Sum of the minimum elements in all connected components of an undirected graph
Given an array A of N numbers where Ai represent the value of the (i+1)th node. Also given are M pair of edges where u… Read More »
Category Archives: Graph
Computer Networks | Cuts and Network Flow
The backbone analysis of any network is broadly accomplished by using Graph Theory and its Algorithms. The performance constraints are Reliability, Delay/Throughput and the goal… Read More »
Largest connected component on a grid
Given a grid with different colors in a different cell, each color represented by a different number. The task is to find out the largest… Read More »
Multi Source Shortest Path in Unweighted Graph
Suppose there are n towns connected by m bidirectional roads. There are s towns among them with a police station. We want to find out… Read More »
Proof that Hamiltonian Path is NP-Complete
Prerequisite : NP-Completeness The class of languages for which membership can be decided quickly fall in the class of P and The class of languages… Read More »
Number of Transpositions in a Permutation
Permutation A permutation is an arrangement of elements. A permutation of n elements can be represented by an arrangement of the numbers 1, 2, …n… Read More »
Number of single cycle components in an undirected graph
Given a set of ‘n’ vertices and ‘m’ edges of an undirected simple graph (no parallel edges and no self-loop), find the number of single-cycle-components… Read More »
Number of shortest paths in an unweighted and directed graph
Given an unweighted directed graph, can be cyclic or acyclic. Print the number of shortest paths from a given vertex to each of the vertices.… Read More »
Check if the given permutation is a valid DFS of graph
Given a graph with N nodes numbered from 1 to N and M edges and an array of numbers from 1 to N. Check if… Read More »
Multistage Graph (Shortest Path)
A Multistage graph is a directed graph in which the nodes can be divided into a set of stages such that all edges are from… Read More »
Transpose graph
Transpose of a directed graph G is another directed graph on the same set of vertices with all of the edges reversed compared to the… Read More »
Shortest path in an unweighted graph
Given a unweighted graph, a source and a destination, we need to find shortest path from source to destination in the graph in most optimal… Read More »
Minimize the number of weakly connected nodes
Given an undirected graph, task is to find the minimum number of weakly connected nodes after converting this graph into directed one. Weakly Connected Nodes… Read More »
Number of Unicolored Paths between two nodes
Given an undirected colored graph(edges are colored), with a source vertex ‘s’ and a destination vertex ‘d’, print number of paths which from given ‘s’… Read More »
Number of loops of size k starting from a specific node
Given two positive integer n, k. Consider an undirected complete connected graph of n nodes in a complete connected graph. The task is to calculate… Read More »