5.7. Worked Example: Nested LoopsΒΆ

Subgoals for Evaluating a Loop

  1. Diagram which statements go together.

  2. Define and initialize variables

    1. Determine the start condition.

    2. Determine the update condition.

    3. Determine the termination condition.

    4. Determine body that is repeated.

  3. Trace the loop.

    1. For every iteration of the loop, write down the values.

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Problem: Given the following code, what is the output?

int i = 0, j = 0, m = 8, n = 5;
while (i < n)
{
  j = 0;
  while (j < m)
  {
        System.out.print("*");
        j++;
  }
  System.out.println();
  i++;
}

SG1: Diagram which statements go together.

nested loops code diagram

SG2: Define and initialize variables

For now, we begin with the variables that control the outer loop.

Start:

i = 0, n = 5

End:

i >= 5

SG3: Trace the loop

Think of an analog clock:

Second hand goes completely around before minute hand moves

Just like inner loop:

Inner loop must finish before outer loop increments once

Clock

Looking at ONLY the outer loop: <NL> is a new line

Counter

Now Repeat for inner loop

SG1: Diagram which statements go together.

Counter

SG2: Define and initialize variables

Start:

j = 0, m = 8

End:

j >= 8

SG3: Trace the loop

Looking at Only the inner loop:

Counter

Remember, this was just for the first iteration of the outer loop, while i is still value 0.

Counter

Continuing to the next iteration of the outer loop, i is 1 and j is re-started at value 0:

Counter

Again, increment i to 2, and j is re-started at 0:

Counter

Note that outer loop goes 5 times,

Inner loop goes 8 times (for each outer loop)

Counter

The final output will be 5 lines of 8 asterisks (*).

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