?? Beware of Common Big O Notation Traps in Job Interviews! ????

You might have encountered some sneaky questions about?Big O Notation if you've been through technical interviews. Today, we’ll cover two classic examples that often trip up candidates.

Scenario 1: Independent Arrays

Let’s start with a question: If you have two arrays of different sizes, array_a, and array_b, and you iterate over them separately using two for loops, what’s the Big O Notation?

Take a moment to think about it before looking at the code below:

The Most Common Mistake: ??

Many candidates rush and assume the complexity is O(n), where n represents the array size. But here’s the catch: the arrays are independent and could be different sizes!

• The first loop iterates over the array_a, with a complexity of O(a).
• The second loop iterates over the array_b, with a complexity of O(b).

?? Don’t fall into the trap of assuming both arrays have the same size! Pay attention to that: The complexity is O(n) only if both arrays have the same size. If not, the correct answer is O(a + b)

Scenario 2: Nested Arrays

Now for a slightly trickier one: If you have two arrays and the second array is nested inside the loop of the first array, what’s the Big O Notation?

Here’s the code:

The Most Common Mistake: ??

In this scenario, many candidates jump to the conclusion that the complexity is O(n2). After all, there are two nested loops, right? But here’s the trap:

• The arrays are not guaranteed to be the same size. Instead of assuming a single variable n for both, you need to analyze them as a (the size of array a) and b (the size of array b).
• The outer loop runs O(a) times.
• For each element in a, the inner loop runs O(b) times.

?? The correct answer is O(a * b), not O(n2). This distinction is critical—when loops are nested, you multiply the complexities based on the size of each array, not square a single variable!

Why do interviewers use these examples?

These questions are designed to test whether you can recognize:

• Independent loops where you add the complexities (O(a + b)).
• Nested loops where you multiply the complexities (O(a * b)).

By rushing or assuming that both arrays are the same size, you might make the common mistake of giving an incorrect complexity like O(n2) or O(n). But now, you can confidently spot the traps and give the correct answers!

?? Interview Tip: Take your time to carefully analyze the structure of the loops and the relationship between inputs. Don’t fall into the habit of assuming that all arrays are of the same size. This attention to detail will set you apart in interviews! ??

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