Ultrasonic distance sensor (HC-SR04) in Arduino - Time & Space Complexity

Time Complexity: Ultrasonic distance sensor (HC-SR04)

O(n)

Understanding Time Complexity

We want to understand how the time taken by the ultrasonic sensor code changes as we measure distances repeatedly.

How does the program's running time grow when we take more distance readings?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const int trigPin = 9;
const int echoPin = 10;
long duration;
int distance;

void setup() {
  pinMode(trigPin, OUTPUT);
  pinMode(echoPin, INPUT);
  Serial.begin(9600);
}

void loop() {
  digitalWrite(trigPin, LOW);
  delayMicroseconds(2);
  digitalWrite(trigPin, HIGH);
  delayMicroseconds(10);
  digitalWrite(trigPin, LOW);

  duration = pulseIn(echoPin, HIGH);
  distance = duration * 0.034 / 2;

  Serial.println(distance);
  delay(500);
}
    

This code sends an ultrasonic pulse, waits for the echo, calculates the distance, and prints it every half second.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The loop() function runs repeatedly, sending pulses and measuring echoes.
• How many times: It runs indefinitely, repeating the distance measurement every 500 milliseconds.

How Execution Grows With Input

Each distance measurement takes roughly the same time regardless of the distance value.

Input Size (n)	Approx. Operations
10 readings	About 10 times the measurement steps
100 readings	About 100 times the measurement steps
1000 readings	About 1000 times the measurement steps

Pattern observation: The total time grows linearly with the number of readings taken.

Final Time Complexity

Time Complexity: O(n)

This means the time to complete n distance measurements grows directly in proportion to n.

Common Mistake

[X] Wrong: "The time to measure distance depends on how far the object is."

[OK] Correct: The sensor waits for the echo pulse, and the code timing depends on the echo time, so time per reading varies slightly with distance but is mostly fixed per measurement cycle.

Interview Connect

Understanding how sensor reading loops scale helps you write efficient embedded programs that handle repeated tasks smoothly.

Self-Check

"What if we added a loop inside loop() to take multiple readings before printing? How would the time complexity change?"

Practice

1. What is the main purpose of the trigger pin on the HC-SR04 ultrasonic sensor?

easy

A. To send a short ultrasonic pulse to start distance measurement

B. To receive the echo signal from the object

C. To power the sensor

D. To reset the sensor

Solution

1. Step 1: Understand the role of the trigger pin

   The trigger pin is used to send a short pulse that starts the ultrasonic burst.

2. Step 2: Differentiate from echo pin

   The echo pin listens for the returning pulse, not the trigger pin.

3. Final Answer:

   To send a short ultrasonic pulse to start distance measurement -> Option A

4. Quick Check:

   Trigger pin sends pulse = A [OK]

Hint: Trigger pin sends pulse, echo pin listens [OK]

Common Mistakes:

• Confusing trigger with echo pin
• Thinking trigger powers the sensor
• Assuming trigger resets the sensor

2. Which Arduino function is used to measure the duration of the echo pulse from the HC-SR04 sensor?

easy

A. digitalWrite()

B. pulseIn()

C. analogRead()

D. delay()

Solution

1. Step 1: Identify function to measure pulse duration

   The pulseIn() function measures the length of a pulse on a pin.

2. Step 2: Exclude other functions

   digitalWrite() sets pin output, analogRead() reads analog values, delay() pauses execution.

3. Final Answer:

   pulseIn() -> Option B

4. Quick Check:

   pulseIn measures pulse length = B [OK]

Hint: Use pulseIn() to measure echo pulse duration [OK]

Common Mistakes:

• Using digitalWrite() to read pulse
• Confusing analogRead() with pulse measurement
• Using delay() instead of measuring pulse

3. What will be the output distance (in cm) if the measured echo time is 1160 microseconds? Use the formula: distance = (echoTime / 2) / 29.1.

medium

A. 80 cm

B. 40 cm

C. 10 cm

D. 20 cm

Solution

1. Step 1: Calculate half of echo time

   Half of 1160 microseconds is 580 microseconds.

2. Step 2: Divide by 29.1 to get distance

   580 / 29.1 ≈ 19.93 cm, approximately 20 cm.

3. Final Answer:

   20 cm -> Option D

4. Quick Check:

   (1160/2)/29.1 ≈ 20 cm [OK]

Hint: Divide echo time by 2 and then by 29.1 [OK]

Common Mistakes:

• Forgetting to divide echo time by 2
• Using wrong divisor instead of 29.1
• Mixing units of time and distance

4. Identify the error in this Arduino code snippet for HC-SR04 distance measurement:

digitalWrite(triggerPin, HIGH);
delayMicroseconds(10);
digitalWrite(triggerPin, LOW);
echoTime = pulseIn(echoPin, LOW);

medium

A. echoTime should be declared as int, not long

B. delayMicroseconds should be delay()

C. pulseIn should measure HIGH pulse, not LOW

D. triggerPin should be set LOW before HIGH

Solution

1. Step 1: Check pulseIn usage

   The echo pulse is HIGH when the echo is received, so pulseIn should measure HIGH pulse.

2. Step 2: Verify other code parts

   delayMicroseconds(10) is correct for 10 microseconds pulse; triggerPin sequence is correct; echoTime type depends on usage but not an error here.

3. Final Answer:

   pulseIn should measure HIGH pulse, not LOW -> Option C

4. Quick Check:

   pulseIn measures HIGH pulse = D [OK]

Hint: pulseIn(echoPin, HIGH) to measure echo pulse [OK]

Common Mistakes:

• Measuring LOW pulse instead of HIGH
• Using delay() instead of delayMicroseconds()
• Setting triggerPin LOW before HIGH incorrectly

5. You want to measure distance continuously and print it every second using HC-SR04. Which code snippet correctly triggers the sensor and calculates distance in cm?

hard

A. digitalWrite(triggerPin, LOW);
delayMicroseconds(2);
digitalWrite(triggerPin, HIGH);
delayMicroseconds(10);
digitalWrite(triggerPin, LOW);
echoTime = pulseIn(echoPin, HIGH);
distance = (echoTime / 2) / 29.1;

B. digitalWrite(triggerPin, HIGH);
delayMicroseconds(10);
digitalWrite(triggerPin, LOW);
echoTime = pulseIn(echoPin, LOW);
distance = echoTime * 29.1 / 2;

C. digitalWrite(triggerPin, LOW);
delay(10);
digitalWrite(triggerPin, HIGH);
echoTime = pulseIn(echoPin, HIGH);
distance = (echoTime / 2) / 29.1;

D. digitalWrite(triggerPin, HIGH);
delayMicroseconds(2);
digitalWrite(triggerPin, LOW);
echoTime = pulseIn(echoPin, HIGH);
distance = (echoTime * 2) / 29.1;

Solution

1. Step 1: Check trigger pulse sequence

   The correct sequence is to set trigger LOW for 2 microseconds, then HIGH for 10 microseconds, then LOW again.

2. Step 2: Verify echo measurement and distance formula

   pulseIn measures HIGH pulse duration; distance = (echoTime / 2) / 29.1 converts time to cm correctly.

3. Final Answer:

   Code snippet C correctly triggers and calculates distance -> Option A

4. Quick Check:

   Trigger LOW-2us-HIGH-10us-LOW, pulseIn HIGH, distance formula = C [OK]

Hint: Trigger LOW-2us, HIGH-10us, then LOW; measure HIGH pulse [OK]

Common Mistakes:

• Skipping initial LOW trigger pulse
• Measuring LOW pulse instead of HIGH
• Incorrect distance formula with wrong multiplication/division