Graph Data Structure

Graph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities.

If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms.

Basics of Graph:

• Introduction to Graphs
• Graph and its representations
• Transpose graph

Easy Problems

• Breadth First Traversal for a Graph
• Depth First Traversal for a Graph
• Shortest path in an unweighted graph
• 0-1 BFS (Shortest Path in a Binary Weight Graph)
• Count number of trees in a forest
• Topological Sorting
• All topological sorts of a Directed Acyclic Graph
• Kahn’s Algorithm for Topological Sorting
• Sum of dependencies in a graph
• Maximum Weight Node

Medium Problems

• Transitive Closure of a Graph using DFS
• Rotten Tomatoes
• Islands in a Graph
• Flood Fill
• Check for Bipartite
• Word Ladder
• Snakes and Ladder
• Water Jug problem
• Shortest Path in Binary Matrix
• Clone a Graph
• Detect Cycle in a Directed Graph
• Detect cycle in an Undirected graph
• Detect a negative cycle in a Graph | (Bellman Ford)
• Cycles of length n in an undirected and connected graph
• Detecting negative cycle using Floyd Warshall
• Clone a Directed Acyclic Graph
• Introduction to Disjoint Set Data Structure or Union-Find Algorithm
• Union By Rank and Path Compression in Union-Find Algorithm
• Dijkstra’s shortest path algorithm
• Bellman–Ford Algorithm
• Floyd Warshall Algorithm
• Johnson’s algorithm for All-pairs shortest paths
• Multistage Graph (Shortest Path)
• Karp’s minimum mean (or average) weight cycle algorithm
• Find minimum weight cycle in an undirected graph
• Prim’s Minimum Spanning Tree (MST)
• Kruskal’s Minimum Spanning Tree Algorithm
• Difference between Prim’s and Kruskal’s algorithm for MST
• Applications of Minimum Spanning Tree Problem
• Minimum cost to connect all cities
• Minimum Product Spanning Tree
• Reverse Delete Algorithm for Minimum Spanning Tree
• Boruvka’s algorithm for Minimum Spanning Tree
• Maximum edges that can be added to DAG so that is remains DAG
• Longest Path in a Directed Acyclic Graph
• Topological Sort of a graph using departure time of vertex
• Find Itinerary from a given list of tickets
• Eulerian path and circuit
• Fleury’s Algorithm for printing Eulerian Path or Circuit
• Strongly Connected Components
• Count all possible walks from a source to a destination with exactly k edges
• Euler Circuit in a Directed Graph
• Paths to travel each nodes using each edge (Seven Bridges of Königsberg)
• Length of shortest chain to reach the target word
• Dynamic Connectivity | Set 1 (Incremental)
• Max Flow Problem Introduction
• Ford-Fulkerson Algorithm for Maximum Flow Problem
• Find maximum number of edge disjoint paths between two vertices
• Maximum Bipartite Matching
• Channel Assignment Problem
• Karger’s Algorithm- Set 1- Introduction and Implementation
• Dinic’s algorithm for Maximum Flow
• Find length of the largest region in Boolean Matrix
• A Peterson Graph Problem
• Clone an Undirected Graph
• Graph Coloring (Introduction and Applications)
• Erdos Renyl Model (for generating Random Graphs)
• Chinese Postman or Route Inspection | Set 1 (introduction)
• Hierholzer’s Algorithm for directed graph
• Check whether a given graph is Bipartite or not
• Snake and Ladder Problem
• Boggle (Find all possible words in a board of characters)
• Hopcroft Karp Algorithm for Maximum Matching-Introduction
• Minimum Time to rot all oranges
• Construct a graph from given degrees of all vertices
• Determine whether a universal sink exists in a directed graph
• Number of sink nodes in a graph
• Two Clique Problem (Check if Graph can be divided in two Cliques)

Hard Problems

• Pacific Atlantic Water Flow
• Total number of Spanning Trees in a Graph
• Longest Path in a Directed Acyclic Graph
• Bridges in a graph
• Articulation Points (or Cut Vertices) in a Graph
• Biconnected Components
• Find if an array of strings can be chained to form a circle
• Tarjan’s Algorithm to find strongly connected Components
• Find minimum s-t cut in a flow network
• Traveling Salesman Problem (TSP) Implementation
• Vertex Cover Problem | Set 1 (Introduction and Approximate Algorithm)
• K Centers Problem | Set 1 (Greedy Approximate Algorithm)