Repetition and loops

by Owen

Published on: Fri, Apr 3, 2015
Lesson Number: 10
Key stage: KS2  
Key Stage Level: Lower  
Teacher Notes: Repetition  
Lesson Plan: Repetition  
Slides: Repetition  
Category: Fundamentals  
Concepts: Repetition  

What You are Going to Learn

In the last two lessons we have looked at how computers programs make decisions.

Now we want to investigate how and why we want computers to repeat small parts of a computer program.

We will introduce the pattern for repetition or loops as they are more commonly known.

How to do Something Again and Again…

In the last lesson we showed you how to use an if else statement to make decisions. You used these to create the timesquestion program. But the timesquestion program had a problem. You could only make one guess each time you ran the program.

But what if you wanted to make more than one guess? What if you wanted to make as may guesses as you liked? Well for that you need to use repetition or as most programmers call them loops. That’s what this lesson is all about.

Once you understand both selection and loops you will be able to write some really useful programs.

Important

Make sure you have completed the lesson about selections before you try this lesson. You will need to understand selection and if statements before you can understand repetition.

Repeating Things

Let’s think about repeating patterns. Lets start with squares. Think about the steps needed to draw a square. You could draw a square like this.

  1. Draw one side
  2. Turn 90 degrees clockwise
  3. Draw another side
  4. Turn 90 degrees clockwise
  5. Draw another side
  6. Turn 90 degrees clockwise
  7. Draw another side
  8. Turn 90 degrees clockwise

Think about multiplication too. A multiplication like this

2 * 4 = ?

Now it is your turn

Can you see the pattern to draw a square? How many times do you have to repeat this pattern to draw a square?

Think about the multiplication. How can you rewrite the multiplication to get the same answer but only use addition?

The pattern in the square drawing is:

  1. Draw one side
  2. Turn 90 degrees clockwise

This pattern draws one side and then turns so that the next side will go in the correct direction. A square has four sides so we need to repeat this pattern four times to draw a square.

The multiplication can be rewritten as

2 + 2 + 2 + 2

Now the pattern is add 2 to the number. Starting with the number 2 you need to do this three times.

Repetition

These are both examples of repetition. If you can spot a pattern and know how to make the pattern repeat, you can change how you write your programs. This is an important idiom (part) of computer programming.

Repetition means that a small part of the program runs over and over again. You are asking the computer to repeat a sequence of instructions.

Most programs are made up of repetition and selection statements.

But Why?

So if that’s what repetition is, why is it useful? Well repetition makes the program both shorter - so less typing - and easier to understand. If you use repetition it will make your program logic much clearer. Both for you and for anyone else who reads your program. Repetition also means that the program more closely resembles the algorithms that it might use. Some algorithms are described in terms of doing things over and over again. For example algorithms that sort lists of numbers are all described by repeating a small sequence of instructions.

Look at the square drawing algorithm. It is clearer to say repeat this four times “Draw a line and then turn 90 degrees clockwise” instead of listing the the pair of steps 4 times - which would be 8 lines in total.

The hard part is spotting a pattern that can be repeated! As you write more and more programs you will get much better as spotting these patterns.

Loops

Programmers normally talk about loops instead of repetition. We call repetition a loop because a sequence of instructions is looped over and over again.

Programmers also talk about different types of loops. So there are loops that repeat while a condition is true - called a while loop. There are loops that repeat for a fixed number of times - called a for loop. There are loops that run forever - called an infinite loop.

The difference between the loops is the presence or absence of a condition that controls how many times the loop goes around. For loops also have the additional property of specifying the step-size of the loop.

We are going to look at while loops first. For loops are just a simple extension to a while loop. We will show you these after we have shown you while loops.

The Loop Pattern

The loop pattern looks very similar to the if pattern. This is the pattern for a loop that repeats while a condition is true is

for condition {
    statements-to-repeat
} // last brace

Go uses the keyword for to indicate a loop, regardless of which type of loop it is.

So how does this work? Well it is actually pretty easy if you already understand if statements.

The first thing to happen is that the condition is tested before the loop starts. If the condition is false then the statements-to-repeat are skipped over and execution continues after the last brace. So a loop behaves in the same way as an if statement when the condition is false. In fact there is an implicit if test in any while or for loop.

If the condition is true the statements-to-repeat are executed. This is also the same as an if statement. The difference comes once all of the statements-to-repeat have been executed. Once these have been executed the condition is tested again. Think of the last brace causing a jump back to the for line.

If the condition is still true the statements-to-repeat are executed again, for a second time. Once the statements-to-repeat have been executed the condition is tested yet again.

When the condition becomes false the statements-to-repeat are skipped over. Execution then continues at the last brace. This is similar to an if statement when its condition is false.

The condition is tested before each time though the loop. Each time though the loop is called a loop iteration so the condition is tested before each loop iteration including the first one.

The loop example shows how to use a for loop to create a loop that repeats until the condition is true.

Lets look at an example. Take a look at this bit of code.

 1var word string
 2var secretWord string
 3secretWord = "Banana"
 4
 5fmt.Println("Guess the secret word.")
 6word = simpleio.ReadStringFromKeyboard()
 7
 8for word != secretWord {
 9    fmt.Println("Sorry that is not the secret word!")
10    fmt.Println("Try and guess again!")
11    word = simpleio.ReadStringFromKeyboard()
12}
13
14fmt.Println("Congratulations!")
Fig-1. The loop example code

Important

This is not a complete program, so you won’t be able to run it. We wanted you to focus on how the loop works rather than look at the rest of the program.

When you are trying to work out what this program does, just look at one line at a time and work out what that line does. It might help you write down the value of the word variable at each stage.

You don’t need a computer to solve this, you just need to think and act like the computer would.

Now it is your turn

Look at the example loop and see if you can work out what happens

  • If your first guess was Goldfish?
  • If your first guess was Banana?
  • If you had three guesses, first Octopus, then Shark, then Banana

Remember whatever you type in as your answer is read by the line

word = simpleio.ReadStringFromKeyboard()

and is stored in the variable called word.

The trick to working out what happens is to look at the condition at the top of the loop. If you don’t guess the secret word then the loop is executed. Inside the loop you are asked to guess again. If you guess correctly then the whole loop is skipped.

So if you guess wrong the program asks you to guess again over and over again until you guess the secret word.

Lets look at how this works.

If your first guess is “Goldfish” it reads it into the variable called word on line 6. The condition on line 8

word != secretWord {

Is true - “Goldfish” is not the same as the secret word “Banana” so the loop statements between the { and } are executed. So the program executes lines 9 and 10 and prints out

Sorry that is not the secret word!
Try and guess again!

and then waits for you to enter the next guess on line 11.

If you entered “Banana” as your first next guess, then word would contain the value “Banana” and the condition would be false. Now that the condition is false the loop is skipped over and the program prints out.

Congratulations!

If your first guess was “Octopus” it will be read into the variable called word on line 6. The condition on line 8

word != secretWord {

Is true - “Octopus” is not the same as the secret word “Banana” so the loop statements between the { and } are executed. So he program executes lines 9 and 10 and prints out

Sorry that is not the secret word!
Try and guess again!

and then waits for you to enter the next guess on line 11.

Now if your second guess was “Shark”. The value in variable word is now Shark. Now that program hits the closing brace, the } on line 12. The last brace forces the program to jump back to line 8. Now the loop has gone around once.

Now that the program is back at line 8, the condition

word != secretWord {

is tested again. This time the value in word is Shark but this is not the same as the secret word. So the condition is false. So the next line to be executed are lines 9 and 10 so the program prints out

Sorry that is not the secret word!
Try and guess again!

again.

Now if your last guess is Banana, the process is similar. Now the value in word is Banana. The last brace forces the loop back to the top on line 8.

But now when loops condition is tested it is true. You have guessed the secret word. Now the program skips over the whole loop and prints out the

Congratulations!

congratulations message.

The timesquiz Program

The timesquiz is an extension of the previous timesquestion program from the if else selection lesson.

Like the timesquestion program the timesquiz program asks you to solve a multiplication question from the 1 to 12 times tables. Also like the timesquestion program the timesquiz program tells you if your guess is too large or too small. But unlike the timesqestion program the timesquiz program will not exit until you guess the answer correctly. If your guess is wrong the program asks for anther guess. The only way to exit the program is to enter the correct answer.

The timesquiz program looks like this

 1package main
 2
 3import (
 4	"fmt"
 5
 6	"github.com/gophercoders/random"
 7	"github.com/gophercoders/simpleio"
 8)
 9
10func main() {
11
12	var a int
13	var b int
14	var answer int
15
16	fmt.Println("The timesquiz shows you how to use loops.")
17	fmt.Println("Can you remember your times tables?")
18	fmt.Println("")
19
20	a = random.GetRandomNumberInRange(1, 12)
21	b = random.GetRandomNumberInRange(1, 12)
22
23	fmt.Print("What is ")
24	fmt.Print(a)
25	fmt.Print(" * ")
26	fmt.Print(b)
27	fmt.Println("?")
28
29	answer = simpleio.ReadNumberFromKeyboard()
30
31	for answer != a*b {
32		if answer > a*b {
33			fmt.Println("Sorry, your guess was to big.")
34		} else {
35			fmt.Println("Sorry your guess was to small.")
36		}
37		fmt.Println("Try again ")
38		answer = simpleio.ReadNumberFromKeyboard()
39	}
40	fmt.Println("Congratulations! You are correct.")
41}
Fig-2. The timesquiz code

If you type the program in and run it then you should see something like this.

The timesquiz shows you how to use loops.
Can you remember your times tables?

What is 11 * 6?
45
Sorry your guess was to small.
Try again
89
Sorry, your guess was to big.
Try again
66
Congratulations! You are correct.

Important

Remember that the numbers for the multiplication are chosen randomly. When you run the programs you will see different numbers.

The program is very similar to the previous timesquestion program.

Lets look at how it works.

Your guess is read on line 29 using the ReadNumberFromKeybaord from the simpleio package. Their guess is stored in the variable answer.

The loop extends from lines 31 to 39. The loop condition

answer != a*b

is on line 31. If you guess correctly on your first guess then this condition is false. The loop is then skipped over and the next line to execute is line 40

fmt.Println("Congratulations! You are correct.")

so the complete output from the program wold be.

The timesquiz shows you how to use loops.
Can you remember your times tables?

What is 11 * 6?
66
Congratulations! You are correct.

So that’s what happens if you are lucky enough to guess the correct answer on your first attempt.

If you guess incorrectly, for example 45, then the condition on line 31 is true so the loop is executed.

The first line in the loop is an if else statement. The condition in the if else statement is

answer > a*b

This is false (45 < 66 in this case) so the next line to be executed is line 35

fmt.Println("Sorry, your guess was to small.")

The output at this point would be

The timesquiz shows you how to use loops.
Can you remember your times tables?

What is 11 * 6?
45
Sorry your guess was to small.

The remainder of the loop lines 37 and 38 now execute. Line 37 asks the you to try another guess. Line 38 is identical to line 29 and stores your new guess in the answer variable.

If you had a guessed 89 the output would be

The timesquiz shows you how to use loops.
Can you remember your times tables?

What is 11 * 6?
45
Sorry your guess was to small.
Try again
89

At this point execution has reached line 39 which forces execution back to line 31 to repeat the loop.

The condition on line 31 is evaluated again and again is true (89 != 66). The loop is therefore executed for a second time.

This time the condition in the if else statement on line 32 is true (89 > 66)

answer > a*b

so the next line to be executed is line 33

fmt.Println("Sorry, your guess was to big.")

The output at this point would be

The timesquiz shows you how to use loops.
Can you remember your times tables?

What is 11 * 6?
45
Sorry your guess was to small.
Try again
89
Sorry, your guess was to big.

The if else statement is now completed so the remainder of the loop, lines 37 and 38 now execute. Line 37 asks you to try another guess. Line 38 is identical to line 29 and stores your new guess in the answer variable.

If you now enter 66 as your next (3rd guess) the output would look like this:

The timesquiz shows you how to use loops.
Can you remember your times tables?

What is 11 * 6?
45
Sorry your guess was to small.
Try again
89
Sorry, your guess was to big.
Try again
66

Again the execution hits line 39 the last brace in the for loop which forces the execution back to line 31.

Now the answer is correct, the value of answer is 66 which is 6 * 11. So the loops condition

answer != a*b

is now false. This breaks the loop. The entire loop body is skipped, lines 32 to 39, and the next line to be executed is line 40

fmt.Println("Congratulations! You are correct.")

This results in the complete output of

The timesquiz shows you how to use loops.
Can you remember your times tables?

What is 11 * 6?
45
Sorry your guess was to small.
Try again
89
Sorry, your guess was to big.
Try again
66
Congratulations! You are correct.

Having printed the congratulations message the program terminates.

Now it is your turn

The objective is to change the timesquz program so that now if you guess incorrectly the program should ask you another new multiplication with two new random numbers.

If you guess correctly the program should work as before.

The output of the revised program would be similar to

The timesquiz shows you how to use loops.
Can you remember your times tables?

What is 12 * 9?
34
Sorry your guess was to small.
Try again
What is 10 * 11?
100
Sorry your guess was to small.
Try again
What is 9 * 5?
95
Sorry, your guess was to big.
Try again
What is 12 * 7?
84
Congratulations! You are correct.

Now you can try and solve it!

The challenge is not a hard as it seems. There are two keys to solving the challenge.

First you need to read the challenge carefully. It states that the behaviour should only be different if the pupils guesses incorrectly. This implies that program behaviour only needs to change when the condition

answer != a*b

is true. This implies that the changes need to be made to the statements that the loop will execute.

The challenge also tells them that the program should still tell them if their guess was too large or small before the new question is presented. This implies that the changes have to happen after the if else statement inside the loop.

Secondly you already have the code to create two new random numbers and to ask a multiplication question earlier in the program. The code you are looking for is in lines 20-27 of the timesquiz program.

Now you should be able to change the timesquiz program so that it solves the challenge.

The solution is simply to copy lines 20-27 and to paste them in between lines 37 and 38.

This gives the complete solution.

The complete solution is

 1package main
 2
 3import (
 4	"fmt"
 5
 6	"github.com/gophercoders/random"
 7	"github.com/gophercoders/simpleio"
 8)
 9
10func main() {
11
12	var a int
13	var b int
14	var answer int
15
16	fmt.Println("The revised timesquiz shows you how to use loops.")
17	fmt.Println("Can you remember your times tables?")
18	fmt.Println("")
19
20	a = random.GetRandomNumberInRange(1, 12)
21	b = random.GetRandomNumberInRange(1, 12)
22
23	fmt.Print("What is ")
24	fmt.Print(a)
25	fmt.Print(" * ")
26	fmt.Print(b)
27	fmt.Println("?")
28
29	answer = simpleio.ReadNumberFromKeyboard()
30
31	for answer != a*b {
32		if answer > a*b {
33			fmt.Println("Sorry, your guess was to big.")
34		} else {
35			fmt.Println("Sorry your guess was to small.")
36		}
37		fmt.Println("Try again ")
38
39        a = random.GetRandomNumberInRange(1, 12)
40        b = random.GetRandomNumberInRange(1, 12)
41
42        fmt.Print("What is ")
43        fmt.Print(a)
44        fmt.Print(" * ")
45        fmt.Print(b)
46        fmt.Println("?")
47
48		answer = simpleio.ReadNumberFromKeyboard()
49	}
50	fmt.Println("Congratulations! You are correct.")
51}
Fig-3. The revised timesquiz code

Lines 39-47 are the new lines.

Lines 39 and 40 generate two new random numbers and store them in the variables a and b.

Lines 42-46 print the question and line 48 reads your answer into the variable answer as before.

Now that the value of the variables in a and b have changed then loop test on line 31 will test the new answer against the new values of a and b and not the previous values.

The loop test itself is now dynamic. It changes each time the loop executes.

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