Dynamic Programming: Master Optimization with Dynamic Programming Techniques

Question 1

Consider the Fibonacci sequence. Which dynamic programming strategy is most suitable for solving it recursively?

Accepted Answer

Top-down approach with memoization

Answer

Bottom-up approach with tabulation

Answer

Top-down approach without memoization

Answer

Bottom-up approach with memoization

Question 2

What is the time complexity of the bottom-up dynamic programming approach for finding the longest common subsequence in two strings of length m and n?

Accepted Answer

O(mn)

Answer

O(m+n)

Answer

O(m)

Answer

O(n)

Question 3

Consider the Fibonacci sequence. What is the optimal number of recursive calls required to compute the nth Fibonacci number using a naive recursive approach?

Accepted Answer

2^n

Answer

n

Answer

n^2

Answer

log n

Question 4

Consider the longest common subsequence (LCS) problem. What is the time complexity of computing the LCS using dynamic programming?

Accepted Answer

n^2

Answer

n

Answer

n log n

Answer

n^3

Question 5

In dynamic programming, what is the purpose of a base case?

Accepted Answer

To identify the smallest subproblems that can be solved directly

Answer

To store the results of subproblems that have already been solved

Answer

To compute the final solution of the problem

Answer

To check if the problem is solvable

Question 6

Which of the following is NOT a step in the dynamic programming approach?

Accepted Answer

Check if the problem is NP-complete

Answer

Define the subproblems

Answer

Recursively solve the subproblems

Answer

Store the results of the subproblems

Question 7

Memoization involves:

Accepted Answer

Storing results of subproblems for later use

Answer

Re-computing results of subproblems every time they are needed

Answer

Estimating the results of subproblems

Answer

Using a greedy algorithm to obtain an optimal solution

Question 8

Which is NOT an advantage of using dynamic programming?

Accepted Answer

Guaranteeing an optimal solution in all cases

Answer

Solving complex problems efficiently

Answer

Reducing memory usage

Answer

Simplifying the coding process

Question 9

Consider the Fibonacci sequence. Which of the following recurrence relations defines the nth Fibonacci number?

Accepted Answer

F(n) = F(n-1) + F(n-2)

Answer

F(n) = F(n-1) * F(n-2)

Answer

F(n) = F(n-1) - F(n-2)

Answer

F(n) = 2 * F(n-1)

Question 10

Which problem involves finding the longest sequence that is a subsequence of two given strings?

Accepted Answer

Longest Common Subsequence

Answer

Shortest Common Supersequence

Answer

Edit Distance

Answer

Knuth-Morris-Pratt Algorithm

Question 11

Tabulation can be optimized in terms of space by using:

Accepted Answer

A 1D array

Answer

A 2D table

Answer

A linked list

Answer

Recursion

Question 12

In dynamic programming, when is memoization more space-efficient than tabulation?

Accepted Answer

When the number of unique subproblems is small.

Answer

When the input size is small.

Answer

When the number of states is large.

Answer

Memoization is never more space-efficient than tabulation.

Question 13

In the context of dynamic programming, what does a subproblem represent?

Accepted Answer

A smaller, independent version of the original problem

Answer

The difference between two states of the problem

Answer

A specific solution to the entire problem

Answer

The complement of the original problem

Question 14

Which dynamic programming algorithm utilizes a bottom-up approach, iteratively building solutions from smaller subproblems?

Accepted Answer

Tabulation

Answer

Memoization

Answer

Greedy

Answer

Divide-and-conquer

Question 15

In dynamic programming, what is the primary purpose of a transition function?

Accepted Answer

To define the relationship between subproblems and their solutions

Answer

To store intermediate results

Answer

To determine the optimal solution

Answer

To generate new subproblems

Question 16

What is the time complexity of the dynamic programming algorithm for solving the Fibonacci sequence problem?

Accepted Answer

O(n)

Answer

O(2^n)

Answer

O(log n)

Answer

O(n^2)

Question 17

When applying dynamic programming, what is a crucial consideration for ensuring efficient implementation?

Accepted Answer

Identifying the optimal substructure and selecting an appropriate data structure

Answer

Using a top-down approach

Answer

Choosing the largest possible subproblems

Answer

Storing all possible subproblems and solutions

Question 18

Which of the following problems is well-suited for solving using dynamic programming?

Accepted Answer

Determining the longest common subsequence of two strings

Answer

Sorting a list of numbers using bubble sort

Answer

Finding the shortest path in a graph using Dijkstra's algorithm

Answer

Searching for an element in a binary tree using depth-first search

Question 19

In dynamic programming, what is the purpose of defining a base case?

Accepted Answer

To provide a stopping condition and initial values for the recursion

Answer

To store intermediate results

Answer

To calculate the optimal solution directly

Answer

To identify the subproblems

Question 20

In a dynamic programming problem with significant subproblem overlap and a large number of subproblems, which approach is likely to yield better performance?

Accepted Answer

Tabulation

Answer

Greedy algorithm

Answer

Recursion

Answer

Memoization

Question 21

Which of the following problems is well-suited for a dynamic programming solution?

Accepted Answer

Finding the longest common subsequence of two strings

Answer

Coloring a graph with the fewest colors

Answer

Solving the traveling salesman problem

Answer

Implementing Prim's algorithm for minimum spanning trees