Blog 1: Graph Fundamentals & Representations
- Adjacency List, Adjacency Matrix, Edge List.
- Directed vs Undirected, Weighted vs Unweighted.
- BFS/DFS basics on graphs.
- Snippet: build graph in Java using adjacency list.
Blog 2: BFS Pattern (Level Order, Shortest Path in Unweighted Graphs)
- BFS traversal explained.
- Shortest path in unweighted graph.
- Classic Problems: Rotten Oranges, Word Ladder, Minimum Steps in Grid.
- Snippet: BFS with queue.
Blog 3: DFS Pattern (Path Exploration, Connectivity, Components)
- DFS recursive & iterative.
- Connected components.
- Detecting cycles with DFS.
- Problems: Number of Islands, Graph Coloring.
- Snippet: DFS recursion & stack-based.
Blog 4: Topological Sort & DAG Problems
- Kahn’s Algorithm (BFS).
- DFS-based topological ordering.
- Problems: Course Schedule, Task Scheduling.
- Snippet: Topo sort with indegree array.
Blog 5: Shortest Path Algorithms
- BFS (unweighted).
- Dijkstra’s (weighted, positive).
- Bellman-Ford (handles negative edges).
- Floyd-Warshall (all pairs).
- Problems: Network Delay Time, Cheapest Flights with K Stops.
Blog 6: Minimum Spanning Tree (MST)
- Kruskal’s (Union-Find).
- Prim’s (Min Heap).
- Applications: Network design, clustering.
- Problems: Connecting Cities with Minimum Cost.
Blog 7: Union-Find / Disjoint Set Pattern
- DSU implementation.
- Path compression & union by rank.
- Detect cycle in undirected graph.
- Problems: Redundant Connection, Accounts Merge.
Blog 8: Strongly Connected Components & Bridges/Articulation Points
- Kosaraju’s algorithm.
- Tarjan’s algorithm (low-link values).
- Bridges in graph (critical connections).
- Problems: Critical Connections in Network, SCC counting.
Blog 9: Advanced Graph Patterns (Flow, Matching, Bipartite)
- Bipartite check with BFS/DFS.
- Max Flow (Ford-Fulkerson, Edmonds-Karp).
- Bipartite Matching.
- Problems: Maximum Bipartite Matching, Water Distribution.
Blog 10: Advanced Graph Tricks & Real-World Applications
⚡ By the end, you’ll have a Graph Pattern Playbook like we built for backtracking — covering all traversals, connectivity, shortest paths, MST, SCC, Union-Find, and advanced flow problems.
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