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This document defines and describes various types of algorithms. It begins by explaining that an algorithm is a step-by-step procedure for solving problems or processing data, and that they are used in mathematics and computer science. It then categorizes algorithms into different types, including recursive, divide and conquer, dynamic programming, greedy, branch and bound, brute force, and randomized algorithms. Examples are provided to illustrate each type of algorithm.
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- 2. Nabia Rahman Farjana Sarmin Name of Group Members MD. Osman Goni Sumayea Musarat
- 3. An algorithm is a procedure or formula for solving a problem. Derives from the mathematician, Mohammed ibn-Musa al-Khwarizmi. Al-Khwarizmi's work is the likely source for the word algebra as well.
- 4. In mathematics and computer science, an algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. A program is one type of algorithm All programs are algorithms Not all algorithms are programs!
- 5. Using a similar problem-solving approach can be grouped together The purpose is not to be able to classify an algorithm as one type or another, but to highlight the various ways in which a problem can be attacked.
- 6. • Simple recursive algorithms • Backtracking algorithms • Divide and conquer algorithms • Dynamic programming algorithms • Greedy algorithms • Branch and bound algorithms • Brute force algorithms • Randomized algorithms
- 7. A simple recursive algorithm: Solves the base cases directly Recurs with a simpler sub problem Does some extra work to convert the solution to the simpler sub problem into a solution to the given problem I call these “simple” because several of the other algorithm types are inherently recursive
- 9. Given a list, find a specific element in the list We will see two types Linear search Binary search
- 12. Given a list, put it into some order We will see Three types Bubble sort Selection sort Quick sort
- 16. In computer science, divide and conquer is an important algorithm design paradigm based on multi-branched recursion. It works by recursively breaking down a problem into two or more sub-problems.
- 17. It is a method for solving complex problems by breaking them down into simpler sub problems.
- 18. It is a general algorithm for finding optimal solutions of various optimization problems. A branch-and-bound algorithm consists of a systematic calculation of all candidate solutions.
- 19. A brute force algorithm simply tries all possibilities until a satisfactory solution is found - Such an algorithm can be: Optimizing - Example: Finding the best path for a travelling salesman Satisfying - Example: Finding a travelling salesman path that is within 10% of optimal
- 20. A randomized algorithm uses a random number at least once during the computation to make a decision Example: In Quicksort, using a random number to choose a pivot Example: Trying to factor a large prime by choosing random numbers as possible divisors