2017-03-26 07:36

# Team Rankings

It��s preseason and the local newspaper wants to publish a preseason ranking of the teams in the local amateur basketball league. The teams are the Ants, the Buckets, the Cats, the Dribblers, and the Elephants. When Scoop McGee, sports editor of the paper, gets the rankings from the selected local experts down at the hardware store, he��s dismayed to find that there doesn��t appear to be total agreement and so he��s wondering what ranking to publish that would most accurately reflect the rankings he got from the experts. He��s found that finding the median ranking from among all possible rankings is one way to go.

The median ranking is computed as follows: Given any two rankings, for instance ACDBE and ABCDE, the distance between the two rankings is defined as the total number of pairs of teams that are given different relative orderings. In our example, the pair B, C is given a different ordering by the two rankings. (The first ranking has C above B while the second ranking has the opposite.) The only other pair that the two rankings disagree on is B, D; thus, the distance between these two rankings is 2. The median ranking of a set of rankings is that ranking whose sum of distances to all the given rankings is minimal. (Note we could have more than one median ranking.) The median ranking may or may not be one of the given rankings.

Suppose there are 4 voters that have given the rankings: ABDCE, BACDE, ABCED and ACBDE. Consider two candidate median rankings ABCDE and CDEAB. The sum of distances from the ranking ABCDE to the four voted rankings is 1 + 1 + 1 + 1 = 4. We��ll call this sum the value of the ranking ABCDE. The value of the ranking CDEAB is 7 + 7 + 7 + 5 = 26.

It turns out that ABCDE is in fact the median ranking with a value of 4.

Input

There will be multiple input sets. Input for each set is a positive integer n on a line by itself, followed by n lines (n no more than 100), each containing a permutation of the letters A, B, C, D and E, left-justified with no spaces. The final input set is followed by a line containing a 0, indicating end of input.

Output

Output for each input set should be one line of the form:

ranking is the median ranking with value value.

Of course ranking should be replaced by the correct ranking and value with the correct value. If there is more than one median ranking, you should output the one which comes first alphabetically.

Sample Input

4
ABDCE
BACDE
ABCED
ACBDE
0
Sample Output

ABCDE is the median ranking with value 4.

• 点赞
• 写回答
• 关注问题
• 收藏
• 邀请回答

#### 2条回答默认 最新

• blownewbee 2017-04-04 15:17
已采纳
• 罗忠浩 2017-03-27 02:58

CSDN (Chinese Software Developer Network) 创立于1999年，是中国最大的IT社区和服务平台，为中国的软件开发者和IT从业者提供知识传播、职业发展、软件开发等全生命周期服务，满足他们在职业发展中学习及共享知识和信息、建立职业发展社交圈、通过软件开发实现技术商业化等刚性需求。拥有超过3000万注册会员（其中活跃会员800万）、50万注册企业及合作伙伴。

点赞 打赏 评论
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}