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The article discusses various algorithms for finding the shortest path in graphs, focusing on different scenarios based on edge weights. It explains the use of BFS for unweighted graphs, Dijkstra's algorithm for non-negative weights, and Bellman-Ford for graphs with negative weights. Additionally, it highlights common pitfalls and when to apply each algorithm effectively.
- ▪BFS is used for unweighted graphs where every edge has the same cost.
- ▪Dijkstra's algorithm is suitable for graphs with non-negative edge weights.
- ▪Bellman-Ford is applicable when edge weights can be negative or for cycle detection.
Opening excerpt (first ~120 words) tap to expand
/ library›shortest-pathShortest Path01 / The shared mechanismFind the shortest route from a source to every other node. The mechanism splits by what the edges carry — uniform costs collapse to BFS, non-negative weights need a priority queue (Dijkstra), negatives demand relaxation rounds (Bellman-Ford), and full transit tables fall to Floyd-Warshall.01Unweighted BFS02Dijkstra03Bellman − Ford04Floyd − Warshall02 / The one-sentence essenceWhen every edge costs the same, the first time you reach a node is the shortest way to reach it — so BFS, which visits nodes in increasing order of step-count, doubles as a shortest-path algorithm.animationcomplexity Problemshortest path from source on an unweighted graphGraphmeshSourceA?A∞B∞C∞D∞E∞F∞Graph has 6 nodes.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at Algorhythm.