Finding The Max of sum of elements in matrix in distinct rows and columns
I have a nxm matrix and I need to find the maximum of sum of its values in distinct rows and columns.
For example considering the following Matrix:
m1 m2 m3
n1 1 2 3
n2 4 5 6
n3 7 8 9
n4 10 11 12
The max will be 12+8+4 = 24
Note that finding the max and eliminating all values belong开发者_JS百科ing to that column or row is not a good solution as it doesn't work for all cases.
The exception for above will be the following:
m1 m2
n1 17 1
n2 18 15
If you find 18 and remove 17 and 15, the sum will be 18+1 = 19. while 17+15 = 32 has a higher value.
Any idea about the algorithm for this question?
The solution is to use Hungarian Algorithm. It's a complicated algorithm. There's a very good lecture on that on youtube:
http://www.youtube.com/watch?v=BUGIhEecipE
This is similar to the N Queen Problem where we have to place N queen in N*N matrix such that no 2 queen should be in the same column or same row.
import java.util.Vector;
public class maxSum {
private static int getMaxSum(int row, int[] col, int n, int[][] mat, int sum,
Vector<Integer> ans) {
if(row >= n) {
System.out.println(ans+"->"+sum);
return sum;
}
int max = Integer.MIN_VALUE;
for(int i=0;i<n;i++) {
if(col[i]==1)
continue;
col[i] = 1;
ans.add(mat[row][i]);
max = Math.max(getMaxSum(row+1,col,n,mat,sum+mat[row][i],ans), max);
ans.remove(ans.size()-1);
col[i] = 0;
}
return max;
}
public static void main(String[] args) {
// TODO Auto-generated method stub
int[][] mat = {{2,5,7,6},{8,5,11,9},{7,3,1,2},{8,7,9,7}};
int n = 4;
int col[] = {0,0,0,0};
Vector<Integer> ans = new Vector<Integer>();
System.out.println(getMaxSum(0,col,n,mat,0,ans));
}
}
精彩评论