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  1. Practice
  2. Interview Preparation Kit
  3. Graphs
  4. BFS: Shortest Reach in a Graph

BFS: Shortest Reach in a Graph

Consider an undirected graph consisting of nodes where each node is labeled from to and the edge between any two nodes is always of length . We define node to be the starting position for a BFS. Given a graph, determine the distances from the start node to each of its descendants and return the list in node number order, ascending. If a node is disconnected, it's distance should be .

For example, there are nodes in the graph with a starting node . The list of , and each has a weight of .

image

Starting from node and creating a list of distances, for nodes through we have .

Function Description

Define a Graph class with the required methods to return a list of distances.

Input Format

The first line contains an integer, , the number of queries.

Each of the following sets of lines is as follows:

  • The first line contains two space-separated integers, and , the number of nodes and the number of edges.
  • Each of the next lines contains two space-separated integers, and , describing an edge connecting node to node .
  • The last line contains a single integer, , the index of the starting node.

Constraints

Output Format

For each of the queries, print a single line of space-separated integers denoting the shortest distances to each of the other nodes from starting position . These distances should be listed sequentially by node number (i.e., ), but should not include node . If some node is unreachable from , print as the distance to that node.

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 there is no connection to node .
  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 print node 's distance to nodes and (respectively) as a single line of space-separated integers: -1 6.

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