题目描述
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.
输入描述:
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.
输出描述:
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.
示例1
输出
复制3
如果左右两边重量相等那么左右两边都是标准重量（将Mark[temp[i]]=0），如果左边重于右，那么遍历左边，如果左边的硬币不仅出现在重的堆里还出现在轻的堆里，那么这个硬币是标准的.
#include<iostream>
using namespace std;
int temp[1000];//保存所有硬币的编号，从1开始
int mark[1000];//有四种状态，初始化为2表示不确定，标准重量的为0，较标准重的为1，较标准轻的为-1.
int t;
bool notin(int n)
{
for(int i=0;i<2*t;i++)
{
if(n==temp[i])return false;
}
return true;
}
int main()
{
int n,k;
while(cin>>n>>k)
{
for(int i=1;i<=n;i++)
mark[i]=2;
while(k--)
{
cin>>t;
for(int i=0;i<2*t;i++)
cin>>temp[i];
char s;
cin>>s;
if(s=='=')
{
for(int i=0;i<2*t;i++)
mark[temp[i]]=0;
}
else if(s=='<')
{
int i=0;
for( i;i<t;i++)
{
if(mark[temp[i]])//不正常的才考虑
{
if(mark[temp[i]]==1)mark[temp[i]]=0;//既出现在重的组又出现在轻的组
else mark[temp[i]]=-1;
}
}
for(;i<2*t;i++)
{
if(mark[temp[i]])//不正常的才考虑
{
if(mark[temp[i]]==-1)mark[temp[i]]=0;//既出现在重的组又出现在轻的组
else mark[temp[i]]=1;
}
}
for(int i=1;i<=n;i++)
{
if(notin(i))
mark[i]=0;
}
}
else if(s=='>')
{
int i=0;
for(i;i<t;i++)
{
if(mark[temp[i]])//不正常的才考虑
{
if(mark[temp[i]]==-1)mark[temp[i]]=0;//既出现在重的组又出现在轻的组
else mark[temp[i]]=1;
}
}
for(i;i<2*t;i++)
{
if(mark[temp[i]])//不正常的才考虑
{
if(mark[temp[i]]==1)mark[temp[i]]=0;//既出现在重的组又出现在轻的组
else mark[temp[i]]=-1;
}
}
for(int i=1;i<=n;i++)
{
if(notin(i))
mark[i]=0;
}
}
}
int count=0,flag=0;
for(int i=1;i<=n;i++)
{
if(!mark[i])count++;//正常的
else flag=i;
}
if(count==n-1)
cout<<flag<<endl;
else cout<<0<<endl;
}
return 0;
}