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35 Dynamic Programming interview questions

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Basic Dynamic Programming Concepts

1.
What is Dynamic Programming and how does it differ from recursion?
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2.
Can you explain the concept of overlapping subproblems?
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3.
Define memoization and how it improves performance in Dynamic Programming.
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4.
What is the difference between top-down and bottom-up approaches in Dynamic Programming?
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5.
Explain the importance of state definition in Dynamic Programming solutions.
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Fundamental Dynamic Programming Problems

6.
Compute the Fibonacci sequence using Dynamic Programming.
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7.
Implement a solution to the Coin Change Problem using DP.
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8.
Use Dynamic Programming approach to solve the 0/1 Knapsack problem.
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9.
Implement an algorithm for computing the longest common subsequence of two sequences.
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10.
Solve matrix chain multiplication problem with Dynamic Programming.
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Optimizing Dynamic Programming Solutions

11.
What are the trade-offs between memoization and tabulation in Dynamic Programming?
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12.
How do you determine the time complexity of a Dynamic Programming algorithm?
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13.
Describe techniques to optimize space complexity in Dynamic Programming problems.
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14.
What is state transition, and how do you derive state transition relations?
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String-related Dynamic Programming Questions

15.
Find the longest palindromic substring in a given string.
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16.
Provide a Dynamic Programming solution for the edit distance problem.
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17.
Explain Dynamic Programming on strings with the example of word break problem.
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Sequence and Subsequence related Problems

18.
Solve the Longest Increasing Subsequence problem using Dynamic Programming.
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19.
Solve the Maximum Sum Increasing Subsequence problem with DP.
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20.
Implement an algorithm for finding the number of subsequences with a given sum in an array.
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Partitioning Problems

21.
Solve the partition problem using Dynamic Programming.
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22.
Provide a Dynamic Programming solution for the subset sum problem.
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23.
Solve the Balanced Partition problem dynamically.
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Path-finding Dynamic Programming Questions

24.
Solve the unique paths problem in a grid with obstacles using DP.
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25.
Use Dynamic Programming to solve the minimum cost path problem in a grid.
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26.
Find the longest path in a matrix with given constraints.
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Advanced Dynamic Programming Problems

27.
Solving the word wrap problem using DP.
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28.
Implement an algorithm for the maximal square problem in a 2D binary matrix.
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29.
Apply Dynamic Programming to solve the maximum profit in job scheduling.
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Dynamic Programming in Graphs

30.
How Dynamic Programming can be used for finding shortest paths in graphs (e.g., Floyd-Warshall algorithm)?
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31.
How to use Dynamic Programming to find the number of ways to reach a given vertex in a directed acyclic graph?
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Game Theory and Dynamic Programming

32.
Implement an algorithm to solve the Nim Game using Dynamic Programming.
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33.
Apply Dynamic Programming to solve the minimax problem in game theory.
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Stochastic Dynamic Programming Questions

34.
Can Dynamic Programming be used to solve problems with probabilistic states? Provide an example.
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35.
How does Stochastic Dynamic Programming differ from deterministic Dynamic Programming, and what are its applications?
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