Visual Problem Solving (Lecture)
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The document discusses algorithms and problem solving techniques like flowcharts and top-down design. It provides examples of using each technique to solve problems like building a barn, operating an ATM, and calculating the Fibonacci sequence. Key steps include breaking problems down into smaller sub-problems, modeling the logic with tools like flowcharts, and refining the models through step-wise decomposition.
Visual Problem Solving (Lecture)
- 1. VISUAL PROBLEM SOLVING Computer Science 20S with Mr. Wachs – Thursday, September 16, 2021
- 2. Algorithm
- 3. Algorithm Flowcharts have applications in many areas other than computer solutions For example, in how-to-build-it instructions and recipes An algorithm is a step-by- step procedure for solving a problem
- 4. Algorithm (cont’d) An algorithm for baking a chocolate cake is the chocolate cake recipe An algorithm for repairing your Mustang carburetor is the instructions in the shop manual A flowchart is a “picture” of the algorithm If it is done well, it is like a road map, and the path to the solution will be smooth
- 5. Algorithm (cont’d) A computer program is a set of instructions that tells a computer to solve a problem in a step-by-step manner The program is written from a logic representation The model we employ when using the computer to find a solution is first the algorithm and then the “picture” A flowchart
- 6. Algorithm (cont’d) From the flowchart we form a computer program, which we use to arrive at the solution We can check the solution either by hand or by running the program Here are two analogous stages to problem solving (with the computer and without)
- 7. Algorithm (cont’d) Without Computer With Computer 1. What is the problem? Same 2. Make a model of the problem Develop an algorithm 3. Analyze the model Use a flowchart? 4. Find the solution Write a computer program 5. Check the solution Run the program
- 8. Problem Solving… Continuing with our analysis of higher-level problem solving techniques, today we will examine the concept of Top Down Design Problem solving often involves breaking a problem down into smaller more manageable parts Then deal with each part individually
- 9. Top Down Design This method is well suited to problem solving It allows us to start with general steps and elaborate on them until the problem is solved The process of making the steps more and more specific in top down design is called stepwise refinement
- 10. Let’s Try it… (1.) The problem: Building a barn This is a big project, so we break the project down into smaller steps
- 11. Top Down Design (cont’d) Let’s Build a Barn Build Foundation Build Walls Build Roof Now continue with the step wise refinement, breaking down each section again
- 12. Top Down Design (cont’d) Build a Barn Build Foundation Build Walls Build Roof step wise refinement could continue even more, but you see the pattern Dig Concrete Framing Paneling Rafters Shingles
- 13. Top Down Design (cont’d) Hierarchy charts do not indicate the flow of data But instead illustrate the tasks, or modules, for each part of the solution The only flow of data important is what should go into and come out of each module
- 14. Another Example… An ATM machine… ATM Machine Get Inputs Give Outputs Perform all Calculations First level hierarchy chart
- 15. The ATM example (cont’d) Second level hierarchy chart for input Get Inputs Get Password Get Transaction Amount Get Transaction Type
- 16. The ATM example (cont’d) Second level hierarchy chart for output Get Outputs Print Error Message Dispense Cash Print Balance
- 17. The ATM example (cont’d) Second and third level hierarchy chart for calculations Perform Calculations Handle Deposits Handle Withdrawals Add amount to balance Check balance Subtract amount from balance Give an error message
- 18. The ATM example (cont’d) The complete hierarchy chart for the ATM Perform all calculations Handle Deposits Handle Withdrawals Add amount to balance Check balance Subtract amount from balance Give an error message Give outputs Print error message Print balance Dispense cash Give Inputs Get password Get transaction Get amount ATM
- 19. Top Down Design (cont’d) The use of top down design, or hierarchy charts is truly a divide and conquer method of problem solving
- 20. Logical Representations A logical representation is some sort of model that represents processes in the real world In some sense, mathematics is a model that represents the logic of natural systems We have already used top down design diagrams and other logic representations Now we’ll examine another method commonly used in computer problem solving, flowcharts
- 22. Flowchart Symbols The common flowchart symbols Start/Stop – necessary for every flowchart Operation – do something Arrow – shows direction of flow
- 23. Flowchart Symbols (cont’d) Decision – answer yes or no Information in – “read in” Information out – “output box” Connector – used for larger flowcharts
- 24. Let’s Try it… (1.) The problem: How do you enter a locked room?
- 25. Solution… First, list all necessary steps (algorithm) Do not take anything for granted Second, put the steps in the correct order 1. Walk to the room 2. Stop at the door 3. Take keys from pocket 4. Choose correct key 5. Put key in lock
- 26. Solution… 6.Turn key 7.Open door 8.Take key out of lock 9.Walk in Now the corresponding flowchart
- 27. Solution… START Take out keys Walk to room Stop at door Choose key Put in lock Turn key Open door Take key out Walk in STOP
- 28. Another one… The problem… You are in a house with a telephone, a doorbell, and a alarm clock You hear one of them ringing, what is the solution
- 29. Solution… START Listen to the bell ringing Is it the telephone? Answer the phone Is it the doorbell? See who is at the door Turn off the alarm STOP N Y Y N
- 30. “Decision Symbol” With this symbol, there is always one arrow coming in, but two arrows (the decision) coming out ? No Yes
- 31. The problem… Flowchart our ATM machine example from earlier
- 32. Solution… Get password Is Password correct Get type and amount Deposit or withdraw Is Amount < balance Add amount to balance Subtract from balance Give error message or response N N N Y Y Y Start Stop
- 33. Last one… The problem… Leonardo Fibonacci of Pisa wrote in 1202 about the number of rabbits that would be found at the end of a year if we started with a single pair of rabbits The pair produced one pair of offspring after the second month Then they stopped breeding Each new pair also produced two more pairs in the same way then stopped breeding
- 34. Problem (cont’d) The answer to the first year is as follows Number of additional pairs 1 1 2 3 5 8 13 21 34 55 89 144 Month 1 2 3 4 5 6 7 8 9 10 11 12 The first 2 months are both 1 (since there is only one additional pair) Each month after, is the sum of the 2 months before it This is know as the Fibonacci sequence
- 35. Problem (cont’d) Looking at it mathematically… F1 = 1 This translates as “first month (F1) equals one pair” F2 = 1 This translates as “second month (F2) equals one additional pair” F3 = F2 + F1 = 1 + 1 This translates as “third month (F3) equals second month plus first month” F4 = F3 + F2 = 2 + 1 = 3 Etc. There is a definite pattern, and thus we have found an algorithm to find all the terms
- 36. Start Let the old Term equal 0 Let the newest Term equal 1 Find sum of Old and new term Is sum > 100? Let old term equal The newest term Let the newest Term equal the sum Write out The sum Stop Y N Solution… For numbers up to 100