LED brightness control with PWM in Arduino - Time & Space Complexity

Time Complexity: LED brightness control with PWM

O(n)

Understanding Time Complexity

When controlling LED brightness using PWM, it's important to understand how the program's running time changes as we adjust brightness levels.

We want to know how the time the program takes grows when we change the brightness steps.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const int ledPin = 9;

void setup() {
  pinMode(ledPin, OUTPUT);
}

void loop() {
  for (int brightness = 0; brightness <= 255; brightness++) {
    analogWrite(ledPin, brightness);
    delay(10);
  }
}
    

This code gradually increases LED brightness from off (0) to fully bright (255) using PWM, pausing briefly at each step.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that runs from 0 to 255 to set brightness levels.
• How many times: 256 times each time the loop runs.

How Execution Grows With Input

As the number of brightness steps increases, the program runs the loop more times, so the total work grows directly with the number of steps.

Input Size (n)	Approx. Operations
10	10 loop cycles
100	100 loop cycles
1000	1000 loop cycles

Pattern observation: The total operations increase in a straight line as input size grows.

Final Time Complexity

Time Complexity: O(n)

This means the time to complete the brightness changes grows directly with the number of brightness levels you set.

Common Mistake

[X] Wrong: "The delay inside the loop doesn't affect the time complexity because it's just a fixed pause."

[OK] Correct: The delay runs every loop cycle, so it adds up and grows with the number of brightness steps, affecting total time linearly.

Interview Connect

Understanding how loops and delays affect program time helps you explain how your code scales, a useful skill in many programming tasks.

Self-Check

"What if we changed the for-loop to increase brightness in steps of 5 instead of 1? How would the time complexity change?"

Practice

1. What does analogWrite(pin, 128) do to an LED connected to the specified pin?

easy

A. Sets the LED brightness to about half of its maximum brightness.

B. Turns the LED fully off.

C. Turns the LED fully on at maximum brightness.

D. Causes the LED to blink on and off repeatedly.

Solution

1. Step 1: Understand PWM value range

   The analogWrite function accepts values from 0 (off) to 255 (full brightness).

2. Step 2: Interpret the value 128

   128 is about half of 255, so the LED brightness will be about half of maximum.

3. Final Answer:

   Sets the LED brightness to about half of its maximum brightness. -> Option A

4. Quick Check:

   PWM value 128 = half brightness [OK]

Hint: Remember 0=off, 255=full brightness, 128=half brightness [OK]

Common Mistakes:

• Thinking 128 turns LED off
• Confusing analogWrite with digitalWrite
• Assuming 128 means blinking

2. Which of the following is the correct syntax to set PWM brightness on pin 9 to maximum in Arduino?

easy

A. analogWrite(255, 9);

B. digitalWrite(9, 255);

C. analogWrite(9, 255);

D. analogRead(9, 255);

Solution

1. Step 1: Recall analogWrite syntax

   The correct syntax is analogWrite(pin, value) where pin is the pin number and value is 0-255.

2. Step 2: Check each option

   analogWrite(9, 255); uses analogWrite(9, 255); which is correct. Others have wrong function names or argument order.

3. Final Answer:

   analogWrite(9, 255); -> Option C

4. Quick Check:

   Correct function and argument order = analogWrite(9, 255); [OK]

Hint: analogWrite(pin, value) sets PWM; pin first, value second [OK]

Common Mistakes:

• Swapping pin and value arguments
• Using digitalWrite instead of analogWrite
• Using analogRead instead of analogWrite

3. What will be the effect of this Arduino code snippet on an LED connected to pin 6?

for (int brightness = 0; brightness <= 255; brightness += 51) {
  analogWrite(6, brightness);
  delay(100);
}

medium

A. The LED will stay at full brightness without change.

B. The LED will blink on and off 5 times quickly.

C. The code will cause a compile error due to wrong syntax.

D. The LED brightness will increase in 5 steps from off to full brightness.

Solution

1. Step 1: Analyze the for loop increments

   The loop variable brightness starts at 0 and increases by 51 until it reaches 255, so values are 0, 51, 102, 153, 204, 255 (6 values, 5 steps).

2. Step 2: Understand analogWrite effect

   Each loop sets LED brightness to the current value, increasing brightness in steps with 100ms delay.

3. Final Answer:

   The LED brightness will increase in 5 steps from off to full brightness. -> Option D

4. Quick Check:

   Brightness steps with delay = gradual brightness increase [OK]

Hint: Loop increments PWM value to fade LED brightness up [OK]

Common Mistakes:

• Counting 6 steps instead of 5 increments
• Thinking LED blinks on/off instead of fading
• Assuming syntax error due to loop

4. Identify the error in this Arduino code that tries to fade an LED on pin 10:

for (int i = 0; i < 256; i++) {
  analogWrite(10, i);
  delay(50);
}
analogWrite(10, 256);

medium

A. The for loop should use <= 256 instead of < 256.

B. The value 256 is invalid for analogWrite; max is 255.

C. Pin 10 cannot be used with analogWrite on Arduino.

D. delay() cannot be used inside a for loop.

Solution

1. Step 1: Check analogWrite value limits

   analogWrite accepts values from 0 to 255. Using 256 is out of range and invalid.

2. Step 2: Verify other code parts

   The for loop correctly uses i from 0 to 255. Pin 10 supports PWM on most Arduino boards. delay() is allowed inside loops.

3. Final Answer:

   The value 256 is invalid for analogWrite; max is 255. -> Option B

4. Quick Check:

   analogWrite max value = 255, 256 causes error [OK]

Hint: PWM values max at 255; never use 256 [OK]

Common Mistakes:

• Using values above 255 for analogWrite
• Thinking delay() is not allowed in loops
• Assuming pin 10 can't do PWM

5. You want to create a smooth breathing LED effect using PWM on pin 3. Which code snippet correctly achieves this effect?

hard

A. for (int b = 0; b <= 255; b++) { analogWrite(3, b); delay(10); } for (int b = 255; b >= 0; b--) { analogWrite(3, b); delay(10); }

B. analogWrite(3, 255); delay(1000); analogWrite(3, 0); delay(1000);

C. for (int b = 0; b < 256; b += 50) { analogWrite(3, b); delay(100); }

D. digitalWrite(3, HIGH); delay(500); digitalWrite(3, LOW); delay(500);

Solution

1. Step 1: Understand breathing LED effect

   A breathing effect smoothly increases brightness from 0 to max, then back down to 0 repeatedly.

2. Step 2: Analyze each option

   for (int b = 0; b <= 255; b++) { analogWrite(3, b); delay(10); } for (int b = 255; b >= 0; b--) { analogWrite(3, b); delay(10); } uses two loops: one increasing PWM from 0 to 255, then decreasing back to 0 with small delays for smoothness. analogWrite(3, 255); delay(1000); analogWrite(3, 0); delay(1000); just turns LED fully on and off abruptly. for (int b = 0; b < 256; b += 50) { analogWrite(3, b); delay(100); } increases brightness in large steps, not smooth. digitalWrite(3, HIGH); delay(500); digitalWrite(3, LOW); delay(500); uses digitalWrite, which only turns LED fully on or off.

3. Final Answer:

   for (int b = 0; b <= 255; b++) { analogWrite(3, b); delay(10); } for (int b = 255; b >= 0; b--) { analogWrite(3, b); delay(10); } -> Option A

4. Quick Check:

   Smooth increase and decrease PWM = breathing LED [OK]

Hint: Use increasing then decreasing PWM values for breathing effect [OK]

Common Mistakes:

• Using digitalWrite instead of analogWrite for brightness
• Skipping the decreasing brightness loop
• Using large PWM steps causing jerky effect