np.full() for custom-filled arrays in NumPy - Time & Space Complexity

Time Complexity: np.full() for custom-filled arrays

O(n)

Understanding Time Complexity

We want to understand how the time needed to create an array filled with a specific value changes as the array size grows.

How does the work increase when we ask numpy to fill bigger arrays?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np

# Create a 1D array of size n filled with the value 7
n = 1000
arr = np.full(n, 7)

This code creates a numpy array of length n, filling every element with the number 7.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Filling each element of the array with the given value.
• How many times: Exactly once for each element, so n times.

How Execution Grows With Input

As the array size grows, the time to fill it grows in direct proportion.

Input Size (n)	Approx. Operations
10	10 fill operations
100	100 fill operations
1000	1000 fill operations

Pattern observation: Doubling the size doubles the work needed to fill the array.

Final Time Complexity

Time Complexity: O(n)

This means the time to create and fill the array grows linearly with the number of elements.

Common Mistake

[X] Wrong: "np.full() fills the array instantly regardless of size because it uses a shortcut."

[OK] Correct: Even though numpy is fast, it must still set each element, so time grows with array size.

Interview Connect

Understanding how array creation scales helps you reason about data preparation speed, a key skill in data science and coding interviews.

Self-Check

What if we changed np.full() to create a 2D array of size n by m? How would the time complexity change?

Practice

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

easy

A. Creates an empty array with no values

B. Creates an array with random values

C. Creates an array with increasing numbers

D. Creates an array filled with the same specified value

Solution

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

   The function np.full() is designed to create arrays where every element has the same value.

2. Step 2: Compare with other array creation functions

   Unlike functions that create random or sequential arrays, np.full() fills the array with a constant value.

3. Final Answer:

   Creates an array filled with the same specified value -> Option D

4. Quick Check:

   np.full() = constant value array [OK]

Hint: Remember: full means fill with one value [OK]

Common Mistakes:

• Confusing np.full() with np.random functions
• Thinking it creates empty or zero arrays
• Assuming it creates sequences of numbers

2. Which of the following is the correct syntax to create a 3x3 NumPy array filled with the value 7 using np.full()?

easy

A. np.full((3, 3), 7)

B. np.full(3, 3, 7)

C. np.full([3, 3], value=7)

D. np.full(7, shape=(3,3))

Solution

1. Step 1: Identify the correct parameter order for np.full()

   np.full() takes the shape as the first argument (tuple), then the fill value as the second argument.

2. Step 2: Check each option's syntax

   np.full((3, 3), 7) uses np.full((3, 3), 7) which matches the correct order and types. Others misuse argument order or syntax.

3. Final Answer:

   np.full((3, 3), 7) -> Option A

4. Quick Check:

   Shape tuple first, fill value second [OK]

Hint: Shape is first tuple, value is second argument [OK]

Common Mistakes:

• Passing shape and value as separate arguments without tuple
• Using keyword arguments incorrectly
• Swapping the order of shape and fill value

3. What is the output of the following code?

import numpy as np
arr = np.full((2, 2), 5)
print(arr)

medium

A. [[5 5]
[5 5]]

B. [[2 2]
[2 2]]

C. [[0 0]
[0 0]]

D. [[5 5 5]
[5 5 5]]

Solution

1. Step 1: Understand np.full() parameters

   The shape is (2, 2), so the array will have 2 rows and 2 columns. The fill value is 5.

2. Step 2: Predict the printed array

   The array will be a 2x2 matrix with all elements equal to 5, printed as [[5 5]\n [5 5]].

3. Final Answer:

   [[5 5] [5 5]] -> Option A

4. Quick Check:

   Shape (2,2) with 5 fills = [[5 5]\n [5 5]] [OK]

Hint: Shape defines size, fill value repeats [OK]

Common Mistakes:

• Confusing shape dimensions
• Expecting zeros instead of fill value
• Misreading the printed array shape

4. Identify the error in this code snippet:

import numpy as np
arr = np.full(3, 4, 2)
print(arr)

medium

A. Fill value must be a string

B. Shape argument must be a tuple

C. The third positional argument `2` is an invalid dtype specifier

D. np.full() cannot create 1D arrays

Solution

1. Step 1: Check np.full() argument count and order

   np.full(shape, fill_value, dtype=None, ...). The call np.full(3, 4, 2) sets shape=3, fill_value=4, dtype=2, but 2 is not a valid dtype (raises ValueError: data type "2" not understood).

2. Step 2: Confirm correct usage

   Correct syntax is np.full(3, 4) for 1D array of 4s, or specify valid dtype like dtype=float. Extra or invalid dtype causes error.

3. Final Answer:

   The third positional argument `2` is an invalid dtype specifier -> Option C

4. Quick Check:

   np.full(3,4,2) -> ValueError: data type "2" [OK]

Hint: Optional dtype must be valid (e.g., float, int) [OK]

Common Mistakes:

• Passing multiple positional arguments instead of tuple shape
• Using wrong data types for shape
• Assuming np.full() needs three arguments

5. You want to create a 4x4 NumPy array filled with the value 9, but only the diagonal elements should be 0. Which code correctly achieves this using np.full() and other NumPy functions?

hard

A. arr = np.zeros((4,4)); arr[:] = 9; print(arr)

B. arr = np.full((4,4), 9); np.fill_diagonal(arr, 0); print(arr)

C. arr = np.full((4,4), 0); np.fill_diagonal(arr, 9); print(arr)

D. arr = np.full(4, 9); np.fill_diagonal(arr, 0); print(arr)

Solution

1. Step 1: Create a 4x4 array filled with 9

   Using np.full((4,4), 9) creates a 4x4 array where every element is 9.

2. Step 2: Replace diagonal elements with 0

   np.fill_diagonal(arr, 0) sets the diagonal elements of the array to 0.

3. Step 3: Verify the output

   Printing arr shows a 4x4 array with 9 everywhere except 0 on the diagonal.

4. Final Answer:

   arr = np.full((4,4), 9); np.fill_diagonal(arr, 0); print(arr) -> Option B

5. Quick Check:

   Fill then fill_diagonal for custom values [OK]

Hint: Fill full array first, then change diagonal [OK]

Common Mistakes:

• Filling zeros first then trying to fill diagonal with 9
• Using wrong shape or 1D array for 2D problem
• Misusing np.fill_diagonal on 1D arrays