Extension of linked list

Zhen Jiang West Chester University

zjiang@wcupa.edu

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

(Single) Linked list

NULL

node

Double Cyclic Linked List

NULL

node

Queue

NULL

node

Insert a new item at the head

Delete an item from the tail

Stack

NULL

node

Insert a new item at the head

Delete an item from the head

Implementation of stack with template http://www.cs.wcupa.edu/~zjiang/

csc513_template.ppt

Use of Stack Project 5

Reading information via file http://www.cs.wcupa.edu/~zjiang/

530_proj5_file.pdf Three stacks, one for each {}, (), and [].

Left => push/insert Right => pop/delete the closest left symbol

Evaluation of (postfix) expression

5 4 + 3 * 5 4 3 + * 5 4 * 3 + 5 4 3 * +

(5 + 4) * 3 5 * (4 + 3) 5 * 4 + 3 5 + (4 + 3)

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

Disorder of the link connection

NULL

node

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.

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

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)

Insertion(p, 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)

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

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)

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

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

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

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)

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

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

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

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.

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

Print Postfix

Construction From infix format http://www.cs.wcupa.edu/~zjiang/

csc530_expressionTree.htm

Network Graph table

http://www.cs.wcupa.edu/~zjiang/csc530_graph_table.pdf

Depth first search http://www.cs.wcupa.edu/~zjiang/csc530_depth.pdf

Width first search http://www.cs.wcupa.edu/zjiang/csc530_width.pdf

Shortest path construction http://www.cs.wcupa.edu/~zjiang/

csc530_shortestpath.pdf

Spanning (travel) Project 7