np.argmin() and np.argmax() in NumPy - Time & Space Complexity

Time Complexity: np.argmin() and np.argmax()

O(n)

Understanding Time Complexity

We want to understand how the time it takes to find the smallest or largest value's position in an array changes as the array gets bigger.

How does the work grow when using np.argmin() or np.argmax() on larger arrays?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np

arr = np.random.rand(1000)
min_index = np.argmin(arr)
max_index = np.argmax(arr)

This code creates an array of 1000 random numbers and finds the positions of the smallest and largest values.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Scanning through each element of the array once to compare values.
• How many times: Each element is checked exactly once for argmin and once for argmax.

How Execution Grows With Input

As the array size grows, the number of comparisons grows in a straight line with it.

Input Size (n)	Approx. Operations
10	About 10 comparisons
100	About 100 comparisons
1000	About 1000 comparisons

Pattern observation: Doubling the array size roughly doubles the work needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the smallest or largest value's position grows directly with the size of the array.

Common Mistake

[X] Wrong: "np.argmin() or np.argmax() instantly find the answer without checking all elements."

[OK] Correct: These functions must look at every element to be sure which is smallest or largest, so they take time proportional to the array size.

Interview Connect

Understanding how simple array scans grow with size helps you explain performance clearly and shows you know how basic operations scale in data tasks.

Self-Check

"What if we used np.argmin() on a 2D array with axis specified? How would the time complexity change?"