Example

lets take the real life example we wants to constuct a contact list for that we need to add contacts and search the contacts :
Now lets deal it with two things Arrays and LinkedList 


Arrays:
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now if we wants to add the contact to the Arrays two things come into play:
1.sorted array 
2.unsorted array


lets see the sorted array first:
[1,2,3,4,5,6,7,8,9]


Now if i have to add the number into the sorted list then the time complexity is O(n) 
if i wants to perform the search operation on the sorted list then my time complexity is O(log n) because it is sorted array 


let see Unsorted Array:
[1,3,2,5,4,7,6,9,8]

Now if i have to add the item into the unsorted array then the time complexity is O(1) because i can add it at any where 
now if i have to perform search operation on the unsorted Array then the time Complexity is O(n) 


Now if we see in Real case we can take time to add the contacts to the list but to search we need it immediately

so sorted array is best with time complexity o(n) and O(log n) 


Linked List:
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now in linked list if we want to add we can do it in the starting in the head so time complexity is O(1) 

If we wants to search the time complexity is O(1) 


so the best is: Arrays sorted list
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As the Time Complexity is O(log n) for searching can we decrease it : 

lets see it by using Bit Sorting 


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