Dynamic Programming Interview Questions and Answers for 2 years experience

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100 Dynamic Programming Interview Questions & Answers

  1. What is dynamic programming?

    • Answer: Dynamic programming is an algorithmic technique for solving optimization problems by breaking them down into smaller, overlapping subproblems, solving each subproblem only once, and storing their solutions to avoid redundant computations. It's typically used when a problem exhibits optimal substructure (optimal solution can be constructed from optimal solutions of its subproblems) and overlapping subproblems (same subproblems are solved multiple times).

  2. Explain the two main approaches in dynamic programming: top-down (memoization) and bottom-up (tabulation).

    • Answer: Top-down (memoization) starts with the main problem and recursively breaks it down into subproblems. It stores the results of each subproblem in a cache (usually a dictionary or array) to avoid recalculating them. Bottom-up (tabulation) starts with the smallest subproblems and iteratively builds up solutions to larger subproblems, storing the results in a table. Bottom-up generally has better space complexity than top-down due to avoiding recursive calls.

  3. What is the time and space complexity of dynamic programming?

    • Answer: The time and space complexity vary greatly depending on the specific problem. However, dynamic programming often reduces the time complexity from exponential (in brute-force approaches) to polynomial. Space complexity depends on the size of the table or cache used to store solutions, which is often related to the input size.

  4. How do you identify if a problem can be solved using dynamic programming?

    • Answer: A problem is a good candidate for dynamic programming if it exhibits optimal substructure and overlapping subproblems. Optimal substructure means the optimal solution to the problem can be constructed from optimal solutions to its subproblems. Overlapping subproblems mean the same subproblems are encountered multiple times during the solution process.

  5. Explain the concept of optimal substructure.

    • Answer: Optimal substructure means that an optimal solution to a problem contains within it optimal solutions to its subproblems. If you can find the optimal solutions to the smaller parts and combine them to get the global optimum, the problem likely has optimal substructure.

  6. Explain the concept of overlapping subproblems.

    • Answer: Overlapping subproblems means that the same subproblems are solved repeatedly in the recursive solution to the problem. Dynamic programming aims to solve each subproblem only once and store the results for later use, avoiding redundant computations.

  7. Solve the Fibonacci sequence using dynamic programming (both top-down and bottom-up).

    • Answer: [Provide code examples for both top-down and bottom-up Fibonacci implementations in a language like Python or Java. Explain the code's logic and time/space complexity.]

  8. Explain how to solve the 0/1 knapsack problem using dynamic programming.

    • Answer: [Provide a detailed explanation with code example of the 0/1 knapsack problem solution using dynamic programming. Explain the concept of the DP table and how it's filled.]

  9. Explain how to solve the longest common subsequence (LCS) problem using dynamic programming.

    • Answer: [Provide a detailed explanation with code example of the LCS problem solution using dynamic programming. Explain the DP table and how it's used to find the length and the actual subsequence.]

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