1.6.8 Australian Voting
PC/UVa IDs: 110108/10142, Popularity: B, Success rate: low Level: 1
Australian ballots require that voters rank all the candidates in order of choice.
Initially only the first choices are counted, and if one candidate receives more than 50%
of the vote then that candidate is elected. However, if no candidate receives more than
50%, all candidates tied for the lowest number of votes are eliminated. Ballots ranking
these candidates first are recounted in favor of their highest-ranked non-eliminated
candidate. This process of eliminating the weakest candidates and counting their ballots
in favor of the preferred non-eliminated candidate continues until one candidate receives
more than 50% of the vote, or until all remaining candidates are tied.
Input
The input begins with a single positive integer on a line by itself indicating the number
of cases following, each as described below. This line is followed by a blank line. There
is also a blank line between two consecutive inputs.
The first line of each case is an integer n ≤ 20 indicating the number of candidates.
The next n lines consist of the names of the candidates in order, each up to 80 characters
in length and containing any printable characters. Up to 1,000 lines follow, each
containing the contents of a ballot. Each ballot contains the numbers from 1 to n in
some order. The first number indicates the candidate of first choice; the second number
indicates candidate of second choice, and so on.
Output
The output of each test case consists of either a single line containing the name of the
winner or several lines containing the names of all candidates who are tied. The output
of each two consecutive cases are separated by a blank line.
Sample Input
1
3
John Doe
Jane Smith
Jane Austen
1 2 3
2 1 3
2 3 1
1 2 3
3 1 2
Sample Output
John Doe