6 problem solving with decisions
- 1. Data Structures and Algorithms The Decision Logic Structure Some examples of conditional expressions are as follows : 1. A < B (A and B are the same the data type) 2. X + 5 >=Z (X and Z are numeric data) 3. E < 5 or F > 10 (E and F are numeric data) 4. DATAOK (DATAOK is a logical datum) Problem Solving with Decisions *Property of STI Page 1 of 40
- 2. Data Structures and Algorithms The Decision Logic Structure Multiple IF/THEN/ELSE There are three types of decision logic you will use to write algorithms for solutions consisting of more than one decision. These types of decision logic include: · Straight-through logic · Positive logic · Negative Logic Problem Solving with Decisions *Property of STI Page 2 of 40
- 3. Data Structures and Algorithms The Decision Logic Structure @ Single Condition – Two Possible Actions or Sets of Actions Problem Solving with Decisions *Property of STI Page 3 of 40
- 4. Data Structures and Algorithms The Decision Logic Structure Straight-through logic @ Means that all of the decisions are processed sequentially, one after the other. @ There is no ELSE part of the instruction; the FALSE branch always goes to the next decision, and the TRUE branch goes to the next decision after the instructions for the TRUE branch have been processed. Problem Solving with Decisions *Property of STI Page 4 of 40
- 5. Data Structures and Algorithms The Decision Logic Structure Positive Logic @ Allows the flow of the processing to continue through the module instead of processing succeeding decisions, once the resultant of a decision is true. @ Whenever the resultant is FALSE (the ELSE part of the decision), another decision in the sequence is processed until the resultant is TRUE, or there are no more decisions to process. @ At that time, the FALSE branch processes the remaining instructions. Problem Solving with Decisions *Property of STI Page 5 of 40
- 6. Data Structures and Algorithms The Decision Logic Structure Negative Logic @ similar to positive logic except that the flow of the processing continues through the module when the resultant of a decision is FALSE @ whenever the resultant is TRUE, another decision is processed until the resultant is FALSE, or there are no more decisions to process @ at that time, the TRUE branch processes the remaining instructions @ the hardest to use and understand Problem Solving with Decisions *Property of STI Page 6 of 40
- 7. Data Structures and Algorithms The Decision Logic Structure Using Straight-through logic Problem: Find the amount to charge people of varying ages for a food ticket. When the person is under 16, the charge is P7; when the person is 65 or over, the charge is P5; all others are charged P10. The conditions are the following : AGE CHARGE AGE < 16 7 AGE >=16 and AGE < 65 10 AGE >=65 5 Problem Solving with Decisions *Property of STI Page 7 of 40
- 8. Data Structures and Algorithms The Decision Logic Structure Solution : Algorithm Flowchart A IF AGE < 16 THEN T CHARGE = 7 IF T AGE < 16 IF AGE >= 16 AND AGE <65 THEN T CHARGE = 10 Charge = 7 IF AGE >= 65 F THEN T CHARGE = 5 IF AGE >= 16 T and AGE < 65 Charge = 10 F IF T AGE >= 65 Charge = 10 F B Problem Solving with Decisions *Property of STI Page 8 of 40
- 9. Data Structures and Algorithms The Decision Logic Structure Problem: Change the value of X to 0 when X becomes greater than 100, and to change the value of Y to 0 when Y becomes greater than 250 Algorithm Flowchart A IF X < 100 THEN IF T T X = 10 X > 100 IF Y > 250 X=0 THEN T F Y=0 IF T Y > 250 Y=0 F B Problem Solving with Decisions *Property of STI Page 9 of 40
- 10. Data Structures and Algorithms The Decision Logic Structure Using Positive Logic Problem: Find the amount to charge people of varying ages for a food ticket. When the person is under 16, the charge is P7; when the person is 65 or over, the charge is P5; all others are charged P10. The conditions are the following : Algorithm IF AGE <16 THEN CHARGE = 7 ELSE IF AGE < 65 THEN CHARGE = 10 ELSE CHARGE = 5 Problem Solving with Decisions *Property of STI Page 10 of 40
- 11. Data Structures and Algorithms The Decision Logic Structure Flowchart A F IF T AGE < 16 F IF T AGE < 65 CHARGE = 7 CHARGE = 5 CHARGE = 10 B Problem Solving with Decisions *Property of STI Page 11 of 40
- 12. Data Structures and Algorithms The Decision Logic Structure Problem: Calculate the commission rate for a salesperson, given the amount of sales. When the salesperson has sold less than or equal to 2,000 worth of goods, the commission is 2%. When the sales total is more than 2,000 and less than or equal to 4,000, the commission is 4%. When sales total is more than 4,000 and less than or equal to 6,000, the commission is 7%. When the person has sold more than 6,000 the commission is 10%. The conditions are the following: SALES COMMISSION <=2000 .02 2001 – 4000 .04 4001 – 6000 .07 > 6000 .10 Problem Solving with Decisions *Property of STI Page 12 of 40
- 13. Data Structures and Algorithms The Decision Logic Structure Solution 1: Algorithm IF SALES <= 2000 THEN COMMISSION = .02 T ELSE IF SALES <= 4000 THEN COMMISSION = .04 T ELSE IF SALES <= 6000 THEN F T COMMISSION = .07 F ELSE F COMMISSION = .1 Problem Solving with Decisions *Property of STI Page 13 of 40
- 14. Data Structures and Algorithms The Decision Logic Structure Solution 1: Flowchart A F T IF SALES <=2000 F T COMMISSION = IF .02 SALES <=4000 COMMISSION F IF T = .04 SALES <=6000 COMMISSION COMMISSION = .1 = .07 B Problem Solving with Decisions *Property of STI Page 14 of 40
- 15. Data Structures and Algorithms The Decision Logic Structure Solution 1: Test 1. TEST FOR 3. TEST FOR SALES = 1500 SALES = 5500 IS SALES <= 2000 IS SALES <= 2000 TRUE FALSE COMMISSION = .02 IS SALES <= 4000 FALSE 2. TEST FOR IS SALES <= 6000 SALES = 3500 TRUE IS SALES <= 2000 COMMISSION = .07 FALSE IS SALES <= 4000 4. TEST FOR TRUE SALES = 7500 COMMISSION = .04 IS SALES <= 2000 FALSE IS SALES <= 4000 FALSE IS SALES <= 6000 TRUE COMMISSION = .1 Problem Solving with Decisions *Property of STI Page 15 of 40
- 16. Data Structures and Algorithms The Decision Logic Structure Solution 2: Algorithm IF SALES > 6000 THEN COMMISSION = .1 T ELSE IF SALES > 4000 THEN COMMISSION = .07 T ELSE IF SALES > 2000 THEN F T COMMISSION = .04 F ELSE F COMMISSION = .02 Problem Solving with Decisions *Property of STI Page 16 of 40
- 17. Data Structures and Algorithms The Decision Logic Structure Solution 2: Flowchart A F T IF SALES > 6000 F T COMMISSION = IF .1 SALES > 4000 COMMISSION F IF T = .07 SALES > 2000 COMMISSION COMMISSION = .02 = .04 B Problem Solving with Decisions *Property of STI Page 17 of 40
- 18. Data Structures and Algorithms The Decision Logic Structure Solution 2: Test 1. SALES = 1500 3. SALES = 5500 IS SALES > 6000 IS SALES > 6000 FALSE FALSE IS SALES > 4000 IS SALES > 4000 FALSE TRUE IS SALES > 2000 COMMISSION = .07 FALSE COMMISSION = .02 2. SALES = 3500 4. SALES = 7500 IS SALES > 6000 IS SALES > 6000 FALSE TRUE IS SALES > 4000 COMMISSION = .1 FALSE IS SALES > 2000 TRUE COMMISSION = .04 Problem Solving with Decisions *Property of STI Page 18 of 40
- 19. Data Structures and Algorithms The Decision Logic Structure Using Negative Logic @ Negative Logic is the hardest for most people to comprehend because they do not think in negative terms. @ In general when you use negative logic you are telling the computer to process another decision when the resultant condition is TRUE; @ If the resultant is FALSE, then the computer processes a consequent set of instructions and then continues processing the module. Problem Solving with Decisions *Property of STI Page 19 of 40
- 20. Data Structures and Algorithms The Decision Logic Structure Negative Logic Solution 1: Algorithm IF AGE >= 16 THEN IF AGE >= 65 THEN CHARGE = 5 ELSE CHARGE = 10 ELSE CHARGE = 7 Problem Solving with Decisions *Property of STI Page 20 of 40
- 21. Data Structures and Algorithms The Decision Logic Structure Negative Logic Solution 1: Flowchart A F T IF AGE >= 16 F T CHARGE = 7 IF AGE >= 16 CHARGE = 10 CHARGE = 5 B Problem Solving with Decisions *Property of STI Page 21 of 40
- 22. Data Structures and Algorithms The Decision Logic Structure Negative Logic Solution 2: Algorithm IF SALES > 2000 THEN IF SALES > 4000 THEN IF SALES > 6000 THEN COMMISSION = .1 ELSE COMMISSION = .07 ELSE COMMISSION = .04 ELSE COMMISSION = .02 Problem Solving with Decisions *Property of STI Page 22 of 40
- 23. Data Structures and Algorithms The Decision Logic Structure Negative Logic Solution 2: Flowchart A IF SALES > 2000 COMMISSION = .02 IF SALES > 4000 COMMISSION = .04 IF SALES > 6000 COMMISSION = COMMISSION = .07 .01 B Problem Solving with Decisions *Property of STI Page 23 of 40
- 24. Data Structures and Algorithms The Decision Logic Structure Negative Logic Solution 2: TEST 1. SALES = 1500 3. SALES = 5500 IS SALES > 2000 IS SALES > 2000 FALSE TRUE COMMISSION = .02 IS SALES > 4000 TRUE 2. SALES = 3500 IS SALES > 6000 IS SALES > 2000 FALSE TRUE COMMISSION = .1 IS SALES > 4000 FALSE 4. SALES = 7500 COMMISSION = .04 IS SALES > 2000 TRUE IS SALES > 4000 TRUE IS SALES > 6000 TRUE COMMISSION = .1 Problem Solving with Decisions *Property of STI Page 24 of 40
- 25. Data Structures and Algorithms The Decision Logic Structure Another Set-Up: Algorithm IF SALES <= 6000 THEN IF SALES <= 4000 THEN IF SALES <= 2000 THEN COMMISSION = .02 ELSE COMMISSION = .04 ELSE COMMISION = .07 ELSE COMMISSION = .1 Problem Solving with Decisions *Property of STI Page 25 of 40
- 26. Data Structures and Algorithms The Decision Logic Structure Another Set-Up: Flowchart A F T IF SALES <= 6000 CHARGE = .1 F T IF SALES <= 4000 COMMISSION = .07 F IF T SALES <= 2000 COMMISSION = COMMISSION = .04 .02 B Problem Solving with Decisions *Property of STI Page 26 of 40
- 27. Data Structures and Algorithms The Decision Logic Structure Another Set-Up: Test 1. SALES = 1500 3. SALES = 5500 IS SALES <= 6000 IS SALES <= 6000 TRUE TRUE IS SALES <= 4000 IS SALES <= 4000 TRUE FALSE IS SALES <= 2000 COMMISSION = .07 TRUE COMMISSION = .02 2. SALES = 3500 4. SALES = 7500 IS SALES <= 6000 IS SALES <= 6000 TRUE FALSE IS SALES <= 4000 COMMISSION = .1 TRUE IS SALES <= 2000 FALSE COMMISSION = .04 Problem Solving with Decisions *Property of STI Page 27 of 40
- 28. Data Structures and Algorithms The Decision Logic Structure Logic Conversion To convert from positive logic to negative logic or vice versa, do the following : 1. Change all < to >= 2. Change all <= to > 3. Change all > to <= 4. Change all >= to < 5. Change all = to <> 6. Change all <> to = 7. Interchange all of the THEN set of instructions with the corresponding ELSE set of instructions. Problem Solving with Decisions *Property of STI Page 28 of 40
- 29. Data Structures and Algorithms The Decision Logic Structure Conversion from Positive to Negative Logic Problem Solving with Decisions *Property of STI Page 29 of 40
- 30. Data Structures and Algorithms The Decision Logic Structure Which Decision Logic? To analyze which type of decision logic would be most efficient for a particular solution, answer the following questions: 1. Which type would make the solution most readable? 2. Which type would make the solution the easiest to maintain or change? 3. Which would require the fewest test when you don’t know anything about the data? 4. Which would require the fewest test when you’re given some data? Problem Solving with Decisions *Property of STI Page 30 of 40
- 31. Data Structures and Algorithms The Decision Logic Structure Four ways to Design a Set of Conditions Problem Solving with Decisions *Property of STI Page 31 of 40
- 32. Data Structures and Algorithms The Decision Logic Structure Decision Tables A decision table consists of four parts: @ The conditions. @ The actions. @ The combinations of TRUE and FALSE for the conditions. @ The action to be taken or the consequences for each combination of conditions. The four steps to develop a flowchart from the decision table are : @ Draw all decisions in flowchart form. @ Compare the true and false sides of each decision, starting with the first one. @ Eliminate any decisions that have the same instructions on both the true and false sides, keeping the true consequence or action. @ Redraw the flowchart. Problem Solving with Decisions *Property of STI Page 32 of 40
- 33. Data Structures and Algorithms The Decision Logic Structure Decision Table Format Problem Solving with Decisions *Property of STI Page 33 of 40
- 34. Data Structures and Algorithms The Decision Logic Structure Problem Solving with Decisions *Property of STI Page 34 of 40
- 35. Data Structures and Algorithms The Decision Logic Structure Elimination of Conditions Problem Solving with Decisions *Property of STI Page 35 of 40
- 36. Data Structures and Algorithms The Decision Logic Structure Final Flowchart Problem Solving with Decisions *Property of STI Page 36 of 40
- 37. Data Structures and Algorithms The Decision Logic Structure Decision Table Problem Solving with Decisions *Property of STI Page 37 of 40
- 38. Data Structures and Algorithms The Decision Logic Structure Starting Flowchart Problem Solving with Decisions *Property of STI Page 38 of 40
- 39. Data Structures and Algorithms The Decision Logic Structure Elimination of Condition Problem Solving with Decisions *Property of STI Page 39 of 40
- 40. Data Structures and Algorithms The Decision Logic Structure Final Flowchart Problem Solving with Decisions *Property of STI Page 40 of 40