Traffic light sequence in PLC Programming - Time & Space Complexity

Time Complexity: Traffic light sequence

O(n)

Understanding Time Complexity

We want to understand how the time it takes to run a traffic light sequence program changes as the program runs longer or handles more steps.

Specifically, we ask: how does the number of operations grow as the sequence repeats?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Simple traffic light sequence
Timer GreenTimer = 10;
Timer YellowTimer = 3;
Timer RedTimer = 7;

while (true) {
  TurnOn(GreenLight);
  Wait(GreenTimer);
  TurnOff(GreenLight);

  TurnOn(YellowLight);
  Wait(YellowTimer);
  TurnOff(YellowLight);

  TurnOn(RedLight);
  Wait(RedTimer);
  TurnOff(RedLight);
}
    

This code runs a traffic light sequence turning lights on and off with fixed wait times in a continuous loop.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The infinite while (true) loop that cycles through turning lights on and off.
• How many times: This loop repeats endlessly, running the sequence over and over.

How Execution Grows With Input

Since the sequence runs forever, the number of operations grows steadily over time.

Input Size (n)	Approx. Operations
10 cycles	About 10 times the steps in one sequence
100 cycles	About 100 times the steps in one sequence
1000 cycles	About 1000 times the steps in one sequence

Pattern observation: The operations increase linearly with the number of cycles completed.

Final Time Complexity

Time Complexity: O(n)

This means the total work grows directly in proportion to how many times the traffic light sequence runs.

Common Mistake

[X] Wrong: "The program runs forever, so the time complexity is infinite or undefined."

[OK] Correct: We measure time complexity by how work grows with input size, not by total runtime. Here, each cycle does a fixed amount of work, so complexity grows linearly with cycles.

Interview Connect

Understanding how loops that run repeatedly affect time helps you explain how programs behave over time, a useful skill in automation and control systems.

Self-Check

What if we added a nested loop inside the sequence that repeated a fixed number of times? How would the time complexity change?

Practice

1. What is the main purpose of a traffic light sequence in PLC programming?

easy

A. To control the order and timing of red, yellow, and green lights

B. To measure the speed of vehicles

C. To detect weather conditions

D. To count the number of cars passing

Solution

1. Step 1: Understand traffic light function

   Traffic lights manage traffic by showing red, yellow, and green lights in a set order.

2. Step 2: Identify PLC role

   PLC programs control the timing and sequence of these lights to keep traffic safe and flowing.

3. Final Answer:

   To control the order and timing of red, yellow, and green lights -> Option A

4. Quick Check:

   Traffic light sequence = control lights order and timing [OK]

Hint: Traffic lights cycle colors in order to manage traffic flow [OK]

Common Mistakes:

• Confusing traffic light sequence with vehicle speed measurement
• Thinking traffic lights detect weather
• Assuming traffic lights count cars

2. Which of the following is the correct way to represent a state for the green light in a PLC program?

easy

A. state = GREEN

B. state = YELLOW

C. state = RED

D. state = OFF

Solution

1. Step 1: Identify the green light state

   The green light state should be named clearly as GREEN to represent that light.

2. Step 2: Match option to green state

   Only state = GREEN assigns the state variable to GREEN, which is correct for the green light.

3. Final Answer:

   state = GREEN -> Option A

4. Quick Check:

   Green light state = GREEN [OK]

Hint: Use clear names like GREEN for green light state [OK]

Common Mistakes:

• Using RED or YELLOW for green light state
• Using OFF which means no light
• Confusing state names

3. Given this PLC pseudocode snippet for a traffic light sequence:

timer = 0
state = 'RED'
if timer < 10:
  light = 'RED'
elif timer < 15:
  light = 'GREEN'
else:
  light = 'YELLOW'

What will be the value of light when timer is 12?

medium

A. 'YELLOW'

B. 'RED'

C. 'GREEN'

D. Error

Solution

1. Step 1: Check timer conditions for 12

   12 is not less than 10, so first if is false. 12 is less than 15, so second condition is true.

2. Step 2: Determine light value

   Since timer < 15 is true, light is set to 'GREEN'.

3. Final Answer:

   'GREEN' -> Option C

4. Quick Check:

   timer=12 <15 -> light='GREEN' [OK]

Hint: Check conditions in order, timer 12 fits second condition [OK]

Common Mistakes:

• Choosing 'RED' because timer is close to 10
• Choosing 'YELLOW' by ignoring conditions order
• Thinking code causes error

4. This PLC code snippet is intended to cycle traffic lights but does not work correctly:

state = 'RED'
if state == 'RED':
  state = 'GREEN'
elif state == 'GREEN':
  state = 'YELLOW'
elif state == 'YELLOW':
  state = 'RED'

What is the main problem?

medium

A. The state variable is misspelled

B. The state changes only once because conditions are checked once

C. The code uses wrong comparison operators

D. The code lacks a timer to delay state changes

Solution

1. Step 1: Analyze state change logic

   The code changes state immediately but only once; no loop or repeated check.

2. Step 2: Identify missing repeated execution

   Without looping or timer, state changes once and stops, so no cycling happens.

3. Final Answer:

   The state changes only once because conditions are checked once -> Option B

4. Quick Check:

   Single run code = no cycling [OK]

Hint: State must update repeatedly, not just once [OK]

Common Mistakes:

• Thinking variable name is wrong
• Believing comparison operators are incorrect
• Ignoring need for timing or looping

5. You want to create a PLC program that cycles traffic lights with these timings: red for 10 seconds, green for 15 seconds, yellow for 3 seconds. Which approach best implements this sequence?

hard

A. Use separate timers for each light but no state variable

B. Use a single timer that counts total time without resetting

C. Use random delays between light changes

D. Use a state machine with a timer that resets after each state duration

Solution

1. Step 1: Understand timing requirements

   Each light needs a specific duration before switching to the next.

2. Step 2: Choose best control method

   A state machine with a timer that resets after each state's time allows precise control and cycling.

3. Final Answer:

   Use a state machine with a timer that resets after each state duration -> Option D

4. Quick Check:

   State machine + timer reset = correct timing control [OK]

Hint: Reset timer each state for exact light durations [OK]

Common Mistakes:

• Using one timer without reset causes wrong timing
• Random delays break predictable sequence
• No state variable causes confusion in sequence