Programming-Foundations-Algorithms

Algorithms purpose

to solve a specific proplem with a sequential sets of steps
for instance : if you need to add different shaped in groups you can use loop by iterate on each shape if its belong to this group or not

Algorithms charachteristics

algorithms complixity
- space complixity
- time complixity
input and output
classification
- serial/parallel
- exact/approximate

common algorithms

searching algo find a specific data from a structure
sorting algo take a set of data and apply a sort order to it
computational algo given a ser of data calculate another (calculator)
collection algo work with collection of data : manipulating and navigating amoung sets of data that are sorted (count a specific items)
exerciese for an algorithm

def greatest common denomonator (a,b)
    while (b != 0)
        t=a
        a=b
        b=t%b
    return a 

print(20,8)

Algorithm performance

how an algorithm will be have based on the size of input set data
big-O to describe algorithm performance as the size of input grows over time it usually describe the worst case senario

Time complixity rank

O(1) operation in question doesnt depend on the number of elements in the given data set (calculating the number is even or odd)
O(log n) finding a specific value in a sorted array using a bionary search so if the number of elements grow it takes logarithmic time relation to find any given item
O(n) searching for an item in an unsorted array as number of items increase it take the corrosponding linear time to complete the search
O(nlogn) sorting algorithm like stack and merge sort
O(n2) as the number of data increase the time it take is squared

Overview on Data structure

1: Array

it has either one dimention or multiple , you can calculate

item index O(1)
insert or delete at beginning or middle O(n)
insert or delete at end : O(1)

2: Linked lists(nodes)

linear collection of data elements each node has a field that refer to the next element in the list
the benifit of it over arrays is that its fast and easy to add and remove items from the list
its not necessary to recognize the essintial memory that hold the data because the individual nodes doesnt have to be stored adjecently like arrays
the linked lists cant do canstant time random access to any item in the list like the array

**you can inserting a new item in the list**

#### 3: stack
**is collection that support two priciples .**
* push
* pop
the last item pushed is the first one poped

is used in
* expression processing
* back tracking
#### 4: Queue
**its collection that supports adding and removing and work like stack but**
the first item added is the first one removed

is used in
* order processing
* massaginh
#### 5: hash tables
**an ability to unique map a given key to a specific value (word during dictionary list)**

it
* is very fast
* for small data sets array is more efficient
* hash table dont order entries in a predictable way
___
### Recursion
* your recursive function return at some point (breaking condition)
* otherwise it leeds to infinite loop
* each time the function called the value of arguments of the previous call are stored aside not written over by the new call (call stack)
### sorting data
####1: bubble sort