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 two arrays of non-negative integers say ‘arr1’ and ‘arr2’. Your task is to find the maximum value of ( ‘A’ xor ‘B’ ) where ‘A’ and ‘B’ are any elements from ‘arr1’ and ‘arr2’ respectively and ‘xor’ represents the bitwise xor operation.

The city of Ninjaland is analogous to the unweighted graph. The city has ‘N’ houses numbered from 1 to ‘N’ respectively and are connected by M bidirectional roads. If a road is connecting two houses ‘X’ and ‘Y’ which means you can go from ‘X’ to ‘Y’ or ‘Y’ to ‘X’. It is guaranteed that you can reach any house from any other house via some combination of roads. Two houses are directly connected by at max one road.

A path between house ‘S’ to house ‘T’ is defined as a sequence of vertices from ‘S’ to ‘T’. Where starting house is ‘S’ and the ending house is ‘T’ and there is a road connecting two consecutive houses. Basically, the path looks like this: (S , h1 , h2 , h3 , ... T). you have to find the shortest path from ‘S’ to ‘T’.

For example

In the below map of Ninjaland let say you want to go from S=1 to T=8, the shortest path is (1, 3, 8). You can also go from S=1 to T=8  via (1, 2, 5, 8)  or (1, 4, 6, 7, 8) but these paths are not shortest.

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