Multiple sensor fusion in Arduino - Time & Space Complexity

Time Complexity: Multiple sensor fusion

O(n)

Understanding Time Complexity

When combining data from multiple sensors, the time it takes to process all inputs matters.

We want to know how processing time grows as we add more sensors.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const int sensorCount = 5;
int sensorValues[sensorCount];

void readSensors() {
  for (int i = 0; i < sensorCount; i++) {
    sensorValues[i] = analogRead(i);
  }
}

void loop() {
  readSensors();
  // process sensorValues here
}
    

This code reads values from multiple sensors one by one and stores them in an array.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop reading each sensor value.
• How many times: It runs once per sensor, so sensorCount times.

How Execution Grows With Input

As the number of sensors increases, the time to read all sensors grows in a straight line.

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

Pattern observation: Doubling the number of sensors doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to read sensors grows directly with the number of sensors.

Common Mistake

[X] Wrong: "Reading multiple sensors takes the same time no matter how many sensors there are."

[OK] Correct: Each sensor read takes time, so more sensors mean more total time.

Interview Connect

Understanding how sensor reading time grows helps you design efficient embedded systems and shows you can think about performance clearly.

Self-Check

What if we read sensors in parallel using interrupts? How would the time complexity change?