Some Notes for Algorithms

Time complexity - Omega of algorithms

a) if statement - O(n) [Omega times n]
b) for loop - O(n) [Omega times n]
c) for loop with a for loop - O(n*n) [Omega times n squared]
d) for loop within a if loop, this if loop is within a for loop - O(n + n*n) [n plus n squared omega]
e) while loop - O(n) [Omega times n]
f) MergeSort - O(nlogn) [Omega n time logarithmic n]
g) HeapSort - O(nlogn) [Omega n time logarithmic n]
h) KMP algorithm - O(m+n) [m plus n omega]

Checklist before selecting the right data structure for a given problem

(i) Analysis the problem in order to determine resource constraints
(ii) Determine the basic operations that need to be supported, such as Insert/Remove/Search
(iii) Now, select the data structure that has minimum cost/benefits to support the required operations

Operation time complexity for a LINKED LIST

The time complexity of handling the operations in a data structure like a LINKED LIST are as follows:

i. Most of the operations are O(n) [i.e. omega times n]
ii. Remove/Insert operations that handles element between elements require O(1) [i.e. omega times one] this is due to references/pointers on both the ends of the list, hence the elements don't require to be shifted. However, due to the references/pointers this data structure requires additional memory!

Operation time complexity for an ARRAY

The time complexity of handling the operations in a data structure like an ARRAY are as follows:

i. Almost all the operations are O(1) [i.e. omega times one]
ii. Remove/Insert operations that handles element between elements require O(n) [i.e. omega times n] because the elements need to be shifted.
Note! Hence, an array as a data structure is used where remove/insert operations are not required.