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 eliminates the need for recursion.
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 is often used in optimizing which aspect of algorithms?
Space complexity
Code readability
Data structure usage
Time complexity
What is the role of a recurrence relation in dynamic programming?
It expresses the solution to a problem in terms of solutions to its smaller subproblems.
It determines the order in which subproblems should be solved.
It defines a non-recursive solution to the problem.
It calculates the time complexity of the dynamic programming algorithm.
Which of the following problems exhibits optimal substructure, making it suitable for a dynamic programming approach?
Sorting an array of integers in ascending order.
Finding the shortest path between two nodes in a graph.
Checking if a given string is a palindrome.
Finding the largest element in an unsorted array.
What is the primary benefit of using a top-down dynamic programming approach (memoization) over a purely recursive approach?
It reduces the need for complex data structures.
It eliminates the need for recursion entirely.
It avoids redundant computations by storing and reusing previously calculated results.
It improves the asymptotic time complexity of all algorithms.
A problem can be solved using dynamic programming if it has:
Both overlapping subproblems and optimal substructure
Optimal substructure
Neither overlapping subproblems nor optimal substructure
Overlapping subproblems
What is the core principle behind the bottom-up approach (tabulation) in dynamic programming?
Building a table of solutions to subproblems, starting from the smallest subproblems and moving up.
Using recursion to break down the problem into smaller subproblems.
Applying a greedy algorithm to find a locally optimal solution at each step.
Solving the problem in reverse order of subproblems.
Which of the following best describes the principle of Dynamic Programming?
Finding the locally optimal solution at each step to reach a globally optimal solution.
Solving a problem by storing and reusing solutions to overlapping subproblems.
Using probabilistic methods to approximate the solution to a problem.
Dividing a problem into smaller subproblems and solving each subproblem independently.
Which data structure is commonly used to implement the tabulation table in a bottom-up dynamic programming solution?
An array or a matrix.
A binary tree.
A linked list.
A stack.
How does Dynamic Programming differ from a greedy algorithm?
Dynamic Programming cannot be used to solve problems that can be solved with a greedy algorithm.
Greedy algorithms always find the globally optimal solution.
Dynamic Programming always results in a faster solution than a greedy algorithm.
Greedy algorithms make locally optimal choices, while Dynamic Programming considers all subproblems.