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| 1 | +\textbf{\LARGE{\color{tumgadPurple}(a,b) Trees}}\\ |
| 2 | +\\ |
| 3 | +\noindent |
| 4 | +Given the following \href{https://sebastianoner.github.io/TUMGAD/src/DataStructures/SearchStructures/ABTrees/ABLTrees}{\underline{(a,b) Tree}} with a = 2 and b = 4: |
| 5 | +%$INITTREE$ |
| 6 | +Perform the following operations in their given order on the tree above: |
| 7 | +\begin{center} |
| 8 | + Delete: $DELETIONS$\\ |
| 9 | + Insert: $INSERTIONS$\\ |
| 10 | +\end{center} |
| 11 | +Use the preprints below to fill in the values (note that there may be more nodes printed than needed)\\ |
| 12 | +\vspace{8px} |
| 13 | +\\ |
| 14 | +Delete: \underline{\hspace{1cm}}\\ |
| 15 | +\begin{center} |
| 16 | + \begin{tikzpicture} |
| 17 | + \tikzstyle{bplus}=[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw] |
| 18 | + \tikzstyle{every node}=[bplus] |
| 19 | + \tikzstyle{level 1}=[sibling distance=25mm] |
| 20 | + \node {\nodepart{two}\nodepart{three}} [->] |
| 21 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 22 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 23 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 24 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 25 | + ; |
| 26 | + \end{tikzpicture} |
| 27 | +\end{center} |
| 28 | +\vspace{8px} |
| 29 | +Delete: \underline{\hspace{1cm}}\\ |
| 30 | +\begin{center} |
| 31 | + \begin{tikzpicture} |
| 32 | + \tikzstyle{bplus}=[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw] |
| 33 | + \tikzstyle{every node}=[bplus] |
| 34 | + \tikzstyle{level 1}=[sibling distance=25mm] |
| 35 | + \node {\nodepart{two}\nodepart{three}} [->] |
| 36 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 37 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 38 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 39 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 40 | + ; |
| 41 | + \end{tikzpicture} |
| 42 | +\end{center} |
| 43 | +\vspace{8px} |
| 44 | +Insert: \underline{\hspace{1cm}}\\ |
| 45 | +\begin{center} |
| 46 | + \begin{tikzpicture} |
| 47 | + \tikzstyle{bplus}=[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw] |
| 48 | + \tikzstyle{every node}=[bplus] |
| 49 | + \tikzstyle{level 1}=[sibling distance=25mm] |
| 50 | + \node {\nodepart{two}\nodepart{three}} [->] |
| 51 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 52 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 53 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 54 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 55 | + ; |
| 56 | + \end{tikzpicture} |
| 57 | +\end{center} |
| 58 | +\vspace{8px} |
| 59 | +Insert: \underline{\hspace{1cm}}\\ |
| 60 | +\begin{center} |
| 61 | + \begin{tikzpicture} |
| 62 | + \tikzstyle{bplus}=[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw] |
| 63 | + \tikzstyle{every node}=[bplus] |
| 64 | + \tikzstyle{level 1}=[sibling distance=25mm] |
| 65 | + \node {\nodepart{two}\nodepart{three}} [->] |
| 66 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 67 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 68 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 69 | + child {node[rectangle split,rectangle split horizontal, rectangle split parts = 3, rectangle split empty part width=0.01mm, rectangle split every empty part={\hspace{0.35cm}}, draw]{\nodepart{two}\nodepart{three}}} |
| 70 | + ; |
| 71 | + \end{tikzpicture} |
| 72 | +\end{center} |
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