What advantages does Dynamic Programming offer over brute-force algorithms?

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here are the Dynamic Programming multiple-choice questions (MCQs) along with their respective answers:

What is the primary objective of Dynamic Programming?
a) Maximizing computational complexity
b) Minimizing memory usage
c) Optimizing solutions by breaking down problems into smaller subproblems
d) Prioritizing sequential algorithms over recursive ones
Answer: c) Optimizing solutions by breaking down problems into smaller subproblems

Which term best describes the fundamental concept behind Dynamic Programming?
a) Divide and Conquer
b) Backtracking
c) Memoization
d) Greedy Algorithm
Answer: a) Divide and Conquer

In Dynamic Programming, what is memoization used for?
a) Storing precomputed results to avoid redundant calculations
b) Tracking recursion depth in algorithms
c) Optimizing loops in iterative algorithms
d) Eliminating the need for conditional statements
Answer: a) Storing precomputed results to avoid redundant calculations

Which type of problems are typically suitable for Dynamic Programming approaches?
a) Problems with no overlapping subproblems
b) Problems involving recursive algorithms only
c) Problems with optimal substructure and overlapping subproblems
d) Problems with purely sequential constraints
Answer: c) Problems with optimal substructure and overlapping subproblems

What is the time complexity of most Dynamic Programming algorithms?
a) O(1)
b) O(log n)
c) O(n)
d) O(n^2) or better
Answer: d) O(n^2) or better

Which step is essential in solving problems using the Dynamic Programming approach?
a) Precomputing results for all subproblems
b) Finding the largest subproblem to solve first
c) Solving problems recursively from smallest to largest
d) Solving problems iteratively from largest to smallest
Answer: a) Precomputing results for all subproblems

What is the purpose of the “bottom-up” approach in Dynamic Programming?
a) Starting computation from the smallest subproblems and working upwards
b) Starting computation from the largest subproblems and working downwards
c) Performing computations on non-overlapping subproblems
d) Utilizing a heuristic approach to problem-solving
Answer: a) Starting computation from the smallest subproblems and working upwards

Which type of Dynamic Programming approach utilizes an auxiliary table to store computed results?
a) Tabulation
b) Recursion
c) Optimization
d) Reduction
Answer: a) Tabulation

What does the term “optimal substructure” imply in the context of Dynamic Programming?
a) Each subproblem’s solution contributes to the global optimum
b) Finding the shortest path in a graph
c) Solving problems using a recursive approach
d) Subproblems do not overlap in their solutions
Answer: a) Each subproblem’s solution contributes to the global optimum

Which classic problem is commonly solved using Dynamic Programming techniques?
a) Tower of Hanoi
b) Quick Sort
c) Longest Common Subsequence
d) Breadth-First Search
Answer: c) Longest Common Subsequence