BigO Notation

Big O Notation describes the efficiency of code as the input approaches infinity. 
We do not have to use concrete units like measuring the time or space. Instead, Big O analyze how time and space scale.
Big O helps use to find better solutions.
Better solutions in the sense that they use least resources - time and space.
This is what we call the Time-Space Complexity.

**Simplifying Big O Notation**
There are two important rules;
The Product Rule and The Sum Rule.
**Product Rule:**
If the Big O is the product of multiple terms, drop the constant term.
For a constant term,the Big O notation is given as O(1).
When using Big O notation, we are analyzing what can possibly slow down the program.
for constant terms, it is easier to measure time and space. Instance, if it takes a painter, two hours to make a portrait,
we can measure how long it will take him to make ten others. However, other paintings like landscape that depends on size and amount of detail becomes a variable.
Therefore, since variables can grow, they are hence analyzed using the Big O notation.

Examples of product rule:
1. O(4*n)
result: O(n)
2. O(n/3) -: This can be rewritten as;
O((1/3) * n )
result: O(n)
3. O(5 * n * n)
result: 0(n^2)

Sum Rule:
If the Big O is a sum of multiple terms, pick the largest value.
Note: if there is a variable, pick the variable. This is because the variable can grow till infinity.

Eg. O(n^2 + n)
result: n^2

2. O(n + 10000 + n^5 + n^3)
result: n^5


CASES OF BOTH PRODUCT AND SUM RULE
In simplifying a complex Big O Notation, first apply the Product Rule and then, the Sum Rule.
O(5n^2 + 100n + 17)
result:
Applying product rule: O (n^2 + n + 1)
Sum Rule: O(n^2);