WORDS1  Play on Words
Some of the secret doors contain a very interesting word puzzle. The team of archaeologists has to solve it to open that doors. Because there is no other way to open the doors, the puzzle is very important for us.
There is a large number of magnetic plates on every door. Every plate has one word written on it. The plates must be arranged into a sequence in such a way that every word begins with the same letter as the previous word ends. For example, the word ``acm'' can be followed by the word ``motorola''. Your task is to write a computer program that will read the list of words and determine whether it is possible to arrange all of the plates in a sequence (according to the given rule) and consequently to open the door.
Input
The input consists of T test cases. The number of them (T, equal to about 500) is given on
the first line of the input file.
Each test case begins with a line containing a single integer number N that indicates the number of plates
(1 <= N <= 100000). Then exactly Nlines follow,
each containing a single word. Each word contains at least two
and at most 1000 lowercase characters, that means only letters 'a
'
through 'z
' will appear in the word. The same word may appear several
times in the list.
Output
Your program has to determine whether it is possible to arrange all the plates in a sequence such that the first letter of each word is equal to the last letter of the previous word. All the plates from the list must be used, each exactly once. The words mentioned several times must be used that number of times.
If there exists such an ordering of plates, your program should print
the sentence "Ordering is possible.
". Otherwise, output
the sentence "The door cannot be opened.
".
Example
Sample input: 3 2 acm ibm 3 acm malform mouse 2 ok ok Sample output: The door cannot be opened. Ordering is possible. The door cannot be opened.
Warning: large Input/Output data, be careful with certain languages
hide comments
sunny_saraff:
20211003 12:26:31
Awesome Problem 

lk03021998:
20190127 10:09:12
if we take each word as a node of a graph then we have to traverse all the node without visiting a node twice but in case of Euler path we have to cover all the edges repetition of vertex is allowed then how it is a Euler path question? 

karan_yadav:
20180727 22:28:46
A really good problem.


coolio_1:
20180606 19:38:00
Euler Path! 

nikhil2504:
20170730 00:14:10
Refer Euler Paths and come back !


sam128:
20170712 09:57:18
Nice problem..Learnt new concepts..Eulerian path


arthur1991:
20170324 21:26:02
i love qianqian 

avisheksanvas:
20160731 11:36:23
Great Problem. :) 

citransvostok:
20160630 17:03:37
thanks to Eliton! helped a lot! AC 

mikeseeley06:
20160507 20:46:06
https://en.wikipedia.org/wiki/Hamiltonian_path 
Added by:  adrian 
Date:  20040606 
Time limit:  20s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  ACM Central European Programming Contest, Prague 1999 