Integer random with integers() in NumPy - Time & Space Complexity

Time Complexity: Integer random with integers()

O(n)

Understanding Time Complexity

We want to understand how the time it takes to generate random integers changes as we ask for more numbers.

How does the work grow when we increase the number of random integers generated?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np

# Generate 1 million random integers between 0 and 9
random_numbers = np.random.default_rng().integers(low=0, high=10, size=1000000)

This code creates an array of one million random integers from 0 to 9.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Generating each random integer one by one internally.
• How many times: Once for each number requested (size of the array).

How Execution Grows With Input

As we ask for more random numbers, the work grows directly with how many numbers we want.

Input Size (n)	Approx. Operations
10	About 10 random numbers generated
100	About 100 random numbers generated
1000	About 1000 random numbers generated

Pattern observation: The number of operations grows in a straight line with the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to generate random integers grows directly with how many numbers you want.

Common Mistake

[X] Wrong: "Generating many random numbers is almost instant no matter how many I ask for."

[OK] Correct: Each number requires some work, so asking for more numbers takes more time.

Interview Connect

Understanding how time grows with input size helps you explain performance clearly and shows you know how algorithms scale in real tasks.

Self-Check

"What if we generate random integers without specifying the size (just one number)? How would the time complexity change?"

Practice

1.

What does the numpy.random.integers(low, high) function do?

easy

A. Generates random numbers only equal to low or high.

B. Generates random whole numbers from low (inclusive) to high (inclusive).

C. Generates a sequence of numbers from low to high.

D. Generates random decimal numbers between low and high.

Solution

1. Step 1: Understand the function purpose

   numpy.random.integers(low, high) generates random integers in a range.

2. Step 2: Check the range behavior

   The function generates from low inclusive to high inclusive (default endpoint=True).

3. Final Answer:

   Generates random whole numbers from low (inclusive) to high (inclusive). -> Option B

4. Quick Check:

   integers() returns [low, high] random integers [OK]

Hint: integers() generates [low, high] by default [OK]

Common Mistakes:

• Thinking it generates decimal numbers
• Thinking high is exclusive
• Confusing with sequence generation

2.

Which of the following is the correct syntax to generate 5 random integers between 1 and 10 using numpy.random.integers()?

import numpy as np
# Your code here

easy

A. np.random.integers(1, 10, size=5)

B. np.random.integers(1, 10, count=5)

C. np.random.integers(low=1, high=10, count=5)

D. np.random.integers(1, 10, length=5)

Solution

1. Step 1: Check the function parameters

   integers(low, high, size=number) generates an array of random integers.

2. Step 2: Identify correct keyword for number of values

   The correct keyword is size, so size=5 generates 5 numbers.

3. Final Answer:

   np.random.integers(1, 10, size=5) -> Option A

4. Quick Check:

   Use size= for array length [OK]

Hint: Use size= to specify number of random integers [OK]

Common Mistakes:

• Using positional third argument without size keyword
• Using wrong keyword like count or length
• Missing import statement

3.

What is the output of the following code?

import numpy as np
np.random.seed(0)
arr = np.random.integers(1, 5, size=4)
print(arr)

medium

A. [5 4 3 5]

B. [1 2 3 4]

C. [3 3 3 3]

D. [4 4 1 3]

Solution

1. Step 1: Set random seed for reproducibility

   Using np.random.seed(0) fixes the random numbers generated.

2. Step 2: Generate 4 random integers between 1 and 5 inclusive

   np.random.integers(1, 5, size=4) produces the array [4 4 1 3] with this seed.

3. Final Answer:

   [4 4 1 3] -> Option D

4. Quick Check:

   Seed 0 + integers(1,5,4) = [4 4 1 3] [OK]

Hint: Use seed to get repeatable random integers [OK]

Common Mistakes:

• Ignoring seed and expecting different output
• Confusing inclusive range with exclusive
• Miscounting size parameter

4.

Find the error in this code snippet and choose the correct fix:

import numpy as np
arr = np.random.integers(0, 10, 5)
print(arr)

medium

A. No error; code runs correctly as is.

B. Change third argument to size=5 to specify array size.

C. Add parentheses around arguments: integers((0,10),5).

D. Replace integers with randint to fix syntax.

Solution

1. Step 1: Check function signature

   integers(low, high, size=...) accepts size as positional or keyword argument.

2. Step 2: Identify argument usage

   Passing 5 as positional third argument works correctly.

3. Final Answer:

   No error; code runs correctly as is. -> Option A

4. Quick Check:

   Positional size argument works [OK]

Hint: size can be positional or keyword in integers() [OK]

Common Mistakes:

• Confusing integers() with randint()
• Using wrong keyword like count or length
• Assuming positional size causes error

5.

You want to generate a 2x3 array of random integers from 10 to 20 using numpy.random.integers() and then filter to keep only even numbers. Which code correctly does this?

hard

A. arr = np.random.integers(5, 10, size=(2,3)) * 2

B. arr = np.random.integers(10, 20, size=(2,3)); arr = arr * 2

C. arr = np.random.integers(10, 20, size=(2,3)); arr = arr[arr % 2 == 0]

D. arr = np.random.integers(10, 20, size=(2,3)); arr = arr[arr % 2 != 0]

Solution

1. Step 1: Generate 2x3 array of integers 10 to 20

   Use np.random.integers(10, 20, size=(2,3)) to get random integers in the range.

2. Step 2: Filter only even numbers

   Use boolean indexing arr[arr % 2 == 0] to keep even numbers only.

3. Final Answer:

   arr = np.random.integers(10, 20, size=(2,3)); arr = arr[arr % 2 == 0] -> Option C

4. Quick Check:

   Filter with modulo 2 equals zero for evens [OK]

Hint: Filter with arr % 2 == 0 to keep even numbers [OK]

Common Mistakes:

• Multiplying random numbers instead of filtering
• Filtering odd numbers by mistake
• Using wrong range for even numbers