Multiple outputs in MATLAB - Time & Space Complexity

Time Complexity: Multiple outputs

O(n)

Understanding Time Complexity

We want to see how the time needed changes when a MATLAB function gives back more than one answer.

How does asking for multiple results affect the work the program does?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function [sumVal, prodVal] = sumAndProduct(arr)
    n = length(arr);
    sumVal = 0;
    prodVal = 1;
    for i = 1:n
        sumVal = sumVal + arr(i);
        prodVal = prodVal * arr(i);
    end
end

This function calculates the sum and product of all elements in an array.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: A single loop that goes through each element of the array once.
• How many times: Exactly as many times as there are elements in the array (n times).

How Execution Grows With Input

As the array gets bigger, the loop runs more times, doing a fixed amount of work each time.

Input Size (n)	Approx. Operations
10	About 10 additions and 10 multiplications
100	About 100 additions and 100 multiplications
1000	About 1000 additions and 1000 multiplications

Pattern observation: The work grows directly with the number of elements. Double the elements, double the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to get both outputs grows in a straight line with the size of the input array.

Common Mistake

[X] Wrong: "Getting two outputs means the program does twice as much work, so the time complexity doubles to O(2n)."

[OK] Correct: The loop still runs once per element doing both tasks together, so the time grows linearly, not doubled in complexity terms.

Interview Connect

Understanding how multiple outputs affect time helps you explain your code clearly and shows you know how work scales in real programs.

Self-Check

"What if the function used two separate loops instead of one to calculate sum and product? How would the time complexity change?"

Practice

1. In MATLAB, how do you define a function that returns multiple outputs?

easy

A. Separate output variables with commas without brackets.

B. Use square brackets around output variables in the function definition.

C. Use parentheses around output variables in the function definition.

D. Define each output in a separate function.

Solution

1. Step 1: Understand MATLAB function output syntax

   MATLAB requires multiple outputs to be enclosed in square brackets in the function definition. Only Use square brackets around output variables in the function definition. correctly uses square brackets; others are invalid syntax or incorrect approach.

2. Final Answer:

   Use square brackets around output variables in the function definition. -> Option B

3. Quick Check:

   Multiple outputs = square brackets [OK]

Hint: Remember: multiple outputs always use square brackets [OK]

Common Mistakes:

• Using parentheses instead of square brackets
• Listing outputs without any brackets
• Trying to define outputs in separate functions

2. Which of the following is the correct syntax to call a MATLAB function myFunc that returns two outputs?

easy

A. [a, b] = myFunc(x);

B. a, b = myFunc(x);

C. (a, b) = myFunc(x);

D. a = myFunc(x); b = myFunc(x);

Solution

1. Step 1: Recall MATLAB function call syntax for multiple outputs

   Multiple outputs must be captured using square brackets on the left side of the assignment. [a, b] = myFunc(x); uses correct square brackets; B and C use invalid syntax; A calls function twice, not multiple outputs.

2. Final Answer:

   [a, b] = myFunc(x); -> Option A

3. Quick Check:

   Multiple outputs call = square brackets [OK]

Hint: Use square brackets to capture multiple outputs when calling [OK]

Common Mistakes:

• Using parentheses or commas without brackets
• Calling function multiple times instead of one call
• Missing brackets around output variables

3. What is the output of this MATLAB code?

function [sumVal, diffVal] = calc(a, b)
    sumVal = a + b;
    diffVal = a - b;
end

[x, y] = calc(5, 3);

What are the values of x and y?

medium

A. x = 5, y = 3

B. x = 2, y = 8

C. x = 8, y = 2

D. x = 15, y = 2

Solution

1. Step 1: Trace function execution and match outputs

   The function returns sumVal = a + b = 5 + 3 = 8 and diffVal = a - b = 5 - 3 = 2. x receives sumVal (8), y receives diffVal (2).

2. Final Answer:

   x = 8, y = 2 -> Option C

3. Quick Check:

   sum = 8, diff = 2 [OK]

Hint: First output = sum, second output = difference [OK]

Common Mistakes:

• Swapping order of outputs
• Confusing inputs with outputs
• Adding instead of subtracting for difference

4. Identify the error in this MATLAB function that tries to return two outputs:

function [a, b] = wrongFunc(x)
    a = x * 2;
    b = x + 3
end

medium

A. Square brackets not allowed in output

B. Function must return only one output

C. Function name does not match file name

D. Missing semicolon after assigning b

Solution

1. Step 1: Check syntax line by line

   Line assigning b lacks a semicolon, causing output to print unexpectedly. Multiple outputs with square brackets are allowed; function name matching file is good practice but not error here.

2. Final Answer:

   Missing semicolon after assigning b -> Option D

3. Quick Check:

   Missing semicolon = syntax error [OK]

Hint: Always end statements with semicolon to avoid output [OK]

Common Mistakes:

• Ignoring missing semicolons
• Thinking multiple outputs are not allowed
• Confusing function name and file name mismatch as error

5. You want to write a MATLAB function stats that takes a vector and returns three outputs: the mean, median, and standard deviation. Which function header and call are correct?

hard

A. Function: function [m, med, s] = stats(v)Call: [meanVal, medianVal, stdVal] = stats(data);

B. Function: function (m, med, s) = stats(v)Call: (meanVal, medianVal, stdVal) = stats(data);

C. Function: function m, med, s = stats(v)Call: meanVal, medianVal, stdVal = stats(data);

D. Function: function stats(v) returns m, med, sCall: stats(data)

Solution

1. Step 1: Verify function header and call syntax

   Multiple outputs must use square brackets in the function header: function [m, med, s] = stats(v) and in the call: [meanVal, medianVal, stdVal] = stats(data);. Others use invalid parentheses, commas without brackets, or incorrect formats.

2. Final Answer:

   Function and call with square brackets for multiple outputs -> Option A

3. Quick Check:

   Multiple outputs = square brackets in header and call [OK]

Hint: Use square brackets for multiple outputs in both function and call [OK]

Common Mistakes:

• Using parentheses instead of square brackets
• Not capturing all outputs in call
• Incorrect function header syntax