ZOJ_1003

ZOJ_1003: Crashing Balloon

Time Limit: 2000 MS Memory Limit: 64 MB
64bit IO Format: %lld

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Description

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.

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.

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.

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.

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.

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.

Input

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

Output

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

Sample Input

343 49
3599 610
62 36

Sample Output

49
610
62

Source

Zhejiang University Local Contest 2001

看了题解以后自己写的。

思路要理清楚，这道题就是要求a，b有没有公共因子

假设a>b

从100到1每次枚举因数p，如果b可以整除p,那么就让b得到这个因子，b=b/p，进入递归，否则 如果a可以整除，就让a=a/p，进入递归

如果a==1了，那么a 合法，如果b==1了那么b合法。此处合法即为没有公共因子的条件下，ab被逐步分解完全。

#include<cstdio>

#include<cstring>

#include<algorithm>

using namespace std;

int n,m;

int t1,t2;

void solve(int a,int b,int p)

{

if(t1)

{

return ;

}

if(a==1)

{

t1=1;

return ;

}

if(b==1)

{

t2=1;

}

while(p)

{

if(b%p==0)

solve(a,b/p,p-1);

else if(a%p==0)

solve(a/p,b,p-1);

p--;

}

return ;

}

int main()

{

while(scanf("%d%d",&n,&m)!=EOF)

{

t1=t2=0;

if(n<m)

swap(n,m);

solve(n,m,100);

if(!t1&&t2)

{

printf("%d\n",m);

}

else

{

printf("%d\n",n);

}

}

return 0;

}