ZOJ1003

Crashing Balloon

Time Limit: 2 Seconds      Memory Limit: 65536 KB

On every June 1st, the Children's Day, there will be a game named "crashing balloon" on TV.   The rule is very simple.  On the ground there are 100 labeled balloons, with the numbers 1 to 100.  After the referee shouts "Let's go!" the two players, who each starts with a score of  "1", race to crash the balloons by their feet and, at the same time, multiply their scores by the numbers written on the balloons they crash.  After a minute, the little audiences are allowed to take the remaining balloons away, and each contestant reports his\her score, the product of the numbers on the balloons he\she's crashed.  The unofficial winner is the player who announced the highest score.

每年的61儿童节,电视里会有一个“打破气球”的游戏。游戏规则非常简单。当场有100个贴有标签的气球,上面写着1到100。裁判法令,游戏开始,两个玩家最初的分数都是1。他们跑向气球,得分就是他们的分数乘以戳破的气球分数。一分钟后,小观众把剩下的气球带走,每一个选手汇报他们的分数,也就是他们戳破的气球的分数。暂时的胜利者是分数最高的选手。

Inevitably, though, disputes arise, and so the official winner is not determined until the disputes are resolved.  The player who claims the lower score is entitled to challenge his\her opponent's score.  The player with the lower score is presumed to have told the truth, because if he\she were to lie about his\her score, he\she would surely come up with a bigger better lie.  The challenge is upheld if the player with the higher score has a score that cannot be achieved with balloons not crashed by the challenging player.  So, if the challenge is successful, the player claiming the lower score wins.

不可避免的是会有争议,争议解决后产生最终的胜利者。分数低的选手可以质疑对手的分数,假设他说的是真话,因为如果他撒谎,他当然会得到一个更高的更好的谎言。如果高分选手的分数可以用气球上的分数相乘得到,那么挑战会受阻。而挑战成功的话,低分的选手获胜。

So, for example, if one player claims 343 points and the other claims 49, then clearly the first player is lying; the only way to score 343 is by crashing balloons labeled 7 and 49, and the only way to score 49 is by crashing a balloon labeled 49.  Since each of two scores requires crashing the balloon labeled 49, the one claiming 343 points is presumed to be lying.

举例来说,如果一个选手得分是343,另一个选手是49,那么明显地是第一个选手在说谎。要获得343分的唯一办法是戳破标签7和49的气球,而得到49分的唯一办法是戳破标签49的气球。因为每个选手的分数都需要戳破49,所以得分343的选手在说谎。

On the other hand, if one player claims 162 points and the other claims 81, it is possible for both to be telling the truth (e.g. one crashes balloons 2, 3 and 27, while the other crashes balloon 81), so the challenge would not be upheld.

另一方面,如果一个选手得分是162,另一个是81分,两个人都可能在说真话。比如一个人的得分是2*3*27,而另一个是81,因此挑战受阻。

By the way, if the challenger made a mistake on calculating his/her score, then the challenge would not be upheld. For example, if one player claims 10001 points and the other claims 10003, then clearly none of them are telling the truth. In this case, the challenge would not be upheld.

挑战者在计算分数时出错的话,挑战将受阻。比如一个选手得分是10001,另一个是10003,那么很明显没有一个人在说真话,挑战受阻。

Unfortunately, anyone who is willing to referee a game of crashing balloon is likely to get over-excited in the hot atmosphere that he\she could not reasonably be expected to perform the intricate calculations that refereeing requires.  Hence the need for you, sober programmer, to provide a software solution.

非常不幸地是,裁判非常有可能过度兴奋而无法执行复杂的计算,因此需要程序员编程解决问题。

Input

Pairs of unequal, positive numbers, with each pair on a single line, that are claimed scores from a game of crashing balloon.

在一行输入一对不相等的数,分别代表游戏中戳破气球得到的分数。

Output

Numbers, one to a line, that are the winning scores, assuming that the player with the lower score always challenges the outcome.

输出获得胜利的分数,假设低分选手经常挑战结果。

Sample Input

343 49
3599 610
62 36

Sample Output

49
610
62

Source: Zhejiang University Local Contest 2001

posted @ 2017-03-10 19:34  RunningYY  阅读(307)  评论(1)    收藏  举报