Introduction to Algorithms

Why do you need algorithms?Good algorithmic training is VERY important for the programmer, but you don’t need to memorize all the algorithmsUnderstanding algorithms gives you:1) Ability to solve incomprehensible problems2) Habit to analyze the effectiveness of each of your solutions3) Ability to skillfully use the existing tools

One more reason: jobs

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

Disclaimer

Some of the terms and words Google-translated.Sorry.

Source code is availigle on GitHub

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.

Formal properties of algorithms1) Finiteness2) Discreteness3) Clarity4) Accuracy5) Mass character6) Definitiveness

FinitenessFiniteness (or effectiviness)

means that algorithm has a finite number of steps to received result.

DiscretenessDiscreteness

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

ClarityClarity

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

AccuracyAccuracy

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

Mass characterMass character

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

DefinitivenessDefinitiveness

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

Test yourselfI want to cut an orange. What’s the plan?

Example of algorithm:How to cut an orange

ClassificationCouple of categories of algorithms (there are a plenty of them)

•Deterministic / Randomized• Exact / Approximation• Sequential / Parallel• etc.

Complexity of algorithms1) 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.

Algorithms: Strings/arraysAlgorithm #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.)

Algorithms: Strings/arraysAlgorithm #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

Algorithms: Strings/arraysAlgorithm #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.

Algorithms: MatrixAlgorithm: Rotate Image

You are given an n x n 2D matrix representing an image.Rotate the image by 90 degrees (clockwise).

Algorithms: Linked ListLinked 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.

Algorithms: Binary TreeBinary 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.

Algorithms: SortingСhances 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

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

Extra resources1) http://www.programcreek.com/2012/11/top-10-algorithms-for-cod

ing-interview/