From 1dde989058d026b7dcec4ad51a5de1c9e7414d4d Mon Sep 17 00:00:00 2001
From: Galina Pokitko
Date: Wed, 5 Aug 2026 16:58:36 -0500
Subject: [PATCH] Fixed Spacing for Chapter 8
---
pretext/Trees/AVLTreeImplementation.ptx | 3 +++
pretext/Trees/AVLTreePerformance.ptx | 3 +++
pretext/Trees/BalancedBinarySearchTrees.ptx | 3 +++
pretext/Trees/BinaryHeapImplementation.ptx | 3 +++
pretext/Trees/BinaryHeapOperations.ptx | 3 +++
pretext/Trees/BinaryHeapPriorityQExample.ptx | 3 +++
pretext/Trees/BinarySearchTrees.ptx | 3 +++
pretext/Trees/DiscussionQuestions.ptx | 3 +++
pretext/Trees/ExamplesofTrees.ptx | 3 +++
pretext/Trees/Glossary.ptx | 3 +++
pretext/Trees/ListofListsRepresentation.ptx | 3 +++
pretext/Trees/Matching.ptx | 3 +++
pretext/Trees/NodesandReferences.ptx | 3 +++
pretext/Trees/Objectives.ptx | 3 +++
pretext/Trees/ParseTree.ptx | 5 ++++-
pretext/Trees/PriorityQueueswithBinaryHeaps.ptx | 3 +++
pretext/Trees/ProgrammingExercises.ptx | 3 +++
pretext/Trees/SearchTreeAnalysis.ptx | 3 +++
pretext/Trees/SearchTreeImplementation.ptx | 3 +++
pretext/Trees/SearchTreeOperations.ptx | 3 +++
pretext/Trees/Summary.ptx | 3 +++
pretext/Trees/SummaryofMapADTImplementations.ptx | 3 +++
pretext/Trees/TreeTraversals.ptx | 3 +++
pretext/Trees/VocabularyandDefinitions.ptx | 3 +++
24 files changed, 73 insertions(+), 1 deletion(-)
diff --git a/pretext/Trees/AVLTreeImplementation.ptx b/pretext/Trees/AVLTreeImplementation.ptx
index 7d2b7681..e40e5a34 100755
--- a/pretext/Trees/AVLTreeImplementation.ptx
+++ b/pretext/Trees/AVLTreeImplementation.ptx
@@ -520,4 +520,7 @@ void rebalance(TreeNode *node){
+
+
+
diff --git a/pretext/Trees/AVLTreePerformance.ptx b/pretext/Trees/AVLTreePerformance.ptx
index 9ffa6090..9a9d828b 100755
--- a/pretext/Trees/AVLTreePerformance.ptx
+++ b/pretext/Trees/AVLTreePerformance.ptx
@@ -90,4 +90,7 @@
equal to a constant(1.44) times the log of the number of nodes in the tree. This
is great news for searching our AVL tree because it limits the search to
O(\log{N}).
+
+
+
diff --git a/pretext/Trees/BalancedBinarySearchTrees.ptx b/pretext/Trees/BalancedBinarySearchTrees.ptx
index 1e9b693a..fefc410d 100755
--- a/pretext/Trees/BalancedBinarySearchTrees.ptx
+++ b/pretext/Trees/BalancedBinarySearchTrees.ptx
@@ -41,4 +41,7 @@
+
+
+
diff --git a/pretext/Trees/BinaryHeapImplementation.ptx b/pretext/Trees/BinaryHeapImplementation.ptx
index d0e9449a..3a03233c 100755
--- a/pretext/Trees/BinaryHeapImplementation.ptx
+++ b/pretext/Trees/BinaryHeapImplementation.ptx
@@ -577,4 +577,7 @@ main()
What is the vector used in the binary tree in the first image of ? Exclude any whitespace.
Is the correct answer!
Remember what has to be at the beginning of the vector to accurately traverse through the binary tree. Look back at chp. 8.9.2.
Refer to section 8.10.1 and 8.10.2
+
+
+
diff --git a/pretext/Trees/BinaryHeapOperations.ptx b/pretext/Trees/BinaryHeapOperations.ptx
index deb9345c..d55baa70 100755
--- a/pretext/Trees/BinaryHeapOperations.ptx
+++ b/pretext/Trees/BinaryHeapOperations.ptx
@@ -239,4 +239,7 @@ main()
+
+
+
diff --git a/pretext/Trees/BinaryHeapPriorityQExample.ptx b/pretext/Trees/BinaryHeapPriorityQExample.ptx
index 9392d63c..ddc03223 100755
--- a/pretext/Trees/BinaryHeapPriorityQExample.ptx
+++ b/pretext/Trees/BinaryHeapPriorityQExample.ptx
@@ -23,5 +23,8 @@
As we continue to complete the homework with the closest deadline we will continue to remove the homeworks in the demostrated fashion until we are done.
+
+
+
diff --git a/pretext/Trees/BinarySearchTrees.ptx b/pretext/Trees/BinarySearchTrees.ptx
index 0154f5c4..beec5b87 100755
--- a/pretext/Trees/BinarySearchTrees.ptx
+++ b/pretext/Trees/BinarySearchTrees.ptx
@@ -8,5 +8,8 @@
case we are not interested in the exact placement of items in the tree,
but we are interested in using the binary tree structure to provide for
efficient searching.
+
+
+
diff --git a/pretext/Trees/DiscussionQuestions.ptx b/pretext/Trees/DiscussionQuestions.ptx
index c154c0e7..61399dc4 100755
--- a/pretext/Trees/DiscussionQuestions.ptx
+++ b/pretext/Trees/DiscussionQuestions.ptx
@@ -106,5 +106,8 @@
+
+
+
diff --git a/pretext/Trees/ExamplesofTrees.ptx b/pretext/Trees/ExamplesofTrees.ptx
index 68292f20..6c893f13 100755
--- a/pretext/Trees/ExamplesofTrees.ptx
+++ b/pretext/Trees/ExamplesofTrees.ptx
@@ -159,5 +159,8 @@
+
+
+
diff --git a/pretext/Trees/Glossary.ptx b/pretext/Trees/Glossary.ptx
index c35e0789..7db0fb0c 100755
--- a/pretext/Trees/Glossary.ptx
+++ b/pretext/Trees/Glossary.ptx
@@ -186,5 +186,8 @@
+
+
+
diff --git a/pretext/Trees/ListofListsRepresentation.ptx b/pretext/Trees/ListofListsRepresentation.ptx
index 71b01009..7851f472 100755
--- a/pretext/Trees/ListofListsRepresentation.ptx
+++ b/pretext/Trees/ListofListsRepresentation.ptx
@@ -237,4 +237,7 @@ main()
+
+
+
diff --git a/pretext/Trees/Matching.ptx b/pretext/Trees/Matching.ptx
index 0f48b6d0..479d276e 100644
--- a/pretext/Trees/Matching.ptx
+++ b/pretext/Trees/Matching.ptx
@@ -83,4 +83,7 @@
+
+
+
diff --git a/pretext/Trees/NodesandReferences.ptx b/pretext/Trees/NodesandReferences.ptx
index b5222571..4610f611 100755
--- a/pretext/Trees/NodesandReferences.ptx
+++ b/pretext/Trees/NodesandReferences.ptx
@@ -380,4 +380,7 @@ main()
+
+
+
diff --git a/pretext/Trees/Objectives.ptx b/pretext/Trees/Objectives.ptx
index f92dd6af..93967a54 100755
--- a/pretext/Trees/Objectives.ptx
+++ b/pretext/Trees/Objectives.ptx
@@ -20,5 +20,8 @@
To implement a priority queue using a heap.
+
+
+
diff --git a/pretext/Trees/ParseTree.ptx b/pretext/Trees/ParseTree.ptx
index 51bf3ebd..26b26892 100755
--- a/pretext/Trees/ParseTree.ptx
+++ b/pretext/Trees/ParseTree.ptx
@@ -576,5 +576,8 @@ def evaluate(parseTree):
-
+
+
+
+
diff --git a/pretext/Trees/PriorityQueueswithBinaryHeaps.ptx b/pretext/Trees/PriorityQueueswithBinaryHeaps.ptx
index 898c2cd3..4bec6e26 100755
--- a/pretext/Trees/PriorityQueueswithBinaryHeaps.ptx
+++ b/pretext/Trees/PriorityQueueswithBinaryHeaps.ptx
@@ -30,5 +30,8 @@
at the front, and the max heap, in which the largest key value is
always at the front. In this section we will implement the min heap. We
leave a max heap implementation as an exercise.
+
+
+
diff --git a/pretext/Trees/ProgrammingExercises.ptx b/pretext/Trees/ProgrammingExercises.ptx
index 3ae339ae..c2486770 100755
--- a/pretext/Trees/ProgrammingExercises.ptx
+++ b/pretext/Trees/ProgrammingExercises.ptx
@@ -54,5 +54,8 @@
constructor, plus the enqueue and dequeue methods.
+
+
+
diff --git a/pretext/Trees/SearchTreeAnalysis.ptx b/pretext/Trees/SearchTreeAnalysis.ptx
index 41adc190..bc75fc02 100755
--- a/pretext/Trees/SearchTreeAnalysis.ptx
+++ b/pretext/Trees/SearchTreeAnalysis.ptx
@@ -73,5 +73,8 @@
+
+
+
diff --git a/pretext/Trees/SearchTreeImplementation.ptx b/pretext/Trees/SearchTreeImplementation.ptx
index 4c13a6f2..4b844a99 100644
--- a/pretext/Trees/SearchTreeImplementation.ptx
+++ b/pretext/Trees/SearchTreeImplementation.ptx
@@ -1279,4 +1279,7 @@ main()
+
+
+
diff --git a/pretext/Trees/SearchTreeOperations.ptx b/pretext/Trees/SearchTreeOperations.ptx
index 68a2d820..037f8885 100755
--- a/pretext/Trees/SearchTreeOperations.ptx
+++ b/pretext/Trees/SearchTreeOperations.ptx
@@ -26,5 +26,8 @@
length() Return the number of key-value pairs stored in the tree.
+
+
+
diff --git a/pretext/Trees/Summary.ptx b/pretext/Trees/Summary.ptx
index 2e2fcdb0..fdefa849 100755
--- a/pretext/Trees/Summary.ptx
+++ b/pretext/Trees/Summary.ptx
@@ -17,5 +17,8 @@
A min heap used to implement a priority queue.
+
+
+
diff --git a/pretext/Trees/SummaryofMapADTImplementations.ptx b/pretext/Trees/SummaryofMapADTImplementations.ptx
index 29bcd9fd..21105f55 100755
--- a/pretext/Trees/SummaryofMapADTImplementations.ptx
+++ b/pretext/Trees/SummaryofMapADTImplementations.ptx
@@ -100,5 +100,8 @@
+
+
+
diff --git a/pretext/Trees/TreeTraversals.ptx b/pretext/Trees/TreeTraversals.ptx
index 43ce1e77..e65b2226 100755
--- a/pretext/Trees/TreeTraversals.ptx
+++ b/pretext/Trees/TreeTraversals.ptx
@@ -455,4 +455,7 @@ Section2.1, Section2.2.1, Section2.2.2, Section2.2,
+
+
+
diff --git a/pretext/Trees/VocabularyandDefinitions.ptx b/pretext/Trees/VocabularyandDefinitions.ptx
index 97c4165b..9f32f370 100755
--- a/pretext/Trees/VocabularyandDefinitions.ptx
+++ b/pretext/Trees/VocabularyandDefinitions.ptx
@@ -154,4 +154,7 @@
+
+
+