## Introduction

This is the first post that I am writing in a while, and it's mostly because I wanted to start working through all the problems on Project Euler. I wanted to do this for a few reasons. First, they are hard problems, so they are good way to practice. Second, they let me keep my math skills sharp. Third, They ley me practice my ruby.

This first problem is fun, but we don't get a chance to look at clever mathematical approaches. But we do get to see some of the methods that we have in ruby.

## Problem Statement

The Following Problem was taken from Project Euler:

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

This is a great problem because it takes a classic problem (FizzBuzz) and adds an extra layer too it. More importantly, it has a single integer result as opposed to an array of integers and strings.

## Breaking it down.

This problem is basically saying that we need to do a few things. First, we need to find all the numbers from 1-999 that are multiples of 3 or 5. Then, we need to sum all those numbers together. This is a pretty straightforward problem. Let's see what we can do.

## Attempt One: Iterative Approach

I remember the first time I was asked to look at FizzBuzz, and the sort of approach that I would take when I first started coding. It would have looked something like this.

```
n = 1
sum = 0
while n < 1000
if n % 3 == 0 || n % 5 == 0
sum += n
end
n += 1
end
return sum
```

This is a pretty short method, but it certainly has room to improves. When we run this code, we get the following result: `233168`

. Spoilers, this is the correct answer. But we can get it in a much more ruby way.

## Attempt Two: Declarative Approach

So the iterative method gets us the correct answer, but can we get there with less code? Yes. If take a more declarative approach and take advantage of ruby's array methods, we can write the following method.

```
[*1...1000].select! { |n| (n % 3).zero? || (n % 5).zero? }.sum
```

So this is doing a lot so let's break it down. First we are using `*`

and a range to create all the values that we need to look at, 1-999. Then we are creating new array by selecting all the value that are multiples of 3 or 5 from the original array. Finally, we find the sum of the newly created array to get our result. The result of this method is `233168`

, which is the same as the above method.

# Comparing Methods

Is either of these approaches better? From a stylistic and readability perspective, the second method is probably better, but you need to know how splats, ranges, and array methods work.

But what about performance? When we benchmark the iterative approach, we get the result in 0.039 milliseconds When we benchmark the declarative approach, we get our result in 0.106 milliseconds. So the iterative approach is a lot quicker. I would need to dive into the implementation details to see why, but my guess is that the declarative method is probably generating a lot of overhead, while the iterative method is just performing the calculations we need.

What is the fastest way we could achieve this result?

What is the most readable way we could get this result?

And finally, what is the best way?

You can checkout the source on my GitHub.

## Discussion (2)

In the iterative approach, you're doing one loop to accumulate the sum. In the declarative approach, you're first selecting the numbers the match, then looping again to sum them.

Actually I think there is a better method,by multiplying numbers from 1 to 333 to 3 we can find all multiples of 3 and then multiplying from 1 to 200 without considering multiples of 3( we've already counted them) to 5. this way we can change the iteration count from n (being the max number indicated) to n mod m ( m being the number we check, i.e 3 or 5) but overall both solutions have time complexity of O(n).