From 80057a1ea9cd717f3a8c78d3d1c70024513b509c Mon Sep 17 00:00:00 2001
From: Antti H S Laaksonen <ahslaaks@cs.helsinki.fi>
Date: Fri, 24 Feb 2017 20:22:45 +0200
Subject: [PATCH] Better array representation

---
 chapter18.tex | 29 ++++++++++++++++++++++++++---
 1 file changed, 26 insertions(+), 3 deletions(-)

diff --git a/chapter18.tex b/chapter18.tex
index 732d404..2be2193 100644
--- a/chapter18.tex
+++ b/chapter18.tex
@@ -266,14 +266,18 @@ is $3+4+3+1=11$.
 \end{center}
 
 The idea is to construct a tree traversal array that contains
-three values for each node: (1) the identifier of the node,
-(2) the size of the subtree, and (3) the value of the node.
+three values for each node: the identifier 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:
 
 \begin{center}
 \begin{tikzpicture}[scale=0.7]
 \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 (1.5,0.5) {$2$};
 \node at (2.5,0.5) {$6$};
@@ -330,6 +334,10 @@ can be found as follows:
 \fill[color=lightgray] (4,-1) rectangle (8,-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 (1.5,0.5) {$2$};
 \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]
 \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 (1.5,0.5) {$2$};
 \node at (2.5,0.5) {$6$};
@@ -491,6 +503,10 @@ the array changes as follows:
 \fill[color=lightgray] (4,-1) rectangle (8,-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 (1.5,0.5) {$2$};
 \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.
 
 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.
 The following array corresponds to the above tree:
 
 \begin{center}
 \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);
 %\node at (-1.1,1.5) {\texttt{node}};
 \node at (0.5,1.5) {$1$};
@@ -781,6 +800,10 @@ can be found as follows:
 
 \begin{center}
 \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] (5,1) rectangle (6,2);
 \fill[color=lightgray] (2,0) rectangle (6,1);