Software Engineer

You have been given an undirected graph with 'N' vertices and 'M' edges. The vertices are labelled from 1 to 'N'.

Your task is to find if the graph contains a cycle or not.

A path that starts from a given vertex and ends at the same vertex traversing the edges only once is called a cycle.

Example :

In the below graph, there exists a cycle between vertex 1, 2 and 3. 

Note:

1. There are no parallel edges between two vertices.

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

3. The graph can be disconnected.

For Example :

Input: N = 3 , Edges =  [[1, 2], [2, 3], [1, 3]].
Output: Yes

Explanation : There are a total of 3 vertices in the graph. There is an edge between vertex 1 and 2, vertex 2 and 3 and vertex 1 and 3. So, there exists a cycle in the graph. 

You are given a non-empty binary tree where each node has a non-negative integer value. Return the maximum possible sum of path between any two leaves of the given tree.

The path is also inclusive of the leaf nodes and the maximum path sum may or may not go through the root of the given tree.

If there is only one leaf node in the tree, then return -1.

You are given a positive integer ‘N’, your task is to return an array/list of integers such that the sum of Euler Totient Function values of each integer of the array is equal to ‘N’.

Euler Totient Function:

In number theory, Euler's totient function counts the positive integers up to a given integer ‘N’ that is relatively prime to ‘N’.

More details about Euler’s Totient Function can be found here

For Example:

For ‘N’ = 10, if we take the array as 1, 2, 5, 10,
The Euler totient function value of 1 is 1.
The Euler totient function value of 2 is 1.
The Euler totient function value of 5 is 4.
The Euler totient function value of 10 is 4.
So, the summation will be 1 + 1 + 4 + 4 = 10.
Hence this is a valid array for ‘N’ = 10.

Note:

The solution will be verified by the actual value of the Euler Totient Function of 'N' and the sum of the Euler Totient Function of all the values returned. In the output, only the 'YES' or 'NO' is printed, according to the correctness of the solution.

You are given a Singly Linked List of integers. Return true if it has a cycle, else return false.

A cycle occurs when a node's next points back to a previous node in the list.

Example:

In the given linked list, there is a cycle, hence we return true.