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Graph Algorithms

27 problems·~12h·4 stages

Networks traversed properly: BFS, DFS, shortest paths, MSTs, PageRank, and max flow. You will implement Dijkstra, Kruskal, Kosaraju-style components, centrality measures, and matching from scratch. Great preparation for both interviews and data-centric engineering work.

Your progress

0/27 · 0%

Path readiness 0%Easy 0% · Medium 0% · Hard 0%

Continue path · Adjacency List Build

What you will learn

  • Represent graphs as lists and matrices and traverse them breadth- and depth-first
  • Find shortest paths and minimum spanning trees
  • Compute centrality, PageRank, and bipartite matchings
  • Handle bridges, strongly connected components, and max flow

Before you start

1Representations and Traversal

0/8

Build adjacency lists and matrices, then walk the graph: BFS order, iterative DFS, connected components, density, degree centrality, and a PageRank sweep.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
SimulationRecommended next stepDijkstra Step-Through

2Paths and Spanning Trees

0/7

Connectivity with cost: cycle detection, Kahn's topological order, BFS shortest paths, Dijkstra with a heap, Prim, Kruskal, and course scheduling.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
SimulationRecommended next stepDijkstra Step-Through

3Centrality and Matching

0/6

Rank nodes and pair them: PageRank to tolerance, closeness, Brandes betweenness, eigenvector centrality, augmenting paths, and maximum bipartite matching.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
SimulationRecommended next stepDijkstra Step-Through

4Robustness and Flow

0/6

Cuts, components, and capacity: articulation points, bridges, Kosaraju SCCs, edge betweenness, Ford-Fulkerson max flow, and negative-cycle path extraction.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
SimulationRecommended next stepDijkstra Step-Through

Capstone

Contest

Close the path with one real artifact from the catalog.

Graph Gauntlet

Build, traverse, and hunt cycles in a timed pass over the graph core.