I want to mension that All of here are just practice, I took notes of the foundamental and relevant concepts on my personal digital NoteBook. In a future I try to add about graphs and document more (specificly the boundary cases of each)

I also am trying to combine with the book( only practices ):
"Data Structures and Algorithms in Java" by Michael T. Goodrich (Author), Roberto Tamassia (Author), Michael H. Goldwasser.

Some Content THat I've Learned

Basic Algorithms

• Define what exactly is an algorithm

• Find a maximum element in an array

• Find a minimum element in an array

• Find the 17th element in the fibonacci sequence

• Calculate the factorial of a number

• Calculate the sum of the digits of a positive integer

• etc.

Algorithms Complexity

Measurement Diff: ( software-agnostic && hardware-agnostic ) && ( Seconds || Millis )

Time Complexity

Space Complexity

Algorithms Analysis

Take in account:

• input >= 0
  • input is a positive integer
• Functions do more work for more input
  • Pass by each(<arr_size_100>) -> 100 times
  • Pass by each(<arr_size_1000>) -> 1000 times
  • Pass by each(<arr_size_n>) -> n times
• Drop all constant factors
  • log_2(n) + 1 -> log_2(n)
  • 3n + 2 -> n
  • 50n -> n
• Ignore lower order terms
  • 3n^2 + 2n + 1 -> n^2
  • 6n^3 + 2n^2 + 3n + 1 -> n^3
• ignore base of logarithm
  • we can change the base, the algorithm will be the same
  • log_2(n) -> log(n)
  • log_10(n) -> log(n)
  • log_3(n) -> log(n)

Asymptotic Notation

• Big-O

  same or faster

• Little-O

  faster

• Big-Omega

  same or slower

• Little-Omega

  slower

• Big-Theta

  O() and Omega() are the same

Examples

• n^3 = O(n^2) -> false

• n^2 = O(n^3) -> true

• n^2 = O(n^2) -> true

• (n(n-1))/2 = O(n^2) -> true

• (n(n-1))/2 = o(n^2) -> false

• n^2 = o(n^3) -> true

• n^2 = o(n^2) -> false

• n^3 = o(n^4) -> true

• n^4 = Ω(n^3) -> true

• log n = Ω(1) -> true

• n = Ω(log n) -> true

• n = Ω(n) -> true

• n = Ω(n^2) -> true

• n^2 = ω(n) -> true

• n^3 = ω(n^2) -> true

• log n = ω(1) -> true

• n = ω(log n) -> true

• n^2 = Θ(n^2) -> true

• n^2 = Θ(n^3) -> false

• n^2 = Θ(n^2) -> true

Understand

OOP

Generic Programming

Recursion concepts

Divide and Conquer