Data-Structures-and-Algorithms.

Data Structures :-

A Data Structure is a way of storing/organising data in the memory in such a way that access, management and modification of data become efficient.

Algorithms :-

An algorithm is a step by step procedure to solve logical and mathematical problems. It is any approach you use to perform operations on data (like searching, sorting, traversing, etc).

This Folder is in the continuation of 01. DataStructures to proceed with the Algorithm part, so the approach will be that we will follow the DSA sheet by LoveBabbar and in the process of solving Questions we will also build up the concept of algorithms in proper sequence and our Data Structures will also get revised because algorithms are something which we apply on Data Structures.

TimeComplexity

Weightage of Algos
1 < log N < sqrt(N) < N < N log N < N² < 2^N < 3^N < N !
10⁸ Operation rule

What is O(log N)?

log N in Mathematics:-

In mathematics log has a default base as 10. e.g., log₁₀ 100
Find value of log 1000 ?
- log₁₀ 1000 = x
- 10^x = 1000
- x=2 So log 1000 = 3 because base is 10.
Find value of log₂ 8 ?
- log₂ 8 = x
- 2^x = 8 OR log 8 / log 2
- x = 3

log N in Computer:-

In CS log has a default base as 2. e.g., log₂ 8

O(log N) means times goes up linearly while N goes up exponentially.

1sec to compute 2elements...log₂ 2 = x ...2^x=2
2sec to compute 4elements...log₂ 4 = x ...2^x=4
3sec to compute 8elements...log₂ 8 = x ...2^x=8

Difference between (Subsequence/Subset) VS (Substring/SubArray)

(Subsequence/Subset) - Elements should be in one direction. Not necessary to include adjacent elements i.e., gaps are possible between elements.
- e.g. arr[]={1, 2, 3, 4, 5, 6, 7}--->{1, 3, 5, 7}, {1, 4, 6, 7}...
(Substring/SubArray) - No gaps are possible between elements. Adjacent elements should be there.
- e.g. arr[]={1, 2, 3, 4, 5, 6, 7}--->{1, 2}, {1, 2, 3}, {4, 5, 6}, {6, 7}...