Which of the following problems exhibits optimal substructure, making it suitable for a dynamic programming approach?
Checking if a given string is a palindrome.
Finding the shortest path between two nodes in a graph.
Sorting an array of integers in ascending order.
Finding the largest element in an unsorted array.
Which of the following is a common technique for implementing memoization in a top-down dynamic programming solution?
Employing a recursive function with a cache (like a dictionary or array) to store results.
Sorting the input data before processing.
Using a stack data structure.
Converting the problem into an iterative approach.
Which data structure is commonly used to implement the tabulation table in a bottom-up dynamic programming solution?
An array or a matrix.
A linked list.
A stack.
A binary tree.
Which statement best describes the difference between top-down and bottom-up approaches in dynamic programming?
Top-down uses recursion, while bottom-up uses iteration
Top-down is more intuitive for understanding the problem, while bottom-up is better for optimization
Top-down solves the main problem first, while bottom-up starts with subproblems
Top-down is generally less efficient than bottom-up
Who is credited as the pioneer of dynamic programming?
Richard Bellman
Edsger W. Dijkstra
Donald Knuth
Alan Turing
What does a recurrence relation in dynamic programming represent?
A formula for breaking down the problem into smaller, self-similar subproblems.
A technique for storing and retrieving previously computed results.
The base case of the recursive algorithm.
The final solution to the overall problem.
Why is dynamic programming often preferred over a purely recursive approach for problems with overlapping subproblems?
Dynamic programming avoids the function call overhead associated with recursion, leading to better time complexity.
Dynamic programming always uses less memory than recursion.
Dynamic programming is easier to implement and understand than recursion.
Recursion cannot solve problems with overlapping subproblems.
What is the primary benefit of using a top-down dynamic programming approach (memoization) over a purely recursive approach?
It avoids redundant computations by storing and reusing previously calculated results.
It reduces the need for complex data structures.
It eliminates the need for recursion entirely.
It improves the asymptotic time complexity of all algorithms.
The computation of the nth Catalan number can be efficiently performed using dynamic programming. What is the primary advantage of employing dynamic programming in this scenario?
Dynamic programming improves the space complexity but does not affect the time complexity.
Catalan numbers have a closed-form solution, making dynamic programming unnecessary.
Dynamic programming reduces the time complexity from exponential to linear.
Dynamic programming eliminates the need for recursion.
Which of the following best describes the principle of overlapping subproblems in dynamic programming?
Breaking down a problem into smaller, independent subproblems.
Storing and reusing the results of already solved subproblems.
Solving the same subproblems multiple times, leading to redundant computations.
Finding the optimal solution without considering all possible solutions.