How does Dynamic Programming differ from a greedy algorithm?
Greedy algorithms always find the globally optimal solution.
Greedy algorithms make locally optimal choices, while Dynamic Programming considers all subproblems.
Dynamic Programming always results in a faster solution than a greedy algorithm.
Dynamic Programming cannot be used to solve problems that can be solved with a greedy algorithm.
What is the core principle behind the bottom-up approach (tabulation) in dynamic programming?
Solving the problem in reverse order of subproblems.
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.
Which of the following terms is NOT directly related to dynamic programming?
Tabulation
Divide and conquer
Optimal substructure
Memoization
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?
Catalan numbers have a closed-form solution, making dynamic programming unnecessary.
Dynamic programming reduces the time complexity from exponential to linear.
Dynamic programming improves the space complexity but does not affect the time complexity.
Dynamic programming eliminates the need for recursion.
What is the role of a recurrence relation in dynamic programming?
It defines a non-recursive solution to the problem.
It calculates the time complexity of the dynamic programming algorithm.
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.
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 avoid redundant computations by storing and reusing previously calculated results.
To define the relationship between the problem and its subproblems.
What is the primary benefit of using memoization in dynamic programming?
Avoiding redundant computations by storing and reusing results
Sorting data more efficiently
Reducing the need for recursion
Eliminating the need for iteration
How does dynamic programming approach the problem of overlapping subproblems?
It solves each subproblem only once and stores its solution for later reuse
It avoids overlapping subproblems altogether by breaking down the problem differently
It uses heuristics to approximate the solutions to overlapping subproblems
It employs backtracking to explore all possible solutions to overlapping subproblems
Which characteristic of a problem suggests that dynamic programming might be a suitable approach?
The problem involves traversing a tree data structure
The problem exhibits optimal substructure, where the optimal solution can be constructed from optimal solutions to subproblems
The problem requires processing data in sorted order
The problem can be broken down into smaller, independent subproblems
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 dealing with unsorted data
When the problem requires finding the shortest path in a graph
When the problem can be solved with a single pass through the data