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CSI 1301 ALGORITHMS - PART 2 CONDITIONAL BRANCH CONTROL STRUCTURE

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Conditional Branch So far, in the method part of our algorithms, the instructions have been executed sequentially However, sometimes we need to vary the order of execution of the instructions. The order will be determined by the value of a condition We will test to determine whether the condition is true or false –If the condition is true, we will execute certain instructions –If the condition is false, we will execute other instructions

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Definition of a Block But first, let us define a block as group of related instructions –A block can contain one or as many instructions as we want BLOCK Get X Get Y Let Z = X + Y Give Z BLOCK Let X = A + B * C /D

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Block The key feature of a block is that it has only one entrance (one way to come in) –By executing the first instruction in the block and only one exit (one way out) –By executing the last instruction in the block You cannot execute any other instruction in the block without starting with the first and ending with the last instructions

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Simple Sequence of Blocks Input Block Get X Get Y Process Block Let X = X + Y Let Y = 2 * Y Let Z = X + Y Output Block Give Z

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Test Blocks By adding a test at the beginning of a block, we let the results of the test determine which block of instructions will be executed TEST True Block Do these Instructions if Test is True False Block Do these Instructions if the Test is False

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What is a Test? The test used in a conditional branching control structure contains a variable or expression that evaluates to either True or False

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Logical Operators in a Test Expression

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Examples of Tests

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Logical Tests In practice, tests contain variables and expressions, not numbers Suppose that X, Y and Z are 3, 5, 8 respectively

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Test Block Indentation is used to show different blocks in an algorithm To write a test block, use an IF statement, and indent the instructions to be executed If (Test) Do this statement Do this statement as well Do this statement after the If statement

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Syntax if (Test) Block1 Interpretation If Test is evaluated to true Block1 is executed, else Block2 is executed. The else is optionnal. Note that the indentation is important. It determines the beginning and the end of each block. Test Block (syntax and interpretation) if (Test) Block1 else Block2

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Algorithm 2.1 Write an algorithm to compute the absolute value of a number. –Name: ABSOLUTE –Givens: Number Change: None –Results: Value –Intermediates: None –Definition: Value := ABSOLUTE (Number) – –Method Get Number If (Number >= 0) Let Value = Number If (Number < 0) Let Value = (-1) * Number Give Value

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Else It is redundant to do the test twice as in IF (X > 0) Do this IF (X <= 0) Do that The test should be written as If (X > 0) Do this Else (or Otherwise) Do that

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Algorithm 2.1 (b) Write an algorithm to compute the absolute value of a number using only one test –Name: ABSOLUTE –Givens: Number Change:None –Results: Value –Intermediates: None –Definition: Value := ABSOLUTE (Number) – –Method Get Number If (Number >= 0) Let Value = Number Else Let Value = (-1) * Number Give Value

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Algorithm 2.2 Write an algorithm which finds the largest of three given numbers General Concept –Keep track of “Biggest so Far” Look at the first two numbers Store the larger of the two numbers in “Biggest so Far” Compare “Biggest so Far” with the third number If the third number is larger, then store it in “Biggest so Far”

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Algorithm 2.2 Write an algorithm which finds the largest of three given numbers Name: BIG3 Givens: N1, N2, N3 Change:None Results:Largest Intermediates: None Definition: Largest := BIG3(N1,N2,N3) Method Get N1 Get N2 Get N3 If (N1 > N2) Let Largest = N1 Else Let Largest = N2 If (N3 > Largest) Let Largest = N3 Give Largest

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Trace 2.1 (1) Get N1 (2) Get N2 (3) Get N3 (4) If (N1 > N2) (5) Let Largest = N1 (6) Else (7) Let Largest = N2 (8) If (N3 > Largest) (9) Let Largest = N3 (10) Give Largest LN N1 N2 N3 Largest Test (8>12) (7>12) 10 Output 12 Trace Algorithm 2.2 with the values 8, 12, 7

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Algorithm 2.3 Write an algorithm which, when given an ordered list X1, X2, & X3, modifies the list so that the values are in ascending order General Concept Look at the first two numbers, X1 and X2. If X1 is larger than X2, swap them (remember the swap algorithm?) Look at X2 and X3. If X2 is larger than X3, swap them –This will put the largest number in the X3 position –X2 may have changed, so we have to look at X1 again Look again at X1 and X2. If X1 is larger than X2, swap them –Now the list is in non-decreasing order

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Algorithm 2.3 –Name: SORT3 –Givens: X1,X2,X3 Change: X1,X2,X3 –Results: None –Intermediates: Temp –Definition: SORT3(X1,X2,X3) –Method – Get X 1, X 2, X 3 If (X 1 > X 2 ) Let Temp = X 1 Let X 1 = X 2 Let X 2 = Temp If (X 2 > X 3 ) Let Temp = X 2 Let X 2 = X 3 Let X 3 = Temp If (X 1 > X 2 ) Let Temp = X 1 Let X 1 = X 2 Let X 2 = Temp Give X 1, X 2, X 3 Write an algorithm which, given an ordered list X1, X2 & X3, modifies it so that the values are in ascending order

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Trace 2.2 Trace algorithm 2.3 with list X having values 3, 8 and 2 respectively (1) Get X (2) If (X 1 > X 2 ) (3) Let Temp = X 1 (4) Let X 1 = X 2 (5) Let X 2 = Temp (6) If (X 2 > X 3 ) (7) Let Temp = X 2 (8) Let X 2 = X 3 (9) Let X 3 = Temp (10) If (X 1 > X 2 ) (11) Let Temp = X 1 (12) Let X 1 = X 2 (13) Let X 2 = Temp (14) Give X LN X TEMP TEST 1 (3,8,2) 2 (3 > 8) 6 (8 > 2) (3,2,2) 9 (3,2,8) 10 (3 > 2) (2,2,8) 13 (2,3,8) 14 Output (2,3,8)

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Multiple Tests Sometimes we need to perform multiple related tests –For example, in assigning grades, a student can receive A+, A, A-….E, F We can add an ELSE IF clause for multiple test results IF (Test 1) Execute block for Test 1 Else IF (Test 2) Execute block for Test 2 Else Execute block for Else

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Algorithm 2.4 Write an algorithm which calculates the amount of money to charge for a ticket. The amount varies with the age of the individual. The charge for a person less than 16 is $7. The charge for a person over age 65 is $5 The charge is $10 for everyone else Name: FARE Givens: Age Change: None Results: Price Intermediates: None Definition: Price := FARE(Age) Method Get Age If (Age < 16) Let Price = $7 Else If (Age > 65) Let Price = $5 Else Let Price = $10 Give Price

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Trace 2.3 Trace algorithm 2.4 with the given age 35 (1) Get Age (2) If (Age < 16) (3) Let Price = $7 (4) Else If (Age > 65) (5) Let Price = $5 (6) Else (7) Let Price = $10 (8) Give Price LN Age Price Test (35<16) 4 (35>65) 7 $10 8 Output $10

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Algorithm 2.5 Given an employee’s eligible medical expenses for a calendar year, write an algorithm which computes the amount of reimbursement from group medical insurance. The insurance does not cover the first $100 of medical expenses. It pays 90% of the remaining amount in the first $2000 of expenses and 100% of any additional expenses.

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Algorithm 2.5 Name: MEDICAL Givens: Expense Change: None Results: Refund Intermediates: LL (Constant 100) UL (Constant 2000) Definition: Refund := MEDICAL(Expense) Method Set LL = 100 Set UL = 2,000 Get Expense If (Expense < LL) Let Refund = 0 Else If (Expense < UL) Let Refund = 90% (Expense-LL) Else Let Refund = 90% (UL-LL) + 100% (Expense - UL) Give Refund

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Trace 2.4 ( 1) Set LL = 100 ( 2) Set UL = 2,000 ( 3) Get Expense ( 4) If (Expense < 100) ( 5) Let Refund = 0 ( 6) Else If (Expense < 2,000) ( 7) Let Refund = 90% (Expense-100) ( 8) Else ( 9) Let Refund = 90% (1,900) + 100% (Expense - 2,000) (10) Give Refund LN UL LL Exp Refund Test 1, K (3K<100) 6 (3K<2K) 9 2, Output 2,710 Trace Algorithm 2.5 for $3,000 worth of expenses

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Additional Material

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Flow Charts

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Logic is implemented with a Diamond Symbol There are two exits, which should be labeled Y/N or T/F The two paths need to join before the end of the flowchart

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Algorithm 2.1(a) Name: ABSOLUTE Givens: Number Change: None Results: Value Intermediates: None Definition: Value := ABSOLUTE (Number)

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Algorithm 2.1(b) Name: ABSOLUTE Givens: Number Change: None Results: Value Intermediates: None Definition: Value := ABSOLUTE (Number)

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Algorithm 2.2 Name: BIG3 Givens: N1, N2, N3 Change:None Results:Largest Intermediates: None Definition: Largest := BIG3(N1,N2,N3)

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Algorithm 2.3 Name: SORT3 Givens: X1,X2,X3 Change: X1,X2,X3 Results: None Intermediates: Temp Definition: SORT3(X1,X2,X3)

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Algorithm 2.4 Name: FARE Givens: Age Change: None Results: Price Intermediates: None Definition: Price := FARE(Age)

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Algorithm 2.5 Name: MEDICAL Givens: Expense Change: None Results: Refund Intermediates: LL (Constant 100) UL (Constant 2,000) Definition: Refund := MEDICAL(Expense)

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NSD

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Tricky to do in Excel Use 2 columns –Merge the 2 cells to form question –Format Cells/Borders Diagonal lines can be put in –Add Y/N cells

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Algorithm 2.1(a) Name: ABSOLUTE Givens: Number Change: None Results: Value Intermediates: None Definition: Value := ABSOLUTE (Number)

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Algorithm 2.1(b) Name: ABSOLUTE Givens: Number Change: None Results: Value Intermediates: None Definition: Value := ABSOLUTE (Number)

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Algorithm 2.2 Name: BIG3 Givens: N1, N2, N3 Change:None Results:Largest Intermediates: None Definition: Largest := BIG3(N1,N2,N3)

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Algorithm 2.3 Name: SORT3 Givens: X1,X2,X3 Change: X1,X2,X3 Results: None Intermediates: Temp Definition: SORT3(X1,X2,X3)

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Algorithm 2.4 Name: FARE Givens: Age Change: None Results: Price Intermediates: None Definition: Price := FARE(Age)

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Algorithm 2.5 Name: MEDICAL Givens: Expense Change: None Results: Refund Intermediates: Definition: Refund := MEDICAL(Expense)

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Homework

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For each of the following questions: Develop an algorithm Trace the algorithm with suitable data Write an algorithm to reverse the digits in a three digit number and then add that number to 500. For example, 468 becomes 864. When added to 500, the result is Write an algorithm to get the names and ages of two people. Return the name of the person who is older (in the format “x is older than y”, where x and y are the names of the two people), unless the two people are the same age, in which case, return the message “x is the same age as y”.

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An automotive sales representative’s commission is calculated as a percentage of the sale: –8% of the first $5, of the sale price –10% on the remainder of the sale price, if the remainder is less than or equal to $80, or –12.5% on the remainder, if the remainder is more than $80, Develop an algorithm that will accept the sale price of the automobile and calculate and display the sales representative’s commission.

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