# Graph Data Structure And Algorithms

**Introduction, DFS and BFS:**

- Graph and its representations
- Breadth First Traversal for a Graph
- Depth First Traversal for a Graph
- Applications of Depth First Search
- Applications of Breadth First Traversal
- Longest Path in a Directed Acyclic Graph
- Find Mother Vertex in a Graph
- Transitive Closure of a Graph using DFS
- Find K cores of an undirected Graph
- Iterative Depth First Search
- Count the number of nodes at given level in a tree using BFS
- Count all possible paths between two vertices
- Minimum initial vertices to traverse whole matrix with given conditions
- Shortest path to reach one prime to other by changing single digit at a time
- Water Jug problem using BFS
- Magical Indices in an array
- Count number of trees in a forest
- BFS using vectors & queue as per the algorithm of CLRS
- Level of Each node in a Tree from source node
- Construct binary palindrome by repeated appending and trimming
- Iterative Deepening Search(IDS) or Iterative Deepening Depth First Search(IDDFS)

- Dijkstra’s shortest path algorithm
- Dijkstra’s Algorithm for Adjacency List Representation
- Bellman–Ford Algorithm
- Floyd Warshall Algorithm
- Johnson’s algorithm for All-pairs shortest paths
- Shortest Path in Directed Acyclic Graph
- Some interesting shortest path questions,
- Shortest path with exactly k edges in a directed and weighted graph
- Dial’s Algorithm
- Printing paths in Dijsktra’s Algorithm
- Shortest path of a weighted graph where weight is 1 or 2

- Find if there is a path between two vertices in a directed graph
- Connectivity in a directed graph
- Articulation Points (or Cut Vertices) in a Graph
- Biconnected graph
- Bridges in a graph
- Eulerian path and circuit
- Fleury’s Algorithm for printing Eulerian Path or Circuit
- Strongly Connected Components
- Transitive closure of a graph
- Find the number of islands
- Count all possible walks from a source to a destination with exactly k edges
- Euler Circuit in a Directed Graph
- Biconnected Components
- Count the number of non-reachable nodes
- Find the Degree of a Particular vertex in a Graph
- Check if a given graph is tree or not
- Karger’s algorithm for Minimum Cut
- Eulerian Path in undirected graph
- Find if there is a path of more than k length
- Length of shortest chain to reach the target word
- Print all paths from a given source to destination
- Find minimum cost to reach destination using train
- Tarjan’s Algorithm to find strongly connected Components

- Graph Coloring (Introduction and Applications)
- Greedy Algorithm for Graph Coloring
- Travelling Salesman Problem (Naive and Dynamic Programming)
- Travelling Salesman Problem (Approximate using MST)
- Hamiltonian Cycle
- Vertex Cover Problem | Set 1 (Introduction and Approximate Algorithm)
- K Centers Problem | Set 1 (Greedy Approximate Algorithm)

- Ford-Fulkerson Algorithm for Maximum Flow Problem
- Find maximum number of edge disjoint paths between two vertices
- Find minimum s-t cut in a flow network
- Maximum Bipartite Matching
- Channel Assignment Problem
- Push Relabel- Set 1-Introduction
- Push Relabel- Set 2- Implementation
- Karger’s Algorithm- Set 1- Introduction and Implementation
- Karger’s Algorithm- Set 2 – Analysis and Applications

**STL Implementation of Algorithms**

- Number of triangles in an undirected Graph
- Number of triangles in directed and undirected Graph
- Check whether a given graph is Bipartite or not
- Snake and Ladder Problem
- Minimize Cash Flow among a given set of friends who have borrowed money from each other
- Boggle (Find all possible words in a board of characters)
- Hopcroft Karp Algorithm for Maximum Matching-Introduction
- Hopcroft Karp Algorithm for Maximum Matching-Implementation
- Minimum Time to rot all oranges
- Construct binary palindrome by repeated appending and trimming
- Find same contents in a list of contacts
- Hypercube Graph
- Check for star graph
- Optimal read list for a given number of days
- Print all jumping numbers smaller than or equal to a given value

**Quizzes on** Graph Traversals , Graph Shortest Paths , Graph Minimum Spanning Tree

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