1029 False coin

False coin
Time Limit: 1000MS
 
Memory Limit: 65536K
Total Submissions: 12014
 
Accepted: 3229
Description
The "Gold Bar"bank received information from reliable sources that in their last group of N coins exactly one coin is false and differs in weight from other coins (while all other coins are equal in weight). After the economic crisis they have only a simple balance available (like one in the picture). Using this balance, one is able to determine if the weight of objects in the left pan is less than, greater than, or equal to the weight of objects in the right pan.
In order to detect the false coin the bank employees numbered all coins by the integers from 1 to N, thus assigning each coin a unique integer identifier. After that they began to weight various groups of coins by placing equal numbers of coins in the left pan and in the right pan. The identifiers of coins and the results of the weightings were carefully recorded.
You are to write a program that will help the bank employees to determine the identifier of the false coin using the results of these weightings.
Input
The first line of the input file contains two integers N and K, separated by spaces, where N is the number of coins (2<=N<=1000 ) and K is the number of weightings fulfilled (1<=K<=100). The following 2K lines describe all weightings. Two consecutive lines describe each weighting. The first of them starts with a number Pi (1<=Pi<=N/2), representing the number of coins placed in the left and in the right pans, followed by Pi identifiers of coins placed in the left pan and Pi identifiers of coins placed in the right pan. All numbers are separated by spaces. The second line contains one of the following characters: '<', '>', or '='. It represents the result of the weighting:
'<' means that the weight of coins in the left pan is less than the weight of coins in the right pan,
'>' means that the weight of coins in the left pan is greater than the weight of coins in the right pan,
'=' means that the weight of coins in the left pan is equal to the weight of coins in the right pan.
Output
Write to the output file the identifier of the false coin or 0, if it cannot be found by the results of the given weightings.
Sample Input

5 3
2 1 2 3 4
<
1 1 4
=
1 2 5
=

Sample Output

3

Source
Northeastern Europe 1998
/*몇 가지 법칙이 있습니다.만약 등호가 나타난다면, 등호 양쪽의 금은 모두 가짜가 아니다.만약 부등호가 나타난다면 반드시 위폐가 존재할 것이다.부등호 밖의 그 금화는 모두 가짜여야 한다.위폐가 나타나는 횟수는 부등호가 나타나는 횟수와 같다.위폐는 반드시 부등호의 같은 끝에 나타나야 한다. 우리는 상기 네 가지 조건을 만족시켜야 한다. */#include#includeinta[1010];int b[1010]; int f[1010]; bool ff[1010]; int cal(int x) { if(x<0) return -x; return x; } int main() {int n,k;while(scanf('%d%d',&n,&k)!=EOF){chars[10];int m,num=0;memset(f,0,sizeof(ff,1,sizeof(ff);for(int i=1;i<=k;i++){scanf('%d',&m);for(int j=1;j+)scanf('%d', &a[j]);for(int j=1;j<=m;j++)scanf('%d', &b[j]);scanf('%s','s);if(s[0]='='){for(int j=1;j<=m;j+) {f[a[j]]=0;f[b[j]=0;/보증1 ff[a[j]=0;ff[b[j]]]=0;}}}else {num++;//부등호 출현 횟수if(s[0]='<') {for(int j=1;j<=m;j+) f[a[j]]-, f[b[j]]++;//보증4}else {for(int j=1;j<=m;j+) f[a[j]+, f[b[j]]]-;/보증4}} int mm=0;int ca=1; for(int i=1;i<=n;i++) if(ff[i]&&cal(f[i])==num) { mm++; ca=i; } if(mm==1) printf("%d/n",ca); else printf("0/n"); } return 0; }