Mathematical constants (pi, e, golden ratio) in SciPy - Time & Space Complexity

Time Complexity: Mathematical constants (pi, e, golden ratio)

O(n)

Understanding Time Complexity

We want to understand how fast we can get values of famous math constants using scipy.

How does the time to get these constants change if we ask for many of them?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

from scipy import constants

values = []
for _ in range(n):
    values.append(constants.pi)
    values.append(constants.e)
    values.append(constants.golden)

This code collects the constants pi, e, and the golden ratio n times into a list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop running n times, each time fetching 3 constants.
• How many times: The loop runs exactly n times, repeating the constant retrieval 3 times per loop.

How Execution Grows With Input

Each time we increase n, the number of operations grows directly with n.

Input Size (n)	Approx. Operations
10	30 (10 loops x 3 constants)
100	300 (100 loops x 3 constants)
1000	3000 (1000 loops x 3 constants)

Pattern observation: The operations increase evenly as n grows; doubling n doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to get all constants grows in a straight line as we ask for more.

Common Mistake

[X] Wrong: "Getting constants like pi or e takes a long time or grows with their value."

[OK] Correct: These constants are stored values in scipy, so fetching them is very fast and does not depend on their size or value.

Interview Connect

Knowing how simple operations like fetching constants scale helps you understand bigger data tasks better.

Self-Check

"What if instead of fetching constants, we computed them with a complex formula inside the loop? How would the time complexity change?"