Class 3'1

1
Class 3.1

• Problem Solving Methods
• and
• Algorithms

2
RAT 3.1

• Close your notes, close you laptops or turn off
  your computer monitors.
• As an individual you have 2 minutes to answer the
  following question.
• Name two common ways to write or describe an
  algorithm.
• Answer Flowcharts and pseudocode

3
Learning Objectives

• Learn to apply the problem solving process
• Learn techniques for error-free problem solving

4
Learning Objectives

• Define an algorithm
• Know what is meant by "decomposition" of a
  problem
• Learn how to write algorithms using flowcharts
  and pseudocodes.
• Know what is meant by "top-down" design method.

5
Difficulties in Problem Solving

• Most common difficulty failure to use known
  information.
• To avoid this problem
• Write the problem in primitive form and sketch an
  accurate picture of the setup (where applicable).
• Transform the primitive statements to simpler
  language.
• Translate verbal problems to more abstract
  mathematical statement(s) and figures, diagrams,
  charts, etc.

6
More Difficulties in Solving Problems(AGAIN)

• Imposing unnecessary constraints
• Association Constraints - unstated constraints
  based on previously learned associations.
• Function Constraints - unstated constraints based
  on previously learned functions.
• World View Constraints - unstated constraints
  imposed by individual's world view.

7
Problem Solving Process

• Define and understand problem
• Gather information
• Generate potential methods and solutions.
• Refine and implement solution.
• Verify and test solution.

8
Define and Understand

• Understand what is being asked
• Describe input/output (I/O)
• what are you given
• knowns
• what are you trying to find
• unknowns
• Sketch the problem

9
Gather Information

• Collect necessary data
• List relevant equations/theories
• State all assumptions

10
Generate Solution Methods

• Apply theories and assumptions.
• Typically, there is more than one approach to
  solving a problem
• Work problem by hand using the potential solution
  methods
• Break problem into parts scale it down etc.
• e.g., if the problem was to calculate the average
  of 1000 numbers, work the problem by hand using,
  say, 10 numbers, in order to establish a method

11
Refine and Implement

• Evaluate solution methods.
• accuracy
• ease of implementation
• etc.
• Implement best solution.

12
Verify and Test

• Compare solution to the problem statement
• Is this what you were looking for?
• Does your answer make sense?
• Clearly identify the solution
• Sketch if appropriate

13
CHECK YOUR WORK!!

• Dont stop at getting an answer!!
• Think about whether the answer makes physical
  sense.
• you are the instructor and you have to turn in
  final grades. In your haste, you calculate the
  average of Susies grades (100, 70, 90) to be 78
  and give Susie a C...

14
Getting It Right

• The problem solving process may be an iterative
  process.
• If at first you dont succeed (i.e. the algorithm
  test fails), try again
• The more thorough you are at each step of the
  problem solving process, the more likely you are
  to get it right the first time!!

15
Individual Exercise-Revisited (5 minutes)

• Required
• a) Sketch the problem
• b) How many acres of land are contained by the
  cone created by her line of site?
• c) How high would the balloon be if, using the
  same procedure, an area four times greater is
  encompassed?

• Given A student is in a stationary hot-air
  balloon that is momentarily fixed at 1325 ft.
  above a piece of land. This pilot looks down 60o
  (from horizontal) and turns laterally 360o.

16
Solution to part A Sketch

• Given An engineering student is in a stationary
  hot-air balloon that is momentarily fixed at 1325
  ft. above a piece of land. This pilot looks down
  60o (from horizontal) and turns laterally 360o.

17
Solution to part B Algorithm
Fundamental trigonometry relationship tan(30o)
Viewing Radius/Elevation Part a) Viewing
Radius R 1325 tan(30o) 765.0 ft Area pR2
p(765.0 ft)2 1.838 x 106 ft2 Area 1.838 x
106 ft2 (1 acre/43,560 ft2) Area 42.21 acres
18
Solution to part C Heuristic
Part b) Area f(Viewing Radius)2 Therefore
to increase the area by a factor of 4, the
viewing radius must increase by a factor of
2. Viewing Radius f(Elevation) Therefore
to increase the viewing radius by a factor of 2,
the elevation must also increase by a factor of
2. Elevation 2(1325 ft) 2650 ft
19
HOMEWORK FORMAT

• See Homework Format 111-112.doc on ENGR 111/112
  file server
• Use this format to solve the balloon problem.
• Submit your solution as In-Class Assignment 3.1

20
VCR Problem Statement

• You own a VCR that has two recording and playback
  speeds 1) standard play (SP) and 2) extended
  play (EP). The speed in the EP mode is 1/3 the
  speed in the SP mode. At the SP setting, the
  video tapes you own can be used to record exactly
  120 minutes of video. Suppose you want to use
  these tapes to record programs longer than 120
  minutes?

21
Step 1 Understand the Problem

• You need to know how long to record at the EP
  speed and at SP speed so that the program fits
  exactly on a 120 minute tape. The EP mode does
  not have quality of resolution of the SP mode, so
  you want to record in the EP mode the minimum
  amount of time.

22
Exercise

• Turn off your monitors or close your laptops.
• As a TEAM, take 15 MINUTES to develop a solution
  to this problem

23
SOLUTION

• Let
• TSP time in SP mode (unknown)
• TEP time in EP mode (unknown)
• LP length of program (known)
• LT length of tape (known)
• Two unknowns, therefore two INDEPENDENT equations
  needed.

24
Solution

• Equation for real time
• TSP TEP LP 1)
• Equation for tape time
• TSP (1/3)TEP LT 2)
• Solve 1) 2) simultaneously for TSP and TEP

25
Solution

• TEP (3/2)(LP - LT) 3)
• TSP (3/2)LT - (1/2)LP 4)
• NOTE LT and LP are KNOWN.
• Check
• LT120 min. let LP300 min.
• then TEP270, TSP30
• Correct?

26
Develop Method

• If LP is greater than 3LT then
• program will not fit on the tape
• if LP is less than or equal to LT then
• TSP LP
• TEP 0
• otherwise (i.e. LP is between LT and 3LT)
• TEP (3/2)(LP - LT)
• TSP (3/2)LT - (1/2)LP

27
Problem Solving Process

• General Problem Solving Method
• Define and understand problem.
• Sketch the problem
• Gather information.
• Generate and evaluate potential solutions.
• Use applicable theories and assumptions.
• Refine and implement solution.
• Verify and test solution.

28
Exercise

• Close your laptops/turn off monitors.
• dont reopen/turn on until instructed
• As a TEAM, take 2 minutes to list what you know
  about pseudocode and flowcharts.

29
Algorithms

• Algorithm a step-by-step procedure for solving
  a problem or accomplishing an end (Webster)
• Algorithms can be described by
• Pseudocode
• Flowcharts

30
Pseudocode

• (you can reopen laptops/turn on monitors now)
• English-like description of each step of
  algorithm
• Not computer code
• Example - take out trash barrels
• while there are more barrels
• take barrel to street
• return to garage
• end

31
Flowcharts

• Graphical description of algorithm
• Standard symbols used for specific operations

32
Flowchart Example
33
Flowchart for VCR Problem
Output Program will not fit on tape.
LPgt3LT?
Input LP Input LT
Yes
Start
No
Output Record entire program in SP.
LPLT?
TEP 3/2(LP-LT) TSP 3/2(LT)1/2(LP)
No
Yes
Output TEP Output TSP
End
34
Top Down Design

• State problem clearly
• Sketch problem
• Describe input/output (I/O)
• Work problem by hand
• Algorithm pseudocode or flowchart
• Decomposition - break problem into steps
• Stepwise refinement - solve each step
• Test the algorithm/check your work!!

35
Getting It Right

• The problem solving process may be an iterative
  process.
• If at first you dont succeed (i.e. the algorithm
  test fails), try again
• The more thorough you are at each step of the
  problem solving process, the more likely you are
  to get it right the first time!!

36
VCR Problem Revisited

• You own a VCR that has two recording and playback
  speeds 1) standard play (SP) and 2) extended
  play (EP). The speed in the EP mode is 1/3 the
  speed in the SP mode. At the SP setting, the
  video tapes you own can be used to record exactly
  120 minutes of video. Suppose you want to use
  these tapes to record programs longer than 120
  minutes?

37
Exercise

• As a TEAM, take 15 MINUTES to develop an
  algorithm to hand in using a flowchart or
  pseudocode to solve the VCR problem.

38
Algorithm (Psedudocode)

• If LP is greater than 3LT then
• program will not fit on the tape
• elseif LP is less than or equal to LT then
• TSP LP
• TEP 0
• else (LP is greater than LT)
• TEP (3/2)(LP - LT)
• TSP (3/2)LT - (1/2)LP
• end

39
Algorithm (Flowchart)
Output Program will not fit on tape.
LPgt3LT?
Input LP Input LT
Yes
Start
No
Output Record entire program in SP.
LPLT?
TEP 3/2(LP-LT) TSP 3/2(LT)1/2(LP)
No
Yes
Output TEP Output TSP
End
40
Think-Pair-Share

• In the next 1 minute as an Individual...
• if I only answer one question . . . specifically
  what topics that we have covered so far
  (including today) are still unclear to you at
  least 3 things
• Now take 2 minutes to merge your list with the
  person sitting next to you AND add 1 new item to
  the list
• In the next 5 minutes share the results with the
  other half of your team, delete questions that
  you can answer for each other, AND prioritize the
  remaining questions your list

41
Assignments

• Assignment 3
• Due 9/24/02
• INDIVIDUAL ASSIGNMENT
• Foundations 3.5, 3.6, 3.12, 3.14
• Assignment 4
• Due 9/24/02
• TEAM ASSIGNMENT
• Foundations 4.5, 4.6, 4.7, plus VCR problem (if
  not completed in class)
• YOU MAY USE FLOW CHARTS OR PSEUDOCODE