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DSA
DSA/Graph Algorithms

Graph Algorithms

A premium, interview-focused graph course. Every problem teaches the pattern first, then the algorithm, then a clean Java 17 implementation — with dry runs and interview guidance. You will progress from modelling a grid as a graph all the way to advanced techniques like union-find, Dijkstra, and articulation points.

25

Curated lessons

10

Learning modules

9h 38m

Est. study time

11

Target companies

What you'll learn

  • Model grids, matrices, and relationships as graphs and traverse them with DFS and BFS.
  • Choose the right shortest-path tool for the edge weights: BFS, Dijkstra, or Bellman-Ford.
  • Apply union-find with path compression for near-constant-time grouping and cycle detection.
  • Recognise topological-sort, bipartite, and advanced-graph patterns under interview pressure.

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problems completed

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Learning roadmap

Work top to bottom — each module builds on the last.

  1. 1

    Graph Traversal

    DFS / BFS over grids and adjacency lists

    The foundation: model a grid or adjacency list as a graph and visit every node exactly once with DFS or BFS.

    5/5 problems1h 27m
  2. 2

    Connected Components

    Component counting with DFS or Union-Find

    Count and group nodes that are reachable from one another — the first place Union-Find competes with DFS/BFS.

    3/3 problems1h 3m
  3. 3

    Cycle Detection

    Cycle detection via Union-Find / DFS parent tracking

    Decide whether an undirected graph contains a cycle — the core check behind trees, forests, and safe merges.

    2/2 problems35m
  4. 4

    Topological Sort

    Kahn's BFS / DFS topological ordering

    Order the nodes of a DAG so every edge points forward — the dependency-resolution pattern interviewers love.

    4/4 problems1h 35m
  5. 5

    Union Find

    Disjoint Set Union (path compression + union by rank)

    Disjoint Set Union with path compression and union by rank — near-constant-time grouping and equivalence.

    3/3 problems1h 3m
  6. 6

    Shortest Path

    BFS / Dijkstra / Bellman-Ford shortest paths

    From unweighted BFS to Dijkstra and Bellman-Ford — pick the right shortest-path tool for the edge weights.

    4/4 problems1h 59m
  7. 7

    Minimum Spanning Tree

    Minimum Spanning Tree (Prim / Kruskal)

    Connect every node at minimum total cost with Prim's or Kruskal's algorithm.

    1/1 problems30m
  8. 8

    Grid Graphs

    Multi-source BFS on grids

    Multi-source BFS on a grid — spreading fronts, distances, and simultaneous starts.

    1/1 problems22m
  9. 9

    Bipartite Graph

    2-colouring with BFS / DFS

    Two-colour a graph to prove it has no odd cycle — conflict-free partitioning.

    1/1 problems24m
  10. 10

    Advanced Graphs

    Tarjan's bridges (DFS discovery + low-link)

    Tarjan's bridges and articulation points — the discovery-time / low-link technique for critical edges.

    1/1 problems40m

Modules

10 themed modules from fundamentals to advanced.

1

Graph Traversal

The foundation: model a grid or adjacency list as a graph and visit every node exactly once with DFS or BFS.

5/5 problems1h 27m
0%
2

Connected Components

Count and group nodes that are reachable from one another — the first place Union-Find competes with DFS/BFS.

3/3 problems1h 3m
0%
3

Cycle Detection

Decide whether an undirected graph contains a cycle — the core check behind trees, forests, and safe merges.

2/2 problems35m
0%
4

Topological Sort

Order the nodes of a DAG so every edge points forward — the dependency-resolution pattern interviewers love.

4/4 problems1h 35m
0%
5

Union Find

Disjoint Set Union with path compression and union by rank — near-constant-time grouping and equivalence.

3/3 problems1h 3m
0%
6

Shortest Path

From unweighted BFS to Dijkstra and Bellman-Ford — pick the right shortest-path tool for the edge weights.

4/4 problems1h 59m
0%
7

Minimum Spanning Tree

Connect every node at minimum total cost with Prim's or Kruskal's algorithm.

1/1 problems30m
0%
8

Grid Graphs

Multi-source BFS on a grid — spreading fronts, distances, and simultaneous starts.

1/1 problems22m
0%
9

Bipartite Graph

Two-colour a graph to prove it has no odd cycle — conflict-free partitioning.

1/1 problems24m
0%
10

Advanced Graphs

Tarjan's bridges and articulation points — the discovery-time / low-link technique for critical edges.

1/1 problems40m
0%

Full curriculum

25 problems and 0 concept lessons in learning order.

Techniques you'll master

BFSBellman-FordBinary SearchBridgeColoringCombinatoricsDFSDSUDijkstraGeometryGraphHash TableHeapLow LinkMatrixMinimum Spanning TreeQueueShortest PathSimulationSortingStringTarjanTopological SortUnion Find