Efficiency of an Algorithm

The algorithm is a set of processes for a task
Efficiency tells how good or bad the algorithm is, can be measured in terms of time and space.

The less time (how fast) and less space (how much memory), the better the operation (algorithm)

Counting Primitive Operations

Simplest analytical way to measure runtime is to count the number of primitive operations
By assuming. that each primitive operation has constant execution time

The more operations, the more running time

Can be used to describe the number of basic operations of data structure of size $n$
It’s normally denoted as $f(n)$
$f(n)$ tells numbers of steps and also time

The more $f(n)$ , the more running time. The less $f(n)$ , the less running time.

Big O notation is a mathematical notation that describes how an algorithm's time or space requirements grow as the size of its input increases. (Maybe to $\infty$ )

f(n) \le c(g(n))

That is $f(n)$ is less than or equal to another function $g(n)$ up to a constant factor and in the asymptotic sense as $n$ grows toward $\infty$
Big-O denotes as $O(…)$ (inside is a function of $n$ $n$ with no coefficient)
- It approximates the performance for a very large $n$
- Given the input size $n$ $n$ , an algorithm analysis focuses only on growth rate of time or space used
  - Ex. $O(n)$ , $O(n^2)$ , $O(\log n)$
- Big-O implies how much space (how much memory) and time (how fast) is needed approximately to run an algorithm
The highest degree term controls the asymptotic growth rate of $f(n)$
Big-O can be used to compare the algorithms’ performances
- เวลา Compare ก็ให้มองเป็นโจทย์แบบเปรียบเทียบ

a_n=a_1+(n-1)d

โดยหา $n$ คือจำนวน Term จากสมการนี้ – เดี๋ยวได้ใช้ ใน For Loop เพื่อนับจำนวนครั้ง
อนุกรมเลขคณิต $\boxed{\ce{S_n}=\frac{n}{2}(a_1+a_n)}$