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Better array representation

This commit is contained in:
Antti H S Laaksonen 2017-02-24 20:22:45 +02:00
parent 9bc5daa8ea
commit 80057a1ea9
1 changed files with 26 additions and 3 deletions
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chapter18.tex
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@ -266,14 +266,18 @@ is $3+4+3+1=11$.
\end{center} \end{center}
The idea is to construct a tree traversal array that contains The idea is to construct a tree traversal array that contains
three values for each node: (1) the identifier of the node, three values for each node: the identifier of the node,
(2) the size of the subtree, and (3) the value of the node. the size of the subtree, and the value of the node.
For example, the array for the above tree is as follows: For example, the array for the above tree is as follows:
\begin{center} \begin{center}
\begin{tikzpicture}[scale=0.7] \begin{tikzpicture}[scale=0.7]
\draw (0,1) grid (9,-2); \draw (0,1) grid (9,-2);
\node[left] at (-1,0.5) {node id};
\node[left] at (-1,-0.5) {subtree size};
\node[left] at (-1,-1.5) {node value};
\node at (0.5,0.5) {$1$}; \node at (0.5,0.5) {$1$};
\node at (1.5,0.5) {$2$}; \node at (1.5,0.5) {$2$};
\node at (2.5,0.5) {$6$}; \node at (2.5,0.5) {$6$};
@ -330,6 +334,10 @@ can be found as follows:
\fill[color=lightgray] (4,-1) rectangle (8,-2); \fill[color=lightgray] (4,-1) rectangle (8,-2);
\draw (0,1) grid (9,-2); \draw (0,1) grid (9,-2);
\node[left] at (-1,0.5) {node id};
\node[left] at (-1,-0.5) {subtree size};
\node[left] at (-1,-1.5) {node value};
\node at (0.5,0.5) {$1$}; \node at (0.5,0.5) {$1$};
\node at (1.5,0.5) {$2$}; \node at (1.5,0.5) {$2$};
\node at (2.5,0.5) {$6$}; \node at (2.5,0.5) {$6$};
@ -438,6 +446,10 @@ For example, the following array corresponds to the above tree:
\begin{tikzpicture}[scale=0.7] \begin{tikzpicture}[scale=0.7]
\draw (0,1) grid (9,-2); \draw (0,1) grid (9,-2);
\node[left] at (-1,0.5) {node id};
\node[left] at (-1,-0.5) {subtree size};
\node[left] at (-1,-1.5) {path sum};
\node at (0.5,0.5) {$1$}; \node at (0.5,0.5) {$1$};
\node at (1.5,0.5) {$2$}; \node at (1.5,0.5) {$2$};
\node at (2.5,0.5) {$6$}; \node at (2.5,0.5) {$6$};
@ -491,6 +503,10 @@ the array changes as follows:
\fill[color=lightgray] (4,-1) rectangle (8,-2); \fill[color=lightgray] (4,-1) rectangle (8,-2);
\draw (0,1) grid (9,-2); \draw (0,1) grid (9,-2);
\node[left] at (-1,0.5) {node id};
\node[left] at (-1,-0.5) {subtree size};
\node[left] at (-1,-1.5) {path sum};
\node at (0.5,0.5) {$1$}; \node at (0.5,0.5) {$1$};
\node at (1.5,0.5) {$2$}; \node at (1.5,0.5) {$2$};
\node at (2.5,0.5) {$6$}; \node at (2.5,0.5) {$6$};
@ -710,13 +726,16 @@ in the array and there are a total of $2n-1$
nodes in the array. nodes in the array.
We store two values in the array: We store two values in the array:
(1) the identifier of the node, and (2) the level of the the identifier of the node and the level of the
node in the tree. node in the tree.
The following array corresponds to the above tree: The following array corresponds to the above tree:
\begin{center} \begin{center}
\begin{tikzpicture}[scale=0.7] \begin{tikzpicture}[scale=0.7]
\node[left] at (-1,1.5) {node id};
\node[left] at (-1,0.5) {level};
\draw (0,1) grid (15,2); \draw (0,1) grid (15,2);
%\node at (-1.1,1.5) {\texttt{node}}; %\node at (-1.1,1.5) {\texttt{node}};
\node at (0.5,1.5) {$1$}; \node at (0.5,1.5) {$1$};
@ -781,6 +800,10 @@ can be found as follows:
\begin{center} \begin{center}
\begin{tikzpicture}[scale=0.7] \begin{tikzpicture}[scale=0.7]
\node[left] at (-1,1.5) {node id};
\node[left] at (-1,0.5) {level};
\fill[color=lightgray] (2,1) rectangle (3,2); \fill[color=lightgray] (2,1) rectangle (3,2);
\fill[color=lightgray] (5,1) rectangle (6,2); \fill[color=lightgray] (5,1) rectangle (6,2);
\fill[color=lightgray] (2,0) rectangle (6,1); \fill[color=lightgray] (2,0) rectangle (6,1);