1. Computer Science 2: Trees

2. Goals/Learning Objectives/Learning Targets/…
Complete a dry run that includes, dynamics, recursion, and multiple pointers!
Use notes to help capture today’s thoughts.
Understand the definition of a Binary Tree.
Be able to demonstrate adding to a tree.
Develop pseudo-code and code for adding to a tree.
Develop pseudo-code and code for showing from a tree.

3. procedure b(top:ptrtype); begin if top^.left<> nil then
program DryRunTree1;
type
ptrtype = ^nodetype;
nodetype = record
score:integer;
left, right:ptrtype;
end;
var
top:ptrtype;
num:integer;
procedure a(var top:ptrtype;count:integer);
begin
if top = nil then
new(top);
top^.score:=count;
top^.left:=nil;
top^.right:=nil;
end
else if count MOD 2 = 0 then
a(top^.right, 2*count)
else
a(top^.left, 2*count);
procedure b(top:ptrtype);
begin
if top^.left<> nil then
b(top^.left);
writeln(top^.score);
if top^.right<> nil then
b(top^.right);
end;
top:=nil;
for num:= 1 to 5 do
a(top,num);
b(top);
end.

4. Binary Trees What is it? Benefits
In computer science, a binary tree is a tree data structure in which each node has at most two children. Typically the child nodes are called left and right. One common use of binary trees is binary search trees.
Benefits
Dynamic size
Fast access (Compared to an insertion linked list)
Sorts data as it is entered. …

5. Node 1,2,3 are children of root
Definitions
root
Nodes 1-6 are
descendants
of node 0
Node 0
Node 1,2,3 are children of root
Node 1
Node 2
Node 3
Node 1 is parent of
Nodes 4,5
Node 4
Node 5
Node 6
leaves
Node 4 and 5 are siblings

6. Binary Search Trees
A binary tree where every node's left sub tree has values less than the node's value, and every right sub tree has values greater. 76 39 80 32 47 79

7. Binary Search Trees Applet: animated BST
How to add to a binary search tree ?
Applet: animated BST

8. Add Pseudo Code If top is nill
Practice Adding:
50, 8, 90, 45, 12, 63, 20, 14, 71
90, 80, 70, 60, 50,40
Pseudo Code
If top is nill
Put it in the tree
Else if bigger than or equal to top’s value
Add value to top’s right
Else
Add value to top’s left

9. Developing the code for adding
procedure add(var top:ptrtype;c:integer);
var
temp:ptrtype;
begin
if top=nil then
new(temp);
top:=temp;
temp^.num:=c;
temp^.left:=nil;
temp^.right:=nil;
end
else if c>= top^.num then
add(top^.right, c)
else
add(top^.left, c);
end;
Pseudo Code
If top is nill
Put it in the tree
Else if >= top’s value
Add value to top’s right
Else
Add value to top’s left
Test it with…
30, 50, 20, 75, 15, 65
3, 6, 8, 30, 27, 90, 100

10. Take 3 minutes to summarize your information about Binary Trees.
Definitions
Parts
Adding algorithm

11. Showing the Information
What is the first number that should be shown? (Low to high)
How can you get there?
How about the second value?
Third…?
How can you do this? 76 39 80 32 47 79

12. Developing code for show
PseudoCode
Show in order (Infix)
If you can go left
Go left
Show
If you can go right
Go right
procedure show(top:ptrtype);
begin
if top^.left<> nil then
show(top^.left);
writeln(top^.num);
if top^.right<> nil then
show(top^.right);
end;

13. Tree 1 Menu Push: Show all (High to low using the same tree)
Add a name
Show All (In order: Low to high)
Push: Show all (High to low using the same tree)
Push: Add a procedure to check is someone is in the tree. (If they are in the tree it says they are, if they are not, it says that are not.)
Push: Make this a boolean function that returns true if they are in the tree and false if they are not.
Push: Delete someone from the tree.
Push: On the Show from a tree, have it show the information like a tree.