The Math Behind Your Commute
Deep Dives
Explore related topics with these Wikipedia articles, rewritten for enjoyable reading:
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Dijkstra's algorithm
10 min read
The article discusses pathfinding algorithms for navigation apps. Dijkstra's algorithm is the foundational weighted graph algorithm that modern GPS and routing systems build upon, extending beyond the unweighted BFS/DFS covered in the article.
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Seven Bridges of Königsberg
12 min read
This is the historical problem that founded graph theory itself. Since the article introduces graph traversal concepts, readers would benefit from understanding how Euler's solution to this 1736 puzzle created the mathematical field underlying all modern routing algorithms.
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A* search algorithm
12 min read
The article mentions that 'modern-day apps are much more sophisticated' than basic BFS/DFS. A* is the specific algorithm that powers most real-world navigation systems, combining Dijkstra's approach with heuristics—the natural next step for curious readers.
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In the modern world, we are used to technology telling us how to travel from our current position to places we have never been. It usually lets us know several ways to get there, including the fastest or cheapest.
In today’s post, I want to present the two most basic algorithms used in real-life scenarios that support a massive part of what our current delivery, location, and transportation services use. Though the mechanisms used in modern-day apps are much more sophisticated, they stand on the shoulders of these two basic but effective methods.
In order, this is our agenda for today:
🍞 Breadth-First Search — a graph traversal that simulates how you would explore a new city.
🥖 Depth-First Search — a graph traversal that would allow you to escape from any maze.
🥞 Connected Components — a graph term to call your hometown if you knew how to get to any place from any location.
Given a graph G = (V, E) and two vertices s and t, the goal is to determine whether there exists a path that starts at s and ends at t. This problem is known as the connectivity problem.
Below are two algorithms for naturally solving this problem: Breadth-First Search and ...
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