Top-Down Dynamic Programming in Ruby

The Power of Top-Down Dynamic Programming in Ruby

The view from the top.

Top-down dynamic programming, also known as memoization, is a technique used to solve problems by breaking them down into simpler subproblems, solving each subproblem just once, and storing their solutions in a memory structure (usually an array or a hash). When a subproblem needs to be solved again, instead of recomputing its solution, the algorithm will simply look up the solution in the memory. This technique is especially useful for solving optimization problems and can significantly reduce the time complexity of brute-force solutions.

In Ruby, implementing top-down dynamic programming typically involves the following steps:

1. Identify the base cases: These are the simplest instances of the problem that can be solved without further recursion.
2. Define the recursive relation: Determine how the solution to a problem can be expressed in terms of solutions to smaller subproblems.
3. Implement the recursive function: This function should check if the solution to the current problem is already stored in memory. If so, it returns the stored solution. If not, it computes the solution using the recursive relation, stores this solution in memory, and then returns it.