Facebook Hacker Cup : Studious Student Problem Solution

Photo Credit : Helen Morgan

The Third and final problem of the Facebook Qualification 2011 Round was Studious Student. The problem goes like this:

Studious Student

You’ve been given a list of words to study and memorize. Being a diligent student of language and the arts, you’ve decided to not study them at all and instead make up pointless games based on them. One game you’ve come up with is to see how you can concatenate the words to generate the lexicographically lowest possible string.

Input

As input for playing this game you will receive a text file containing an integer N, the number of word sets you need to play your game against. This will be followed by N word sets, each starting with an integer M, the number of words in the set, followed by M words. All tokens in the input will be separated by some whitespace and, aside from N and M, will consist entirely of lowercase letters.

Output

Your submission should contain the lexicographically shortest strings for each corresponding word set, one per line and in order.

Constraints

1 <= N <= 100
1 <= M <= 9
1 <= all word lengths <= 10

Example input

5
6 facebook hacker cup for studious students
5 k duz q rc lvraw
5 mybea zdr yubx xe dyroiy
5 jibw ji jp bw jibw
5 uiuy hopji li j dcyi

Example output

cupfacebookforhackerstudentsstudious
duzklvrawqrc
dyroiymybeaxeyubxzdr
bwjibwjibwjijp
dcyihopjijliuiuy

Analysis and Solution

This problem is a most confusing out of the lot. Me myself made a silly mistake while solving this problem. On first look it looks like the problem should get solved by sorting and joining the strings, but its not like that.

Consider this following input:

jibw ji jp bw jibw

By sorting and concatenate, the answer should be is:

bwjijibwjibwjp

However, lexicographically lowest possible string will be:

bwjibwjibwjijp

Notice in the above words, "ji" is the prefix of "jibw". The "sort and concatenate" method definitely does not work when there is a case where a word is a prefix of one or more other words.

Some of the contestants solved this problem with brute force, as input range was not that big. With M<=9 one could have only 9!= 362880 possible permutations. And answer can be obtained by sorting these permutations.

However, I didn’t went this approach. I used python internal Sort function with custom compare. Here is my code