PIR motion sensor in Arduino - Time & Space Complexity

Time Complexity: PIR motion sensor

O(n)

Understanding Time Complexity

When using a PIR motion sensor with Arduino, the program often checks sensor input repeatedly.

We want to understand how the time the program takes grows as it keeps checking the sensor.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int sensorPin = 2;
int ledPin = 13;

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

void loop() {
  int motion = digitalRead(sensorPin);
  if (motion == HIGH) {
    digitalWrite(ledPin, HIGH);
  } else {
    digitalWrite(ledPin, LOW);
  }
}
    

This code reads the PIR sensor repeatedly and turns an LED on or off based on motion detection.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The loop() function runs forever, repeatedly reading the sensor.
• How many times: It runs continuously, checking the sensor once every cycle.

How Execution Grows With Input

Each time the loop runs, it performs a fixed number of steps regardless of input size.

Input Size (n)	Approx. Operations
10	10 sensor reads and LED updates
100	100 sensor reads and LED updates
1000	1000 sensor reads and LED updates

Pattern observation: The number of operations grows directly with how many times the loop runs, but each loop does the same fixed work.

Final Time Complexity

Time Complexity: O(n)

This means the total work grows linearly with the number of loop iterations, but each loop cycle takes constant time.

Common Mistake

[X] Wrong: "The time to read the sensor grows if motion is detected because the LED turns on."

[OK] Correct: Turning the LED on or off is a simple command and takes the same time regardless of sensor state, so the time per loop stays constant.

Interview Connect

Understanding how repeated sensor checks affect program speed helps you write efficient embedded code and shows you can think about how programs behave over time.

Self-Check

What if we added a delay inside the loop that depends on how long motion is detected? How would the time complexity change?

Practice

1. What does a PIR motion sensor detect in an Arduino project?

easy

A. Light intensity changes

B. Sound levels in the environment

C. Movement by sensing infrared changes

D. Temperature variations

Solution

1. Step 1: Understand PIR sensor function

   A PIR sensor detects motion by sensing changes in infrared radiation emitted by objects.

2. Step 2: Compare with other options

   Sound, temperature, and light sensors detect different things, not motion via infrared.

3. Final Answer:

   Movement by sensing infrared changes -> Option C

4. Quick Check:

   PIR sensor = Motion detection [OK]

Hint: PIR sensors detect heat movement, not sound or light [OK]

Common Mistakes:

• Confusing PIR with sound or light sensors
• Thinking PIR detects temperature directly

2. Which Arduino code line correctly reads the PIR sensor connected to digital pin 7?

easy

A. int motion = digitalWrite(7);

B. int motion = digitalRead(7);

C. int motion = analogRead(7);

D. int motion = pinMode(7, INPUT);

Solution

1. Step 1: Identify correct function to read digital input

   digitalRead(pin) reads the digital value from a pin, suitable for PIR sensor output.

2. Step 2: Eliminate incorrect functions

   analogRead reads analog pins, digitalWrite sets output, pinMode sets pin mode but does not read value.

3. Final Answer:

   int motion = digitalRead(7); -> Option B

4. Quick Check:

   Use digitalRead for digital sensor input [OK]

Hint: Use digitalRead to get sensor state from digital pins [OK]

Common Mistakes:

• Using analogRead on digital pin
• Using digitalWrite instead of digitalRead
• Confusing pinMode with reading value

3. What will be the output on the Serial Monitor when the following Arduino code runs and the PIR sensor detects motion?

const int pirPin = 8;
void setup() {
  pinMode(pirPin, INPUT);
  Serial.begin(9600);
}
void loop() {
  int motion = digitalRead(pirPin);
  if (motion == HIGH) {
    Serial.println("Motion detected!");
  } else {
    Serial.println("No motion.");
  }
  delay(1000);
}

medium

A. Motion detected! printed every second when motion is present

B. No output because Serial.begin is missing

C. Motion detected! printed once and then stops

D. Syntax error due to missing semicolon

Solution

1. Step 1: Analyze the loop behavior

   The loop reads the PIR sensor pin every second and prints "Motion detected!" if motion is HIGH, else "No motion.".

2. Step 2: Check Serial setup and output

   Serial.begin(9600) is correctly called in setup, so output will appear on Serial Monitor continuously.

3. Final Answer:

   Motion detected! printed every second when motion is present -> Option A

4. Quick Check:

   Serial prints motion status each second [OK]

Hint: Loop prints sensor state every second with delay(1000) [OK]

Common Mistakes:

• Thinking Serial.begin is missing
• Assuming output prints only once
• Confusing syntax errors

4. Identify the error in this Arduino code snippet using a PIR sensor on pin 9:

void setup() {
  pinMode(9, OUTPUT);
  Serial.begin(9600);
}
void loop() {
  int motion = digitalRead(9);
  if (motion == HIGH) {
    Serial.println("Motion detected");
  }
  delay(500);
}

medium

A. Pin 9 should be set as INPUT, not OUTPUT

B. Serial.begin should be in loop()

C. digitalRead cannot be used on pin 9

D. Missing semicolon after Serial.println

Solution

1. Step 1: Check pinMode for sensor input

   PIR sensor output is digital input, so pin 9 must be set as INPUT, not OUTPUT.

2. Step 2: Verify other code parts

   Serial.begin is correctly in setup, digitalRead works on pin 9, and semicolon is present.

3. Final Answer:

   Pin 9 should be set as INPUT, not OUTPUT -> Option A

4. Quick Check:

   Input pins must use pinMode(INPUT) [OK]

Hint: Set sensor pins as INPUT, not OUTPUT [OK]

Common Mistakes:

• Setting sensor pin as OUTPUT
• Moving Serial.begin to loop
• Ignoring pinMode settings

5. You want to turn on an LED connected to pin 13 only when the PIR sensor on pin 2 detects motion. Which Arduino code snippet correctly implements this behavior?

hard

A. pinMode(2, INPUT);
pinMode(13, OUTPUT);
if (digitalRead(2) == LOW) {
digitalWrite(13, HIGH);
}

B. pinMode(2, OUTPUT);
pinMode(13, INPUT);
if (digitalRead(13) == HIGH) {
digitalWrite(2, HIGH);
}

C. pinMode(2, INPUT);
pinMode(13, OUTPUT);
if (digitalRead(2) == HIGH) {
digitalWrite(13, HIGH);
}

D. pinMode(2, INPUT);
pinMode(13, OUTPUT);
digitalWrite(13, digitalRead(2));

Solution

1. Step 1: Set correct pin modes

   Pin 2 is sensor input, so INPUT; pin 13 is LED output, so OUTPUT.

2. Step 2: Use digitalRead to control LED

   digitalWrite(13, digitalRead(2)) sets LED HIGH when sensor reads HIGH, LOW otherwise.

3. Step 3: Eliminate other options

   pinMode(2, OUTPUT); pinMode(13, INPUT); if (digitalRead(13) == HIGH) { digitalWrite(2, HIGH); } has wrong pin modes and logic. pinMode(2, INPUT); pinMode(13, OUTPUT); if (digitalRead(2) == HIGH) { digitalWrite(13, HIGH); } turns LED on for motion but lacks else clause to turn off when no motion. pinMode(2, INPUT); pinMode(13, OUTPUT); if (digitalRead(2) == LOW) { digitalWrite(13, HIGH); } reverses logic.

4. Final Answer:

   pinMode(2, INPUT); pinMode(13, OUTPUT); digitalWrite(13, digitalRead(2)); -> Option D

5. Quick Check:

   LED state = PIR sensor state [OK]

Hint: Write LED pin to sensor pin state directly for simplicity [OK]

Common Mistakes:

• Setting sensor pin as OUTPUT
• Reversing HIGH/LOW logic
• Confusing input/output pin modes
• Omitting else clause to turn off LED