Physical constants (speed of light, Planck) in SciPy - Time & Space Complexity

Time Complexity: Physical constants (speed of light, Planck)

O(n)

Understanding Time Complexity

We want to see how the time to get physical constants changes as we ask for more constants.

How does the work grow when we retrieve many constants like speed of light or Planck's constant?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

from scipy.constants import physical_constants

constants_to_get = ["speed of light in vacuum", "Planck constant", "electron mass"]
results = []
for name in constants_to_get:
    value = physical_constants[name]
    results.append(value)

This code fetches values for a list of physical constants one by one from scipy.

Identify Repeating Operations

• Primary operation: Looping over the list of constant names and fetching each constant.
• How many times: Once for each constant in the list.

How Execution Grows With Input

Each new constant adds one more fetch operation, so the work grows directly with the number of constants.

Input Size (n)	Approx. Operations
10	10 fetches
100	100 fetches
1000	1000 fetches

Pattern observation: The time grows in a straight line as we ask for more constants.

Final Time Complexity

Time Complexity: O(n)

This means the time to get constants grows directly with how many constants you ask for.

Common Mistake

[X] Wrong: "Fetching multiple constants is instant and does not depend on how many I ask for."

[OK] Correct: Each constant requires a separate lookup, so more constants mean more work and more time.

Interview Connect

Understanding how work grows with input size helps you explain efficiency clearly and shows you can think about performance in real tasks.

Self-Check

"What if we stored all constants in a dictionary once and then accessed them repeatedly? How would the time complexity change?"