SDE - Intern

You are given an array of positive integers, ‘VERTICES’ that represent the vertices in a graph. Two vertices, ‘V1’ and ‘V2’, have an edge between them if and only if ‘V1’ and ‘V2’ share a common factor greater than 1. Your task is to return the size of the largest connected component in the graph.

You are given a Singly Linked List of integers and an integer array 'B' of size 'N'. Each element in the array 'B' represents a block size. Modify the linked list by reversing the nodes in each block whose sizes are given by the array 'B'.

Note:

1. If you encounter a situation when 'B[i]' is greater than the number of remaining nodes in the list, then simply reverse the remaining nodes as a block and ignore all the block sizes from 'B[i]'. 

2. All block sizes are contiguous i.e. suppose that block 'B[i]' ends at a node cur, then the block 'B[i+1]' starts from the node just after the node cur.

Example

Linked list: 1->2->3->4->5
Array B: 3 3 5

Output: 3->2->1->5->4

We reverse the first block of size 3 and then move to block 2. Now, since the number of nodes remaining in the list (2) is less than the block size (3), we reverse the remaining nodes (4 and 5) as a block and ignore all the block sizes that follow.

Given an undirected graph of V vertices and E edges. Your task is to find all the bridges in the given undirected graph. A bridge in any graph is defined as an edge which, when removed, makes the graph disconnected (or more precisely, increases the number of connected components in the graph).

For Example :

If the given graph is :

Then the edge between 0 and 4 is the bridge because if the edge between 0 and 4 is removed, then there will be no path left to reach from 0 to 4.and makes the graph disconnected, and increases the number of connected components.

Note :

There are no self-loops(an edge connecting the vertex to itself) in the given graph.

There are no parallel edges i.e no two vertices are directly connected by more than 1 edge.

Given an undirected graph of ‘V’ vertices (labeled 0,1,..., V-1) and ‘E’ edges . Your task is to check whether the graph is bipartite or not.

A bipartite graph is a graph whose vertices can be divided into two sets such that each edge of the graph connects one vertex from the first set and another vertex from the second set.
We can also define a bipartite graph as a graph which can be colored using two colors such that no two adjacent vertices have the same color. 

For example: 
Input: 
4 4
0 1
0 2
1 3
2 3

An undirected graph to the above input is shown below:

In the given input, the number of vertices is 4, and the number of edges is 4.
In the input, following the number of vertices and edges, a list of pairs of numbers is given where each pair (u, v) denotes an edge between vertex u and v.
As per the input, there is an edge between vertex 0 and vertex 1.
The vertices 0 and 2 have an edge between them.

The vertices 1 and 3 have an edge between them.
The vertices 2 and 3 have an edge between them.

As the graph can be colored using two colors, and no adjacent vertices share the same color, the graph is bipartite. 

Design a mechanism such that there should not be any packet loss while transmitting the information over a network, and also to come up with a way, the credentials can be securely transmitted over a network.