The document provides an introduction to algorithms, emphasizing their importance for programmers in problem-solving and solution analysis. It covers definitions, properties, classifications, and complexities of algorithms, as well as examples for practical application. Additionally, it includes resources for further learning about algorithms used in coding interviews.

1. Introduction to Algorithms

2. Why do you need algorithms?
Good algorithmic training is VERY important for the programmer, but
you don’t need to memorize all the algorithms
Understanding algorithms gives you:
1) Ability to solve incomprehensible problems
2) Habit to analyze the effectiveness of each of your solutions
3) Ability to skillfully use the existing tools
One more reason: jobs

3. Outline
• Definition of algorithm
• Formal properties of algorithms
• Some classification of algorithms
• Complexity of algorithms
• ALGORITHMS

4. Disclaimer
Some of the terms and words Google-translated.
Sorry.
Source code is availigle on GitHub

5. Definition of algorithm
Simple:
Algorithm is a set of rules for solving a problem in a finite
number of steps
Less simple:
Algorithm is a finite set of unambiguous instructions that, given some
set of initial conditions, can be performed in a prescribed sequence to
achieve a certain goal and that has a recognizable set of end
conditions.

6. Formal properties of algorithms
1) Finiteness
2) Discreteness
3) Clarity
4) Accuracy
5) Mass character
6) Definitiveness

7. Finiteness
Finiteness (or effectiviness)
means that algorithm has a finite number of steps
to received result.

8. Discreteness
Discreteness
means that algorithm has to be broken down into
a sequence of steps performed

9. Clarity
Clarity
means that algorithm must contain only the
commands that are part of a set of commands
that can perform a particular executor

10. Accuracy
Accuracy
means that any step of an algorithm should be
definite and unambiguous

11. Mass character
Mass character
means that once algorithm is made up it must
solve similar problems with different input data

12. Definitiveness
Definitiveness
means that the same set of input data will
produce the same result, i.e. the result is uniquely
determined by the initial data.

13. Test yourself
I want to cut an orange.
What’s the plan?

14. Example of algorithm:
How to cut an orange

15. Classification
Couple of categories of algorithms (there are a plenty of them)
•Deterministic / Randomized
•Exact / Approximation
•Sequential / Parallel
•etc.

16. Complexity of algorithms
1) Confusing explanation
2) Clear explanation (must read)
The idea is Big-O notation
Big-O notation is a relative representation of the
complexity of an algorithm.

18. Algorithms: Strings/arrays
Algorithm #1: Remove Element
Given an array and a value, remove all instances of
that value in place and return the new length.
(Note: The order of elements can be changed. It doesn't matter
what you leave beyond the new length.)

19. Algorithms: Strings/arrays
Algorithm #2: Search Insert Position
Given a sorted array and a target value, return the
index if the target is found. If not, return the index
where it would be if it were inserted in order. You
may assume no duplicates in the array.
[1,3,5,6], 5 -> 2
[1,3,5,6], 2 -> 1
[1,3,5,6], 7 -> 4
[1,3,5,6], 0 -> 0

20. Algorithms: Strings/arrays
Algorithm #3: Anagrams
Given an array of strings, return all groups of strings that are
anagrams.
An anagram is a type of word play, the result of rearranging the
letters of a word or phrase to produce a new word or phrase,
using all the original letters exactly once; for example Torchwood
can be rearranged into Doctor Who.
If two strings are anagram to each other, their sorted sequence is
the same. Therefore, this problem can be seen as a problem of
finding duplicate elements.

21. Algorithms: Matrix
Algorithm: Rotate Image
You are given an n x n 2D matrix representing an image.
Rotate the image by 90 degrees (clockwise).

22. Algorithms: Linked List
Linked list is a linear collection of data elements, called nodes pointing
to the next node by means of pointer
Algorithm: Reverse Linked List
Reverse a singly linked list.

23. Algorithms: Binary Tree
Binary tree is a tree data structure in which each node has at most two
children, which are referred to as the left child and the right child
Algorithm: Binary Tree Maximum Path Sum
Given a binary tree, find the maximum path sum. The path may
start and end at any node in the tree.

24. Algorithms: Sorting
Сhances that you will need to write a sorting algorithm are close to
zero.
http://www.sorting-algorithms.com/
https://www.youtube.com/watch?v=kPRA0W1kECg

25. Today:
• Learn some theory (definition properties, complexity)
• Overview several algorithms

26. Extra resources
1) http://www.programcreek.com/2012/11/top-10-algorithms-for-
coding-interview/