Analysis Of Algorithms is to determine the amount of resources necessary to execute
it. Most algorithms are designed to work with inputs of arbitrary length.Algorithm
analysis is an important part of a broader computational complexity theory, which
provides theoretical estimates for the resources needed by any algorithm which solves
a given computational problem.Run-time analysis is a theoretical classification
that estimates and anticipates the increase in running time of an algorithm as its
input size increases.

Data structures and algorithms (DS&A) is an integral part of computer science. All
written software stores and manipulates information (data) in one form or another.
Data structures are standardized, efficient, and robust ways of temporarily storing
information in memory. An algorithm, defined as a sequence of precise programming
steps, allows us to further manipulate stored data in order to achieve meaningful
results. Sorting, searching, and merging are just some of the algorithms commonly
used nowadays, bundled into readily available development platforms. Similarly,
the developer's toolset features a huge variety of data structures to choose from.
Although a programming task may be achievable by more than one structure or algorithm
(or specific implementations of them), choosing the right one may have a tremendous
impact on efficacy, efficiency and scalability.

A typical data structures and algorithms course may involve any combination of the
following topics:

- Arrays and Lookup Tables

- Linked Lists

- Circular Linked Lists

- Double Linked Lists

- Stacks

- Queues

- Priority Queues

- Hash Tables (Dictionaries), Maps, and Graphs

- - Binary Trees and Heaps

- Advanced Data Structures, Collections, and Generics

- Fixed (Immutable) and Variable (Dynamic) Size Implementation of Data Structures

- Implementation of Data Structures in Various Programming Languages, with C/C++
and Java being the most common.

- Pointers and Pointer Arithmetic

- Abstract Data Types (ADTs)

- Detailed Comparison of Available Data Structures

- Sort Algorithm Implementation and Comparison, such as Quick Sort, Bubble Sort,
and Insertion Sort

- Search Algorithms and Techniques such as Linear Search, Binary Search Tree, Brute
Force Search, and Heuristics

- Algorithm Analysis (Performance, Complexity)

- Big O Notation (e.g. O(n) and O(n log n))

- Algorithmic Thinking and Algorithm Design

In the subject of computer science, the analysis of algorithms is the purpose of
the number of resources (such as time and storage) necessary to execute them. Most
algorithms are designed to work with inputs of arbitrary length. Usually the efficiency
or running time of an algorithm is stated as a function relating the input length
to the number of steps (time complexity) or storage locations (space complexity).

Algorithm analysis is an imperative part of a broader computational complexity theory,
which provides theoretical estimates for the resources needed by any algorithm which
solves a given computational problem. These estimates provide an insight into reasonable
directions of search for efficient algorithms.

In hypothetical analysis of algorithms it is common to approximate their complexity
in the asymptotic sense, i.e., to estimate the complexity function for arbitrarily
large input. Big O notation, Big-omega notation and Big-theta notation are used
to this end. For instance, binary search is said to run in a number of steps proportional
to the logarithm of the length of the list being searched, or in O(log(n)), colloquially
"in logarithmic time". Usually asymptotic estimates are used because different implementations
of the same algorithm may differ in efficiency. On the other hand the efficiencies
of any two "reasonable" implementations of a given algorithm are related by a constant
multiplicative factor called a concealed constant.

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