Traffic light simulation in Raspberry Pi - Time & Space Complexity

Time Complexity: Traffic light simulation

O(n)

Understanding Time Complexity

When simulating a traffic light, we want to know how the program's running time changes as we add more cycles or lights.

We ask: How does the time to run the simulation grow when we increase the number of light changes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

for cycle in range(num_cycles):
    turn_on_red()
    wait(red_duration)
    turn_on_green()
    wait(green_duration)
    turn_on_yellow()
    wait(yellow_duration)
    
# End of simulation

This code runs a traffic light sequence for a set number of cycles, turning lights on and waiting for their durations.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that repeats the light changes for each cycle.
• How many times: Exactly num_cycles times, once per cycle.

How Execution Grows With Input

Each cycle runs the same fixed steps of turning lights on and waiting.

Input Size (num_cycles)	Approx. Operations
10	About 10 cycles of light changes
100	About 100 cycles of light changes
1000	About 1000 cycles of light changes

Pattern observation: The total work grows directly with the number of cycles; doubling cycles doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to run the simulation grows in a straight line as you add more cycles.

Common Mistake

[X] Wrong: "The time to run the simulation stays the same no matter how many cycles we have."

[OK] Correct: Each cycle repeats the same steps, so more cycles mean more total time.

Interview Connect

Understanding how loops affect running time helps you explain how programs scale, a key skill in many coding tasks.

Self-Check

"What if we added a nested loop inside each cycle to blink the yellow light multiple times? How would the time complexity change?"

Practice

1. What is the main purpose of using GPIO pins in a Raspberry Pi traffic light simulation?

easy

A. To control the LEDs turning on and off

B. To increase the Raspberry Pi processing speed

C. To connect the Raspberry Pi to the internet

D. To store the traffic light timing data

Solution

1. Step 1: Understand GPIO pin function

   GPIO pins on Raspberry Pi are used to send signals to external devices like LEDs.

2. Step 2: Connect GPIO pins to LEDs

   In traffic light simulation, GPIO pins turn LEDs on or off to show red, yellow, or green lights.

3. Final Answer:

   To control the LEDs turning on and off -> Option A

4. Quick Check:

   GPIO pins control LEDs = A [OK]

Hint: GPIO pins control hardware like LEDs in simulations [OK]

Common Mistakes:

• Thinking GPIO speeds up the CPU
• Confusing GPIO with internet connection
• Assuming GPIO stores data

2. Which of the following Python code snippets correctly sets up GPIO pin 17 as an output for the traffic light LED?

easy

A. GPIO.output(17, GPIO.IN)

B. GPIO.setup(17, GPIO.OUT)

C. GPIO.setup(17, GPIO.IN)

D. GPIO.output(17, GPIO.OUT)

Solution

1. Step 1: Identify correct GPIO setup function

   GPIO.setup(pin_number, mode) is used to set pin mode; mode can be GPIO.OUT or GPIO.IN.

2. Step 2: Choose correct mode for LED output

   LEDs need output mode, so GPIO.OUT is correct for pin 17.

3. Final Answer:

   GPIO.setup(17, GPIO.OUT) -> Option B

4. Quick Check:

   Setup pin as output = B [OK]

Hint: Use GPIO.setup(pin, GPIO.OUT) to set output pins [OK]

Common Mistakes:

• Using GPIO.output instead of GPIO.setup to set mode
• Setting pin as GPIO.IN instead of GPIO.OUT
• Confusing setup and output functions

3. What will be the output behavior of this Python code snippet controlling a traffic light LED on GPIO 18?

GPIO.output(18, GPIO.HIGH)
time.sleep(3)
GPIO.output(18, GPIO.LOW)

medium

A. The LED on pin 18 stays off permanently

B. The LED on pin 18 blinks rapidly for 3 seconds

C. The program will cause a syntax error

D. The LED on pin 18 turns on for 3 seconds, then turns off

Solution

1. Step 1: Analyze GPIO.output commands

   GPIO.HIGH turns the LED on; GPIO.LOW turns it off.

2. Step 2: Understand time.sleep effect

   time.sleep(3) pauses the program for 3 seconds while LED stays on.

3. Final Answer:

   The LED on pin 18 turns on for 3 seconds, then turns off -> Option D

4. Quick Check:

   HIGH then sleep then LOW = C [OK]

Hint: HIGH turns LED on, LOW turns it off; sleep pauses timing [OK]

Common Mistakes:

• Thinking LED blinks rapidly without loop
• Assuming syntax error due to time.sleep
• Confusing HIGH with LOW states

4. Identify the error in this traffic light simulation code snippet:

GPIO.setup(22, GPIO.OUT)
GPIO.output(22, HIGH)
time.sleep(2)
GPIO.output(22, LOW)

medium

A. HIGH and LOW should be prefixed with GPIO.

B. GPIO.setup should use GPIO.IN instead of GPIO.OUT

C. time.sleep cannot be used with GPIO.output

D. Pin 22 cannot be used for output

Solution

1. Step 1: Check usage of HIGH and LOW constants

   HIGH and LOW must be written as GPIO.HIGH and GPIO.LOW to be recognized.

2. Step 2: Verify other code parts

   GPIO.setup with GPIO.OUT is correct; time.sleep works fine; pin 22 is valid.

3. Final Answer:

   HIGH and LOW should be prefixed with GPIO. -> Option A

4. Quick Check:

   HIGH/LOW require GPIO. prefix = D [OK]

Hint: Always prefix HIGH/LOW with GPIO. to avoid NameError [OK]

Common Mistakes:

• Omitting GPIO. prefix for HIGH/LOW
• Changing pin mode incorrectly
• Thinking time.sleep causes error

5. You want to simulate a traffic light cycle with red, yellow, and green LEDs connected to GPIO pins 5, 6, and 13 respectively. Which Python code snippet correctly cycles through the lights with 2 seconds red, 1 second yellow, and 3 seconds green, repeating forever?

hard

A. GPIO.output(5, GPIO.HIGH)
GPIO.output(6, GPIO.HIGH)
GPIO.output(13, GPIO.HIGH)
time.sleep(6)
GPIO.output(5, GPIO.LOW)
GPIO.output(6, GPIO.LOW)
GPIO.output(13, GPIO.LOW)

B. for light in [5,6,13]:
GPIO.output(light, GPIO.HIGH)
time.sleep(2)
GPIO.output(light, GPIO.LOW)

C. while True:
GPIO.output(5, GPIO.HIGH)
time.sleep(2)
GPIO.output(5, GPIO.LOW)
GPIO.output(6, GPIO.HIGH)
time.sleep(1)
GPIO.output(6, GPIO.LOW)
GPIO.output(13, GPIO.HIGH)
time.sleep(3)
GPIO.output(13, GPIO.LOW)

D. while True:
GPIO.output(13, GPIO.HIGH)
time.sleep(3)
GPIO.output(13, GPIO.LOW)
GPIO.output(6, GPIO.HIGH)
time.sleep(1)
GPIO.output(6, GPIO.LOW)
GPIO.output(5, GPIO.HIGH)
time.sleep(2)
GPIO.output(5, GPIO.LOW)

Solution

1. Step 1: Check order and timing of lights

   Traffic lights cycle red (2s), yellow (1s), green (3s) in that order repeatedly.

2. Step 2: Verify code matches timing and order

   while True: GPIO.output(5, GPIO.HIGH) time.sleep(2) GPIO.output(5, GPIO.LOW) GPIO.output(6, GPIO.HIGH) time.sleep(1) GPIO.output(6, GPIO.LOW) GPIO.output(13, GPIO.HIGH) time.sleep(3) GPIO.output(13, GPIO.LOW) uses while True loop, turns on red (pin 5) for 2s, then yellow (pin 6) for 1s, then green (pin 13) for 3s, turning off each after delay.

3. Final Answer:

   while True loop with red (2s), yellow (1s), green (3s) -> Option C

4. Quick Check:

   Correct order and timing in loop = A [OK]

Hint: Use while True and sequence GPIO.output with time.sleep [OK]

Common Mistakes:

• Wrong order of lights
• Using for loop without timing per light
• Turning all LEDs on at once