doc: update document

Author: hhow09

Diff for: README.md

@@ -16,4 +16,8 @@ link when you’re done.
 8. Split it up into a frontend and a backend (use the MERN stack)
 9. Using typescript will be a bonus.
 10. Please avoid using the eval-cmd of the JS math library
-11. The more effort you put into it (e.g. design wise, documentation wise) the better the rating will be.
+11. The more effort you put into it (e.g. design wise, documentation wise) the better the rating will be.
+
+## How to start
+1. follow the instructions in [backend/README.md](backend/README.md#run-at-local) to start backend server
+2. follow the instructions in [frontend/README.md](frontend/README.md#run-at-local) to start frontend

Diff for: backend/README.md

@@ -16,7 +16,27 @@ npm run start
 npm run test
 ```
 
-## Limitations on calculation
+## Features
+- [x] It supports 2 types of operations requested via websocket
+    - `operation`: evaluate an expression and return the result.
+    - `history`: get the latest 10 commands and results.
+- [x] [Express](https://expressjs.com/) is used for the server and router.
+- [x] [Socket.io](https://socket.io/) is used for WebSocket communication.
+- [x] [MongoDB](https://www.mongodb.com/) is used for storing chat history.
+    - [Array $slice](https://www.mongodb.com/docs/manual/reference/operator/update/slice/) is used to keep only the latest history.
+- [x] [Jest](https://jestjs.io/) is used for unit testing.
+- [x] [Github Workflows](../.github/workflows/ci.yaml) is used for continuous integration.
+
+## Math Calculation
+### Evalutaion Algorithm
+1. Parse the expression string by splitting by `+` and `-`, resulting a list of sub-expressions (`ExpressionMD`).
+2. For each sub-expression, turn it into a `Fraction`.
+3. Sum all fractions by `Fraction.add(Fraction)`.
+    - It uses **lowest common multiple** to add fractions.
+    - [Decimal.js](https://mikemcl.github.io/decimal.js/) is used for the basic arithmetic operations.
+4. Evaluate the result by `Fraction.evaluate()`.
+
+### Limitations
 - All whitespace is ignored, therefore `1 + 2 3` will consider as `1 + 23`
 - `negative sign` is only allowed at the beginning of an expression but not after multiplication or division
     - e.g. `-5*3 + 1` will return `-14`

Diff for: frontend/README.md

@@ -6,7 +6,7 @@ npm install
 cp .env.example .env # modify as needed
 ```
 
-## Start Locally
+## Run at Local
 ```
 npm run build
 npm run preview