A binary search tree (BST) is a binary tree with labelled vertices such that for any vertex all vertices in the left subtree are less than itâ€™s label and all vertices in the right subtree are greater.

To build the tree, order the vertices then select the root via: \[ \left \lfloor \frac{{min} + {max}}{2} \right \rfloor \] Repeat for each subtree.

As an example, a 14 element BST can be visualised as below

```
\begin{document}
\begin{tikzpicture}[thick,level/.style = {sibling distance = 60mm/#1}]
\node {7}
child {
node {3}
child {
node {1}
child[missing]
child {node {2}}
}
child {
node {5}
child {node {4}}
child {node {6}}
}
}
child {
node {11}
child {
node {9}
child {node {8}}
child {node {10}}
}
child {
node {13}
child {node {12}}
child {node {14}}
}
};
\end{tikzpicture}
\end{document}
```

The height of a binary search tree can be found via the following \[ h = \left\lceil \log_2(n+1) \right\rceil \] This height defines the maximum number of comparisons required to find an stored element.