In what scenarios is dynamic programming most effective compared to greedy algorithms?
When the locally optimal choice doesn't always lead to the global optimum
When the problem requires finding the shortest path in a graph
When the problem can be solved with a single pass through the data
When dealing with unsorted data
What is the primary purpose of memoization in dynamic programming?
To optimize space complexity by storing only the most recent subproblem results.
To reduce the need for recursion in the algorithm.
To define the relationship between the problem and its subproblems.
To avoid redundant computations by storing and reusing previously calculated results.
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.
Solving the problem in reverse order of subproblems.
Applying a greedy algorithm to find a locally optimal solution at each step.
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.
Which of these problems is well-suited for a top-down dynamic programming approach?
Sorting an array of integers in ascending order.
Calculating the factorial of a number.
Finding the Fibonacci sequence.
Finding the shortest path in a directed acyclic graph.
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 improves the asymptotic time complexity of all algorithms.
It eliminates the need for recursion entirely.
It reduces the need for complex data structures.
Dynamic programming is often used in optimizing which aspect of algorithms?
Space complexity
Time complexity
Code readability
Data structure usage
What is the fundamental principle behind dynamic programming?
Using brute-force to explore all possible solutions
Breaking down problems into smaller, overlapping subproblems
Sorting data to find the optimal solution
Always choosing the locally optimal choice
What is the primary benefit of using memoization in dynamic programming?
Reducing the need for recursion
Sorting data more efficiently
Avoiding redundant computations by storing and reusing results
Eliminating the need for iteration
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.
Finding the largest element in an unsorted array.