Tabulation vs. Memoization in Ruby: A Deep Dive

Tabulation and memoization are both optimization techniques employed, especially in the domain of algorithms and computation. However, they have different approaches and uses. Using Ruby, a language known for its expressiveness, we can demonstrate and differentiate the two.

Tabulation:

What is Tabulation?
Tabulation is a bottom-up dynamic programming technique where you solve all the subproblems first. You then use the solutions of these subproblems to build the solution to bigger problems.

Approach in Ruby:

Let’s consider the classic problem of computing the nth Fibonacci number.

def fibonacci(n)
 return n if n <= 1
 table = [0, 1]
 (2..n).each do |i|
   table[i] = table[i - 1] + table[i - 2]
 end
 table[n]
end

In the above example, we use an array table to store solutions to subproblems. We then combine these solutions to find the desired Fibonacci number.

Memoization:

What is Memoization?
Memoization is a top-down dynamic programming technique where you break down a problem into subproblems. It involves storing the result of expensive function calls and returning the cached result when the same inputs occur again.