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.


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.


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.".


Sample input:

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: 2021-10-03 12:26:31

Awesome Problem

lk03021998: 2019-01-27 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: 2018-07-27 22:28:46

A really good problem.
Refer to the Wikipedia article "Eulerian path". Personally, I found the Wikipedia article to be better than Geeksforgeeks article.

coolio_1: 2018-06-06 19:38:00

Euler Path!

nikhil2504: 2017-07-30 00:14:10

Refer Euler Paths and come back !

sam128: 2017-07-12 09:57:18

Nice problem..Learnt new concepts..Eulerian path

arthur1991: 2017-03-24 21:26:02

i love qianqian

avisheksanvas: 2016-07-31 11:36:23

Great Problem. :)

citransvostok: 2016-06-30 17:03:37

thanks to Eliton! helped a lot! AC

mikeseeley06: 2016-05-07 20:46:06


Added by:adrian
Time limit:20s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Resource:ACM Central European Programming Contest, Prague 1999