Slicing with start:stop:step in NumPy - Time & Space Complexity

Time Complexity: Slicing with start:stop:step

O(1)

Understanding Time Complexity

We want to understand how the time it takes to slice a numpy array changes as the array gets bigger.

Specifically, how does using start, stop, and step in slicing affect the work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np
arr = np.arange(1000)
sliced = arr[10:900:5]

This code creates an array of 1000 numbers and then slices it from index 10 to 899, taking every 5th element.

Identify Repeating Operations

• Primary operation: Adjusting metadata (offset, shape, strides) to create a view of the original array. No data copying.
• How many times: Constant time, performed once regardless of array size or slice parameters.

How Execution Grows With Input

As the array size grows, the slicing operation remains constant time because it creates a view, not a copy.

Input Size (n)	Approx. Operations
10	1 (metadata adjustment)
100	1
1000	1

Pattern observation: The work is constant, independent of array size, slice length, or step size.

Final Time Complexity

Time Complexity: O(1)

This means the time is constant, as NumPy slicing creates a zero-copy view by adjusting metadata only.

Common Mistake

[X] Wrong: "Slicing copies the selected elements, so time proportional to output size (O(k))."

[OK] Correct: NumPy slicing returns a view with adjusted strides—no data is copied. Use .copy() for actual copying, which is O(k).

Interview Connect

Knowing slicing is O(1) helps optimize code by avoiding unnecessary copies, crucial for large datasets in data science pipelines.

Self-Check

"What if we changed the step size to 1? How would the time complexity change?"

Answer: Still O(1), as it's always a view.

Practice

1. What does the step value control in a NumPy array slice like arr[start:stop:step]?

easy

A. How many elements to skip between each selected element

B. The total number of elements to select

C. The starting index of the slice

D. The ending index of the slice

Solution

1. Step 1: Understand the slice syntax

   The slice arr[start:stop:step] selects elements from start up to but not including stop, moving by step.

2. Step 2: Identify the role of step

   The step determines how many elements to skip between each selected element. For example, step=2 picks every second element.

3. Final Answer:

   How many elements to skip between each selected element -> Option A

4. Quick Check:

   Step controls skipping elements = A [OK]

Hint: Step is the gap between elements in slicing [OK]

Common Mistakes:

• Confusing step with start or stop index
• Thinking step is total count of elements
• Ignoring that step can be negative

2. Which of the following is the correct syntax to slice a NumPy array arr to get every 3rd element from index 1 to 10?

easy

A. arr[10:1:3]

B. arr[1:3:10]

C. arr[1:10:3]

D. arr[3:1:10]

Solution

1. Step 1: Recall slice order

   The slice syntax is arr[start:stop:step]. Here, start=1, stop=10, step=3 means from index 1 up to 9, every 3rd element.

2. Step 2: Check each option

   arr[1:10:3] matches the correct order and values. Others have wrong order or values that don't match the requirement.

3. Final Answer:

   arr[1:10:3] -> Option C

4. Quick Check:

   Correct slice syntax = D [OK]

Hint: Remember slice is start:stop:step in order [OK]

Common Mistakes:

• Mixing up stop and step positions
• Using step as stop index
• Reversing start and stop incorrectly

3. Given arr = np.array([10, 20, 30, 40, 50, 60, 70]), what is the output of arr[1:6:2]?

medium

A. [10 30 50 70]

B. [20 30 40 50 60]

C. [30 50]

D. [20 40 60]

Solution

1. Step 1: Identify slice indices

   The slice arr[1:6:2] starts at index 1 (value 20), stops before index 6, stepping by 2.

2. Step 2: Select elements

   Indexes selected: 1 (20), 3 (40), 5 (60). So output is [20 40 60].

3. Final Answer:

   [20 40 60] -> Option D

4. Quick Check:

   Elements at 1,3,5 = [20 40 60] [OK]

Hint: Pick elements at start, start+step, ... until stop-1 [OK]

Common Mistakes:

• Including stop index element
• Using wrong step size
• Starting from index 0 instead of 1

4. What is wrong with this code snippet?
arr = np.array([1,2,3,4,5])
slice = arr[4:1:-1]
What will slice contain?

medium

A. [4 3 2]

B. [5 4 3]

C. Empty array

D. IndexError

Solution

1. Step 1: Understand negative step slicing

   With step=-1, slicing goes backwards from start index 4 down to stop index 1 (exclusive).

2. Step 2: Identify elements selected

   Indexes selected: 4 (5), 3 (4), 2 (3). So slice contains [5 4 3].

3. Final Answer:

   [5 4 3] -> Option B

4. Quick Check:

   Backward slice from 4 to 2 = [5 4 3] [OK]

Hint: Negative step slices backward, stop is exclusive [OK]

Common Mistakes:

• Expecting forward slice with negative step
• Including stop index element
• Thinking it causes error

5. You have a NumPy array arr = np.arange(20). How would you slice it to get every 4th element in reverse order starting from the last element?

hard

A. arr[19::-4]

B. arr[::4]

C. arr[19:0:4]

D. arr[0:19:-4]

Solution

1. Step 1: Understand array and goal

   arr = np.arange(20) creates array from 0 to 19. We want every 4th element backward starting from last element (index 19).

2. Step 2: Check slicing options

   arr[19::-4] starts at index 19, goes backward to start (index 0), stepping by 4, which matches the goal.

3. Step 3: Verify other options

   A: arr[::4] every 4th forward [0,4,8,...], wrong direction. C: arr[19:0:4] positive step with start>stop gives empty. D: arr[0:19:-4] start<stop with negative step gives empty.

4. Final Answer:

   arr[19::-4] -> Option A

5. Quick Check:

   Reverse every 4th from last = arr[19::-4] [OK]

Hint: Use start index with negative step for reverse slicing [OK]

Common Mistakes:

• Using positive step with decreasing indices
• Wrong start or stop indices
• Assuming arr[::-4] always starts at last element