📄️ Basics of Graph
Graph theory is a mathematical discipline that studies the properties and relationships of graphs, which consist of nodes (vertices) connected by edges, enabling analysis of various real-world systems and phenomena.
📄️ Breadth First Search
Breadth-first search (BFS) is a fundamental graph traversal algorithm widely used in Artificial Intelligence (AI) for finding the shortest path between nodes in a graph. BFS explores all vertices at the present depth level before moving on to vertices at the next depth level, ensuring that the shortest path to each vertex is discovered first. This characteristic makes BFS particularly useful in AI applications where optimal solutions are required. For example, in navigation systems like Google Maps, BFS is employed to determine the shortest route between two locations. When a user inputs a starting point and a destination, BFS calculates the shortest path by systematically exploring all possible routes and selecting the one with the minimum number of steps or distance. Another concrete example is in social network analysis, where BFS can be used to find the shortest connection path between two individuals, helping to identify degrees of separation and influential nodes within the network. Additionally, BFS is utilized in AI for solving puzzles and games, such as the shortest path to solve a maze or the optimal sequence of moves in board games. Overall, BFS is a powerful tool in AI for efficiently solving problems that require finding the shortest path in complex graphs.
📄️ Depth First Search
Depth-first search (DFS) is a crucial graph traversal algorithm that explores as far as possible along each branch before backtracking. This depth-wise exploration makes DFS particularly effective for tasks such as topological sorting, cycle detection, and solving puzzles. Topological sorting is used to order tasks based on dependencies, ensuring that prerequisite tasks are completed first. For example, in project management software, DFS can help determine the sequence of tasks to optimize workflow. Cycle detection is another important application, where DFS identifies cycles in graphs, which is essential for detecting deadlocks in operating systems or circular dependencies in software packages. Additionally, DFS is employed in solving puzzles with a unique solution, such as mazes or Sudoku. By systematically exploring all possible paths, DFS can find the correct sequence of moves to solve the puzzle.