CubeIT Tech - Algorithms
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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.
![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](https://image.slidesharecdn.com/cubeit-tech-algorithms-160217031207/85/CubeIT-Tech-Algorithms-19-320.jpg)
CubeIT Tech - 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
Editor's Notes
- #3: First, is the ability to solve the problem of incomprehensible. The vague wording of vital problems to see the possible strict interpretation. Comprehensively analyze the various options and choose the most suitable. Obviously, it is not enough just to know the algorithms. You must be able to "see them", to recognize the possibilities of their application. Secondly, algorithmic training should get you the habit of analyzing the effectiveness of each of your solutions. Third, algorithmic training should help skillfully use the existing tools. Databases are continuous data structures and algorithms. And conceptually quite simple and clear - search trees, hash table For example, knowing that the database index - it's just a search tree, it is easy to understand which requests can be met quickly and which ones are doomed to full-scan.
- #6: http://dictionary.reference.com/browse/algorithm https://books.google.ca/books?id=uI1ytRzul8MC&pg=PA5&lpg=PA5&dq=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&source=bl&ots=QLftG8AKmM&sig=EMu5Y74g3c9qrZowCNpYEr9VOJ4&hl=ru&sa=X&ved=0ahUKEwi7gMvQwvzKAhXBnIMKHZutDpoQ6AEIHDAA#v=onepage&q=finite%20set%20of%20unambiguous%20instructions%20that%2C%20given%20some%20set%20of%20initial%20conditions%2C%20can%20be%20performed%20in%20a%20prescribed%20sequence%20to%20achieve%20a%20certain%20goal%20and%20that%20has%20a%20recognizable%20set%20of%20end%20conditions&f=false
- #7: http://learnpascal.ru/vvedenie-v-paskal/algoritm.html
- #8: 1) SIMPLE: the algorithm must eventually terminate. Something endless is not an algorithm
- #9: Example: Do that – then that – then that. Not like do that or that – then that – but before you should do that
- #10: Example: if you need to perform a mathematical algorithm you will probably use calculator or something like that, you can only do mathematical operations with that (like division, multiplication, addition, substraction, power etc). Calculator cannot do barrel roll to do that math algorithm
- #12: I’ll try to give examples of that properties later
- #15: 1) Finiteness – we need 5 steps to get result 2) Discreteness – each step is discrete 3) Clarity – we have comands like lay orange and cut 4) Accuracy - cut the orange in half vertically (NOT HORISONTALLY) but also that tutorial is specially designed for oranges. 5) Mass character – using that tutorial we can cut not only that but anyof the oranges in the world 6) Definiteness – if we follow these steps we will always have 6 pieces of orange in the end
- #16: I won’t spend a lot of time on classification. Here I’d like to stress that in general algorithms never contain random processes. Here randomized means that in such of algorithms are used another algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. 2 – clear 3 – example of making a soup. We can put water to boil and peel and cut potatoes during that.
- #17: Обозначение логарифма: log 𝑏 𝑁 = x Эта запись равнозначна следующей: bx = N .
- #19: I want to show you some algorithms, explain them code programming Strings/arrays are easy to understand, but the interview problems often require advanced algorithm to solve, such as dynamic programming, recursion, etc.
- #25: But it’s still important to know when one sorting algorithm is better than another