Common Big O Misconceptions: What Your Interviewer Really Wants to Hear
During technical interviews, there are certain expectations from interviewers about time complexity and big O notation. In this blog post, we'll explore what interviewers are really expecting to hear through when running into common Big O notation misconceptions.
Misconception 1: "Constants Never Matter"
While it's true that we simplify Big O notations (e.g., O(2n) becomes O(n)), this doesn't mean constants are irrelevant in the real world. Make sure to mention it to your interviewer.
What your interviewer wants to hear: "The time complexity of this function is O(n), but it performs twice as many operations as a single loop. In practice, the constant factor can significantly impact performance. While we simplify to O(n) in Big O notation, it's important to consider the real-world implications."
Misconception 2: "All Nested Loops are O(n²)"
As we covered in our nested loops trap post, not all nested loops result in O(n²) complexity. Here's another example:
When interviewing, make sure to explain why this function is O(n) rather than O(n²).
What your interviewer wants to hear: "While this contains a nested loop, the inner loop only processes a maximum of 3 elements for each iteration of the outer loop. As a result, each element is processed a constant number of times, making this O(n) rather than O(n²)."
Misconception 3: "Average Case Doesn't Matter"
More often than not focusing on the worst-case complexity is the right thing to do. But there are times where average case complexity is as important. When discussing specific algorithms like sorting ones, mentioning both complexities and explaining why the average case is more representative of real-world performance is crucial.
What your interviewer wants to hear: "QuickSort has a worst-case complexity of O(n²), but its average case is O(n log n). In practice, it often performs better than algorithms with a consistent O(n log n) like MergeSort complexity due to better cache utilization and simpler operations."
Misconception 4: "The Stack Doesn't Count for Space Complexity"
Space complexity isn't just about data structures created. Recursive calls also consume space on the call stack which adds to the space complexity of an algorithm.
What your interviewer wants to hear: "The space complexity of the recursive approach is O(n) due to the recursive calls consuming space on the call stack. In contrast, the iterative approach has a space complexity of O(1) because it doesn't require additional as the input grows."
Misconception 5: "O(1) Means Fast"
Constant time complexity doesn't always mean fast execution. In practice, the constant factor can have a significant impact on performance. Make sure to discuss this with your interviewer.
What your interviewer wants to hear: "While this function is O(1) because it performs a fixed number of operations regardless of input size, it's not necessarily fast. Big O notation describes how the runtime scales with input size, not the absolute performance."
Takeaways
• Be precise in your complexity analysis, but also demonstrate practical understanding
• Explain theoretical complexity but always tie it back to real-world implications
• Consider and discuss multiple cases (best, average, worst) when appropriate
• Don't forget about space complexity, including recursion stack
Remember, interviewers are looking for nuanced understanding. Don't just state the Big O complexity - explain your reasoning and demonstrate awareness of real-world implications.
