# Solve your sudoku puzzles with Elixir — Part-3

# Introduction

Now, we can solve easy sudoku puzzles with our algorithm and this is great !

In our implementation, I made a simplification on the **ApplyValues** module.

It just sets the value but do not apply constraints on the units containing the value. Which means if we apply {0,0} -> 3, the 3 units containing {0,0} have to remove the value 3 from the possibilities.

It’s huge because it removes 24 possibilities:

`row + column + box = 27 possibilities`

and as the element {0,0} appears 3 times, once in each unit

27 - 3 = 24

In this part we will update our apply values process to do what we have just said. Then use a new strategy to reduce the number of possibilities before using backtracking. And to finish, we will create a **Main** module to orchestrate our algorithms.

# Project structure

`├── _build`

...

├── config

│ └── config.exs

├── index.js

├── lib

│ ├── sudoku

│ │ ├── board.ex

│ │ ├── backtracking.ex

│ │ ├── data_structure_utils.ex

│ │ ├── strategies

│ │ │ ├── apply_values.ex <-- (update)

│ │ │ └── naked_single.ex <--

│ │ ├── main.ex <--

│ │ └── validation.ex

│ └── sudoku.ex

├── mix.exs

├── package.json

├── README.md

├── stuff.js

└── test

├── sudoku_board_test.exs

├── sudoku_apply_values_test.exs <--

├── sudoku_naked_single_test.exs <--

├── sudoku_test.exs

└── test_helper.exs

# Improve the apply values process

Let’s refactoring our **Sudoku.ApplyValues** module.

Remember ourupdate_mapfrom theBacktrackingmodule ?

Every time this function is called in order to apply new values now, it removes up to 24 possibilities !!

Let’s try that in iex.

Wow in part-2 **input_str_5** took us ~15s and now it’s less than a sec ! It’s time to try our “out of memory” puzzles

Fast !!!

OMG… again ?! It took us ages to solve this one ! but we solved it … **input_str4** is probably one of the most difficult ! but anyway it’s too long ! What can we do now ? Well it turns out that there are a lot of strategies in sudoku ! We will use a simple one call naked single

# Using the naked single strategy

# Introduction

Here is an example of what it does:

On row 0, There is only one element where we can apply 6 ! so apply it !

# Implementation

This function is the most important to understand this strategy, again, if you want you can try to implement it yourself copy/paste my test file and use mix test to see if it’s green.

Then continue implementing or copy/paste my files

# Create the Main module to orchestrate algorithms

Is it enough for our well known revolted sudoku called **input_str_4** ? Well as usual try it in iex !

# Conclusion

Well I guess it’s over ! we reach the goal ! There are tons of way to improve this project but for now it’s fast enough for what I want to do with it ;)

I’m counting on you to improve it.

I feel really comfortable writing this project thanks to Exercism.io. so again use it without moderation.

Thank you for reading.

PS: I solve Euler project n96 do you ?