Cell array creation in MATLAB - Time & Space Complexity

Time Complexity: Cell array creation

O(n)

Understanding Time Complexity

We want to understand how the time needed to create a cell array changes as the size grows.

How does the work increase when we make bigger cell arrays?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

n = 1000;
C = cell(1, n);
for i = 1:n
    C{i} = i^2;
end

This code creates a cell array of size n and fills each cell with the square of its index.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that runs from 1 to n.
• How many times: Exactly n times, once for each cell assignment.

How Execution Grows With Input

Each time we increase n, the loop runs more times, doing more assignments.

Input Size (n)	Approx. Operations
10	10 assignments
100	100 assignments
1000	1000 assignments

Pattern observation: The work grows directly with n; doubling n doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to create and fill the cell array grows in a straight line with the number of cells.

Common Mistake

[X] Wrong: "Creating a cell array is instant and does not depend on size."

[OK] Correct: Even though the cell array structure is created quickly, filling each cell with data takes time proportional to the number of cells.

Interview Connect

Understanding how loops affect time helps you explain and improve code that handles collections like cell arrays.

Self-Check

"What if we preallocate the cell array but fill only half of the cells? How would the time complexity change?"

Practice

1. What is the correct way to create a cell array in MATLAB that contains a number, a string, and a logical value?

easy

A. myCell = [42, 'hello', true];

B. myCell = (42, 'hello', true);

C. myCell = {42, 'hello', true};

D. myCell = <42, 'hello', true>;

Solution

1. Step 1: Understand cell array syntax

   Cell arrays use curly braces { } to hold mixed data types.

2. Step 2: Identify correct syntax for mixed types

   myCell = {42, 'hello', true}; uses curly braces with different types: number, string, logical.

3. Final Answer:

   myCell = {42, 'hello', true}; -> Option C

4. Quick Check:

   Curly braces create cell arrays [OK]

Hint: Use curly braces { } for cell arrays, not square brackets [ ] [OK]

Common Mistakes:

• Using square brackets instead of curly braces
• Using parentheses instead of curly braces
• Using angle brackets which are invalid

2. Which of the following is the correct syntax to create a 2x2 cell array with elements 1, 'a', 3.14, and false?

easy

A. C = [1, 'a'; 3.14, false];

B. C = {1, 'a'; 3.14, false};

C. C = {1; 'a'; 3.14; false};

D. C = (1, 'a'; 3.14, false);

Solution

1. Step 1: Recall cell array 2D syntax

   Use curly braces { } with semicolons for rows and commas for columns.

2. Step 2: Check each option

   C = {1, 'a'; 3.14, false}; correctly uses { } with two rows and two columns separated by ; and ,.

3. Final Answer:

   C = {1, 'a'; 3.14, false}; -> Option B

4. Quick Check:

   Curly braces + semicolon for rows = correct 2D cell array [OK]

Hint: Use semicolon to separate rows inside curly braces [OK]

Common Mistakes:

• Using square brackets which create numeric arrays
• Using commas instead of semicolons for rows
• Using parentheses which are invalid for arrays

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

myCell = {10, 'MATLAB'; 'false', 3.5};
disp(myCell{2,1});

medium

A. false

B. 3.5

C. 'MATLAB'

D. 10

Solution

1. Step 1: Understand cell content access

   Using curly braces with indices accesses the content inside the cell.

2. Step 2: Identify the element at row 2, column 1

   myCell{2,1} is the element in second row, first column, which is 'false' as a string.

3. Final Answer:

   'false' -> Option A

4. Quick Check:

   myCell{2,1} = 'false' [OK]

Hint: Use curly braces { } to get cell content, not parentheses ( ) [OK]

Common Mistakes:

• Using parentheses instead of curly braces to access content
• Confusing row and column indices
• Expecting the whole cell instead of content

4. Consider this MATLAB code snippet:

C = {1, 2, 3; 4, 5, 6};
val = C(2,3);

What is the issue with this code if you want to get the number 6 as a value?

medium

A. C(2,3) returns a cell, not the content inside the cell

B. C(2,3) is invalid syntax for cell arrays

C. C(2,3) returns the number 6 directly

D. C(2,3) returns an error because of wrong indexing

Solution

1. Step 1: Understand difference between () and {}

   Parentheses () return a cell array subset, curly braces {} return content.

2. Step 2: Analyze C(2,3)

   C(2,3) returns a 1x1 cell containing 6, not the number 6 itself.

3. Final Answer:

   C(2,3) returns a cell, not the content inside the cell -> Option A

4. Quick Check:

   Use curly braces to get content: C{2,3} [OK]

Hint: Use curly braces { } to get cell content, parentheses () return cells [OK]

Common Mistakes:

• Using parentheses expecting content instead of cell
• Confusing cell array indexing with numeric array indexing
• Expecting direct numeric output from parentheses indexing

5. You want to create a cell array that stores a numeric vector, a string, and another cell array inside it. Which of the following correctly creates such a nested cell array?

hard

A. nestedCell = {[1, 2, 3], 'text', [true; false]};

B. nestedCell = {[1, 2, 3], 'text', [true, false]};

C. nestedCell = {[1, 2, 3], 'text', (true, false)};

D. nestedCell = {[1, 2, 3], 'text', {true, false}};

Solution

1. Step 1: Identify nested cell array syntax

   To nest a cell array inside another, use curly braces { } inside the main cell array.

2. Step 2: Check each option for correct nesting

   nestedCell = {[1, 2, 3], 'text', {true, false}}; uses {true, false} as a nested cell array inside the main cell array.

3. Final Answer:

   nestedCell = {[1, 2, 3], 'text', {true, false}}; -> Option D

4. Quick Check:

   Curly braces inside curly braces create nested cells [OK]

Hint: Use curly braces inside curly braces for nested cell arrays [OK]

Common Mistakes:

• Using square brackets for nested cell arrays
• Using parentheses which are invalid
• Using semicolons inside nested cell arrays incorrectly