Problem Description
A university network is composed of N computers. System administrators gathered information on the traffic between nodes, and carefully divided the network into two subnetworks in order to minimize traffic between parts.
A disgruntled computer science student Vasya, after being expelled from the university, decided to have his revenge. He hacked into the university network and decided to reassign computers to maximize the traffic between two subnetworks.
Unfortunately, he found that calculating such worst subdivision is one of those problems he, being a student, failed to solve. So he asks you, a more successful CS student, to help him.
The traffic data are given in the form of matrix C, where Cij is the amount of data sent between ith and jth nodes (Cij = Cji, Cii = 0). The goal is to divide the network nodes into the two disjointed subsets A and B so as to maximize the sum ∑Cij (i∈A,j∈B).
Input
The first line of input contains a number of nodes N (2 <= N <= 20). The following N lines, containing N space-separated integers each, represent the traffic matrix C (0 <= Cij <= 10000). <br>Output file must contain a single integer -- the maximum traffic between the subnetworks. <br>
Output
Output must contain a single integer -- the maximum traffic between the subnetworks.
Sample Input
3
0 50 30
50 0 40
30 40 0
Sample Output
90
很多点直接有距离，把这些点分成两和集合，就两个集合最大的分法。
思路：
用dfs（）不断循环把点分到两个集合。
代码：
#include <cstring>
#include <cstdio>
using namespace std;
int n;
int map[22][22];
int po[22];
int sum=0;
int sun;
int dfs(int k)
{
if(k==n+1)
{
if(sum<sun)sum=sun;
return 0;
}
int an=0;
for(int j=1;j<=k-1;j++)
{
if(po[j]){
an+=map[k][j];
}
}
sun+=an;
dfs(k+1);
sun-=an;
po[k]=1;
an=0;
for(int j=1;j<=k-1;j++)
{
if(!po[j]){
an+=map[k][j];
}
}
sun+=an;
dfs(k+1);
sun-=an;
po[k]=0;
}
int main()
{
while(cin>>n)
{ memset(map,0,sizeof(map));
memset(po,0,sizeof(po));
sum=0;
sun=0;
for(int i=1;i<=n;i++)
{
for(int j=1;j<=n;j++)
{
scanf("%d",&map[i][j]);
}
}
po[1]=1;
dfs(1);
printf("%d\n",sum);
}
return 0;
}