Ontario 10 Applied (MFM2P)
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Loops
Lesson
Roller Coaster

 

Loops (or iterations) are steps that are repeated a number of times in an algorithm.  They make algorithms simpler because they don’t need to include groups of unnecessary steps.

For example, the steps involved in eating breakfast could be:

  1. Fill bowl with cereal
  2. Pour milk onto cereal
  3. Place spoon in bowl and scoop up cereal and milk
  4. Lift spoon to mouth and empty contents of the spoon into mouth
  5. Eat spoonful of cereal and milk
  6. Place spoon in bowl and scoop up cereal and milk
  7. Lift spoon to mouth and empty contents of the spoon into mouth
  8. Eat spoonful of cereal and milk
  9. Place spoon in bowl and scoop up cereal and milk
  10. Lift spoon to mouth and empty contents of the spoon into mouth
  11. Eat spoonful of cereal and milk
  12. Place spoon in bowl and scoop up cereal and milk
  13. Lift spoon to mouth and empty contents of the spoon into mouth
  14. Eat spoonful of cereal and milk

    ........continue these steps until bowl is finished (could be a large number of steps)

          End

This algorithm could be rewritten using a loop:

  1. Fill bowl with cereal
  2. Pour milk onto cereal
  3. While there is cereal in the bowl
  4.              Place spoon in bowl and scoop up cereal and milk
  5.              Lift spoon to mouth and empty contents of the spoon into mouth
  6.              Eat spoonful of cereal and milk
  7. End

 

When writing algorithms in pseudocode we can use a WHILE loop.  A while loop states a condition at the start of the loop which determines how many times a loop is repeated in an algorithm.

Look at this algorithm written in pseudocode, and the explanation of each line of code

START start
SET a = 2 give the variable a, the value 2
SET sum = 0 give the variable sum, the value 0
WHILE a < 5 while a has a value less than 5 repeat the next 2 steps
     sum = sum + a add a to the value of sum 
     a = a + 1 add 1 to the value of a
END WHILE stop the loop when a is no longer less than 5
PRINT sum print the final value of sum
END end

This loop contains 2 steps   sum = sum + a  
                                               a = a + 1

these will be repeated until a is no longer less than 5.  The values of the variables a and sum for each loop are:

  sum a
initially $0$0 $2$2
after first loop $0+2=2$0+2=2 $2+1=3$2+1=3
after second loop $2+3=5$2+3=5 $3+1=4$3+1=4
after third loop $5+4=9$5+4=9 $4+1=5$4+1=5

At the end of the third loop the value of a is 5 and so the condition for the loop to end has been reached. The final value of sum is 9.  This is the value that will be printed (OUTPUT) from the algorithm.

Worked Examples

Question 1

Look at the pseudocode below:

START
SET a = 2
SET sum = 0
WHILE a < 9
    sum = sum + a
    a = a + 1
END WHILE
PRINT sum
END
  1. The initial value of a is $\editable{}$.

  2. What is the OUTPUT of this code?

    OUTPUT: $\editable{}$

Question 2

Consider the algorithm represented by the flow chart:

  1. Rearrange the letters $A$A, $B$B, $C$C, $D$D, $E$E, $F$F and $G$G so the corresponding pseudocode correctly represents the flow chart's algorithm.

    $C$C: a = a + 1
    $E$E: SET a = 1
    $A$A: WHILE a ≠ 5
    $F$F: PRINT sum
    $B$B: sum = sum + a
    $G$G: END WHILE
    $D$D: SET sum = 0
    START
    Line 1 $\editable{}$
    Line 2 $\editable{}$
    Line 3 $\editable{}$
    Line 4 $\editable{}$
    Line 5 $\editable{}$
    Line 6 $\editable{}$
    Line 7 $\editable{}$
    END

Question 3

Look at the pseudocode below:

Note that the symbol < represents the statement 'less than'.

START
SET a = 2
WHILE a < 10
    PRINT a
    a = a + 2
END WHILE
END
  1. What is the OUTPUT of this code? Write each value on the same line, separated by a comma.

    OUTPUT: $\editable{}$

 

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