shunfurh 于 2017.09.07 11:14 提问

Marriage is Stable

Problem Description
Albert, Brad, Chuck are happy bachelors who are in love with Laura, Marcy, Nancy. They all have three choices. But in fact, they do have some preference in mind. Say Albert, he likes Laura best, but that doesn't necesarily mean Laura likes him. Laura likes Chuck more than Albert. So if Albert can't marry Laura, he thinks Nancy a sensible choice. For Albert, he orders the girls Laura > Nancy > Marcy.

For the boys:

Albert: Laura > Nancy > Marcy
Brad: Marcy > Nancy > Laura
Chuck: Laura > Marcy > Nancy

For the girls:

Laura: Chuck > Albert > Brad
Marcy: Albert > Chuck > Brad
Nancy: Brad > Albert > Chuck

But if they were matched randomly, such as

Albert <-> Laura
Chuck <-> Nancy

they would soon discover it's not a nice solution. For Laura, she likes Chuck instead of Albert. And what's more, Chuck likes Laura better than Nancy. So Laura and Chuck are likely to come together, leaving poor Albert and Nancy.

Now it's your turn to find a stable marriage. A stable marriage means for any boy G and girl M, with their choice m[G] and m[M], it will not happen that rank(G, M) < rank(G, m[G]）and rank(M, G) < rank(M, m[M]).

Input
Each case starts with an integer n (1 <= n <= 500), the number of matches to make.

The following n lines contain n + 1 names each, the first being name of the boy, and rest being the rank of the girls.

The following n lines are the same information for the girls.

Process to the end of file.

Output
If there is a stable marriage, print n lines with two names on each line. You can choose any one if there are multiple solution. Print "Impossible" otherwise.

Print a blank line after each test.

Sample Input
3
Albert Laura Nancy Marcy
Brad Marcy Nancy Laura
Chuck Laura Marcy Nancy
Laura Chuck Albert Brad
Marcy Albert Chuck Brad
Nancy Brad Albert Chuck

Sample Output
Albert Nancy
Chuck Laura

1个回答

caozhy      2017.09.22 08:34

RT，该问题可解决n男n女配对问题：每个人有自己理想对象排名，而要使配对后不存在一对男女不是配偶且对于彼此的好感优于当前配偶。 算法流程： 1.每一轮未订婚的男士向其未求过婚的女士求婚； 2.女士若有男士X向其求婚，如该女士之前没有未婚夫，则直接将男士X作为该女士临时的未婚夫，如已有未婚夫且对该男士X的好感比未婚夫更高，则把未婚夫甩了，重新加入单身狗队列，把X作为未婚夫。 不断执行上述过程，
POJ3487 The Stable Marriage Problem

HDU 1522 Marriage is Stable 稳定婚姻匹配
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hdu 3081 Marriage Match II【并查集+二分+最大流Dinic+建图】
Marriage Match II Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 3597    Accepted Submission(s): 1165 Problem Description Presumably,
POJ 3487(稳定婚姻问题)
Language: Default The Stable Marriage Problem Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 1941   Accepted: 827 Description 稳定婚姻系统问题如下 集合M 表示n个男性
stable marriage