Reshaping arrays in MATLAB - Time & Space Complexity

Time Complexity: Reshaping arrays

O(1)

Understanding Time Complexity

When we reshape arrays in MATLAB, we change their shape without changing the data.

We want to know how the time to reshape grows as the array size grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

A = 1:1000;          % Create a row vector with 1000 elements
B = reshape(A, 100, 10); % Reshape into a 100x10 matrix

This code reshapes a 1D array into a 2D matrix by rearranging elements.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Updating shape metadata (dimensions array). No element copying or traversal.
• How many times: Constant time, independent of array size (n).

How Execution Grows With Input

As the number of elements grows, the time to reshape stays roughly constant.

Input Size (n)	Approx. Operations
10	About 5 operations
100	About 5 operations
1000	About 5 operations

Pattern observation: The time is constant regardless of the number of elements.

Final Time Complexity

Time Complexity: O(1)

This means the time to reshape is constant and does not grow with the number of elements. MATLAB reshape updates metadata without copying data.

Common Mistake

[OK] Correct thinking: "Reshaping is instant and does not depend on array size."

[X] Why the wrong one fails: Reshape does not copy or process elements; it only updates metadata, so no O(n) cost.

Interview Connect

Understanding how reshaping scales helps you reason about data manipulation efficiency in real tasks.

Self-Check

"What if we reshape a very large array multiple times in a loop? How would the time complexity change?"

Practice

1. What does the MATLAB function reshape do to an array?

easy

A. Sorts the array elements in ascending order

B. Changes the data values but keeps the shape the same

C. Deletes elements from the array

D. Changes the shape of the array without changing its data

Solution

1. Step 1: Understand the purpose of reshape

   The reshape function changes how the array is organized in terms of rows and columns but does not modify the actual data values.

2. Step 2: Confirm data remains unchanged

   The total number of elements stays the same, so no data is lost or changed, only rearranged.

3. Final Answer:

   Changes the shape of the array without changing its data -> Option D

4. Quick Check:

   reshape changes shape, not data [OK]

Hint: Remember reshape only rearranges elements, data stays same [OK]

Common Mistakes:

• Thinking reshape changes data values
• Assuming reshape deletes elements
• Confusing reshape with sorting

2. Which of the following is the correct syntax to reshape a 1x6 vector A into a 2x3 matrix in MATLAB?

easy

A. reshape(A, 2, 3)

B. reshape(2, 3, A)

C. reshape(A, [3 2])

D. reshape(A, 3, 2)

Solution

1. Step 1: Recall reshape syntax

   The correct syntax is reshape(array, rows, columns). So the array comes first, then the new dimensions.

2. Step 2: Check dimensions for 2x3

   To reshape into 2 rows and 3 columns, use reshape(A, 2, 3). Options with swapped dimensions or wrong order are incorrect.

3. Final Answer:

   reshape(A, 2, 3) -> Option A

4. Quick Check:

   reshape(array, rows, cols) [OK]

Hint: Syntax is reshape(array, rows, columns) [OK]

Common Mistakes:

• Putting dimensions before the array
• Swapping rows and columns
• Using brackets incorrectly

3. What is the output of the following MATLAB code?

A = 1:6;
B = reshape(A, 3, 2);
disp(B);

medium

A. [1 4; 2 5; 3 6]

B. [1 2; 3 4; 5 6]

C. [1 3 5; 2 4 6]

D. [1 2 3; 4 5 6]

Solution

1. Step 1: Understand reshape fills column-wise

   MATLAB fills the reshaped matrix column by column from the original vector. The vector A = [1 2 3 4 5 6].

2. Step 2: Fill 3 rows and 2 columns

   Fill first column: 1, 2, 3; second column: 4, 5, 6. So matrix B is:
   [1 4;
   2 5;
   3 6]

3. Final Answer:

   [1 4; 2 5; 3 6] -> Option A

4. Quick Check:

   reshape fills column-wise [OK]

Hint: Remember MATLAB fills columns first in reshape [OK]

Common Mistakes:

• Assuming row-wise filling
• Mixing up rows and columns
• Confusing output format

4. Identify the error in this MATLAB code:

A = 1:8;
B = reshape(A, 3, 3);

medium

A. Variable A is not defined correctly

B. reshape dimensions do not match number of elements

C. Syntax error in reshape function

D. No error, code runs fine

Solution

1. Step 1: Count elements in A

   Vector A has 8 elements (1 to 8).

2. Step 2: Check reshape target size

   reshape tries to make a 3x3 matrix which needs 9 elements, but A has only 8.

3. Final Answer:

   reshape dimensions do not match number of elements -> Option B

4. Quick Check:

   Elements must match reshape size [OK]

Hint: Check total elements before reshaping [OK]

Common Mistakes:

• Ignoring element count mismatch
• Assuming reshape pads missing elements
• Thinking reshape auto adjusts size

5. Given a 3D array A of size 2x3x4, which MATLAB command correctly reshapes it into a 6x4 matrix without changing the order of elements?

hard

A. reshape(A, [2 3 4])

B. reshape(A, 4, 6)

C. reshape(A, [6 4])

D. reshape(A, [4 6])

Solution

1. Step 1: Calculate total elements

   Original size is 2x3x4 = 24 elements total.

2. Step 2: Confirm reshape size matches total elements

   6x4 = 24 elements, so reshape to [6 4] is valid.

3. Step 3: Use correct syntax for reshape with vector size

   reshape accepts size as a vector, so reshape(A, [6 4]) is correct and clearer for multi-dimensional arrays.

4. Final Answer:

   reshape(A, [6 4]) -> Option C

5. Quick Check:

   Use vector size for multi-dim reshape [OK]

Hint: Use reshape(A, [rows cols]) for multi-dim arrays [OK]

Common Mistakes:

• Swapping rows and columns
• Using wrong syntax without brackets
• Ignoring total element count