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.

## Approach in Ruby:

For the same Fibonacci problem:

`def fibonacci(n, memo = {})`

return n if n <= 1

return memo[n] if memo.has_key?(n)

memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo)

end

Here, we use a **memo** hash to store results of subproblems. When a result is not in the **memo**, we compute it and save it to **memo** for future reference.

## Differences:

**Approach:****Tabulation:**Bottom-up approach. Solve smaller subproblems first.**Memoization:**Top-down approach. Solve bigger problems first by breaking them down.**Data Structure:****Tabulation:**Usually employs arrays (but not limited to them).**Memoization:**Commonly uses hashes (dictionaries).**Space Efficiency:****Tabulation:**Might sometimes use more space as it solves and stores solutions for all subproblems…