finish the readme

.gitignore

@@ -60,6 +60,7 @@ dkms.conf
 # Executable
 push_swap
 checker
+checker_linux
 
 # File obj
 obj/

README.md

@@ -1,5 +1,80 @@
-This project has been created as part of the 42 curriculum by mteriier[, dgaillet].
+*This project has been created as part of the 42 curriculum by dgaillet[, mteriier].*
 
 ## Description
 
-The *Push swap* project goal is to sort values with push swap operations beetween 2 stack (*a* and *b*)
+The **Push swap** project goal is to sort values with push swap operations beetween 2 stack (*a* and *b*)
+with different algorithms. Depends on the difficulties to solve the stacks. We will select a certain algorithms.
+
+The difficulty is calculate with a disorder function *(compute_disorder)*. Disorder result will be between 0 and 1.
+
+Selected algo depends on the disorder:
+
+**Disorder < 0.2 ( O(n2) ):**
+- Insertion sort adaptation ( len = 500 > complexity = 30 000)
+
+**0.2 >= Disorder < 0.5 ( O(n√n) ):**
+- Bucket sort adaptations with √n buckets ( len = 500 > complexity = 11900)
+
+**Disorder >= 0.5 ( O(n log n) ):**
+- Radix sort adaptation (LSD or MSD) ( len = 500 > complexity = 8000)
+
+## Instructions
+
+### 1. Command to compile push_swap :
+```
+make
+```
+### 2. Command to compile bonus :
+
+```
+make bonus
+```
+### 3. Command to delete all objects and exec :
+
+```
+make fclean
+```
+### 3. Command exemples how to use push_swap :
+
+```
+./push_swap 7 5 8 12 30 -20
+```
+```
+ARG="7 5 8 12 30 -20"; ./push_swap $ARG
+```
+
+### 4. Command exemples how to use checker :
+
+```
+./checker 7 5 8 12 30 -20
+(put the command like pa,ra,rr,rrr ...)
+```
+### 5. Command exemples how to use checker and push_swap together :
+
+```
+ARG="7 5 8 12 30 -20"; ./push_swap $ARG | ./checker $ARG
+```
+
+## Resources
+
+- **For the algorithms**  
+https://en.wikipedia.org/wiki/Sorting_algorithm
+
+- **For BUCKET SORT**  
+https://www.meilisearch.com/blog/bucket-sort-guide
+
+- **For BUCKET SORT**  
+https://www.geeksforgeeks.org/dsa/radix-sort/
+
+## Additional sections may be required depending on the project 
+
+### Justification to why we chose this algorithms
+- **Insertion sort**  
+We select **Insertion** cause that was the more simple to implement with the restrictions.
+
+- **Bucket sort**  
+We select **Bucket** cause i like how the algorithms sort.
+ Define the range and the number of buckets.
+
+- **Radix sort**  
+We select **Radix** cause that was the more simple to implement with the restrictions.