10 Expert Top DSA Interview Questions with Answers: Part-4

Welcome to the final chapter of our series! In Parts 1-3, we covered the “what” and the “how.” Now, we dive into the “how fast” and “how smart.” Understanding Big-O and advanced DP problems like LCS is essential for senior-level Top DSA Interview Questions with Answers.

41. What is Longest Common Subsequence (LCS)?

The LCS problem is a classic example of Dynamic Programming found in Top DSA Interview Questions with Answers. It asks for the longest sequence that appears in the same relative order in two strings, but not necessarily in contiguous blocks.

• Real-world use: Used by the diff command in Git/Linux and in bioinformatics for DNA sequencing.
• Complexity: Typically solved using DP in O(n times m) time.

42. What is Longest Increasing Subsequence (LIS)?

LIS is another favorite among Top DSA Interview Questions with Answers. It finds the length of the longest subsequence in an array such that all elements are sorted in increasing order.

• Standard DP: O(n^2)
• Optimized: Using Binary Search (Patience Sorting), you can achieve O(n log n). This optimization is a favorite “follow-up” question for interviewers.

43. What is a Palindrome Substring problem?

This involves finding the longest palindromic part of a string.

1. Expand Around Center: O(n^2) — Check each character as a potential center.
2. Dynamic Programming: O(n^2) — Use a 2D boolean table.
3. Manacher’s Algorithm: O(n) — An advanced algorithm used specifically to solve this in linear time.

44. Difference between Greedy and Dynamic Programming?

Both are used for optimization, and distinguishing them is key when answering Top DSA Interview Questions with Answers.

• Greedy: Makes the “best” choice at the current moment without looking back. It is fast but doesn’t always find the global optimum (e.g., Fractional Knapsack).
• DP: Considers all possible subproblems and stores their results. It guarantees the most optimal solution (e.g., 0/1 Knapsack).

45. What is Big-O Notation?

Big-O is the language of Top DSA Interview Questions with Answers. It describes the limiting behavior of a function when the argument tends towards a particular value or infinity. In DSA, it describes the worst-case scenario.

• Common Orders: O(1) < O(log n) < O(n) < O(n log n) < O(n^2) < O(2^n).

46. Time vs. Space Complexity?

• Time Complexity: How the runtime of an algorithm increases as the input size $n$ grows.
• Space Complexity: The extra memory (excluding input) the algorithm needs to run.
• The Trade-off: Often, we can use more memory (Space) to make an algorithm faster (Time), such as in Memoization.

47. How to find time complexity of recursive functions?

We use Recurrence Relations. For many Top DSA Interview Questions with Answers, the Master Theorem can be used:

• Binary Search: T(n) = T(n/2) + O(1) rightarrow O(log n)
• Merge Sort: T(n) = 2T(n/2) + O(n) rightarrow O(n log n)

48. What are Amortized Time Complexities?

Amortized complexity is the average time taken per operation over a long sequence of operations.

• Example: In a Dynamic Array (ArrayList in Java), most insertions are O(1). However, when the array is full, it must resize (O(n)). Because resizes happen rarely, the amortized cost remains O(1).

49. What is Tail Recursion?

A recursive function is “tail-recursive” if the recursive call is the very last thing the function does.

• Benefit: Modern compilers can optimize tail recursion by reusing the current stack frame, effectively turning the recursion into a loop and preventing StackOverflowError.

50. How to solve coding questions in interviews?

Mastering Top DSA Interview Questions with Answers is only half the battle. Your process matters:

1. Clarify: Don’t start coding immediately. Ask about constraints (e.g., “Is the array sorted?”).
2. Brute Force: Explain the simple solution first to show you understand the logic.
3. Optimize: Identify bottlenecks (look for O(n^2) loops) and apply the techniques from Parts 1-3.
4. Dry Run: Trace your code with a small example before telling the interviewer you are finished.