BOTTOM - The Bottom of a Graph
We will use the following (standard) definitions from graph theory.
V be a nonempty and finite set, its elements being called vertices (or nodes).
E be a subset of the Cartesian product
V×V, its elements being called edges.
G=(V,E) is called a directed graph.
n be a positive integer, and let
p=(e1,...,en) be a sequence of length
n of edges
ei∈ E such that
ei=(vi,vi+1) for a sequence of vertices
p is called a path from vertex
v1 to vertex
G and we say that
vn+1 is reachable from
Here are some new definitions.
v in a graph
G=(V,E) is called a sink, if for every node
G that is reachable from
v is also reachable from
The bottom of a graph is the subset of all nodes that are sinks, i.e.,
You have to calculate the bottom of certain graphs.
The input contains several test cases, each of which corresponds to a directed graph
Each test case starts with an integer number
v, denoting the number of vertices of
G=(V,E), where the vertices will be identified by the integer numbers in the set
You may assume that
That is followed by a non-negative integer
e and, thereafter,
e pairs of vertex identifiers
v1,w1,...,ve,we with the meaning that
There are no edges other than specified by these pairs.
The last test case is followed by a zero.
For each test case output the bottom of the specified graph on a single line. To this end, print the numbers of all nodes that are sinks in sorted order separated by a single space character. If the bottom is empty, print an empty line.
3 3 1 3 2 3 3 1 2 1 1 2 0
1 3 2
I didn't understand the 2nd test case. There is an edge from 1->2 and implicitly from 2->2. Going by this implication, in the first test case, we should also have had 1->1, 2->2 and 3->3, in addition to 1->3 and 3->1. Could someone please explain this to me?
My first SCC Problem :)
can someone suggest me tricky test case..i'm constantly getting wa ....all the test cases in the problems and comments are passing :(
Yes..We All Are Strongly Connected...
cake walk :) simple scc problem
nice one..AC in one go..
nice one !!
What is to be done when a graph has multiple bottoms?do we have to print the nodes of bottom with maximum size? If yes, in second case there are two bottoms both of size 1, why is only 2 printed.
For people getting WAs, please keep in mind that reachability doesn't mind the vertices have to be directly connected. Overlooking this costed me 2 WAs.