SDE - 1

You have been given an undirected graph of ‘V’ vertices (labeled 0,1,..., V-1) and ‘E’ edges. Each edge connecting two nodes (‘X’,’Y’) will have a weight denoting the distance between node ‘X’ and node ‘Y’.

Your task is to find the shortest path distance from the source node, which is the node labeled as 0, to all vertices given in the graph.

Example:

Input:
4 5
0 1 5
0 2 8
1 2 9
1 3 2
2 3 6

In the given input, the number of vertices is 4, and the number of edges is 5.

In the input, following the number of vertices and edges, three numbers are given. The first number denotes node ‘X’, the second number denotes node ‘Y’ and the third number denotes the distance between node ‘X’ and ‘Y’.

As per the input, there is an edge between node 0 and node 1 and the distance between them is 5.

The vertices 0 and 2 have an edge between them and the distance between them is 8.
The vertices 1 and 2 have an edge between them and the distance between them is 9.
The vertices 1 and 3 have an edge between them and the distance between them is 2.
The vertices 2 and 3 have an edge between them and the distance between them is 6.

Note:

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

2. There can be parallel edges i.e. two vertices can be directly connected by more than 1 edge.

You are given a Directed Acyclic Graph (DAG) with ‘E’ edges and ‘V’ vertices. A DAG is a type of graph with no directed cycles.

You have been given a source vertex ‘S’. Your task is to find the distance between ‘S’ and the farthest vertex reachable from ‘S’?

Example: Given a DAG graph :

Source node: 1
The farthest vertex in the above graph from vertex 1 is 2 via the route of vertex 3. So, the distance is 2.

Given a string S containing digits from 2 to 9 inclusive. Your task is to find all possible letter combinations that the number could represent.

A mapping from Digits to Letters (just like in Nokia 1100) is shown below. Note that 1 does not map to any letter.

Designing top K trending hashtags.