Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g. in memory or on disk) by an algorithm.
Big O notation will always assume the upper limit where the algorithm will perform the maximum number of iterations.
important tool when dealing with algorithms that need to operate at scale, allowing you to make the correct choices and acknowledge trade-offs when working with different data sets.
algorithm that will always execute in the same time (or space) regardless of the size of the input data set.
algorithm whose performance will grow linearly and in direct proportion to the size of the input data set.
algorithm whose performance is directly proportional to the square of the size of the input data set.
common with algorithms that involve nested iterations over the data set.
Deeper nested iterations will result in O(N³), O(N⁴) etc.
### 4- O(2^N) : algorithm whose growth doubles with each addition to the input data set.
The growth curve of an O(2^N) function is exponential — starting off very shallow, then rising meteorically.
extremely efficient when dealing with large data sets.
growth curve that peaks at the beginning and slowly flattens out as the size of the data sets increase.
Doubling the size of the input data set has little effect on its growth as after a single iteration of the algorithm the data set will be halved
(data strucutre)
has 3 types: 1- singly: each node refer to the node next to it but the last one refer to null
2-doubly: each node refers to the node befor and the node after
3- circuler: same as singly but the last node refers to the first node in the list
is often linked with big O notation
big o notation: is a way to discripe how efficent somthing is (algorithems,dataStrucre) how will do it perform and how memory does it need
you can think about them like grades
constant time (no matter if you add or delete it will take the same amount of time or memory(depend on condiditon)) O(1)
example: adding item to the beginning of a linked-list
so add to link list method takes O(1)
take avergae score
perform in a linear form where n present the number of the nodes in the linked-list.
to add somthing to the end of linked list you have to go throw each elemnt of the list a lot of nodes it will take longer as the list size increases
quadatric time
as the input gorws it will takes double the time or memory from befor adding that input
linked -list : uses O(1) for adding to start of array while array uses O(n) because it will have to update all elemnts index to add so we should use O(1) for this useCase
searching for item is easier in array more than linked list because index will help us to find what we want more quickly
the size of the list and what we want to do with list items are keys to help us pick the right approch
1-nams are assigned independintly
2- names refers to the value (not to other names)
3- in python memroy is managed dynamicly (vaule live untill there is now referce to it)
4- asssignment never copy data (only refer to the same value and not copy it) so if you change a value in (ex:list) all the names will have that change because they all refer to the same list (this is the cast in mutable data type)
5- in imutable data type (string,tuples,int) when change there values the new value value wont be stored in that refernce but it will store the value in new reffernce (do not change in place)
str='aaa'
nums=[1,2,3]
x=1
x=x+1
str=str+'aa'
cant be mutated
nums.append(4)
assignment is the same in all values but changing is different and that what gives a different behaviour
write function that do not mutate list but return new list mkae the code alot eaiser to understand
you can start evalute data structre base on how they evalute different things (like insert) you need to use somthing that will abetter grade big O that the other