Variable arguments (varargin, varargout) in MATLAB - Time & Space Complexity

Time Complexity: Variable arguments (varargin, varargout)

O(n)

Understanding Time Complexity

When using variable input or output arguments in MATLAB functions, it is important to understand how the number of inputs or outputs affects the time the function takes to run.

We want to know how the function's running time changes as we pass more or fewer arguments.

Scenario Under Consideration

Analyze the time complexity of the following MATLAB function using varargin and varargout.

function varargout = exampleFunc(varargin)
    n = length(varargin);
    for k = 1:n
        varargout{k} = varargin{k} * 2;
    end
end

This function takes any number of inputs, doubles each one, and returns the results as outputs.

Identify Repeating Operations

Look for loops or repeated steps that depend on input size.

• Primary operation: The for-loop that doubles each input argument.
• How many times: The loop runs once for each input argument, so n times.

How Execution Grows With Input

As you add more input arguments, the function does more work by doubling each one.

Input Size (n)	Approx. Operations
10	10 doubling steps
100	100 doubling steps
1000	1000 doubling steps

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

Final Time Complexity

Time Complexity: O(n)

This means the time to run the function grows in a straight line with the number of input arguments.

Common Mistake

[X] Wrong: "Using varargin or varargout makes the function slower in a way that grows faster than the number of inputs."

[OK] Correct: The function only processes each input once, so the time grows linearly, not faster. The variable arguments themselves don't add hidden loops.

Interview Connect

Understanding how variable arguments affect time helps you write flexible functions without surprises about speed. This skill shows you can think about how code scales with input size.

Self-Check

"What if the function called another function inside the loop that itself loops over the input? How would the time complexity change?"

Practice

1. What does varargin do in a MATLAB function?

easy

A. Returns multiple output arguments as a cell array

B. Collects all input arguments into a cell array

C. Limits the number of input arguments to one

D. Specifies the data type of input arguments

Solution

1. Step 1: Understand the role of varargin

   varargin is used to collect any number of input arguments passed to a function into a single cell array.

2. Step 2: Differentiate from varargout

   varargout is used for output arguments, not input. So it does not collect inputs.

3. Final Answer:

   Collects all input arguments into a cell array -> Option B

4. Quick Check:

   varargin = input collector [OK]

Hint: Remember: 'varargin' collects inputs, 'varargout' returns outputs [OK]

Common Mistakes:

• Confusing varargin with varargout
• Thinking varargin limits inputs
• Assuming varargin specifies data types

2. Which of the following is the correct way to define a MATLAB function that accepts a fixed input followed by any number of additional inputs using varargin?

easy

A. function output = myFunc(input1, varargin)

B. function output = myFunc(varargout)

C. function output = myFunc(varargin)

D. function output = myFunc(varargin, input1)

Solution

1. Step 1: Check correct varargin placement

   varargin must be the last input argument to collect all remaining inputs.

2. Step 2: Evaluate options

   function output = myFunc(input1, varargin): function output = myFunc(input1, varargin) correctly places varargin after the fixed input input1. function output = myFunc(varargout) incorrectly uses varargout as an input. function output = myFunc(varargin) has no fixed input. function output = myFunc(varargin, input1) places varargin before a fixed input, which is invalid.

3. Final Answer:

   function output = myFunc(input1, varargin) -> Option A

4. Quick Check:

   varargin must be last input [OK]

Hint: Put varargin last in input list to accept extra arguments [OK]

Common Mistakes:

• Placing varargin before fixed inputs
• Using varargout as input
• Omitting parentheses in function definition

3. What will be the output of the following MATLAB code?

function varargout = exampleFunc(varargin)
  n = length(varargin);
  for k = 1:n
    varargout{k} = varargin{k} * 2;
  end
end

[a, b] = exampleFunc(3, 5); disp([a, b]);

medium

A. Error: varargout not assigned properly

B. [3 5]

C. [6 10]

D. [9 25]

Solution

1. Step 1: Understand varargin and varargout usage

   varargin collects inputs {3, 5}. The loop doubles each input and assigns to varargout.

2. Step 2: Calculate output values

   3 * 2 = 6, 5 * 2 = 10. So outputs are 6 and 10.

3. Final Answer:

   [6 10] -> Option C

4. Quick Check:

   Each input doubled = output [OK]

Hint: varargin inputs, varargout outputs; loop doubles inputs here [OK]

Common Mistakes:

• Confusing input and output values
• Forgetting to assign varargout elements
• Assuming varargout is a numeric array, not cell

4. Identify the error in this MATLAB function using varargin:

function result = sumAll(varargin)
  total = 0;
  for i = 1:varargin
    total = total + varargin{i};
  end
  result = total;
end

medium

A. Incorrect indexing of varargin with parentheses

B. Missing output argument varargout

C. No error, function works correctly

D. Using varargin as a number in the for loop

Solution

1. Step 1: Check for loop range

   The for loop uses 1:varargin, but varargin is a cell array, not a number.

2. Step 2: Correct way to get number of inputs

   Use length(varargin) or nargin to get number of inputs for the loop.

3. Final Answer:

   Using varargin as a number in the for loop -> Option D

4. Quick Check:

   Loop needs numeric length, not cell array [OK]

Hint: Use length(varargin) to loop over inputs, not varargin itself [OK]

Common Mistakes:

• Using varargin directly as a number
• Forgetting to use curly braces for cell access
• Assuming varargout is required for outputs

5. You want to write a MATLAB function that accepts any number of numeric inputs and returns their squares as multiple outputs. Which function definition and body correctly uses varargin and varargout to achieve this?

hard

A. function varargout = squareAll(varargin)
for k = 1:length(varargin)
varargout{k} = varargin{k}^2;
end
end

B. function varargout = squareAll(varargin)
for k = 1:nargin
varargout{k} = varargin(k)^2;
end
end

C. function varargout = squareAll(varargin)
for k = 1:length(varargin)
varargout(k) = varargin{k}^2;
end
end

D. function varargout = squareAll(varargin)
for k = 1:nargout
varargout{k} = varargin{k}^2;
end
end

Solution

1. Step 1: Check input count method

   Using length(varargin) correctly gets the number of inputs. nargin inside the function counts all inputs including fixed ones, but here only varargin inputs matter.

2. Step 2: Check cell indexing and assignment

   Accessing inputs with varargin{k} and assigning outputs with varargout{k} using curly braces is correct. Parentheses would cause errors.

3. Final Answer:

   function varargout = squareAll(varargin) for k = 1:length(varargin) varargout{k} = varargin{k}^2; end end -> Option A

4. Quick Check:

   Use length(varargin) and curly braces for cell access [OK]

Hint: Use length(varargin) and curly braces {} for cell arrays [OK]

Common Mistakes:

• Using parentheses instead of curly braces for cell access
• Using nargin instead of length(varargin)
• Assigning outputs with parentheses instead of curly braces