Prison rearrangement
| Time Limit: 3000MS | Memory Limit: 10000K | |
| Total Submissions: 2008 | Accepted: 906 |
Description
In order to lower the risk of riots and escape attempts, the boards of two nearby prisons of equal prisoner capacity, have decided to rearrange their prisoners among themselves. They want to exchange half of the prisoners of one prison, for half of the prisoners of the other. However, from the archived information of the prisoners' crime history, they know that some pairs of prisoners are dangerous to keep in the same prison, and that is why they are separated today, i.e. for every such pair of prisoners, one prisoners serves time in the first prison, and the other in the second one. The boards agree on the importance of keeping these pairs split between the prisons, which makes their rearrangement task a bit tricky. In fact, they soon find out that sometimes it is impossible to fulfil their wish of swapping half of the prisoners. Whenever this is the case, they have to settle for exchanging as close to one half of the prisoners as possible.
Input
On the first line of the input is a single positive integer n, telling the number of test scenarios to follow. Each scenario begins with a line containing two non-negative integers m and r, 1 < m < 200 being the number of prisoners in each of the two prisons, and r the number of dangerous pairs among the prisoners. Then follow r lines each containing a pair xi yi of integers in the range 1 to m,which means that prisoner xi of the first prison must not be placed in the same prison as prisoner yi of the second prison.
Output
For each test scenario, output one line containing the largest integer k <= m/2 , such that it is possible to exchange k prisoners of the first prison for k prisoners of the second prison without getting two prisoners of any dangerous pair in the same prison.
Sample Input
3101 0
3 3
1 2
1 3
1 1
8 12
1 11
21 3
1 4
2 5
3 5
4 5
5 5
6 6
7 6
8 7
8 8
Sample Output
500
3
Source
所有危险囚犯对是可以分割整个二部图为几个集合的，也就是说，比如位于1号监狱的甲如果需要到2号监狱，那么位于2好监狱的所有和甲敌对的囚犯必须得到1号监狱，这样的话可以蔓延这种关系最后形成一个整数对x; y 保证如果甲到2号监狱那么一共要有x个囚犯从1号监狱到2号监狱，而y个囚犯从2号监狱必须得到1号监狱。现在在我们分割二部图为一些整数对后，我们希望选择一部分整数对使它们的和为Sum(x) = Sum(y)，并且是小于n=2的最大数。
dp[ i ][ j ]表示可以用一号监狱的 i 个人跟二号监狱的 j 个人换
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
bool mp[222][222],dp[222][222];
bool prison1[222],prison2[222];
int r,l,n,m,T;
void dfs(int x,int tem)
{
if(tem==1)
{
prison1[x]=true;
}
else if(tem==2)
{
prison2[x]=true;
}
if(tem==1)
{
r++;
for(int i=1;i<=n;i++)
{
if(mp[x]&&prison2==false)
{
dfs(i,2);
}
}
}
else if(tem==2)
{
l++;
for(int i=1;i<=n;i++)
{
if(mp[x]&&prison1==false)
{
dfs(i,1);
}
}
}
return ;
}
int main()
{
scanf("%d",&T);
while(T--)
{
int i,j,k;
memset(mp,false,sizeof(mp));
memset(dp,false,sizeof(dp));
memset(prison1,false,sizeof(prison1));
memset(prison2,false,sizeof(prison2));
int x,y;
scanf("%d%d",&n,&m);
for(int i=0;i<m;i++)
{
scanf("%d%d",&x,&y);
mp[x][y]=true;
}
dp[0][0]=true;
for(i=1;i<=n;i++)
{
if(prison1==false)
{
l=0;r=0;
dfs(i,1);
for(j=n/2;j>=r;j--)
{
for(k=n/2;k>=l;k--)
{
if(dp[j-r][k-l]==true)
dp[j][k]=true;
}
}
}
}
for(i=1;i<=n;i++)
{
if(prison2==false)
{
l=0;r=0;
dfs(i,2);
for(j=n/2;j>=r;j--)
{
for(k=n/2;k>=l;k--)
{
if(dp[j-r][k-l]==true)
dp[j][k]=true;
}
}
}
}
for(i=n/2;i>=0;i--)
if(dp)
break;
printf("%d
",i);
}
return 0;
}