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Category Archives: Graph

A Bipartite Graph is a graph whose vertices can be divided into two independent sets, U and V such that every edge (u, v) either… Read More
Given a directed graph, find out if a vertex j is reachable from another vertex i for all vertex pairs (i, j) in the given… Read More
Given a graph and a source vertex src in graph, find shortest paths from src to all vertices in the given graph. The graph may… Read More
We recommend reading the following two posts as a prerequisite of this post.1. Greedy Algorithms | Set 7 (Dijkstra’s shortest path algorithm) 2. Graph and its representationsWe… Read More
  Given a graph and a source vertex in the graph, find the shortest paths from the source to all vertices in the given graph.Dijkstra’s… Read More
We recommend to read following two posts as a prerequisite of this post.1. Greedy Algorithms | Set 5 (Prim’s Minimum Spanning Tree (MST)) 2. Graph and… Read More
  We have discussed Kruskal’s algorithm for Minimum Spanning Tree. Like Kruskal’s algorithm, Prim’s algorithm is also a Greedy algorithm. It starts with an empty spanning tree.… Read More
A graph is a data structure that consists of the following two components: 1. A finite set of vertices also called as nodes. 2. A finite set… Read More
What is Minimum Spanning Tree? Given a connected and undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects… Read More
In the previous post, we introduced union find algorithm and used it to detect cycle in a graph. We used following union() and find() operations… Read More
A disjoint-set data structure is a data structure that keeps track of a set of elements partitioned into a number of disjoint (non-overlapping) subsets. A… Read More
  Given a boolean 2D matrix, find the number of islands. A group of connected 1s forms an island. For example, the below matrix contains… Read More
  The Floyd Warshall Algorithm is for solving the All Pairs Shortest Path problem. The problem is to find shortest distances between every pair of… Read More
Hamiltonian Path in an undirected graph is a path that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a Hamiltonian Path… Read More
Given an undirected graph and a number m, determine if the graph can be coloured with at most m colours such that no two adjacent… Read More