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?"

Practice

1. What does the function np.argmin() do in NumPy?

easy

A. Finds the index of the smallest value in an array

B. Finds the index of the largest value in an array

C. Returns the smallest value in an array

D. Returns the largest value in an array

Solution

1. Step 1: Understand the purpose of np.argmin()

   The function np.argmin() returns the index (position) of the smallest value in a NumPy array.

2. Step 2: Differentiate from similar functions

   Unlike np.min() which returns the smallest value itself, np.argmin() returns where that value is located.

3. Final Answer:

   Finds the index of the smallest value in an array -> Option A

4. Quick Check:

   np.argmin() = index of smallest value [OK]

Hint: Remember: argmin = position of minimum value [OK]

Common Mistakes:

• Confusing np.argmin() with np.min()
• Thinking it returns the smallest value, not the index
• Mixing up np.argmin() with np.argmax()

2. Which of the following is the correct NumPy function syntax to find the index of the largest value in a NumPy array arr?

easy

A. np.argmin(arr)

B. arr.argmax()

C. np.argmax(arr)

D. arr.argmin()

Solution

1. Step 1: Recall the function to find largest value index

   np.argmax(arr) returns the index of the largest value in the array arr.

2. Step 2: Check other options

   arr.argmax() is valid but not the function syntax asked; np.argmin() and arr.argmin() find smallest value index, not largest.

3. Final Answer:

   np.argmax(arr) -> Option C

4. Quick Check:

   np.argmax(arr) = index of max value [OK]

Hint: Use np.argmax() to get largest value index [OK]

Common Mistakes:

• Using np.argmin() instead of np.argmax()
• Confusing method call arr.argmax() with function np.argmax()
• Mixing up largest and smallest value functions

3. Given the array arr = np.array([3, 1, 4, 1, 5]), what is the output of np.argmin(arr)?

medium

A. 3

B. 1

C. 0

D. 4

Solution

1. Step 1: Identify the smallest value in the array

   The array is [3, 1, 4, 1, 5]. The smallest value is 1.

2. Step 2: Find the index of the first occurrence of the smallest value

   The first 1 appears at index 1 (0-based indexing).

3. Final Answer:

   1 -> Option B

4. Quick Check:

   np.argmin([3,1,4,1,5]) = 1 [OK]

Hint: np.argmin() returns first smallest value index [OK]

Common Mistakes:

• Choosing the last occurrence index instead of first
• Confusing values with indices
• Using np.argmax() by mistake

4. Consider the code:

import numpy as np
arr = np.array([[2, 5, 1], [7, 3, 9]])
index = np.argmax(arr, axis=1)

What is the correct output of index?

medium

A. [1 2]

B. [0 2]

C. [2 1]

D. [2 2]

Solution

1. Step 1: Understand np.argmax with axis=1

   axis=1 means find the index of the largest value in each row.

2. Step 2: Find largest values per row and their indices

   Row 0: [2, 5, 1], max is 5 at index 1; Row 1: [7, 3, 9], max is 9 at index 2.

3. Step 3: Check options carefully

   [2 2] shows [2 2], which is incorrect because first row max index is 1, not 2. [1 2] is [1 2], which matches the correct indices.

4. Final Answer:

   [1 2] -> Option A

5. Quick Check:

   np.argmax(arr, axis=1) = [1 2] [OK]

Hint: axis=1 finds max index per row [OK]

Common Mistakes:

• Mixing up axis parameter
• Confusing row and column indices
• Assuming global max index instead of per row

5. You have a 2D NumPy array representing exam scores of 4 students in 3 subjects:

scores = np.array([[88, 92, 79], [95, 85, 91], [70, 78, 88], [90, 91, 85]])

How do you find the subject index where each student scored the lowest?

hard

A. np.argmax(scores, axis=0)

B. np.argmin(scores, axis=0)

C. np.argmax(scores, axis=1)

D. np.argmin(scores, axis=1)

Solution

1. Step 1: Understand the array and axis meaning

   Each row is a student, columns are subjects. axis=1 means operate across columns (subjects) per student.

2. Step 2: Use np.argmin with axis=1 to find lowest score subject per student

   np.argmin(scores, axis=1) returns the index of the smallest score in each student's row.

3. Final Answer:

   np.argmin(scores, axis=1) -> Option D

4. Quick Check:

   Lowest subject per student = np.argmin(scores, axis=1) [OK]

Hint: Use axis=1 to find min per row (student) [OK]

Common Mistakes:

• Using axis=0 which finds min per subject, not per student
• Using np.argmax instead of np.argmin
• Confusing rows and columns in axis parameter