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  1. Prepare
  2. Algorithms
  3. Graph Theory
  4. Breadth First Search: Shortest Reach

Breadth First Search: Shortest Reach

Consider an undirected graph where each edge weighs 6 units. Each of the nodes is labeled consecutively from 1 to n.

You will be given a number of queries. For each query, you will be given a list of edges describing an undirected graph. After you create a representation of the graph, you must determine and report the shortest distance to each of the other nodes from a given starting position using the breadth-first search algorithm (BFS). Return an array of distances from the start node in node number order. If a node is unreachable, return for that node.

Example
The following graph is based on the listed inputs:

image

// number of nodes
// number of edges

// starting node

All distances are from the start node . Outputs are calculated for distances to nodes through : . Each edge is units, and the unreachable node has the required return distance of .

Function Description

Complete the bfs function in the editor below. If a node is unreachable, its distance is .

bfs has the following parameter(s):

  • int n: the number of nodes
  • int m: the number of edges
  • int edges[m][2]: start and end nodes for edges
  • int s: the node to start traversals from

Returns
int[n-1]: the distances to nodes in increasing node number order, not including the start node (-1 if a node is not reachable)

Input Format

The first line contains an integer , the number of queries. Each of the following sets of lines has the following format:

  • The first line contains two space-separated integers and , the number of nodes and edges in the graph.
  • Each line of the subsequent lines contains two space-separated integers, and , that describe an edge between nodes and .
  • The last line contains a single integer, , the node number to start from.

Constraints

Sample Input

2
4 2
1 2
1 3
1
3 1
2 3
2

Sample Output

6 6 -1
-1 6

Explanation

We perform the following two queries:

  1. The given graph can be represented as:
    image
    where our start node, , is node . The shortest distances from to the other nodes are one edge to node , one edge to node , and an infinite distance to node (which it is not connected to). We then return an array of distances from node to nodes , , and (respectively): .

  2. The given graph can be represented as:
    image
    where our start node, , is node . There is only one edge here, so node is unreachable from node and node has one edge connecting it to node . We then return an array of distances from node to nodes , and (respectively): .

Note: Recall that the actual length of each edge is , and we return as the distance to any node that is unreachable from .