Mastering Dynamic Programming: Interview-Level Quiz Quiz

1. Q1. Memoization vs. Tabulation

   What is the primary difference between memoization and tabulation techniques in dynamic programming?

   1. Memoization is bottom-up, while tabulation is top-down.
   2. Memoization stores results of subproblems, while tabulation builds a table iteratively.
   3. Tabulation uses recursion, while memoization uses iteration.
   4. There is no difference; they are interchangeable.

2. Q2. Fibonacci Sequence - DP

   Which of the following is the time complexity of a dynamic programming solution for calculating the nth Fibonacci number?

   1. O(2^n)
   2. O(n log n)
   3. O(n)
   4. O(log n)

3. Q3. 0/1 Knapsack - State Definition

   In the 0/1 Knapsack problem, what does the state dp[i][w] typically represent?

   1. The maximum value obtainable with items up to index i and a maximum weight of w.
   2. The minimum weight required to obtain a value of w with items up to index i.
   3. The total weight of items up to index i, given a capacity of w.
   4. The number of items selected up to index i, with a weight limit of w.

4. Q4. Longest Common Subsequence - Recurrence

   What is the correct recurrence relation for the Longest Common Subsequence (LCS) problem, where s1 and s2 are the strings, and i and j are their respective indices?

   1. dp[i][j] = max(dp[i-1][j], dp[i][j-1]) + (s1[i] == s2[j])
   2. dp[i][j] = dp[i-1][j-1] + (s1[i] == s2[j] ? 1 : 0)
   3. dp[i][j] = max(dp[i-1][j], dp[i][j-1], dp[i-1][j-1] + (s1[i] == s2[j] ? 1 : 0))
   4. dp[i][j] = min(dp[i-1][j], dp[i][j-1])

5. Q5. Coin Change - Optimization

   Which optimization technique can be used in the Coin Change problem to reduce space complexity from O(amount * number of coins) to O(amount)?

   1. Using a 2D array instead of a 1D array.
   2. Reusing the same array in each iteration, overwriting previous results.
   3. Sorting the coins.
   4. Using memoization instead of tabulation.

6. Q6. Bottom-Up vs. Top-Down

   In what scenario is a bottom-up dynamic programming approach generally preferred over a top-down approach?

   1. When the solution requires calculating only a small subset of possible states.
   2. When the problem has overlapping subproblems that are never revisited.
   3. When there is a clear topological order for solving the subproblems.
   4. When the recursion depth becomes a limiting factor.

7. Q7. Space Complexity Optimization

   Which type of dynamic programming problems are most suitable for space complexity optimization by reducing the dimensionality of the DP table?

   1. Problems with complex dependencies between states.
   2. Problems where the current state only depends on the immediately previous row or column.
   3. Problems involving strings with large alphabets.
   4. Problems requiring high precision floating-point arithmetic.

8. Q8. Real-World DP Scenario

   In which real-world application is dynamic programming frequently used for optimal decision-making?

   1. Database management systems.
   2. Compiler optimization.
   3. Network routing algorithms.
   4. All of the above.

9. Q9. Edit Distance - Understanding

   What does the Edit Distance problem aim to find?

   1. The longest common subsequence between two strings.
   2. The shortest path between two nodes in a graph.
   3. The minimum number of operations required to transform one string into another.
   4. The maximum number of matching characters between two strings.

10. Q10. DP State Variables

    What determines the number of state variables needed to define a dynamic programming solution?

    1. The number of input elements.
    2. The number of possible function calls.
    3. The number of dimensions of the DP table.
    4. The minimum number of parameters required to uniquely identify each subproblem.

11. Q11. Minimum Cost Path - Application

    Dynamic programming is commonly used to solve the Minimum Cost Path problem in a grid. What does this path typically represent?

    1. The path with the fewest number of cells.
    2. The path with the largest sum of values in the cells.
    3. The path with the smallest sum of values in the cells.
    4. The path that avoids all obstacles.

12. Q12. Partition Problem

    What is the core objective of the Partition Problem solvable with dynamic programming?

    1. To find the largest subset of a set.
    2. To divide a set into two subsets such that the difference of subset sums is minimized.
    3. To sort the elements of a set in ascending order.
    4. To find the median element of a set.

13. Q13. Optimal Binary Search Tree

    What problem does Dynamic programming offer a solution for in case of Optimal Binary Search Tree?

    1. Optimizing the height of the BST
    2. Minimizing the average search cost in a BST
    3. Maximizing the number of nodes in a BST
    4. Balancing the BST structure

14. Q14. Matrix Chain Multiplication

    Which problem does dynamic programming optimize when addressing Matrix Chain Multiplication?

    1. The order of matrix storage in memory.
    2. The number of matrices to be multiplied.
    3. The order in which matrices are multiplied to minimize the total number of scalar multiplications.
    4. The size of the resulting matrix.

15. Q15. Cutting a Rod

    What is the goal when using dynamic programming to solve the 'Cutting a Rod' problem?

    1. To find the shortest way to cut the rod.
    2. To determine the maximum number of cuts possible.
    3. To find the optimal way to cut a rod into smaller pieces to maximize the total value.
    4. To minimize the amount of material wasted during cutting.