding
\usepackage{amsmath}                                    % Math
\usepackage{empheq}
\usepackage{tensor}
\usepackage{xcolor}
\usepackage{synttree}

\begin{document}

\begin{figure}[h]
\centering
\scalebox{0.8}
{
\branchheight{0.4in}
\childsidesep{1em}
\childattachsep{0.1in}
\synttree
[$\nabla$
    [$\triangle$
        [$\nabla$
            [5]
            [1]
            [4]
        ]
        [$\nabla$
            [2]
            [7]
            [9]
        ]
        [$\nabla$
            [3]
            [5]
            [7]
        ]
    ]
    [$\triangle$
        [$\nabla$
            [10]
            [2]
            [1]
        ]
        [$\nabla$
            [5]
            [1]
            [4]
        ]
        [$\nabla$
            [8]
            [9]
            [2]
        ]
    ]
    [$\triangle$
        [$\nabla$
            [3]
            [1]
            [2]
        ]
        [$\nabla$
            [7]
            [6]
            [5]
        ]
        [$\nabla$
            [9]
            [8]
            [9]
        ]
    ]
]
}
\caption{Minimax tree}
\end{figure}
\end{document}

Answer 1

If you are willing to switch to the powerful forest package (the syntax is really similar), you will have access to the full power of TikZ, besides the nice features provided by the package. You can then use a decoration for defining s style to be easily applied to the desired edges; a little example:

\documentclass[10pt,a4paper]{article}
\usepackage{forest}
\usetikzlibrary{decorations.markings}

\newsavebox\mybox
\savebox\mybox{%
  \tikz{
    \draw[ultra thick,red] (-4pt,-4pt) -- (4pt,4pt);
    \draw[ultra thick,red] (-4pt,4pt) -- (4pt,-4pt);
  }%
}  

\tikzset{
myedge/.style={
  decoration={
   markings,
   mark=at position 0.5 with \node {\usebox\mybox};
  },
  postaction=decorate
  }
}
\begin{document}

\begin{figure}[h]
\centering
\scalebox{0.8}
{%
\begin{forest}
[$\nabla$
    [$\triangle$,edge={myedge}
        [$\nabla$
            [5]
            [1,edge={myedge}]
            [4]
        ]
        [$\nabla$,edge={myedge}
            [2]
            [7]
            [9]
        ]
        [$\nabla$
            [3]
            [5,edge={myedge}]
            [7]
        ]
    ]
    [$\triangle$
        [$\nabla$
            [10]
            [2,edge={myedge}]
            [5]
        ]
        [$\nabla$
            [5]
            [6]
            [4,edge={myedge}]
        ]
        [$\nabla$
            [8]
            [9]
            [2,edge={myedge}]
        ]
    ]
    [$\triangle$
        [$\nabla$
            [3]
            [7]
            [2,edge={myedge}]
        ]
        [$\nabla$,edge={myedge}
            [7]
            [6]
            [5]
        ]
        [$\nabla$,edge={myedge}
            [9]
            [8]
            [9]
        ]
    ]
]
\end{forest}
}
\caption{Minimax tree}
\end{figure}

\end{document}

Answer 2

Forgive me if I've mistaken your intent, but is this the sort of thing you seek? If so, I just used a \stackinset. The syntax is

\stackinset{H-anchor:l,c,r}{H-offset}{V-anchor:t,c,b}{V-offset}{inset}{base image}

The insets may be nested, as I've shown here. This is a method of last resort, because the labels are placed (after the fact) on the tree by specifying physical lengths on the base image, rather than using logical indicators within the scope of the tree coding.

\documentclass[10pt,a4paper]{article}

\usepackage[T1]{fontenc}
\usepackage[bitstream-charter]{mathdesign}
\usepackage{subfig}
\usepackage[latin1]{inputenc}                           % Input encoding
\usepackage{amsmath}                                    % Math
\usepackage{empheq}
\usepackage{tensor}
\usepackage{xcolor}
\usepackage{synttree}
\usepackage{stackengine}
\def\bigX{\sffamily\bfseries\Huge\textcolor{red}{$\times$}}
\begin{document}

\begin{figure}[h]
\centering
\stackinset{c}{-1.8cm}{c}{0.8cm}{\bigX}{%
\stackinset{c}{-0.5cm}{c}{}{\bigX}{%
\scalebox{0.8}
{
\branchheight{0.4in}
\childsidesep{1em}
\childattachsep{0.1in}
\synttree
[$\nabla$
    [$\triangle$
        [$\nabla$
            [5]
            [1]
            [4]
        ]
        [$\nabla$
            [2]
            [7]
            [9]
        ]
        [$\nabla$
            [3]
            [5]
            [7]
        ]
    ]
    [$\triangle$
        [$\nabla$
            [10]
            [2]
            [1]
        ]
        [$\nabla$
            [5]
            [1]
            [4]
        ]
        [$\nabla$
            [8]
            [9]
            [2]
        ]
    ]
    [$\triangle$
        [$\nabla$
            [3]
            [1]
            [2]
        ]
        [$\nabla$
            [7]
            [6]
            [5]
        ]
        [$\nabla$
            [9]
            [8]
            [9]
        ]
    ]
]
}}}
\caption{Minimax tree}
\end{figure}
\end{document}