Dynamic Programming Questions
The main difference between top-down and bottom-up approaches in Dynamic Programming lies in the order in which subproblems are solved.
In the top-down approach, also known as memoization, the problem is divided into smaller subproblems, and the solutions to these subproblems are stored in a memoization table. The algorithm starts by solving the original problem and recursively solves the subproblems by retrieving the solutions from the memoization table. This approach typically uses recursion and is more intuitive and easier to implement.
On the other hand, the bottom-up approach, also known as tabulation, starts by solving the smallest subproblems and iteratively builds up to the larger problem. It uses an iterative loop and a table to store the solutions to subproblems. This approach avoids recursion and solves all subproblems in a systematic manner, leading to a more efficient solution.
In summary, the top-down approach solves the problem by breaking it down into smaller subproblems and solving them recursively, while the bottom-up approach solves the subproblems iteratively and builds up to the original problem.