How does dynamic programming approach the problem of overlapping subproblems?
It solves each subproblem only once and stores its solution for later reuse
It employs backtracking to explore all possible solutions to overlapping subproblems
It uses heuristics to approximate the solutions to overlapping subproblems
It avoids overlapping subproblems altogether by breaking down the problem differently
Who is credited as the pioneer of dynamic programming?
Edsger W. Dijkstra
Richard Bellman
Alan Turing
Donald Knuth
Which of these problems is well-suited for a top-down dynamic programming approach?
Finding the Fibonacci sequence.
Sorting an array of integers in ascending order.
Finding the shortest path in a directed acyclic graph.
Calculating the factorial of a number.
Which statement best describes the difference between top-down and bottom-up approaches in dynamic programming?
Top-down solves the main problem first, while bottom-up starts with subproblems
Top-down is more intuitive for understanding the problem, while bottom-up is better for optimization
Top-down uses recursion, while bottom-up uses iteration
Top-down is generally less efficient than bottom-up
Which of the following problems exhibits optimal substructure, making it suitable for a dynamic programming approach?
Finding the largest element in an unsorted array.
Checking if a given string is a palindrome.
Finding the shortest path between two nodes in a graph.
What is the difference between memoization and tabulation in dynamic programming?
Memoization is less efficient than tabulation in terms of space complexity.
Memoization solves the problem top-down, while tabulation solves it bottom-up.
Memoization uses iteration, while tabulation uses recursion.
Memoization stores results in a table, while tabulation uses a recursive stack.
Which of the following best describes the principle of Dynamic Programming?
Using probabilistic methods to approximate the solution to a problem.
Finding the locally optimal solution at each step to reach a globally optimal solution.
Dividing a problem into smaller subproblems and solving each subproblem independently.
Solving a problem by storing and reusing solutions to overlapping subproblems.
What is the primary benefit of using memoization in dynamic programming?
Sorting data more efficiently
Eliminating the need for iteration
Avoiding redundant computations by storing and reusing results
Reducing the need for recursion
What is the fundamental principle behind dynamic programming?
Using brute-force to explore all possible solutions
Breaking down problems into smaller, overlapping subproblems
Always choosing the locally optimal choice
Sorting data to find the optimal solution
What is the primary benefit of using a top-down dynamic programming approach (memoization) over a purely recursive approach?
It improves the asymptotic time complexity of all algorithms.
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.