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 node NULL

Double Cyclic Linked List node NULL

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

Stack node NULL 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 node NULL

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->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 Construction Postfix From infix format http://www.cs.wcupa.edu/~zjiang/csc530_expressionTree.htm

Network Graph table Depth first search Width first search 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