"In mathematics and computer science, an algorithm is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation."
The methods and strategies used to solve computational problems, such as sorting, searching, and graph traversal.
Data Structures: The organization and storage of data in a computer's memory, including arrays, linked lists, trees, and graphs.
Sorting Algorithms: The process of arranging a list of items in a certain order, like alphabetical or numerical.
Searching Algorithms: The process of finding a specific item within a data structure.
Time Complexity Analysis: Measuring the amount of time an algorithm takes to execute as a function of its input size.
Space Complexity Analysis: Measuring the amount of memory an algorithm uses as a function of its input size.
Dynamic Programming: An optimization strategy for solving complex problems by breaking them down into smaller subproblems and solving each subproblem only once.
Divide and Conquer: A strategy for solving a problem by breaking it down into smaller subproblems that are easier to solve independently.
Greedy Algorithms: An algorithmic paradigm that follows the problem-solving heuristic of making the locally optimal choice at each stage with the hope of finding a global optimum.
Backtracking Algorithms: A general algorithmic technique for solving problems by incrementally building candidate solutions and using the information gathered so far to unbuild the candidate as soon as it becomes clear it cannot lead to a valid solution.
Graph Algorithms: Algorithms that operate on graphs, which are mathematical structures used to model pairwise relations between objects.
Optimization Problems: A problem in which the goal is to find the best solution among a set of possible solutions.
Simulation Algorithms: The process of creating an artificial world or system that simulates a real-world system.
Cryptographic Algorithms: Algorithms used for encrypting, decrypting, and securing data.
Network Algorithms: Algorithms used for managing and routing different types of networks, including computer networks and social networks.
Machine Learning Algorithms: Algorithms used for training and testing machine learning models, including decision trees, neural networks, and support vector machines.
Sorting Algorithms: These are used to arrange data in ascending or descending order. Examples include Bubble Sort, Quick Sort, and Merge Sort.
Searching Algorithms: These are used to search for a specific data item in a collection of data. Examples include Linear Search and Binary Search.
Graph Algorithms: These are used to represent problems in the form of graphs and solve problems related to graph theory. Examples include Breadth-First Search, Depth-First Search, and Dijkstra's Algorithm.
Dynamic Programming Algorithms: These are used to solve complex problems by breaking them down into sub-problems and solving them separately. Examples include the Fibonacci series algorithm and the Knapsack problem.
Backtracking Algorithms: These are used to solve problems by generating all possible solutions and choosing the best one. Examples include the N-Queens problem and Sudoku solving algorithms.
Greedy Algorithms: These are used to make optimal choices based on the current best option without considering the future. Examples include Huffman coding and Kruskal's Algorithm.
Divide and Conquer Algorithms: These are used to break down a problem into smaller sub-problems that are easier to solve. Examples include the Merge Sort algorithm and the Binary Search algorithm.
Randomized Algorithms: These are used to randomly generate solutions to problems. Examples include Quicksort and Monte Carlo Simulation.
Genetic Algorithms: These are used to solve optimization problems by mimicking the process of natural selection. Examples include the Traveling Salesman Problem and Machine Learning models.
Algorithmic Game Theory: These are used to model and analyze strategic interactions in multi-agent systems. Examples include Auction Algorithms and Nash Equilibrium algorithms.
"Algorithms are used as specifications for performing calculations and data processing."
"In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results."
"Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as 'memory,' 'search,' and 'stimulus'."
"More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually."
"As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function."
"Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing 'output' and terminating at a final ending state."
"The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input." I have provided eight study questions along with relevant quotes from the paragraph. If you need additional questions or quotes, please let me know.