For the set of {\(1, 4, 5, 10, 16, 17, 21\) } of keys, draw binary search trees of heights 2, 3, 4, 5 and 6.
Height of 2:
Height of 3:
Height of 4:
Height of 5:
Height of 6:
The following blocks of LaTeX code were used to generate the above binary search trees:
Height of 2:
\documentclass[border = 5pt, tikz]{standalone}
\begin{document}
\begin{tikzpicture}[
every node/.style = {minimum width = 2em, draw, circle},
level/.style = {sibling distance = 30mm/#1}
]
\node {10}
child {node {4}
child {node {1}}
child {node {5}}
}
child {node {17}
child {node {16}}
child {node {21}}
};
\end{tikzpicture}
\end{document}Height of 3:
\documentclass[border = 5pt, tikz]{standalone}
\begin{document}
\begin{tikzpicture}[
every node/.style = {minimum width = 2em, draw, circle},
level/.style = {sibling distance = 30mm/#1}
]
\node {10}
child {node {5}
child {node {4}
child {node {1}}
child {edge from parent[draw = none]}
}
child {edge from parent[draw = none]}
}
child {node {17}
child {node {16}}
child {node {21}}
};
\end{tikzpicture}
\end{document}Height of 4:
\documentclass[border = 5pt, tikz]{standalone}
\begin{document}
\begin{tikzpicture}[
every node/.style = {minimum width = 2em, draw, circle},
level/.style = {sibling distance = 30mm/#1}
]
\node {5}
child {node {4}
child {node {1}}
child {edge from parent[draw = none]}
}
child {node {10}
child {edge from parent[draw = none]}
child {node {16}
child {edge from parent[draw = none]}
child {node {17}
child {edge from parent[draw = none]}
child {node {21}}
}
}
};
\end{tikzpicture}
\end{document}Height of 5:
\documentclass[border = 5pt, tikz]{standalone}
\begin{document}
\begin{tikzpicture}[
every node/.style = {minimum width = 2em, draw, circle},
level/.style = {sibling distance = 30mm/#1}
]
\node {17}
child {node {16}
child {node {10}
child {node {5}
child {node {4}
child {node {1}}
child {edge from parent[draw = none]}
}
child {edge from parent[draw = none]}
}
child {edge from parent[draw = none]}
}
child {edge from parent[draw = none]}
}
child {node {21}};
\end{tikzpicture}
\end{document}Height of 6:
\documentclass[border = 5pt, tikz]{standalone}
\begin{document}
\begin{tikzpicture}[
every node/.style = {minimum width = 2em, draw, circle},
level/.style = {sibling distance = 30mm/#1}
]
\node {1}
child {edge from parent[draw = none]}
child {node {4}
child {edge from parent[draw = none]}
child {node {5}
child {edge from parent[draw = none]}
child {node {10}
child {edge from parent[draw = none]}
child {node {16}
child {edge from parent[draw = none]}
child {node {17}
child {edge from parent[draw = none]}
child {node {21}}
}
}
}
}
};
\end{tikzpicture}
\end{document}