String comparison in MATLAB - Time & Space Complexity

Time Complexity: String comparison

O(n)

Understanding Time Complexity

When we compare two strings in MATLAB, the time it takes depends on how long the strings are.

We want to know how the work grows as the strings get longer.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

str1 = 'hello world';
str2 = 'hello there';

isEqual = true;
for i = 1:length(str1)
    if str1(i) ~= str2(i)
        isEqual = false;
        break;
    end
end
    

This code compares two strings character by character until it finds a difference or reaches the end.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop comparing each character of the two strings.
• How many times: Up to the length of the shorter string (n times).

How Execution Grows With Input

As the strings get longer, the number of comparisons grows roughly the same as the string length.

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

Pattern observation: The work grows directly with the length of the strings.

Final Time Complexity

Time Complexity: O(n)

This means the time to compare grows in a straight line as the strings get longer.

Common Mistake

[X] Wrong: "Comparing two strings always takes the same time regardless of length."

[OK] Correct: Actually, the program checks each character until it finds a difference or finishes, so longer strings usually take more time.

Interview Connect

Understanding how string comparison time grows helps you explain efficiency clearly and shows you know how basic operations scale with input size.

Self-Check

"What if the strings are always very different at the first character? How would the time complexity change?"