Understanding Algorithms: Sorting, Graph, Greedy, Dynamic Programming, and Searching

Study Notes

Understanding Algorithms: Sorting, Graph, Greedy, Dynamic Programming, and Searching

An algorithm is a finite sequence of well-defined, computer-implementable instructions, typically to solve a class of problems or to perform a computation. They come in various forms, each designed to tackle specific problems effectively. Here, we explore five major categories of algorithms: sorting, graph, greedy, dynamic programming, and searching.

Sorting Algorithms

Sorting algorithms are used to arrange elements in ascending order. Some popular examples are:

Selection Sort: Iteratively select the smallest element and swap it with the largest unsorted element until all elements are sorted.
Insertion Sort: Iteratively insert elements into a sorted list while maintaining the list in sorted order.
Quick Sort: Divide the array into two parts by choosing a pivot and swapping elements accordingly.
Merge Sort: Splitting the unordered list into smaller lists, comparing those lists recursively until combining them into a single, sorted list.

Graph Algorithms

These algorithms are designed to analyze graphs, which are sets of nodes and edges connecting pairs of nodes. Common graph algorithms include:

Breadth First Search (BFS): Traverses each node in breadth order.
Depth First Search (DFS): Traverses depth order, exploring all paths of a node before proceeding to the next node.
Minimum Spanning Tree: Connects vertices without cycles using the minimum possible edge length.

Greedy Algorithms

Greedy algorithms make the locally optimal choice at each stage, hoping to find a global optimum. Examples include:

Dijkstra's Shortest Path Algorithm: Calculates the shortest path between two points in a weighted graph.
Floyd-Warshall Algorithm: Determines the shortest route between every pair of vertices in a graph.
Prim's Algorithm: Constructs a minimum spanning tree.

Dynamic Programming Algorithms

Dynamic programming algorithms involve breaking down a problem into smaller, overlapping subproblems, solving each subproblem once, and reusing these solutions to solve larger problems. Key dynamic programming algorithms include:

Top-Down Tabulation Method: Breaks a problem into smaller subproblems and solves them recursively.
Bottom-Up Memoization Method: Solves a problem step-by-step and stores intermediary solutions to avoid redundant calculations.

Searching Algorithms

Searching algorithms help locate specific values or items within an ordered collection. Noteworthy search algorithms are:

Linear Search: Sequentially searches through a list for a desired value.
Binary Search: Halves the search space at each step by eliminating half of the remaining possibilities until finding the target.

Description

Explore the fundamental concepts of sorting, graph theory, greedy algorithms, dynamic programming, and searching. Learn about popular algorithms like Selection Sort, Breadth First Search, Dijkstra's Shortest Path Algorithm, and Binary Search.