1. Problem Solving & Algorithms
Diego Aguirre

2. Problem Solving
There is little consensus in how to organize concepts, techniques, approaches, etc. in problem solving.
Different people have come up with different strategies. Some may categorize methods as separate while others may see them as sub- categories.

3. Strategy
We are going to start with a simple problem-solving strategy or framework
IDEAL

4. I D E A L
Can you guess what the I stands for?

5. I D E A L
Identify the Problem

6. I D E A L Let’s define the word Problem
What does the word Problem mean?

7. I D E A L
Problem:
A matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome.
The difference between what is observed and what is expected.
The discrepancy between “what we get and what we want.”

8. I D E A L
Problem:
A problem exists when there is a discrepancy between an initial state and a goal state

9. I D E A L
Source: The IDEAL Problem Solver

10. I D E A L Identify the Problem Problems are often ill-stated unclear
understated

11. I D E A L Before solving a problem, we need to understand it!
What does it mean to understand a problem?

12. I D E A L Before solving a problem, we need to understand it!
What does it mean to understand a problem?
Implications
Understanding a problem -> Understanding what factors/components make it harmful/unwelcomed

13. I D E A L
In this stage, we sense the existence of a problem

14. I D E A L
Can you guess what the D stands for?

15. I D E A L
Define your goals

16. I D E A L Define your goals
Once you understand the problem, you need to think about the format of the solution.
How does a solution look like?
What do you want to happen?

17. I D E A L

18. I D E A L
How would a solution for this problem look like? Can you define a goal?

19. I D E A L
Source: The IDEAL Problem Solver

20. I D E A L
Can you guess what the E stands for?

21. I D E A L
Explore possible strategies or solutions

22. I D E A L
Source: The IDEAL Problem Solver

23. I D E A L This often involves a reanalysis of your goals
options or strategies to achieve those goals

24. I D E A L I am going to ask a question…
I want you to respond as fast as possible….

25. I D E A L
How much is 1 + 1?

26. I D E A L
Let’s do it again…
Ready?

27. I D E A L
What day follows the day before yesterday if two days from now will be Sunday?

28. I D E A L
Why couldn’t you just solve the problem as fast as the first one?

29. I D E A L Good problem solvers break problems into smaller ones…
Remember our Computational Thinking class?
What sub-problems can you find here:
What day follows the day before yesterday if two days from now will be Sunday?

30. I D E A L What is today if two days from now will be Sunday?
If today is Friday, what is the day before yesterday?
What day follows Wednesday?

31. I D E A L What is today if two days from now will be Sunday?
Friday
If today is Friday, what is the day before yesterday?
What day follows Wednesday?

32. I D E A L What is today if two days from now will be Sunday?
Friday
If today is Friday, what is the day before yesterday?
Wednesday
What day follows Wednesday?

33. I D E A L What is today if two days from now will be Sunday?
Friday
If today is Friday, what is the day before yesterday?
Wednesday
What day follows Wednesday?
Thursday

34. I D E A L
What if we had another problem like this, but longer?

35. I D E A L What if we had another problem like this, but longer?
Need external tools

36. I D E A L
A man had four chains, each three links long. He wanted to join the four chains into a single, closed chain. Having a link opened cost 2 cents and having a link closed cost 3 cents. The man had his chains joined into a closed chain for I 5 cents. How did he do it?

37. I D E A L
Another general strategy that good problem solvers often use is to work out a complex or abstract problem by focusing on a simpler, specific situation.
Building scale models or performing experiments that simulate certain characteristics of a real-world environment are good examples of this strategy.

38. I D E A L
You are the director for an upcoming racquetball tournament, and I03 people have entered the open single-elimination tournament (after losing once, the player is eliminated).
If you need a score card for each match, how many cards will you need if each player shows up? (Hint Work out the problem for a very simple case first.)

39. I D E A L
So far we have seen general strategies, like working out small examples or using external resources. However, good problem solvers use specialized knowledge.
Example:
How does Google Maps know what the best route is?
How do physicists solve complex problems?
How do doctors diagnose patients?

40. I D E A L

41. I D E A L The main point here is:
Good problem-solvers must become effective at learning about relevant conceptual tools

42. I D E A L
Computational Thinking?

43. I D E A L A?

44. I D E A L
Anticipate Outcomes and Act

45. I D E A L
Once a strategy is selected, it is important to anticipate possible outcomes and then act on that strategy.
Trash example
What if we decide to ban plastic bags?
What if we charge people for plastic bags?
Space?
What if we tax companies that generate a lot of trash? People?

46. I D E A L L?

47. I D E A L
Look and learn

48. I D E A L
Look at the actual effects of your strategy and learn from the experience.

49. I D E A L
There are 12 cannonballs. They all look alike, but one is the oddball. The oddball is either heavier or lighter than the other balls.
You are supplied with a balance scale that can hold as many cannonballs as you like on each side. The problem is, in four weighings (four uses of the scale), find the oddball.

50. I D E A L
What’s the first thing you would try?

51. Problem Solving
Let’s solve some problems using IDEAL and Computational Thinking!

52. Problem 1

53. Problem Solving We need passwords for everything!
Facebook
Snapchat
UTEP
Gmail
Bank Account
Does this cause any problems? What problems?

54. Problem Solving We need passwords for everything!
Facebook
Snapchat
UTEP
Gmail
Bank Account
Does this cause any problems? What problems?
Solutions???

55. Problem Solving
Algorithms!

56. Problem 2

57. Problem Solving
Hidden object! You cool instructor can find a hidden object in the classroom super quick!

58. Problem 3

59. Problem Solving
Pretend for that you want to send a private message to a friend. The only way you can deliver the message is to write it on a board that is observable by anyone who passes by. What could you and your friend do to ensure that you are the only people who can understand the message? Example:

60. Problem Solving
The characters are divided into two groups: (1) characters for which the image of their uppercase form has an enclosed area (such as P or O) and (2) characters that do not have an enclosed area in in the image of their uppercase form (such as I or Z).
Sort the two groups alphabetically, with group 1 first and then group 2.

61. Problem Solving Applying rule 1:
Group 1:  {A, B, D, O, P, Q, R}            Group 2: {C, E, F, G, H, I, J, K, L, M, N, S, T, U, V, W, X, Y, Z}
Applying rule 2: A, B, D, O, P, Q, R, C, E, F, G, H, I, J, K, L, M, N, S, T, U, V, W, X, Y, Z

62. Problem Solving 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 A B D O P Q R C E F G H I J K L M N S T U V W X Y Z

63. Problem Solving 1 2 3 4 5 6 7 8 9 A N B O C P D Q E R F S G T H U I V
Crate a second Alphabet Mapping #2. 1 2 3 4 5 6 7 8 9 A N B O C P D Q E R F S G T H U I V J W K X L Y M Z

64. Problem Solving Get in teams of two and create two mappings
Encode a simple message using Mapping #1
Encode a simple message using Mapping #2
Encode a simple message using Mapping #1 and then Mapping #2

65. Problem Solving How would you do this on a computer?
Try to decipher other teams codes!