BOTTOM  The Bottom of a Graph
We will use the following (standard) definitions from graph theory. Let $V$ be a nonempty and finite set, its elements being called vertices (or nodes). Let $E$ be a subset of the Cartesian product $V \times V$, its elements being called edges. Then $G = (V, E)$ is called a directed graph.
Let $n$ be a positive integer, and let $p = (e_1, \ldots, e_n)$ be a sequence of length $n$ of edges $e_i \in E$ such that $e_i = (v_i, v_{i+1})$ for a sequence of vertices ($v_1, \ldots, v_{n+1}$). Then $p$ is called a path from vertex $v_1$ to vertex $v_{n+1}$ in $G$ and we say that $v_{n+1}$ is reachable from $v_1$, writing $(v_1 \to v_{n+1})$.
Here are some new definitions. A node $v$ in a graph $G = (V, E)$ is called a sink, if for every node $w$ in $G$ that is reachable from $v$, $v$ is also reachable from $w$. The bottom of a graph is the subset of all nodes that are sinks, i.e., $\mathrm{bottom}(G) = \{v \in V \mid \forall w \in V : (v \to w) \Rightarrow (w \to v) \}$. You have to calculate the bottom of certain graphs.
Input Specification
The input contains several test cases, each of which corresponds to a directed graph $G$. 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 $V = \{1, \ldots, v\}$. You may assume that $1 \le v \le 5000$. That is followed by a nonnegative integer $e$ and, thereafter, $e$ pairs of vertex identifiers $v_1, w_1, \ldots, v_e, w_e$ with the meaning that $(v_i, w_i) \in E$. There are no edges other than specified by these pairs. The last test case is followed by a zero.
Output Specification
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.
Sample Input
3 3 1 3 2 3 3 1 2 1 1 2 0
Sample Output
1 3 2
hide comments
ayush:
20160713 19:12:59
@code_master5 i somehow figured it out later that day, anyways thanks for coming up. :) a simple SCC indeed. 

avisheksanvas:
20160705 10:06:08
Simple SCC problem. The entire problem in one statement : (v→w)⇒(w→v)!


Rohit Agarwal:
20160701 17:42:03
Should we print is descending order or ascending order? The output says sorted order but doesn't specify which one. Are both valid?


code_master5:
20160629 17:28:04
@ayush because if a vertex u is directed towards another vertex v (i.e. u>v), where u and v belong to different SCCs, then


ayush:
20160629 16:09:49
if a vertex belongs to one component and has a neighbour of other component (by component i mean a SCC group), why the whole SCC group of that vertex is discarded, as given by test case:


code_master5:
20160626 21:56:03
Finally! I got ac.. But I was getting WA when I was using low[] values as id for an SCC (yeah! u guessed right, I was using Tarjan's Algo for finding SCC). I was assuming that low value will be different for each SCC. Can anyone explain where I went wrong!!! 

Abhishek Naik:
20160626 19:04:21
@kshubham02: Your comment was really very helpful. Got my code accepted! Thank you! :) Last edit: 20160626 19:04:57 

code_master5:
20160625 20:10:46
@deerishi If u're suggesting this case:


deerishi:
20160625 01:19:56
Nice Problem. For those getting WA consider the case of a single vertex with a self loop. 

code_master5:
20160623 22:37:38
Please help me! I'm constantly getting WA. I've tried all the given testcases (including those in comments!!!). Help me find bugs in my last submission... 
Added by:  Wanderley Guimarăes 
Date:  20070921 
Time limit:  0.254s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JS 
Resource:  University of Ulm Local Contest 2003 