1. Extension of linked list
Zhen Jiang
West Chester University

2. Outline Double Cyclic Linked List Queue & Stack Binary Tree
Expression Tree
Networks

3. (Single) Linked list
node
NULL

4. Double Cyclic Linked List
node
NULL

5. Queue node Delete an item from the tail NULL
Insert a new item at the head

6. Stack node NULL Insert a new item at the head
Delete an item from the head

7. Implementation of stack with template

8. Use of Stack Project 5 Reading information via file
Three stacks, one for each {}, (), and [].
Left => push/insert
Right => pop/delete the closest left symbol
Evaluation of (postfix) expression

9. * *
5 4 * 3 +
5 4 3 * +
(5 + 4) * 3
5 * (4 + 3)
5 * 4 + 3
5 + (4 + 3)

10. Read the formula from left to right Number => push
Binary operator => 2 pops
Right number popped first
Then, left number popped.
Calculate result = <second> op <first>
Push (result)
Until expression reading finishes and only one (final) result is left in stack

11. Disorder of the link connection
node
NULL

12. Tree Definition Each node u has n(u) children
Considering the parent-child relationship is undirected, there is no cycle in a tree
There is only one node called the root in the entire tree. It has children only but no parent.

13. Binary Tree Definition Definition of tree (3)
For each node u, n(u)<3
L<S<R
< is a relation between any two nodes in the tree

14. Constructor
Assume each node has a number value so that we have the relation <
Given a sequence: n1, n2, n3, …, ni, …
n1 -> set root unit (node)
ni -> call insertion(node, ni)

15. Insertion(p, n) If (p->v < n) If (p->v > n)
If p->R not empty
Insertion (p->R, n)
else
Set p->R
If (p->v > n)
Similar to the case (p->v < n)

16. Travel (print out all node values)
Infix travel, L->S->R
Postfix travel, L->R->S
Prefix travel, S->L->R

17. Infix travel If node is not empty, Infix_print (node); Infix_print (p)
If (p->L) infix_print(p->L)
Cout << p->v
If(p->R) infix_print (p->R)

18. Search If node is not empty, Search (node, n); Search (p, n)
If (p->v == n) return true
If (p->v < n) return Search (p->R, n)
If (p->v > n) return Search (p->L, n)
Terminating condition: if (!p) return false

19. Deletion Delete the root node If node is empty
If node->L (or node->R) is empty
tmp = node->R (or node->L)
Delete node
node = tmp

20. If neither node->L nor node->R is empty
If node->L->R is empty
node -> v = node->L->v
tmp = node->L->L
Delete node->L
node->L = tmp
Else
tmp = node->L
While (tmp->R->R) tmp = tmp->R
node->v = tmp->R->V
tmp2 = tmp->R->L
Delete tmp->R
tmp->R = tmp2

21. See if you can find a certain value in the tree and delete it!
Delete (n)
If (node->v == n) delete node;
If (node->v < n)
deletion (node, node-R, n, 1)
If (node->v > n)
deletion (node, node-L, n, 0)

22. Deletion (parent, start, value, flag)
If start is empty // not found, done!
If start->v < value
If start->v > value
Else //start->v == value
If both start->L and start->R are empty
Delete start
If (flag)Parent ->R = NULL
Else Parent -> L = NULL
If start->L (or start->R) is empty

23. Deletion (parent, start, value, flag)
Else //start->v == value
If start->L (or start->R) is empty
If (flag) Parent-R = Start->R (or start->L)
Else Parent->L = Start->R
Delete start
If neither start->L nor start->R is empty

24. If start->L->R is empty
start -> v = start->L->v
tmp = start->L->L
Delete start->L
start->L = tmp
Else
tmp = start->L
While (tmp->R->R) tmp = tmp->R
start->v = tmp->R->V
tmp2 = tmp->R->L
Delete tmp->R
tmp->R = tmp2

25. Expression Tree Definition Definition of binary tree (5)
All leaves are numbers, and all intermediate nodes are operators
To simplify the discussion in this class, we use binary operators only.

26. Evaluation If node is not empty, R_E(node); R_E(p)
If p->v is not digit
Lvalue = R_E(p->L);
Rvalue = R_E(p->R);
Return Lvalue <p->v> Rvalue;
Else
Return p->v

27. Print Construction Postfix From infix format

28. Network Graph table Depth first search Width first search
Depth first search
Width first search
Shortest path construction

29. Spanning (travel)
Project 7