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Graph

Single Source Shortest Path(SSSP)

  1. BFS: O(V+E)
  2. Dijkstra[Using Priority Queue(Best)]: O((V+E)logV)
  3. Dijkstra[Using set(when update is required)]: O((V+E)logV)
  4. Bellman-Ford: O(VE)

All Pair Shortest Path

  1. Floyd-Warshall: O(N^3)

Topological Sort

  1. Topological sort[Using BFS]
  2. Topological sort[Using DFS]
  3. Questions:
    1. https://codeforces.com/problemset/problem/825/E

Disjoint Set (Union-Find) Data Structure

  1. DSU using size
  2. DSU using rank

Problems:

  1. city and flood
  2. city and campers
  3. city and fireman vincent
  4. city and soldiers
  5. city and campers 2
  6. colourful array Nice problem🔥🔥🤯🤯
  7. Remove Max Number of Edges to Keep Graph Fully Traversable

Cycle Detection

  1. Khan's Algorithm[BFS for topological sort]: It only works for Directed Graph.
  2. Union-Find Method: Uses the Union-Find data structure to detect cycles during the union operation. It only works for an Un-Directed Graph
  3. DFS Method: Uses depth-first search to detect back edges. It works for both.

Minimum Spanning Tree(MST)

  1. Prim's Algo
  2. Cruskal's Algo

Strongly connected components(scc) -> Kosaraju Algo: follow three steps:

  1. Sort the nodes on the basis of finishing time of dfs.
  2. Reverese the edges
  3. Run the dfs on nodes in their sorted finishing time.
  4. Code

Problem Patterns

  1. Graph Coloring

Monotonic Stack Resource:

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