# 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.

## 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, whether needed or not.**Memoization:**Generally more space efficient as it only stores solutions to encountered subproblems.**Implementation Complexity:****Tabulation:**Often straightforward and iterative.**Memoization:**Can be more intuitive, especially for problems that have recursive nature, but might lead to stack overflow for deep recursions if not handled well.

## Conclusion:

Both tabulation and memoization serve as powerful techniques to optimize algorithms in Ruby. The choice between the two often depends on the specific problem and the programmer’s familiarity and comfort with each technique.

## Further Reading:

- [Dynamic Programming in Ruby](https://www.rubyguides.com/2018/02/ruby-dynamic-programming/)
- [Ruby Hash Documentation](https://ruby-doc.org/core-2.7.0/Hash.html)

(Note: This article provides an overview of tabulation and memoization, and the code snippets serve as basic implementations for demonstration. Readers are encouraged to dive deeper into both techniques for complex scenarios.)