dsa2 min read
Bellman-Ford — SSSP with Negative Edges and Cycle Detection
Compute single-source shortest paths in graphs with negative weight edges using Bellman-Ford. V-1 relaxation passes detect negative cycles on the Vth pass.
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A* Search — Heuristic Shortest Path for Grid Problems
A* combines Dijkstra's correctness with a heuristic to guide search toward the goal. Uses f(n)=g(n)+h(n) priority. Optimal when heuristic is admissible.
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Topological Sort — Advanced Applications (DFS, Kahn, Cycle Detection)
Advanced topological sort: DFS-based with 3-color marking for cycle detection, Kahn's BFS approach, and applications in course scheduling, build systems, and task ordering.
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Dijkstra Advanced — Modified Dijkstra Patterns (K Stops, States, Constraints)
Advanced Dijkstra patterns: state-space Dijkstra for problems with extra constraints like K stops, fuel limit, or restricted nodes. The key is augmenting the state beyond just the node.
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Graph Coloring and Bipartite Check
Check if a graph is bipartite using BFS 2-coloring. A graph is bipartite if and only if it contains no odd-length cycles — equivalent to being 2-colorable.
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