Relational expressions in MATLAB - Time & Space Complexity

Time Complexity: Relational expressions

O(n)

Understanding Time Complexity

Relational expressions compare values and return true or false. We want to see how the time to evaluate these expressions changes as input size grows.

How does the number of comparisons grow when we check many values?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

A = rand(1, n);  % Create an array of n random numbers
count = 0;
for i = 1:n
    if A(i) > 0.5
        count = count + 1;
    end
end

This code counts how many numbers in the array are greater than 0.5 using a relational expression inside a loop.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The relational check A(i) > 0.5 inside the loop.
• How many times: This check runs once for each element, so n times.

How Execution Grows With Input

Each new element adds one more comparison. So if you double the input size, you double the work.

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

Pattern observation: The number of operations grows directly with the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to finish grows in a straight line as the input gets bigger.

Common Mistake

[X] Wrong: "Relational expressions inside loops run in constant time no matter the input size."

[OK] Correct: Each relational check happens once per element, so more elements mean more checks and more time.

Interview Connect

Understanding how simple comparisons add up helps you explain how your code scales. This skill shows you can think about efficiency clearly.

Self-Check

"What if we replaced the loop with a vectorized relational expression? How would the time complexity change?"

Practice

1. Which of the following relational operators in MATLAB checks if two values are NOT equal?

easy

A. ==

B. <=

C. >=

D. ~=

Solution

1. Step 1: Understand the meaning of relational operators

   The operator == checks equality, ~= checks inequality, and >=, <= check greater or equal and less or equal respectively.

2. Step 2: Identify the operator for NOT equal

   The operator ~= means NOT equal in MATLAB.

3. Final Answer:

   ~= -> Option D

4. Quick Check:

   NOT equal operator = ~= [OK]

Hint: Remember: ~= means NOT equal in MATLAB [OK]

Common Mistakes:

• Confusing == with ~=
• Using = instead of ==
• Mixing up >= and >

2. Which of the following is the correct syntax to check if variable a is greater than or equal to 10 in MATLAB?

easy

A. a >== 10

B. a >= 10

C. a =< 10

D. a => 10

Solution

1. Step 1: Recall MATLAB relational operator syntax

   MATLAB uses >= to mean greater than or equal to.

2. Step 2: Check each option for correct syntax

   a >= 10 uses >= correctly. Options A, B, and C use invalid or reversed operators.

3. Final Answer:

   a >= 10 -> Option B

4. Quick Check:

   Greater or equal operator = >= [OK]

Hint: Use >= for greater or equal, not => or =< [OK]

Common Mistakes:

• Writing => instead of >=
• Writing =< instead of <=
• Adding extra = signs

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

a = 5; b = 7;
result = (a < b) & (b <= 7);
disp(result);

medium

A. 1

B. 0

C. Error

D. [1 0]

Solution

1. Step 1: Evaluate each relational expression

   a < b is 5 < 7 which is true (1). b <= 7 is 7 <= 7 which is true (1).

2. Step 2: Apply logical AND operator &

   Both expressions are true, so (1 & 1) equals 1 (true).

3. Final Answer:

   1 -> Option A

4. Quick Check:

   True & True = 1 [OK]

Hint: True & True gives 1, false & anything gives 0 [OK]

Common Mistakes:

• Confusing & with &&
• Expecting output as logical word instead of 1
• Misreading <= operator

4. Identify the error in this MATLAB code snippet:

x = 10;
if x = 10
    disp('Equal to 10');
end

medium

A. Using = instead of == in if condition

B. Missing semicolon after disp statement

C. Incorrect use of end keyword

D. Variable x is not initialized

Solution

1. Step 1: Check the if condition syntax

   In MATLAB, = is assignment, == is comparison. Using = in if causes error.

2. Step 2: Confirm other parts are correct

   Semicolon after disp is optional, end is correctly used, x is initialized.

3. Final Answer:

   Using = instead of == in if condition -> Option A

4. Quick Check:

   Comparison needs ==, not = [OK]

Hint: Use == for comparison inside if, not = [OK]

Common Mistakes:

• Using = instead of ==
• Thinking semicolon is mandatory after disp
• Misplacing end keyword

5. Given a vector v = [3, 6, 9, 12], which MATLAB expression returns a logical array indicating elements greater than 5 and less than or equal to 10?

hard

A. v > (5 & v) <= 10

B. v > 5 && v <= 10

C. (v > 5) & (v <= 10)

D. (v > 5) | (v <= 10)

Solution

1. Step 1: Understand vector relational operations

   Relational operators applied to vectors return logical arrays element-wise.

2. Step 2: Combine conditions correctly with parentheses and &

   Use parentheses around each condition: (v > 5) & (v <= 10) to get elements satisfying both.

3. Step 3: Check other options for syntax errors

   v > 5 && v <= 10 uses short-circuit &&, invalid for vectors. v > (5 & v) <= 10 is invalid syntax. (v > 5) | (v <= 10) uses OR instead of AND.

4. Final Answer:

   (v > 5) & (v <= 10) -> Option C

5. Quick Check:

   Use parentheses with & for combined conditions [OK]

Hint: Always use parentheses around each relational condition [OK]

Common Mistakes:

• Using && instead of & for array operations
• Using | instead of & for AND
• Writing invalid combined expressions