Dynamic Programming Interview Questions and Answers for internship

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100 Dynamic Programming Interview Questions and 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 relies on the principle of optimality, which states that an optimal solution can be constructed from optimal solutions to its subproblems.

  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. Solutions to subproblems are stored in a cache (e.g., a dictionary or array) to avoid recomputation. Bottom-up (tabulation) starts by solving the smallest subproblems and builds up to the solution of the main problem by iteratively using the solutions of smaller subproblems. It typically uses an array or matrix to store the solutions.

  3. What are the characteristics of a problem suitable for dynamic programming?

    • Answer: A problem is suitable for dynamic programming if it exhibits overlapping subproblems (the same subproblems are solved multiple times) and optimal substructure (an optimal solution can be constructed from optimal solutions to its subproblems).

  4. How does dynamic programming differ from recursion?

    • Answer: Recursion solves subproblems repeatedly, leading to inefficiency. Dynamic programming avoids this redundancy by storing and reusing the solutions to subproblems, either through memoization (top-down) or tabulation (bottom-up).

  5. Explain the concept of overlapping subproblems.

    • Answer: Overlapping subproblems occur when a recursive algorithm solves the same subproblem multiple times. Dynamic programming optimizes by solving each subproblem only once and storing its solution.

  6. Explain the concept of optimal substructure.

    • Answer: Optimal substructure means that an optimal solution to the problem contains optimal solutions to its subproblems. This allows us to build up the overall optimal solution from the optimal solutions of smaller parts.

  7. Describe how you would use dynamic programming to solve the Fibonacci sequence problem.

    • Answer: Both memoization and tabulation can be used. Memoization would recursively calculate Fibonacci numbers, storing results in a dictionary. Tabulation would iteratively build an array where each element represents the Fibonacci number at that index.

  8. Explain how dynamic programming can be used to solve the 0/1 knapsack problem.

    • Answer: A 2D array can be used to store the maximum value that can be achieved for a given weight capacity and a subset of items. The array is filled bottom-up, considering whether to include or exclude each item based on its weight and value.

  9. How would you use dynamic programming to solve the longest common subsequence (LCS) problem?

    • Answer: A 2D array is used to store the length of the LCS for prefixes of the two input sequences. The array is filled bottom-up, considering whether the last characters of the prefixes match. The actual LCS can then be reconstructed by backtracking through the array.

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