Dynamic Programming

Answer: A technique for designing efficient algorithms by breaking down a problem into smaller subproblems

Explanation: Dynamic programming is a technique used in computer science to solve complex problems by breaking them down into smaller, more manageable subproblems. It involves storing solutions to subproblems in memory and reusing them to solve larger problems. This technique can greatly improve the performance of algorithms by reducing redundant computations.

Answer: Divide and conquer

Explanation: Divide and conquer is a different algorithmic technique that involves breaking a problem into smaller subproblems, solving each subproblem independently, and combining the results. Dynamic programming, on the other hand, involves solving subproblems in a way that allows solutions to be reused to solve larger problems.

Answer: Computing the nth Fibonacci number

Explanation: The Fibonacci sequence is a classic example of a problem that can be solved using dynamic programming. The nth Fibonacci number is defined as the sum of the two preceding numbers in the sequence, and computing it involves solving many overlapping subproblems.

Answer: The process of storing solutions to subproblems in memory

Explanation: Memoization is a technique used in dynamic programming to speed up the process of solving complex problems by storing solutions to subproblems in memory. This allows the program to avoid redundant computations and greatly improve performance.

Answer: O(n)

Explanation: The dynamic programming algorithm for computing the nth Fibonacci number has a time complexity of O(n) because it involves solving a linear number of subproblems.

Answer: Computing the nth Fibonacci number

Explanation: The bottom-up approach in dynamic programming involves solving smaller subproblems first and storing their solutions in memory, then using those solutions to solve larger problems. This approach is well-suited to problems like computing the nth Fibonacci number, where the solutions to smaller subproblems can be used to efficiently compute the solution to the overall problem.

Answer: A method of solving problems by starting with the overall problem and recursively breaking it down into smaller subproblems

Explanation: The top-down approach in dynamic programming involves starting with the overall problem and recursively breaking it down into smaller subproblems. This approach can be implemented using recursion, and it typically involves storing the solutions to subproblems in memory to avoid redundant computations.

Answer: Computing the edit distance between two strings

Explanation: Memoization is a technique used in dynamic programming to speed up the process of solving complex problems by storing solutions to subproblems in memory. Problems like computing the edit distance between two strings can benefit from memoization because they involve solving many overlapping subproblems.

Answer: O(n)

Explanation: The dynamic programming algorithm for computing the nth Fibonacci number using memoization has a space complexity of O(n) because it involves storing the solutions to n subproblems in memory.

Answer: Dynamic programming involves breaking a problem down into smaller subproblems and reusing solutions to those subproblems, while brute force involves exhaustively searching through all possible solutions.

Explanation: The main difference between dynamic programming and brute force is that dynamic programming involves breaking a problem down into smaller subproblems and reusing solutions to those subproblems, while brute force involves exhaustively searching through all possible solutions. This makes dynamic programming much more efficient than brute force for many types of problems.