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Preface

Im just kinda taking notes and taking the slides from a yt vid so i can maybe remember stuff / copy stuff for later
also to partially increase my typing speed without looking at my keyboard and idk maybe get better at typing given i dont use the standerd asdf jkl; hand position
rather i do shift+awr jop' layout and use alot of range for my index fingers and spread them out its not optimal but this is realy all i need coz im a gamer lmfao

also [] is my ring finger and all numbers are my ring fingers wish i had an ergo keyboard lol

https://www.youtube.com/watch?v=RBSGKlAvoiM&ab_channel=freeCodeCamp.org

Example page, and literal first 6 minutes of the video


Why Data Structures?

  • They are essential Ingredients in creeating fast and powerfull algorithms.
  • they help to manage and organize data.
  • they make code cleaner and easier to understand. (even if it lowers efficiency)

Abstract Data Types VS. Data Structures

Abstract data type

An abstract data type (ADT) is an abstraction of a data structure which provides only the interface to which a data structure must adhere to which a data structure must adhere to.

the interface does not give any specific details about how something should be implemented or in what programming language.

Examples
Abstraction (ADT)
Implementation (DS)
List

Dinamic Array Linked List

Queue
Linked List based Queue
Array based Queue
Stack based Queue
Map

Tree Map

Hash Map / Hash Table

Vehicle

Golf Cart

Bicycle

Smart Car


Complexity Analysis

As programmers, we often find ourselves asking the same two questions over and over again:

  1. How much time does this algorithm need to finish?
    1. if it takes the length of the universe to complete its useless
  2. How much space does this algorithm need for its computation?
    1. likewise if it takes the entire bit size of internet its also useless

Big-O Notation 

yes it's the letter O not the number 0
Big-O Notation gives an upper bound of the complexity in the worst case, helping to quantify performance as the input size becomes arbitrarily large.

Ex, looking for the number 7 in a list, and it occurring last. this scenario would include all values in that list, if allocating space per number, you'd allocate the entire list.

n - The size of the input
Complexities ordered in from smallest to largest

Constant Time:

O(1)

Logarithmic Time:

O(log(n))

Linear Time:
O(n)
Linearithmic Time:
O((n)log(n))
Quadratic Time:
O(n^2)
Cubic Time:
O(n^3)
Exponential time:
O(b^n), b >1
Factorial Time:
O(n!)

Big-O Properties

O(n + c) =
O(n)
O(cn
=
O(n), c > 0

*c = constant, n = number
if your constant is large, like 2 billion its likely to have substantial run-time penalties

let f be a function that describes the running time of a particular algorithm for an input of size n:

f(n) = 7log(n)^3 + 15(n)^3 + 15n^2 + 8 
this is Quadratic because theres ^3 then ^2 then ^1 or a regular value at the end

O(f(n)) = O(n3)

The folloing run in constant time: O(1)

a := 1
i := 0
b := 2 While i < 11 do
c := a + 5*b
i = i + 1

:= is used to explicitly signal the initialization or assignment of a new value to a variable. and is usually used for pseudo code

The Following runs in Linear time: O(n)

:0
While i < n Do
  i = i + 1
:0
While i < n Do
  i = i + 3
  f(n) = n
  O(f(n)) = O(n)

f(n) = n/3

0(f(n)) = O(n)