Comparison operators in MATLAB - Time & Space Complexity

Time Complexity: Comparison operators

O(n)

Understanding Time Complexity

We want to understand how long it takes to compare values in MATLAB as the input size grows.

How does the time needed change when we compare many elements?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

arr = randi(100, 1, n);
count = 0;
for i = 1:n
    if arr(i) > 50
        count = count + 1;
    end
end

This code counts how many numbers in the array are greater than 50.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Comparing each element to 50 using the > operator inside a loop.
• How many times: Exactly once for each element in the array, so n times.

How Execution Grows With Input

As the array gets bigger, the number of comparisons grows directly with the size.

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

Pattern observation: Doubling the input doubles the number of comparisons.

Final Time Complexity

Time Complexity: O(n)

This means the time to finish grows in a straight line with the number of elements.

Common Mistake

[X] Wrong: "Comparison operators take constant time no matter how many elements we have."

[OK] Correct: While one comparison is quick, doing many comparisons one after another adds up, so total time grows with the number of elements.

Interview Connect

Understanding how simple comparisons add up helps you explain how your code handles bigger data smoothly and efficiently.

Self-Check

"What if we compared pairs of elements inside two nested loops? How would the time complexity change?"

Practice

1. What does the MATLAB expression 5 > 3 return?

easy

A. 0 (false)

B. 1 (true)

C. Error

D. 5

Solution

1. Step 1: Understand the comparison operator

   The operator > checks if the left value is greater than the right value.

2. Step 2: Compare the values 5 and 3

   Since 5 is greater than 3, the expression returns true, which is represented as 1 in MATLAB.

3. Final Answer:

   1 (true) -> Option B

4. Quick Check:

   5 > 3 = 1 [OK]

Hint: Greater than means left number bigger than right [OK]

Common Mistakes:

• Confusing true (1) with false (0)
• Thinking it returns the bigger number
• Using wrong operator like < instead of >

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

easy

A. a = 10

B. a === 10

C. a != 10

D. a == 10

Solution

1. Step 1: Identify the equality operator in MATLAB

   MATLAB uses double equal signs == to test equality, not a single equal sign.

2. Step 2: Check each option

   a = 10 assigns 10 to a, not compare. a == 10 correctly compares a to 10. a === 10 uses triple equals which is invalid in MATLAB. a != 10 uses not equal operator incorrectly.

3. Final Answer:

   a == 10 -> Option D

4. Quick Check:

   Equality test uses == [OK]

Hint: Use double equals (==) to compare, single equals (=) assigns [OK]

Common Mistakes:

• Using single = instead of ==
• Using === which is not MATLAB syntax
• Confusing != with ~= for not equal

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

a = [1 3 5]; b = [2 3 4]; result = a <= b;

medium

A. [1 1 0]

B. [1 0 0]

C. [0 1 1]

D. [0 0 1]

Solution

1. Step 1: Understand element-wise comparison

   The operator <= compares each element of a with the corresponding element of b.

2. Step 2: Compare each pair

   1 <= 2 is true (1), 3 <= 3 is true (1), 5 <= 4 is false (0).

3. Final Answer:

   [1 1 0] -> Option A

4. Quick Check:

   Element-wise <= comparison = [1 1 0] [OK]

Hint: Compare arrays element-wise for <= operator [OK]

Common Mistakes:

• Thinking it returns a single value
• Mixing up < and <= operators
• Forgetting element-wise comparison

4. Identify the error in this MATLAB code snippet:

if a = 5
    disp('Equal');
end

medium

A. Missing semicolon after assignment

B. disp function is incorrect

C. Using = instead of == in if condition

D. if statement needs parentheses

Solution

1. Step 1: Check the if condition syntax

   In MATLAB, the if condition requires a logical expression, not an assignment.

2. Step 2: Identify the operator mistake

   The code uses = which assigns 5 to a, instead of == which compares a to 5.

3. Final Answer:

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

4. Quick Check:

   Comparison uses ==, not = in conditions [OK]

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

Common Mistakes:

• Using = instead of ==
• Adding unnecessary parentheses
• Misusing disp function

5. Given two arrays A = [4 7 2 9] and B = [5 7 3 8], write a MATLAB expression using comparison operators to create a logical array that is true where elements of A are greater than or equal to B and false otherwise. What is the resulting array?

hard

A. [0 1 0 1]

B. [1 1 1 1]

C. [0 0 0 0]

D. [1 0 1 0]

Solution

1. Step 1: Use element-wise comparison operator

   Use the operator >= to compare each element of A with B element-wise.

2. Step 2: Compare each element pair

   4 >= 5 is false (0), 7 >= 7 is true (1), 2 >= 3 is false (0), 9 >= 8 is true (1).

3. Final Answer:

   [0 1 0 1] -> Option A

4. Quick Check:

   A >= B = [0 1 0 1] [OK]

Hint: Use >= for element-wise greater or equal comparison [OK]

Common Mistakes:

• Using > instead of >=
• Confusing logical array with numeric values
• Mixing element-wise with matrix operations