Reading analog sensors through ADC in Raspberry Pi - Time & Space Complexity

Time Complexity: Reading analog sensors through ADC

O(n)

Understanding Time Complexity

When reading analog sensors through an ADC on a Raspberry Pi, it's important to understand how the time taken grows as we read more sensor values.

We want to know how the program's running time changes when we increase the number of sensor readings.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import spidev
import time

def read_adc(channel, spi):
    adc = spi.xfer2([1, (8 + channel) << 4, 0])
    data = ((adc[1] & 3) << 8) + adc[2]
    return data

spi = spidev.SpiDev()
spi.open(0, 0)

for i in range(100):
    value = read_adc(0, spi)
    time.sleep(0.01)

This code reads analog values from channel 0 of an ADC 100 times, pausing briefly between each read.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that calls read_adc 100 times.
• How many times: Exactly 100 times in this example, but this number can change based on input.

How Execution Grows With Input

Each sensor reading takes roughly the same time, so if we double the number of readings, the total time roughly doubles too.

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

Pattern observation: The total work grows directly with the number of readings.

Final Time Complexity

Time Complexity: O(n)

This means the time to complete the readings grows in a straight line as you increase the number of sensor reads.

Common Mistake

[X] Wrong: "Reading multiple sensors at once will take the same time as reading one sensor."

[OK] Correct: Each sensor read requires communication with the ADC, so reading more sensors means more time spent overall.

Interview Connect

Understanding how sensor reading time grows helps you write efficient code for real devices, showing you can think about performance in practical situations.

Self-Check

"What if we changed the code to read from 4 different channels inside the loop? How would the time complexity change?"