Update introduction.md

Author: SNEAXIII

exercises/practice/gigasecond/.approaches/introduction.md

@@ -1,22 +1,136 @@
-# Dig deeper
-There is only one correct and safe way to deal with date and datetime in python. We are going to use the built-in `datetime` module. A `datetime` object contains multiple attributes, like `year`, `month`, `day`, `hour`, `minute` and `second`.
-But you can't update a `datetime` object directly like:
+# Dig Deeper
+When working with dates and datetime in Python, it's essential to use the built-in `datetime` module. 
+
+## General Guidance
+### How to represent one gigasecond (1 billion)?
+In python, there are multiple ways to represent 1 billion in numerical form:  
+| Method              | Value                                              |  
+| ------------------- | -------------------------------------------------- |  
+| Exponentiation      | 10**9                                              |  
+| Power function      | pow(10, 9), math.pow(10, 9) and numpy.pow(10,9)    |  
+| Scientific notation | 1e9                                                |  
+| Underscore notation | 1_000_000_000                                      |  
+| Literal integer     | 1000000000                                         |
+
+### What is a `datetime` and a `timedelta` ?
+A `datetime` object is a way to represent a specific point in time, including the date and time of day. It contains multiple attributes, such as `year`, `month`, `day`, `hour`, `minute`, and `second`. However, updating a `datetime` object directly is not possible. Instead, we'll explore various approaches to solve the problem of adding a gigasecond to a given `datetime`.
+The key to solving this problem lies in using the `timedelta` object, which represents a time interval. We can add or subtract a `timedelta` from a `datetime` object to create a new `datetime` object with the updated values.
+Here is a quick example of how to use a date and time:
 ```py
 from datetime import datetime
 datetime_2000_01_25 = datetime(year = 2000, month = 1, day = 25)
 wrong_date = datetime_2000_01_25 + "2 weeks" # This won't work at all
 ```
-Instead, we have to use another one object, `timedelta`. It will be used to accomplish the same thing as shown in the previous example. This object is a time interval, which can be used to modify a `datetime` object. We can add or subtract the `timedelta` to a `datetime` object to create a new `datetime` object with the updated values.
+Instead, we have to use another one object, `timedelta`. It will be used to accomplish the same thing as shown in the previous example. This object is a time interval, which can be used to modify a `datetime` object. We can add or subtract the `timedelta` to a given `datetime` object to create a new `datetime` object with the updated values.
 ```py
 from datetime import timedelta, datetime
 datetime_2000_01_01 = datetime(year = 2000, month = 1, day = 1)
-delta = timedelta(weeks=2)
+delta = timedelta(weeks=2) 
 datetime_2000_01_15 = datetime_2000_01_01 + delta
 ```
-In the exercise, we have one `datetime` parameter, so one of the correct answer is:
+To create a `timedelta`, you can use positional or named arguments. 
+```py
+# By default, timedelta is equal to:
+a = timedelta(days=0, seconds=0, microseconds=0, milliseconds=0, minutes=0, hours=0, weeks=0)
+# Is equal to:
+a = timedelta(0, 0, 0, 0, 0, 0, 0)
+a = timedelta()
+# Which can be confusing with large functions.
+# For an example "days=0" mean "days" is an optional argument, and by default it is equal to 0.
+# In python functions, arguments is positionnal, that mean if you want a 10 seconds "timedelta", you can do:
+ten_seconds = timedelta(0, 10) # 0 days, 10 seconds
+# Or you can directly name the argument:
+ten_seconds = timedelta(seconds=10)
+```
+### Defining variables
+
+You have several options for defining your variables
+You can define variables with a global scope (outside functions) or local functions (inside).
+Note that there are no immutable `constants` in python. To symbolize a constant, we write it in uppercase with underscore to replace spaces (Screaming Snake Case). Here is a quick example:
+```py
+GLOBAL_CONSTANT = "global" # Global scope variable (defined outside a function), in Screaming Snake Case (constant)
+def test():
+    LOCAL_CONSTANT = "local" # Local scope variable (defined inside a function), only accessible inside this function
+```
+You can choose both, with their pros and cons.
+#### Global variables
+You should define a global variable when:
+* you want to reduce the size of functions
+```py
+def test():
+    str1 = "abc"
+    str2 = "def"
+    return str1 + str2
+    
+# Became
+
+STR1 = "abc"
+STR2 = "def"
+def test():
+    return STR1 + STR2 
+```
+* you need to reuse a value multiple times, like constants (for example, the 1 trillion number)
+```py
+def add_number(n):
+    return n + 10
+
+def add_number_2_times(n):
+    return n + 20
+
+# Became
+
+BONUS = 10
+def add_number(n):
+    return n + BONUS 
+
+def add_number_2_times(n):
+    return n + BONUS * 2
+```
+* you don't want to execute multiple times the same function, or creating a variable (for example, creating the `timedelta` object)
+```py
+def is_vowel(char):
+    # This array will be recreated each time this function is executed.
+    vowels = ["a","e","i","o","u"]
+    return char in vowels
+
+# Became
+
+VOWELS = ["a","e","i","o","u"]
+def is_vowel(char):
+    return char in VOWELS
+```
+#### Local variables
+You should define a local variable when:
+* you don't need to reuse the variable
+* the variable consumes too much memory (like a big array)
+## Approach
+### Approach: global variable with scientific notation
+```py
+from datetime import timedelta, datetime
+ONE_BILLION = 1e9
+GIGASECOND = timedelta(seconds=ONE_BILLION )
+def add(moment: datetime) -> datetime: 
+    return moment + GIGASECOND 
+```
+### Approach: without variable with exponentiation
 ```py
 from datetime import timedelta, datetime
 def add(moment: datetime) -> datetime: 
     return moment + timedelta(seconds=10**9)
 ```
-For more information, check the official [datetime documentation](https://docs.python.org/3/library/datetime.html#datetime.datetime.year)
+### Approach: global number variable with underscore notation
+```py
+from datetime import timedelta, datetime
+ONE_BILLION = 1_000_000_000
+def add(moment: datetime) -> datetime: 
+    return moment + timedelta(seconds=ONE_BILLION) 
+```
+### Approach: local variable with pow()
+```py
+from datetime import timedelta, datetime
+def add(moment: datetime) -> datetime: 
+    ONE_BILLION = pow(10, 9)
+    GIGASECOND = timedelta(seconds=ONE_BILLION )
+    return moment + GIGASECOND  
+```
+For more information, check the official [timedelta documentation](https://docs.python.org/3/library/datetime.html#timedelta-objects)