4.5. Loop Analysis

In this lesson, you will practice tracing through code with loops and analyzing loops to determine how many times they run.

4.5.1. Tracing Loops

A really important skill to develop is the ability to trace the values of variables and how they change during each iteration of a loop.

You can create a tracing table that keeps track of the variable values each time through the loop as shown below. This is very helpful on the exam. Studies have shown that students who create tables like this do much better on code tracing problems on multiple choice exams.

../_images/traceTable.png

Figure 1: A trace table showing the values of all of the variables each time through the loop. The 0 means before the first loop.

coding exercise Coding Exercise

Here is a complex loop. See if you can trace the code on paper by making a tracing table like above to predict what the code will do when you run it. Click on the this Java visualizer link to help you step through the code. Then, add in output statements like System.out.println("var1: " + var1 + " var2: " + var2); before the loop and inside the loop to keep track of the variables and run.

Did you trace table look like the following?

../_images/whileLoopTrace.png

Figure 2: A table showing the values of all of the variables each time through the loop. The 0 means before the first loop.

exercise Check your understanding

    4-5-1: What are the values of var1 and var2 when the code finishes executing?

    int var1 = 0;
    int var2 = 2;
    
    while ((var2 != 0) && ((var1 / var2) >= 0))
    {
       var1 = var1 + 1;
       var2 = var2 -1;
    }
    
  • var1 = 1, var2 = 1
  • The loop stops one of two ways, when var2 = 0 or when var1 / var2 = 0 - neither is true in this case
  • var1 = 2, var2 = 0
  • The loop stopped because var2 = 0. After the first execution of the loop var1 = 1 and var2 = 1. After the second execution of the loop var1 = 2 and var2 = 0. This stops the loop and doesn't execute the second part of the complex conditional.
  • var1 = 3, var2 = -1
  • The loop stops one of two ways, when var2 = 0 or when var1 / var2 = 0 - neither is true in this case
  • var1 = 0, var2 = 2
  • The loop stops one of two ways, when var2 = 0 or when var1 / var2 = 0 - neither is true in this case
  • The loop will cause a run-time error with a division by zero
  • Even though var1 = 2 and var2 = 0 when the conditional is executed the first condition is true so the rest of the complex conditional won't execute.

    4-5-2: What are the values of x and y when the code finishes executing?

    int x = 2;
    int y = 5;
    
    while (y > 2 && x < y)
    {
       x = x + 1;
       y = y - 1;
    }
    
  • x = 5, y = 2
  • This would be true if the and (&&) was an or (||) instead. But in a complex conditional joined with and (&&) both conditions must be true for the condition to be true.
  • x = 2, y = 5
  • This would be true if the loop never executed, but both conditions are true so the loop will execute.
  • x = 5, y = 2
  • This would be true if the values were swapped, but they are not.
  • x = 3, y = 4
  • This would be true the loop only executed one time, but it will execute twice.
  • x = 4, y = 3
  • The first time the loop changes to x = 3, y = 4, the second time x = 4, y = 3 then the loop will stop since x is not less than y anymore.

4.5.2. Counting Loop Iterations

Loops can be also analyzed to determine how many times they run. This is called run-time analysis or a statement execution count.

coding exercise Coding Exercise

How many stars are printed out in this loop? How many times does the loop run? Figure it out on paper before you run the code.

If you made a trace table, you would know that the loop runs when i = 3, 4, 5, 6 but finishes as soon as i becomes 7 since that is not less than 7. So, the loop runs 4 times. Or you can use the shortcut formula in the note below.

Note

The number of times a loop executes can be calculated by (largestValue - smallestValue + 1). By the largest value I mean the largest value that allows the loop to execute and by the smallest value I mean the smallest value that allows the loop to execute. So in the code above the largest value is 6 (which is the largest value < 7) and the smallest value that allows the loop to execute is 3 so this loop executes (6 - 3 + 1 = 4 times).

coding exercise Coding Exercise

How many stars are printed out by the following loops? How many times do the loops run? Calculate on paper before you run the code.

Note

The number of times a nested for loop body is executed is the number of times the outer loop runs times the number of times the inner loop runs.

For the example above, the outer loop executes 4-0+1= 5 times and the inner 9-0+1=10 times so the total is 5 * 10 = 50.

4.5.3. groupwork Programming Challenge : POGIL Analyzing Loops

We encourage you to do this activity as a POGIL (Process Oriented Guided Inquiry Learning) group activity. POGIL groups are self-managed teams of up to 4 students where everyone has a POGIL role and works together to solve the problems, making sure that everyone in the team participates and learns.

Do the following exercises in your group. Make sure you draw the trace tables keeping track of all the variables in the loops. Use the formulas to determine how many times the loops run. If your group finishes early, do some of the multiple-choice problems in the 4.6 Practice and Summary section of this unit.

    4-5-3: How many times does the following code print a *?

    for (int i = 3; i < 8; i++)
    {
        for (int y = 1; y < 5; y++)
        {
            System.out.print("*");
        }
        System.out.println();
    }
    
  • 40
  • This would be true if the outer loop executed 8 times and the inner 5 times, but what is the initial value of i?
  • 20
  • The outer loop executes 7-3+1=5 times and the inner 4-1+1=4 so this will print 5 * 4 = 20 stars.
  • 24
  • This would be true if the outer loop executed 6 times such as if it was i <= 8.
  • 30
  • This would be true if the inner loop executed 5 times such as if it was y <= 5.

    4-5-4: What does the following code print?

    for (int i = 2; i < 8; i++)
    {
        for (int y = 1; y <= 5; y++)
        {
            System.out.print("*");
        }
        System.out.println();
    }
    
  • A rectangle of 8 rows with 5 stars per row.
  • This would be true if i was initialized to 0.
  • A rectangle of 8 rows with 4 stars per row.
  • This would be true if i was initialized to 0 and the inner loop continued while y < 5.
  • A rectangle of 6 rows with 5 stars per row.
  • The outer loop executes 8-2+1=6 times so there are 6 rows and the inner loop executes 5-1+1=5 times so there are 5 columns.
  • A rectangle of 6 rows with 4 stars per row.
  • This would be true if the inner loop continued while y < 5.

    4-5-5: What does the following print?

    for (int i = 3; i <= 9; i++)
    {
       for (int j = 6; j > 0; j--)
       {
           System.out.print("*");
       }
       System.out.println();
    }
    
  • A rectangle of 9 rows and 5 stars per row.
  • Did you notice what i was initialized to?
  • A rectangle of 6 rows and 6 stars per row.
  • It would print 6 rows if it was i < 9.
  • A rectangle of 7 rows and 5 stars per row.
  • It would print 5 stars per row if it was j > 1.
  • A rectangle of 7 rows and 6 stars per row.
  • The outer loop executes 9 - 3 + 1 = 7 times and the inner 6 - 1 + 1 = 6 times.

4.5.4. Summary

  • A trace table can be used to keep track of the variables and their values throughout each iteration of the loop.

  • We can determine the number of times a code segment will execute with a statement execution count. This is called run-time analysis.

  • The number of times a loop executes can be calculated by (largestValue - smallestValue + 1) where these are the largest and smallest values of the loop counter variable possible in the body of the loop.

  • The number of times a nested for-loop runs is the number of times the outer loop runs times the number of times the inner loop runs.

You have attempted of activities on this page
Next Section - 4.6. Unit 4 Summary