dsa2 min read
Kruskal's Algorithm — Minimum Spanning Tree with Union-Find
Find the minimum spanning tree of a weighted graph using Kruskal's algorithm. Sort edges by weight, use Union-Find to avoid cycles. O(E log E) time.
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Prim's Algorithm — MST via Min-Heap Greedy Expansion
Build the minimum spanning tree using Prim's algorithm: start from any vertex, greedily expand by always adding the minimum-weight crossing edge using a min-heap.
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Tarjan's Algorithm — Strongly Connected Components
Find all strongly connected components in a directed graph using Tarjan's single-pass DFS algorithm with discovery time, low-link values, and a stack.
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Bridges and Articulation Points — Graph Vulnerability Detection
Find all bridge edges and articulation point vertices in an undirected graph using a single DFS pass with discovery time and low-link tracking.
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Floyd-Warshall — All-Pairs Shortest Path
Compute shortest paths between all pairs of vertices using Floyd-Warshall's O(V³) DP. Handles negative weights and detects negative cycles.
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