Uniform distribution in SciPy - Time & Space Complexity

Time Complexity: Uniform distribution

O(n)

Understanding Time Complexity

We want to understand how the time to generate uniform random numbers grows as we ask for more numbers.

How does the cost change when we increase the amount of data we create?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np
from scipy.stats import uniform

# Generate 1D array of n uniform random numbers between 0 and 1
n = 1000
samples = uniform.rvs(size=n)
    

This code generates n random numbers from a uniform distribution between 0 and 1.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Generating each random number independently.
• How many times: Exactly n times, once per sample.

How Execution Grows With Input

Each additional number requires one more generation step, so the total work grows directly with n.

Input Size (n)	Approx. Operations
10	10 random number generations
100	100 random number generations
1000	1000 random number generations

Pattern observation: Doubling n doubles the work needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to generate samples grows in a straight line with the number of samples requested.

Common Mistake

[X] Wrong: "Generating multiple uniform samples is constant time because it's just one function call."

[OK] Correct: Each sample requires work, so more samples mean more time, not the same time.

Interview Connect

Understanding how data generation scales helps you explain performance when working with simulations or sampling in real projects.

Self-Check

"What if we generated a 2D array of samples instead of 1D? How would the time complexity change?"