Crashing Balloon
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
问题简述：两个小朋友去爆气球，气球标号1-100，初始分数是1，每个人爆一个气球就乘以相应的分数，最后向裁判报告自己的得分。
分数低的可以提出质疑，如果分数报的高的同学算错了并且分数低的同学没算错，判分低的同学胜利，否则判分高的同学胜利。假设
分低的同学的分数只要合理便没计算错。
思路：深度优先搜索，每一个气球有三个状态，被同学1爆，被同学2爆，或不爆。被某个同学爆时需满足其目前的分数能被该气球的标号
所整除，所以实际的时间复杂度并不高。
直接贴代码:
1 #include<stdio.h> 2 int flag1 ,flag2 ; 3 4 void dfs(int a,int b,int k){ 5 if(b==1){ 6 flag2 = 1; 7 if(a==1){ 8 flag1 = 1; 9 return; //两个均匹配成功 10 } 11 } 12 if(k==1){ 13 return; //匹配失败 14 } 15 if(a%k==0) dfs(a/k,b,k-1); 16 if(b%k==0) dfs(a,b/k,k-1); 17 dfs(a,b,k-1); 18 19 } 20 21 int main(){ 22 int a,b; 23 while(scanf("%d %d",&a,&b)!=EOF){ 24 if(a < b){ 25 int temp = a; 26 a = b; 27 b = temp; 28 } 29 flag1 = flag2 = 0; 30 dfs(a,b,100); 31 if(!flag1&&flag2){ 32 printf("%d\n",b); 33 }else{ 34 printf("%d\n",a); 35 } 36 37 } 38 39 return 0; 40 }