"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."
An overview of what algorithms and data structures are, why they are important, and the fundamental concepts associated with them.
Algorithm Design and Analysis: This involves the design of efficient algorithms and analyzing their time and space complexity.
Sorting Algorithms: Sorting algorithms are an essential topic to learn about. They include Bubble Sort, Insertion Sort, Selection Sort, Merge Sort, Quick Sort, and Heap Sort.
Searching Algorithms: Searching algorithms enable you to find a specific item in a collection of data, including Linear Search, Binary Search, and Interpolation Search.
Data Structures: Data structures are used to organize, store, and retrieve data efficiently. Examples include arrays, linked lists, stacks, queues, trees, and graphs.
Dynamic Programming: This method of solving problems utilizes previously solved subproblems to solve progressively larger problems, eliminating repetitive computations.
Divide and Conquer: This strategy involves breaking down a problem into smaller sub-problems, solving them, and then combining results to solve the original problem.
Greedy Algorithms: These algorithms make locally optimal choices at each step, hoping to find the global optimum.
Hash Tables: Hash tables offer fast retrieval and insertion of data, making them useful in many practical applications.
Graph Algorithms: Graph algorithms are essential for modeling and analyzing a variety of real-world problems, including shortest path algorithms, minimum spanning trees, and network flow algorithms.
String Algorithms: These include pattern matching algorithms, parsing algorithms, and compression algorithms.
Computational Complexity Theory: This topic studies the computational complexity of algorithms and problems, including the P vs. NP problem.
Recursion: Recursion is a technique used in algorithms where a function calls itself to solve a problem by reducing it to one or more simpler subproblems.
Backtracking Algorithms: These algorithms involve a trial-and-error approach to solving problems, examining potential solutions and "backtracking" when the solution does not work well.
Bit Manipulation: This refers to manipulating individual bits to solve problems, optimize storage and computations, and enhance security.
Sorting Algorithms: Sorting Algorithms are used to arrange the given data in a particular order.
Searching Algorithms: Searching Algorithms are used to find a particular element within a given dataset.
Greedy Algorithms: Greedy Algorithms are used to find the optimal solution for a problem that involves making a sequence of decisions.
Dynamic Programming Algorithms: Dynamic Programming Algorithms are used to solve complex problems by breaking them down into manageable subproblems.
Backtracking Algorithms: Backtracking Algorithms are used to find all possible solutions to a given problem by incrementally building candidates to the solutions.
Divide and Conquer Algorithms: Divide and Conquer Algorithms are used to solve a problem by dividing it into two or more subproblems of the same or related type.
Graph Algorithms: Graph Algorithms are used to work with graphs, i.e., sets of vertices and edges that connect them.
String Algorithms: String Algorithms are used to work with strings, i.e., sequences of characters.
Geometric Algorithms: Geometric Algorithms are used to solve mathematical problems related to geometry.
Numerical Algorithms: Numerical Algorithms are used to solve mathematical problems that involve the manipulation of numbers.
"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.