Data structure and algorithm main topic

Data structure and algorithm main topic -

Data structure - 

It is the way to arrange data in main memory for efficient use and more reliable use and in different way you can explain it way to organize data in computer memory so that we can use in a effective way for example : store a list of items having the same data-type using the array data structure

Algorithm -

A sequence of steps to solve a given problem or statement  or you can say a certain way of procedure to solve a problem or given question step by step to get accurate output algorithm sort the items in a certain way thats called algorithm \

for example - lets we take an array 

a[4]-1,7,9,2

sort array is - 1,2,7,9

Time complexity -

Time taken by algorithm by running scalling or in other word you say number of operation to complete its task (consider each operation take same time) algorithm which complete the task in less number of operation is consider more efficient in term of time complexity 

Asymptotic Notations -

The  languages that allow us to analyze an algorithm’s running time by identifying its behavior as the input size for the algorithm increases and algorithm efficiency and performance in a meaningful way. It describes the behaviour of time or space complexity for large instance characteristics

Type of Asymptotic Notations -

1. Big-O -

Big-O notation is a standard metric that is used to measure the performance of functions and it  notation is a standard metric that is used to measure the performance of functions.Big-O notation is a standard metric that is used to measure the performance of functions.

2. Big-Omega -

big Omega(Ω) function is used in computer science to describe the performance or complexity of an algorithm and The function g(n) is Ω(f(n)) iff there exists a positive real constant c and a positive integer n0 such that g(n) ≥ c f(n) for all n > n0

3. Big Theta -

asymptotically tight bound and f(n) = o(g(n)),if there exists constant c1, c2, and n0 such that c1.

The three case are :

Best Case Analysis-

  the minimum number of steps on input data of n elements in a funcation are called best case analysis .

Worst Case Analysis -

worst case happens when the item we are searching is in the last position of the array or the item is not in the array. we need to go through all n items in the array. The worst case runtime is, therefore, O(n).Worst case performance is more important than the best case performance in case of linear search because of the following reasons.

1.The item we are searching is rarely in the first position. If the array has 1000 items from 1 to 1000. If we randomly search the item from 1 to 1000, there is 0.001 percent chance that the item will be in the first position.

2.Most of the time the item is not in the array (or database in general).

Average Case Analysis - 

we calculate it.