Day 21: Shortest Path Algorithms
Shortest Path Algorithms #
Welcome to Day 21 of our 60 Days of Coding Algorithm Challenge! Today, we’ll dive into shortest path algorithms, focusing on two fundamental algorithms: Dijkstra’s Algorithm and the Bellman-Ford Algorithm. These algorithms are crucial for solving problems involving finding the most efficient path between nodes in a graph.
Introduction to Shortest Path Problems #
The shortest path problem is about finding a path between two vertices in a graph such that the sum of the weights of its constituent edges is minimized. This problem has numerous real-world applications, including:
- GPS Navigation systems
- Network routing protocols
- Flight itinerary planning
- Robot motion planning
Dijkstra’s Algorithm #
Dijkstra’s algorithm finds the shortest path from a single source vertex to all other vertices in a weighted graph with non-negative edge weights.
Algorithm: #
- Initialize distances to all vertices as infinite and distance to the source as 0.
- Create a set of unvisited vertices.
- For the current vertex, consider all its unvisited neighbors and calculate their tentative distances.
- When we are done considering all …
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