Stacks

1
Stacks Queues(Ch. 4 5 in text)
2
Base-Conversion Algorithm

• Convert a base-10 number to base-2
• Algorithm input, output, steps
• Use Stack data structure
• Push the remainders into the stack
• Pop the data out
• DIY by hand 2710 - XXXX2, show the stack
  contents on each step

3
Implementing a Stack class

• Data members data type
• How do you store the items in a stack?
• Use array (any drawback?)
• Add an indicator for the top pointer of an array
  (still, this implementation has the capability
  issue)
• Linked list
• Member functions
• Empty
• Push
• Pop

4
Exercise 4.2

• Problem 10 the railroad switching network
• When push, the car on the right (before the
  intersection) will go into the siding. When
  move, the car goes directly to the left. When
  pop, the car on the top of the siding will go to
  the left.
• For n3, there are totally 6321 permutations.
  What operations will be needed for each one? Is
  there a permutation not possible (312)
• Homework 10(b)

5
Reverse Polish Notation (RPN)

• Infix notation 2(34)
• Postfix 234
• Note no parenthesis is needed
• Application Compiler. Postfix expressions are
  easier to evaluate mechanically

6
Evaluation RPN

• Scanned the expression from left to right until
  an operator is found
• The last two operands are combined using this
  operator just found
• Replace the sub-expression with the value
  calculated, obtain a reduced RPN
• Repeat the above process until the result is
  yield and no more operator exists

7
RPN Evaluation examples

• 15841--
• 2495-

8
Converting Infix Expressions to RPN

• Using expression trees
• ab
• a(bc)
• (ab)(c/(d-e))
• Traverse the tree in a Left-Right-Parent order
• ab
• ?
• ?

9
Converting (from infix to postfix) algorithm

• Fully parenthesize the expression
• Replace each right parenthesis by the
  corresponding operator
• Erase all left parenthesis
• Example ((ab)c)
• - ((ab) c
• - ((a b c
• - abc

10
Exercises 4.3

• 1-11
• 12-14
• 15-22
• 28-35
• 46-52

11
Basics of Queues
front
back

• FIFO or FIFS
• Basic operations in text
• Empty
• AddQ (add an element at the back of the queue)
• Front (retrieve the element at the front of the
  queue)
• RemoveQ (remove the element at the front of the
  queue)

12
Implementation of Queues

• Array-based
• The shift back issue (page 221) cause
  inefficiency
• Can be avoided by thinking of the array as
  circular, with first element following the last
  (page 222)

13
Exercises 5.2

• 1-4
• 14