Dynamic Programming Quiz

What is dynamic programming?

• A method for solving complex problems by brute force, trying every possible solution until the correct one is found.

• A method for solving complex problems by using pre-defined formulas and equations.

• A method for solving complex problems by randomly guessing and checking different solutions until the correct one is found.

• A method for solving complex problems by breaking them down into simpler overlapping subproblems and solving each subproblem only once, storing the solution to each subproblem in a table to avoid redundant calculations.

What are the key characteristics of a problem that can be solved using dynamic programming?

• randomized algorithm and divide and conquer

• greedy algorithm and exhaustive search

• backtracking and branch and bound

• overlapping subproblems and optimal substructure

What is the difference between top-down and bottom-up approaches in dynamic programming?

• The top-down approach solves subproblems from the bottom to the top.

• The bottom-up approach solves subproblems from the top to the bottom.

• The top-down approach is more efficient than the bottom-up approach.

• The difference between top-down and bottom-up approaches in dynamic programming is the order in which the subproblems are solved.

What is memoization in dynamic programming?

• Memoization is a technique used in dynamic programming to optimize the execution time of a function by caching its results.

• Memoization is a technique used in dynamic programming to reduce the number of function calls.

• Memoization is a technique used in dynamic programming to randomize the execution time of a function.

• Memoization is a technique used in dynamic programming to increase the memory usage of a function.

What is the time complexity of a dynamic programming solution?

• O(log n)

• O(1)

• Varies

• O(n)

What is the principle of optimality in dynamic programming?

• The principle of optimality in dynamic programming states that an optimal solution to a problem can be achieved by solving the problem in a brute force manner.

• The principle of optimality in dynamic programming states that an optimal solution to a problem can be achieved by solving the problem iteratively.

• The principle of optimality in dynamic programming states that an optimal solution to a problem can be achieved by solving the problem randomly.

• The principle of optimality in dynamic programming states that an optimal solution to a problem can be achieved by breaking it down into smaller subproblems and solving each subproblem optimally.

What is the overlapping subproblem property in dynamic programming?

• The solution to a problem can be obtained by solving smaller overlapping subproblems.

• The overlapping subproblem property means that dynamic programming can only be used for problems with a linear time complexity.

• The overlapping subproblem property refers to the fact that dynamic programming can only be used for problems with a recursive structure.

• The overlapping subproblem property states that dynamic programming can only be applied to problems with a single subproblem.

What is the optimal substructure property in dynamic programming?

• The optimal substructure property is not applicable in dynamic programming.

• The optimal solution to a problem is always the same as the optimal solution to its subproblems.

• An optimal solution to a problem can be constructed from optimal solutions to its subproblems.

• An optimal solution to a problem cannot be constructed from optimal solutions to its subproblems.

What is the Fibonacci sequence and how can it be solved using dynamic programming?

• The Fibonacci sequence is a series of numbers in which each number is the sum of the three preceding ones. Dynamic programming can be used to solve the Fibonacci sequence by using a backtracking algorithm.

• The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. Dynamic programming can be used to solve the Fibonacci sequence by storing the previously calculated values in an array or table.

• The Fibonacci sequence is a series of numbers in which each number is the difference of the two preceding ones. Dynamic programming can be used to solve the Fibonacci sequence by using a greedy algorithm.

• The Fibonacci sequence is a series of numbers in which each number is the product of the two preceding ones. Dynamic programming can be used to solve the Fibonacci sequence by using a recursive algorithm.

What are some common applications of dynamic programming?

• Database management, network security, artificial intelligence

• Optimization problems, bioinformatics, computer graphics

• Machine learning, data analysis, web development

• Game development, natural language processing, robotics