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CS1 Python Subgoals

Section 6.11 Nested Loops

Subgoals for Evaluating a Loop.

  1. Determine Loop Components
    1. Start condition and values
    2. Iteration variable and/or update condition
    3. Termination/final condition
    4. Body that is repeated based on indentation
  2. Trace the loop, writing updated values for every iteration or until you identify the pattern

Subsection 6.11.1

Problem: Given the following code, what is the output?
i = 0
j = 0
m = 8
n = 5
while i < n:
    j = 0
    while j < m:
        print("*", end="")
        j += 1
    print()
    i += 1

Subsection 6.11.2 Determine loop components

Starting values:
i = 0
j = 0
m = 8
n = 5
Termination condition: When i is greater than n
Body that is repeated based on indentation:
j = 0
while j < m:
    print("*", end="")
    j += 1
print()
i += 1

Subsection 6.11.3 SG2: Trace the loop, writing updated values for every iteration or until you identify the pattern

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
A picture of an analog clock showing the second hand moving faster than the minute hand
Figure 6.11.1.
Looking at ONLY the outer loop: <NL> is a new line
Trace table showing the values of i and n, and the output.
Figure 6.11.2.
Now Repeat for inner loop

Subsection 6.11.4 SG1: Determine loop components

Starting values:
j = 0
m = 8
Termination condition: When j is less than m.
Body that is repeated based on indentation:
print("*", end="")
j += 1

Subsection 6.11.5 SG2: Trace the loop, writing updated values for every iteration or until you identify the pattern

Looking at Only the inner loop:
Trace table showing the values of j and m, and the output.
Figure 6.11.3.
Remember, this was just for the first iteration of the outer loop, while i is still value 0.
Trace table showing the values of j and m, and the output; but only for the first iteration of the outer loop (i=0).
Figure 6.11.4.
Continuing to the next iteration of the outer loop, i is 1 and j is re-started at value 0:
Trace table showing the values of j and m, and the output; but only for the second iteration of the outer loop (i=1).
Figure 6.11.5.
Again, increment i to 2, and j is re-started at 0:
Trace table showing the values of j and m, and the output; but only for the third iteration of the outer loop (i=2).
Figure 6.11.6.
Note that outer loop goes 5 times,
Inner loop goes 8 times (for each outer loop)
Final output of the code (5 lines of 8 asterisks)
Figure 6.11.7.
The final output will be 5 lines of 8 asterisks (*).
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