Algorithms are step-by-step procedures or formulas for solving problems. They are fundamental to computer science and are used in a variety of applications, from basic calculations to complex data analysis. Here’s an overview of key concepts and types of algorithms:

Key Concepts

1. Input: The data or parameters the algorithm receives to process.
2. Output: The result produced by the algorithm after processing the input.
3. Efficiency: Often measured in terms of time (how fast it runs) and space (how much memory it uses). This is commonly analyzed using Big O notation.
4. Correctness: An algorithm is correct if, for every input, it produces the correct output.
5. Deterministic vs. Non-deterministic: Deterministic algorithms produce the same output for the same input every time, while non-deterministic algorithms might produce different outputs for the same input.

Types of Algorithms

1. Sorting Algorithms: Arrange data in a specific order.
   • Bubble Sort: Simple but inefficient; compares adjacent elements and swaps them if they are in the wrong order.
   • Merge Sort: Efficient; divides the array into halves, sorts them, and merges them back together.
   • Quick Sort: Efficient; selects a pivot element and partitions the array around it, then recursively sorts the partitions.
2. Search Algorithms: Find specific elements within data structures.
   • Linear Search: Checks each element in the array until it finds the target.
   • Binary Search: Efficient for sorted arrays; repeatedly divides the array in half to find the target.
3. Graph Algorithms: Operate on graph structures (nodes and edges).
   • Dijkstra’s Algorithm: Finds the shortest path from a starting node to all other nodes in a weighted graph.
   • A Algorithm*: Similar to Dijkstra’s but uses heuristics to improve efficiency for pathfinding.
   • Breadth-First Search (BFS): Explores all neighbors at the present depth level before moving on to nodes at the next depth level.
   • Depth-First Search (DFS): Explores as far down a branch as possible before backtracking.

Dynamic Programming: Solves problems by breaking them down into simpler subproblems and storing the results to avoid redundant computations.

• Fibonacci Sequence: A classic example where the nth Fibonacci number is the sum of the two preceding ones.
• Knapsack Problem: Finds the most valuable combination of items without exceeding a weight limit.

Greedy Algorithms: Make the locally optimal choice at each step with the hope of finding a global optimum.

• Huffman Coding: Constructs an optimal prefix-free binary tree for data compression.
• Prim’s Algorithm: Finds a minimum spanning tree for a weighted undirected graph.